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bim_early-english-books-1641-1700_scisme-unmaskt-_percy-john-alias-fisher_1658_17 | English-PD | Open Culture | Public Domain | 1,658 | Scisme unmask't, ... 1658 | Percy, John alias Fisher and Fairfax. | English | Spoken | 7,511 | 12,844 | lam contra ſenſum omninm Corfacerdotum, contra morem @ inſtituta majorum rebaptt= zandum eſſe cenſebat. © Long ago, faith * he, Agrippinas of venerable meinory, * Biſhop of Carthage, the firſt of all men * living, againſt the divine Canon, againſt Thefixth Miſronceipt aiſcevered. $47 | ec again(t che rule of theuniverſal Church, « againſt the tenet of all his fellow-Bi- « ſhops, againſt che cuſtome and decrees | © of his Predeceſfours, thought that Re- © baptization was to be uſed- Que pre- [amptio tantum mali-invexit, ut non ſolu! Hereticts onmmbns' formam ſacrilegrs , ſed etiart quibuſdam Gathilicis kecafionem prebuerit errori;. | ** Which preſumpti- «on, faith this eloquent and: ancient «© Authour, brought in ſo muctrevill, thar © it gave not onelya form of fſacriledge * to Heretiques,- but afforded:al{aan oc- * caſt@n of errour;to fame; Gatholiques: 1 And yet all this, according to Pe arrrn faultleſſe, ment, muſt have been free arid fa | yea, and no-way to be corrected, or re- | ptehended, jin_Agrippinas , the queſtion bavins then never brett defined by a Es ', And — | riot onely defends, but moſt highly ,ex- tolls the pious and pure. zeal of Pope Stephen, (which we ſhall preſently treat) and thence comes again, to'our putpoſe, to the cuſtome of the Church; Deniqae in Epiſtol4, que tunc ad Africam miſſa eft, idem his vertis ſanxit. Nuhil inno- . vandum, niſi quod traditum. eft : Intells= gebat $43 The fxth Miſconceipt diſcovered. gebat enim vir ſanftus & prudens, nihit |. alimd ratienem pictatis admittere , wifi at | omria, que fide a patribus ſuſpepra forent, ealem fide filits confignarentur. © Final- * ly ſaith he , in the Epiſtle which was * ſent to Africa, the ſame { Stephen ) de- * creed intheſe words, Ler nothing be in- ' * novated, bur chat which is delivered,(by © tradition.) For this holy and prudent | * man underſtood, that rhe rule of piety « admitted nothing elſe, then that all * things which were received by faith * from_ our Forefathers., by the ſame * faicrh ſhould .be committed to our © Children. bo Now if it had been entirely in the free power of every Biſhop to do, or held, whatſoever he pleaſed, why ſhould Liri- »enfis have praifed Stephen for conſtitu- ting ſucha reſtraining decree, whereby he cook that liberty from them : And if Stephen were to be praifed in that decree, then all thoſe who violated it, were to be judged: offenders , andif they proceeded to exorbitancy , why might Szephen alſo not have been praiſed tor uſing even the cenſure of Excommunication to reftrain them ? Atthe leaſt St, Aguſtin excuſes | Stephen PR*Qs The fixth Miſconceipt diſcovered. 549 ' Stephen (as *we have proved above)from | allSchiſme, even whileſt he judged thoſe Rebaptizers to be excommunicated ; which cannot ſtand , if it had followed from his dorine,that excommunicating, or threatening Excommunication , for holding andpraRiſing that errour , had been <chiſmaricall. And if you give cre- dit to Lirinenſis(as we doubt not but you do) you muſt acknowledge, that-you dif- race *t. Cyprian not a little , in making im{asyou doin this Paragraph) account Stephen te:proceed tyrannically , in iſſu- ing-out ſacha reſtraining and coercive de- cree or command , againſt thoſe of his party : whereby theit liberty aſſigned to them by St. Cypriax was taken away 2 which Zirinenſss praiſeth ſo much in this ſentence. | You ſpend many lines in. preſing again and again this Argument again us, viz. That if St. Cyprian, accordin to Saint A#gyſtins interpretation of his words, thought, chat Biſhops were not to be judged by other Biſhops in'matrers not fully decermined, but to be left to their own freedom , and for this reaſon would not judge, or exclude any who Ng contradicted PT er HIFI dP II ee ae $59 Thefrxth Miſcorceipt diſcovered. contradicted bim in 4his particular mat- | ter of Rebaptuzation , ſeeing Saint Ay- guſtin affirms, that this of Rebaptization was noc then determined, but examined and -diſpured, ſome bolding_ ic, and others denying it , both he and St. Cy- prian muit condemn Stephen for Excom- municarzng thoſe Biſhops and Provinces, who beld againft him in this undetermi- ned point..-; And; -bence you'prels it fur» ther to your preſent purpoſe, that ſeeing St. Auguſtin excules'St. Cyprian from ſchiſme , becauſe: he-did not- Excommu- nicate thoſe, who contradicted him in this difficult and doubtfull queſtiony mui alſo conſequently, by: the rule of con» traries, imply, that Stephen was! guilty | of ſchiſme for doing quite contraty to St. Cyprian, in Excommunicating thoſe of the Eaſt for contradicting him in ir, before it wasfully. determined. This to | my beſt conceiving your words, is the full force, of your-argument ; and it is well deſerving an anſwer, Firſt , - therefore we anſwer , that though the queſtion itſelf were difputed andapitated-in the Church, yer the ipras Cice of not-Rebaptizing was clear and out The (ixth Miſconceipt diſcovered. 551 #F outofqueſtion,, at keaſt by St. (ypriar and his party ; who granted it to be an Ancient, Univerſall practice, though, as- hechought, not Apoſtolicall,, Now for as much as can be gathered: (for ought we yet have ſeen) from the relation of Stephens proceedings , his prohibition his threat of Excommunication ; an acuall Excommunicating thoſe of the Eaſt , was the aRual infringing:of this ancient cuſtome by Rebaptizarion, &c, and for the diſobeying of his command in this. For whatſoever might be dif- puted againſt it by particular Do&ours, yet ſeeing it was an-univerſall, ancient | practice, Pope Stephen would have it to beobſerved, till the whole matter were fully determined by the Church. $o thatif this can be proved , Stephen Ex- communicated, none at all for diſputing the,queſtion, or. holding contrary opini- onsto him and others init, but for actu- ally proceeding in practice by Rebaptiza- tion, as thoſe of the Eaſt did, according to the opinion which they held-in this. For the matter bejng. yet in diſpute, and many .mQre, as.St. Augnſtin now Cited, witneſſech , holding wich Srephes, Hen | wit becauſe St. Cyprian would have been io '552 The fixth Miſconceipt diſcovered. with St. Cyprian init , whatſoever mens particular reaſons perſwaded chem, was not to be eſteemed ſocertain, that con- trary to the opinion of other as wife, learned, and holy as chey were, and much more in number , they ſhould proceed to a contrary practice, unuſed and un- heard of amongft Chriſtians, The ex- communication therefore was for their diſobedience in praice (which was cer-. tain and naqueſtionable, ) and not for their particular opinions, which were diſpured and doubtfall. The diſparity therefore berwixt S:ephers and St. Cypre- «1:5 Cafes conlifts in this, that St. Cyprian would not excommunicate any for hold- ing an opinion in this againſt him, in a matter diſputable and undetermined ; and Stephen would and did excommnni- cate thoſe, who broke for their particular Opinion ina doubtfull point, an undoubt- ed, Univerſall , and Ancient Practice: which diſparity granted, it follows not, |' that Srephen was either to be cenſured as args unjuſtly and uncharicably, or (much lefſe) condemned of Schiſme for excommunicating others , for one thing, 1 for The ſixth Miſconceipt atſcovered. 553 for excommunicating others for a quite other cauſe. Now that Srephens com. mand and excommunication were con- | cerning the violation of this practice one- ly, and not for the ſpeculation it ſelf, ap- pears (ſo faras weare able to judge) evi- dencly. For firſt, the reaſon which Sre- phey gives in Exſebixs of his excommuni- cating thoſe of the Faſt, is onely the contrary praftice, Qzia Hereticos bapti- 2ant ; Becauſe they. baptize Heretiques. Secondly, his command recited by St. Cy- prian, is onely concerning praQtice. N;- hil innevetur , nfs quod traditum eft , ut manus eis imponantur ad panitentiam. ** Let noting be innovated , but onely ©* that hands be impoſed upon them to * penance. ' Thirdly, St. Angaſtin now cited, ſayes thus, Stephan autem etiam abſtinendos putaverat , qui ae ſuſcipiendrs Hereticis priſcam conſuetudinem ronvellere conabantur. ** Stephen allo thought, * that thoſe were to be exommunicated, © or abſtained, who endeavoured to vio- « [ate the ancient cuftome in receiving of « Heretiques. Fourthly, becauſe St. Cy- prian, and thoſe with him, though of a contrary opinion from Stephen, and the - Bb greater <-> 554 The fixth Miſconceipt diſcovered. oreater part of the Biſhops , were not excommunicated by Srephex : which was ' a manifeſt argument , that Srephens ex- communication was not inflicted for holding the ſole opinion of Rebaptiza= tion, (which St. Cyprian and his did) and that they abſtained , till the matter were- more fully determined, and their difficul- ties ſatisfied from violating the former pratice by aCtuall Rebaptization, (afcer they had received Stephexs command) at leaſt publique and notorious , either be- cauſe the occaſion offered not it it ſelf in choſe ſhort and troubleſome times of per- ſecution, ; or becauſe they bare reſpe&t to the command of Srzephern in pradtice, whatſoever their ſpeculative and uncer- rain oPinion dittated to them again it, Thus the African Biſhops carried them- ſelves in practice conformable to Pope _ _ Zozimws aboutthe Councell'of. Sardire*s decree for appeals, which he citedin the name of the Nicene Conncel, though they could not finde any ſuch decree, af- cer many diligences ufed amongft thoſe of the Councell of Nite. Atid'Dimy/i- us Alexandrinas', though ſpeculatively favouring the opinion of Rebaptization; | yet i aa... 9d. tan tm... an as >. > act fronts wo eo a "P "SD Y%Y yy ES ow » 2:2 »* Ww- wy FT Voc *s a DW ov 1H 9 © 2 9$ W VO VW way The fixth Miſcenceipt diſcovered. 555 yet in._praQtice , as he relates. himſelf in Euſeb. lib.4. cap. 8, 9. hePproceeded ac- cording t6 Stephens command +, and the common cuſtome. 7 Now though it could be proved , that Stephens Excommunication might be ex- tended, even to ſuch as defended pub- liquely and peremptorily Rebaptization, yet the caſes of Stephen and St. Cyprian are very different. For'St. Cyprians opi- nion had neither antiquity, norpradtice, nor cuſtome, nor {6 greata number of Biſhops forit by many degrees; as Ste- phens had. For the far greater part then, and all cheir more ancient Predeceſſours, through the whole Church, were of Sze- wer perſwaſion : whereas St. Cyprian d but ſome of Africa, and Firmilian, and others, ſome of the Eaſt, who ſided with then; ſome, and'thoſe very few, of theit latter Predeceſſours , and none of che more Aricient; ' So that if we reſpe&t the ſole externall authority for St. perſwaſion, which at the firſt ſight could not be ſolved; though within a ſhort proceſſe of time the fallacy was diſcover- | ed, and thetruth found out, as St. Augu- ftin witneſſes: nay , notwithſtanding all that was ſaid againſt Srephens perſwaſi- on, the Authority of St. {yprians party was ſo inconfiderable , that even whileſt they oppoſed it , the” whole Chriſtian world was eſteemed to agree with Stephen, as we ſhall preſently ſee. For the Doctrine of receiving thoſe, who were baptized by Heretiques, with- out rebaptization , may be conſidered in four different ſtates. The firſt was in the-univerſall cuſtom and tradition of it amongſt Chriſtians, betore'it was called into queſtion. The ſecond, the retenti- on of it by the Chriftian world, eyen whileſt it was :called into queſtion: by ſome. .. The third, thefinding it out to, | be true, and diſcovering the. fallaciouſ- neſs of the Arguments, which by ſome were brought againſt it, even; by thoſe who brought them, andupon that 'diſco- } very . their relinquiſhing .the contrar opinion, and conforming.chem(elves bot in ſpeculation and praCtice to the gene- rall The fixth Miſconceipt diſcovered. 557 rall and ancient cuſtome: Fourthly, the confirmation of it, and the reje&jon of the contrary Dofrine in the Occume- nicall Councell of Nice. Inevery one. of theſe ſtates, even whileſt it was deeply yo by ſome, it ſtill retained by orce of Cuſtome, to be the Tenet of the. Chriſtian world: and though ſpecula- tively it was made diſputable, becauſe the difficulties were great , which were againſt it, yet practically it was held cer- tain amonglt the generality of Chriſti- ans, by reaſon thatit had been received by univerſall Tradition , whileſt the-con- trary ' opinion never gained to haye more, then by the ſhew of ſeeming plau- fible reaſons, to cauſe a futuation and wavering in the mindes of ſome againft the generall Tradition; and a private perſwaſion 'in others, that it was to be altered. | All this, which I have here delivered, is moſt clearly taught by St. Aguſtin, lib. 2. Contr. Donatiſh, cap. $. where ſpeaking 'of the generall Councell of Nice ,” he fayes thus, Nondum autem fattum erat, quiu conſuetudints robore te- nebatur orbu terrarum ; & kec ſola oppo- 3 nebatur 558 The ſixth Miſconceipt diſcovered. nebatur inducere. volentibus movitatem, quia non poterant apprehendere veritatem ; | Poſtea werd. dum inter multes ex utraque parte trattlatur & queritur , yon ſolun mnventa eſt, ſed etiam ad plenarij Concilij authuritatem roburque perdutta ; poſt {, y- priani quidem paſſionem, ſed antequam nes | ati eſſemns. It (the Councell of Nice} Was not yet celebrated, becauſe the world was held up, or eftabliſhed, by the ftirength of Cuſtom , (here is mentioned the firſt ſtate. of Stephens Tenet, viz. Ancient and Univerſal Cuſtome and Frodiepe) and this alone was appeſed againſt thoſe, w deſired to FP? Nets w w/c they could not Prins Verity. , (Her was the ſecond, That Tradition aver- Fraged ihe particular reaſons of vrivate perions, raiſed up againſtit;), Tet after 3: was treated and ſought into amongſt; ma- » on both ſides, it was not onely found, (Here you ſee a third ſtate, the: finding out the truth ofthis Tradition,), bat was alſo brought to the authority and. firength of a plenary , & generall Connell, (This _ he lait.and moſt fully defined ſtate OT It; From theſe excellent words of this holy _ Doctour, © BD VS '* Ve © "ww Tf? VV 2a. 1, | The fexth M1 iſconcespt diſcovered. 559 DoRour, we draw theſe Truths, in con+- . firmation of what we. have already ſaid, and of our DoErine againſt you. Frit, Thar before a general! Councell be ce- .ſebrated for the determination of points_ in Religion, there may. be the conſent of the whole Chriſtian world in that very point, which it afterwards defines. Non- dam antem' fatium erat , (Concilium) quia tenebatur orbis terrarum, &c, Se- condly, That this conſent of the whole Chriſtian world in any point of Religion, isan eſtabliſhment of Chriſtians in thar. point , .Tencbatur owrbis terrarym, &C.. Thirdly , That univerſall Tradicion, Cuſtome , and Practice of Chriſtians in ” matter of Religion, is ſufficient, to bold them conſtant.ia.the profeſſion and' 'belief of that. /praRice. (o/yc19di- 9%. rahore tenchatur orbis terrarum. 'Fourtbly, Fhat it is ſufficient for Catho- | liques-.to oppoſe. the. ſole. Univerſall Cyſtome of the whole. Chriſtian world, again(t all who endeavour to ipfringe it. Et hec ſola opponebatur- inducere volenti- bus novitatem. Fifthly, That the oppo- fition made by St. Cyprian and thoſe of: his party, no in the opinion of Ef Bb 4 Sr, 560 The fixth Miſconceipt diſcovered. St. Ano»ſiin, that Qlill thoſe, who ad- hered to Stephen in defence of that Anci- ent univerſall Tradicion, were deſerved[y ſiled orbss terravum , the whole Chriſtian world, Sixthly , that notwithſtanding St. Cyprian ſaid , That this Tradition was a corruptics and abuſe , crept into the Church, ana no Apeſtelicall Tradition, Cy- prian. Ep. ad Pompeium. And Firmiki- an, That the Tradition of the Eaſt Church was the cintrary, and that this, maintained by theſe of Rome,was a meer humane T ra- dition, Firmilian. Ep. ad Cyprian. yet be- cauſe they neither did , nor could ſhew when it preciſely begun , and it was uni- verſally obſerved, before they oppoſed it, time out of minde, it was, according to St. Auguſtin, to prevail in the mindes of Chriſtians, as an Apoſticall, Divine, and uncorrupted Tradition, and to have ftrengch ſufficient to eſtabliſh the Church init: Conſuetudinss robore tenebatnr orbis zerrarum, * Seventhly , That notwith- ſtanding all the fair, bur falſe, pretenſions from Scripture, which St. Cyprian and his Councels brought againſt it , it ſtill ſtood as a wall of defence unſhaken to prote&t the Catholique Church, in the dotine, * and — 5. Wy WW 7. # . GG riots: dk... SR bat T he fixth Miſconceipe diſcovered. FG6x and obſervance of it : Er hec ſola appone- batur inducere wolentibus movitatem. Eighthly , chat ſeeing this univyerſall pra- | Rice was ſo ſtrongand impregnable,that the whole Church was ſecured and eſta- bliſhed by the ſtrength of it , who can ra- tionally condemn or blame, and not ra- ther , with: Vincentias. Lirinenſss bighly praiſe. him , and that: the very Donatiſts themſelves confeſs, that he adminiftred the office of his Popedom :/bate, with- out blemiſh, and deſerved to be ftiled Sani#xs,an Holy Biſhop and Martyr, and that not- onely the Weſt , but the Eaſt * Church alſo , Celebrate his Feaſt with a. moſt hight reverence to his holy.and hero. ick actions, which Z:rinenſis give him, in proceeding even to | excommunicate a- Sainſt thoſe, who endeavoured.co violate this cuſtome : for in the violation of that they battered the -bulwark and fortreſs of the Catholique Church. Ninthly, hence - we ſee clearly the difference betwixt the caſe of St: Cyprian , who had confeſſedly no ſuch cuſtome for him, and thag of Sce- phen ; that it would have been gyranny, and occaſionally , or interpretively ſchi{-- - maticall in him , to have-excommunica- emp — Oh Bb.5, red . , ul $i 562 The þxth Miſconceipt. diſcavered ted thoſe who contradicted him. in de-. fence of this. Catholique praQtice- and tradition,” becauſe it would both have. - cauſed a command to.revoke that excom- j; municationfrom ſuperiour-authoricy,the- | rejection whereof would have been for-. mall Schiſmein St. Cypriay., and might: have been interpreted an Excommuniratis. - on for keeping- due Cathdlique Communic in maintaining this ancient- Catholique- praQtice; andinvolvedan interpretative- obſtinate rejetion of the command of- Srephen to the contrary, and conſequent- ly of his authority , and thereby a ſepa- ration from the Church , which we have above proved to be Schiſmaticall:; where- as Stephen did what he had done in de- fence of Catholique Communion anduni- formity, and agreement. amongſt Chri- ſtians in the generalliobſervance: of the. ancient. univerſall-cuftome through the whole- Church, Tenthly , hence ap- pears.in what ſenſe Saint. Auguſtin faid; That this. Queſtion was notfully defined; but diſputed and agitated-in St; Cyprians time- For he can. have po-other meaning - | (if wemake bim, ſpeak. wirchout- contra-. diction, as we mult, and be certainly did). Li WF. 8 bh, rates ce * o Ws FF 9" 0 00 9 00 CON WO OO The fexth Miſconceipt diſcovered, $6; - then this; that the ſpeculative Reaſons alledged againft this practice , were agi- tated amongſt many, though the practice were certain; yet it was for thoſe Rea- ſons denied to be Apoſtolicall by ſome ; The laſt determination therefore added to.it, was that of the Councel of Nice, wherein this pratice was embraced as an - Apoſtolicall Tradition , and. declared to be ſuch to thewbole Church... |, + __ And: hence your: Argument is fully ſolved, by ſhewing that St. Cypriaz had - heen exceedingly blame-worthy , had he - excommunicated. others- for diſſenting from him in this matter then,icalled-into | queſtion by him; and Srepher blameleſle - or -excommunicating thoſe, who viola- ted (as he then moſt cruly. thought and * taught) to be an Apoſtolicall Tradition and Divine truth. For if the þ ppt | by ſome few the univerſall and immemo. - riall Cyſtomes of the Church, could be a ſufficient reaſon to obſtrud the exerci- fing--the full.. obſervance and belief of , them, the gate will be laid open toallun- certainties; andall conſtancy'in Chriſti. anPraftices and Faith will be ſhaken.. * Though. therefore. the Decree: of the | Eos ES = $64 - The ſixth Mifconceipt diſcovered. General! Covuncell. of Nice had not been - yetenacted, yet the truth of this que- ftion was found out, as St. Anſtiy ac- knowledges in the forefaid words,- and } is made manifeſt by Diony ſix and Saint | Hiercme above cited; and all the - Bi- ſhops both of the Eaſt and Africa, whe had adbered to Firmilian and: ve. {y- prian , diſcovered and: revoked' their er- rqur, and reunited themſelves to Srephey, and to the Chriſtian world, (as St _Au- guſtin ayes). adhering to him. And aſl this was effeted (as St. Hierome wits nefles) by- the- force 6f the univerſall practice obſerved' amongſt their Prede- cellours. Hieronym. contra Lucifer. verſ. finem. Demque illi ip Epiſcops qui rebaſtizandos cum eo (Cypriano) ftatu- erant, ad antiquam conſuetudinem revoly- 23, movum emiſere decretum; nid: faci- mu ? tra & nebss majores noſtri, & illths ſui tradidere majores. © Laſtly ,- faith } *«St.' Hierome, thoſe very Biſhops, who 4. had decreed with-him;, (St: Cyprizn) | *« returning again | to their ancient- Cu. -} ** {tome publiſhed a new Dectee.' What «© do we?: Thus our - Predeceffours-delk. a vered to 0s, and theirs to-them; to - UK, Ss T5 Sis | WT = | f The þxth Miſeonceipt diſcovered. 565 & wit, tothoſe who denied Rebaptiza- * tion. Thistruth therefore having'been fo fully diſcovered, and profeſſed by all the Biſhops and people of the: viſible Church , even before the Councell of Nice, what Chriſtian can doubr, that ic- had been not onely in/o/evt madneſs (as St. Auguſtin affirms) to queſtion , or diſpute againſt it, but no leſs. then the crime of Hereſie obſtinately to contra... dict it, and conſequently that before the Councel of N:ce, there was ſufficient ground given to Excommunicate- any, who after this agreement of the whole- Chriſtian world, ſhould have either Re- baptized Heretiques, or maintained, that: they were to be Rebaptized. Nay, even before this truth was fo fully diſcovered: and univerſally agreed upon by all par- ties, ſeeing it was- moſt- manifeſt, that. it bad been not many years before uni- verſally practiſed and believed by all the Biſhops of the viſible Church , *though- ſome few moved ſpeculative difficulties- againſt it , which ſtartled others, not: being well able to ſolve them at the firſt: hearing ,_ yet tlie contradiQing that unj- verſall praftice and belief; vpon the meer- Pro-- 466 The fixth Miſconceipt diſcovered. Propoſition of new difficulties (accord. ing to the Maximes of crue Church.Go- -verament) required both: a command to have that practice obſerved , andan Ex- communication of thoſe who pertinaci- oully infringed that. command, - \ Sy ©'7, 7. «4 "be ſeventh Miſconcip Haven, E:. 19. FE endour anſwer;to all you have vv ar5po with the- _ bs Mikonceipe.. You affirm rr rn _ fore-cited wards accuſe Stepben. the Rope as. Schiſmaticall , for excompmunicating thoſe. Biſhops., who- held Reboptiarion of Heretjques: wheve- in the thing it ſelfis.teve; :wx. /thatſome- for holding too peremptorily that errour were excommunicated by him, v5z.thofe- of the Eaft, and among thereft, as: we- have ſaid; Firmilian, which-is: lwfkciently roved: by. the words of - Fixmilian. cited | en Butto affirm, that any'/Cacha-- e Biſhdp of cliole times, ntianel- . that: wo mir Or Near ales, or evir ſince, accounted = phen a Schilmarique, isoneof the the theſe deals car edt That- ould from pen nated: = % , - 1s he it) in the. whole carriage of- that. affair > Why did D 70nyfus Alexanadrinus inter- cede to him for the: abſolution of Firmi- lian, and thoſe of the Eaſt of his party, _ -aswitneſſeth Exſebins libr,7. Hiftor, cap. : 4. and St. Hierome de Scriptoribus Ecceſi- afticis , in Dionyſro. And why. did whole Chuch, fave ſome few tainted with that errour, an&excommunicated by him i for it, communicate with him? Nay, -why did St. Cyprian himſelf that implaca- -ble deteſter of Schiſme:, and: his- Col- * "a teagues continue to their very deaths in _ his Communion ? ſeeing they knew it was Schiſmaticall to communicate with. Schiſmatiques> Andcertainly St. Cypri- an for his part was as ready ito. have fuf- Fered Martyrdom ,” rather then tochave - communicated ' with a - Schiſmatique, as he was, and did gloriouſly ſuffer it, 'rather then to relinquiſh the Chriſtian \ To thatwhich you urge from-St. A- fins words, ibr. 2. cap. 6: 8c. of St. Cy- prian and his Colleagues being Schiſma- ti ques, > $68 The ſeventh Miſconceipt diſcovered, _—_ for that Excommunication, why o highly commended by Vincentizs Lirinen ſis (who could not be ignorant of . 4 _ an aw a. a ak & t- eo EY ot A SS. tc ad, ns ns on Oe Pots ng TS 4 RE, 7 TE In , F Theſeventh Miſconceipt diſcovered, 569 | tiques, If they had excommunicated their | - Bret bren for denying Rebaptizamton , &C- We anſwer, that it is very true, that they ; had been Schiſmatiques in that caſe i1- F riative and occaſionaliter at leaſt, not, as you imagine, preciſely for an unjuſt Ex- communication oe , or under that ſole notion, but becauſe St. Cyprian and his | party could not have excommunicated thoſe of the contrary opinion , without ſeparating himſelf, in thoſe circumſtances wherein he then was from the whole vili- ble Church , which communicated with Stephen,and all the other Catholick Patri- archs, even in the-contrary do&rine and practice. So that the others with Cy- | Prian being but a party , and having all * | thechief Paſtoursand.cheir flocks againft them, would preſently have brought a Schiſme into the Church, as being aſiding with one party againſt the body of the whole Church. For whoſoever in this _ caſe had been caſt out of the Church by . St. Cyprian, would preſently have appeal- . ed to- his higher Prelates and Patriarchs, that he was excommunicated for commu- nicating with them and theirs : and they muſt have vindicated him againſt St. Cy- prian þ iz them coreſtore him again to Communi. on: Which if, be had obſtinately refuſed, and rejeced-their Authority , he had. G ſeparated | himſelf from the whole þ. Church, and ſo becomea formall Schiſ. matique. To excuſeyour ſelyes from faying,chat Stephen was a Schiſmatique, you anſwer, | that one a& Schiſmatica}l, or of formall 'Schiſme , is not enough to produce an habit, or to denominate one a Schiſma- * tique ; ; becauſe habits are acquired by frequentation of -a&ts: and. no man. is faid to bea Drunkard,, v. gy. for having .been oneedrunk. Bur, firſt, this doQrine | reliſheth much more of Moral Philoſo- phy, then of true Divinity, /\ For though in acquited: natural}, and mo» | paſt babies. yet it'ha*s no place atalll in tnfuſcd ſupernaturallhabics, fuch as that | of Chriſtian Faith. Hope,Cbarity ,&c. are. For who can deny , that wh. citesone a@ of true Faith, is not t denominated :Fidelzs, 'one 'of the Faith- full > or he who exerciſeth ane at of: | Charity, or Love of God, is not Ami- cu Dea, Gods triend and childe ' of 570 The ſeventh Miſconceipt diſcovered. | þ 'prien.and his party, and commanded | Ft ae as it a oa AS dt _ dit. ai ci... an A. 6k. As. oo (ak a— << Bas. o. wwe er elb- A | d. þ T he ſeventh Miſconcript d/covered. 571 | God? and contrariwiſe , theſe Habits _ are loſt byevery mortal ſin of Infidelity, | Hereſie, or Hate of God; and by thoſe {. very acts, which deſtroy the ſaid ſperna-. turall Habits , oneis truly denominated an Infidell, an Heretique , an Enemy of God, &c. otherwiſeit would follow, that one might for want of frequentation of | aRs , neither be reckoned amongſt" the faithfull , nor amongſt the unfaichfull, that one might-be neither a friend , nor an enemy of God, &c. In like manner exery formall a& of Schiſine makes one a formal] Schuſmazique, otherwiſe one ight; be in denomination. a Chriſtian, cage 4 formall AG of Sebi, o gr- of ſeparation. trom.the Church , god vet be neither C Ly -atholique nar Sctulma- % : # Lque. Secing therefore you accule Fte- phen of an-a& of forma)l Schiſme, you muſt make him a Schiſmarique. Second- ' ly, though this your doRrine of Habits had been true, yet you fail.io the applica- tion of it : For you, .in your; Principles, muſt confeſle, that Sceghen committed ., not One onely,. but many, and.very many | ads of -Schiſme, both in aſſuming a pow- er over his Brethren, not due co hum , and im JR OW UBER SELINA I. oe ts er 572 The ſeventh Miſconceipt diſcovered. - in uſing it tyrannically , and in giving decrees and commands againſt the free- dom of the Biſhops , and in excommuni- cating ſo many Churches and perſons,and in proceeding ſo inhumanely with the Le- cates ſent to him, &c. andin continuing, reiterating, and confirming theſe and the hkeaQs many times over. ah The Lines, which next follow, are | ſpentin a fole repetition of what had been ſaid and. 74. weanſwered, that thoſe words, $4» cerdotes Dei, &c. are not in Eraſmus his | Edition, and ſono certain proof. You | ſay, he was , according,to St. Cypria, | A friend of Heretiques; and conſequently | of Schiſmatiques ;' and ſo by bring a friend | of Schiſmatiques communicates with them, and by that communion became a Schiſma- tique : and yet, though we - count one another ſchiſmatiques , we doubt not but you are our friends, -and we hope you think 'the ſame'of us, without all communion able to make one another _ ſchiſmatiques. Thirdly , you fay, that St, —_ — CC ——_ ro unoony—ACoa Emmet wy rr ge >> >> nn Ste oe one — yams ag——— _ _ OW” <2 Aer engR, EDEMA I> 14 yn HED i tony > ans ned A Ser ka. A ad 2: I PP” W's Wn © 7 WO ' The ſeventh Miſconceipt diſcovered, $73 ' St. Cyprian kept communion with Firmi- lian, thongh we account him Excommuni- cated. Therefore why might he nat keep communion with Stephen, though he ac- counted him 4 Sciſmatique ? Weanſwer, That we read of no other communion betwixt Firmilian and St. Cyprian, then ſending a Meſſage, and receiving a Let- ter , and that might have been done, be- fore St. Cyprian underſtood of Firmilians Excommunication, by reaſon of the Sreat diſtance of place betwixt them, Now after St. Cyprian received that E- piſtle, perceiving that he held the errour ; of the Qaarto decimani in it, and ex- | preſſed himſelf ſo uncharitably and diſ- | reſpectfully againſt Srephes (as we have ſhewed) it is not unlikely , that he cut « off all further correſpondence with him : ' Beſide, if he had continned it by Letters onely, and Meſſages, it had not been (at leaft in thoſe dayes) forbidden by ver- - tue of Excommunication, - Do not we familiarly write and ſend meſſages to yon, (though we efteem you Excommu- nicated), and ye: conceive not, that we communicate with you ? : You ſay farther, as touching Legs is ee IE _ $74 The ſeventh Mfiſconceipt diſcovered, his commendation of Srephen in this ri that it is not expreſſed in him whar we ſay) that he commends him" Þ the whale carriage of that affair. | fore Lirinesſis praiſed him in that 'very thing, which you condemn-in him. Now, as I have ſaid, Lirimenſis could not fight- | ly praiſe Stephex for doing that , which was beyond his power, and injurious to .| the Eccleſiaſtical power of other Biſhops: Therefore the making ſach a Decree,and 1 _—_ it to the African Biſhops,” was within his power: and if he had power to ena@ this Law; and inſtitute this Decree, thoſe to whom he ſent it, as his Law'and Dectee, were obliged t6 obey it; aridin caſe: of diſbbedithce , pertinacity , and contempt , he who had power to make that Law, had power to puniſh them for that difobedience': and if the difobedi- ence had gone ſo-far'as'it required and deſerved Exedinimunication, he had alſo powet to Excortimunicate them, atid all this before any full determination =_ , made | $76 The ſeventh Miſconceipt diſcovered, | made of this point by any generall Coun-.# cel. Stand to Lirinenſis his authority; and Þ anſwer,we pray you, punctually this diffi-.F culty. | $49. } Next you come to Dionyſcus Alexan- i drinss, who (firſt) you ſay, might inter. cede for theſe Biſhops, as to an angry man, to pacifie his wrath. But what need had either Dionyſus, or thoſe Biſhops, to have regarded, whether Stephen were an- ory, or well pleaſed, if he had nothing at all to do with them , nor no more power - over them , thea they over him 2 What wiſe man would ſupplicate any one, much} _ lefſe every one for himſelf, or others, | - whom he knows to- be wrongfully and] | undeſervedly offended with them, and of} 1 whom one hath no dependance at all?J r Secondly, you fay it appears not, that this] 1 ſupplication was made. for cho/e Biſbops, | 7 but for thoſe things, or proceedings of | tt Stephen, becauſe it is not v' asg mwv7wr, but | Þ: Tgs Teyrey ; As though the ſupplicati- | I« on made for others, were not concerning | 01 them ; or as though we may. not ſuppli- | Þ: cate another as. well concerning perſons as | of things, Beſide, ſeeing in the forementi-| E3 oned letter of Srephento thoſe of Cappa-| UP | pj N docia,| fu Theſeventh Miſconceipt diſcovered. 577 decia, &c there is no diverlity of things mentioned, but onely of Biſhops and countries, that 7#pi ='y7w muſt neceſſari- ly be referred to the perſons there menti- oned,as it is expreſſed inthe Latine tranſ- lation, Vr pro omnibus his Epiſccpts, &C. Moreover the word Jevuer > ſignifying, as Lexicoris render that verb , ndigeo, r6- of go,/applico, deſidero, careo aliqua re, con- n-| wemoaliquem, quarito, requiro, ſupplex at | deprecor, ef mihi opus, imploro, poſtals, cu- er} p12, peto, oro, wolo , obſecro, flagito , exoro, ath precibus utor, ſum indignus, ſum inferior, chil /i-m pauper, expeto, precibus contendo, ve- rs, | - 25am oro, it muſt conſequently here ſigni- nd} fie, (as I have already noted) that one off ftandsin need , or is necſlitated to have 11>} recourſe to him by an bumble and fub- his | miſle petition, as to a perſon of an higher 2s, | rank and dignity , and who hath power of | to aſliſt me in this my humble recourſe to wt | him. Though cherefore it were refer- ti. | red to the precedent things before menti- ing oned by Dion7/ius, yet becauſeit is, as you Mi- | bave put it «7Lv7ov, thatis, al, and every -as| of them, it muſt comprehend alſo, thar \ti-| Excommunication inflicted by Srephey - upon the ſaid Biſhops; and ſo muſt be a ia,| ſupplication to Stephen , that he would Cc remit. .S &. Be. | 578 The ſeventh Miſconceipt b[covert y [ remit that Excommunication to the ſaid Biſhops, being now penitent and revo- king their errour, as he had ſaid before, Whence appears, that your interpretati.. on, that this was onely to move Srephey, to retra& his at, which you ſuppoſe was injurious, tyrannicall, and ſchiſmaticall, is far from the matter: for then he ſhould I not have ſubmiſly ſupplicated him , but juſtly expoſtulated with him , eſpecially, ifhe were a perſon having no authority at all over thoſe, whom he had injured as you eſteem Srephea to have had none, | For we'think, you your ſelves would be very far now, to ſend an humble ſuppli- cation to the Pope, to retra the excom- munication, which he hath laid upon you and your Brethren, either for your ſelves, or for them, or be content, that any other perſon in union with the Pope, ſhould ſend the like ſupplication to him in your behalf, This ſupplication there- fore ſuppoſes an acknowledgement of Srepheas Authority over Dionyſins , and over all thoſe, in whoſe behalf he wrote it, if they knew it, or conſented to it. To our generall Anſyer to your Au-| thority, A bin find pp we Ld hens wh 4 ig | womd not give the leaſt occa/70s; to it by The ſeventh HMiſconceipt aiſcovered, 579 thority, you onely deny what we faid, without giving any other reaſon, then by alledging a Text of St. Auguſtin , much like to the former, to which we have an- ' ſwered, andto which our faid Anſwer reaches, For there St, Angsſtia dif. putes 4 minore ad majus , thatif St. Cy- were ſo far from Schiſme , that he abſtaining others from himſelf, they were wholly inexcuſable , for the very ſame reaſon, to commit formall Schiſme 7 /e- parating themſelves from the whole Church; wherein we conſtitute the eſſence of Schiſme, and Saint Angyt1z with us. Thus we have endeavoured to return the foreſaid Miſconceipts to that origin, from whence (as we conceive) they firſt iſſued: and thereby wholly diſinabled your inſtance of Firmilian , groundedin them, from giving any the leaſt ſupport to your definition : and could wiſh a ſpeedy diſpatch of theſe indirect diſcour- ſes, to make a ready paſſage to the main Controverhie, CEe2 T ns + * —_— * Thi: & the @nd of our laſt reading, concern- ing their Argument drawn from the example of Fumilian, ro which we never zet (having expeft- c4 above a twelve-moneth) have received any * Anſwer at all from our eAdverſarics. A Re-1 , AF MF FT BY OPEN lan Re- | ; 1 Schiſme unmaskt. In a 'Recapitulation of the chief Paſſages, wherein may be ſeen in brief the Sum of what hath paſſed in thu Confer ence. to colle& into a ſhort Abridgement ( accord- ing to our agreement) the iſſues of each different Head in this E think it now neceſſary view, what hath been ſo largely diſperſed in the former debates , and drawn out at length by force of incident diſputes, that ſuch Readers, as are not verſedin Logi- call Contentions, or Metaphyſicall For- malities, may be rendered capable of the ſubſtance in each precedent difficultie, by | Conference, and behold,as it were,at one -| a plain and.eafie explication of them,, | Which ſhall be performed by a referring the Reader diſtin&tly in each of them, to | thePagesin this printed Treatiſe, where- CE 3 TK $82 A Recapitalation. in they are” reſpe&edly delivered. In the firſt Section of the firſt Chapter it appears, page 1. That the queſtion whether cf us two are Schiſmatiques, Was ſtated by the Proteſtant Diſputants, and fo acknowledged to be their queſtion , the declining of this main,and dire que. tion to the definition of Schiſme was alſo theirs, as appears - p. 2. Prot. 2. The Definition of Schiſme given by the Ca- | tholiques, was allowed as 4 true Propoſi- tion by their Adverſaries, p.2. The Cath. ' Defenants preſently offered'to return to the main queſtion, and were not admifted to it by the Prot. Diſp. who proceeded in tie oppoſitiou of the Cath. Detinition, p. 2. Cath, 3. and, 3. Prot. 4. whence undeniably appears, that this whole Dif- pute upon. the indire& queſtton of the definition of Schiſme, and diverſion from the main queſtion proceeded originally from the Prot. Diſputants. WE In the fame Section , their Argumen drawn from juſt Excommunication, as be- ing a voluntary Separation of one part from the whole true viſible Church of Chriſt, p. 3, 4. and fo contained under- our detiniti- on, is convinced to be a pure fallacy, both Ew? becauſe BL ac Meet aide WESOSY A Reca pitulatiun, 583 becauſe oye part in the definition of ſchiſm _ is taken byall, as related to the part ſe- parating onely, p.5,6,7,8. And the word voluntary ſignifies in the definition of Schiſme, not onely a free, bur an irr4- tiozall, paſſunate , and cauſeleſſe leparati- on, P. 11.c.8. ſuchas no juſt Excomm.u- nication can be; and the word ſeparation, a compleat, and poſitive ſeparation p. 12.13. Where one part oppoſes and rc- jects the other, from whom they ſepa- race, which is not done by vertue. of fole Juſt Excommunication, and the Adverſa- ry bad no other way to fay any thing to our diſtintion of the different figniti- cations of the word voluntary , . then by miſciting our Text , and thereby bearing ' their Readers in hand, that we framed our diftintion of the thing ſignified, when * we framed.it onely of the word ſignifying, or different acceptions of the word volun- tary , as moſt evidently appears, by what they fay in a later anſwer to us, (which is to be related to the firſt Seion, as the laſt part of it) they ſpeak therefore to us - in this manner. P.: I. And becauſe we have upon this occaſion Cc-4. mentioned - 584 A Recapitulatiosn. mentioned that your diftinftion, that we b* ner troubled again to ſpeak to it, wewill a little here examine it. Pag. 17. We diſtinguiſh (/ay y:#) vo- ſuntary (a main ingredient into your defi» zition ) into two Claſſes. For voluntary is (/ay you) either taken in oppoſition to involuntary ad not-free, (where you mult therefore mean by voluntary,free,) or 1n oppolition to reaſonable and pru- dent proceeding. S$o that whereas you ebjetted to us, that according to 24, all more tall fins would be Schiſmes, which we have refuted, according to yon, onely fins would be voluntary ; for mthing but ſiu ts @ pre= cipitous, heady , unreaſonable , imprudeut and wilful atling ( as you there deſcribe voluntary of-the ſecond acception.) But © have Artiſts heardof ſuch a diftinflion of a word into two Claſſes , whereof one mem- ber includes all the other within it ? and.yet ſuch 75 here that your diſtinftion. For .if all precipitous, heady, unreaſonable, impru- dent, and wilful aftings, and acception of things voluntary (which is your ſecona Claſſis) be attual ſins, as certainly they are, and all aliual ſins be alwaies volunta= ry. and free (which is your firſt Claſlis, aud A Recapitnlation, 585 aud acception of things voluntary) as ſure - they are, then moſt evidently it follows, that - your firſt acception includes in it all of your ſecond acception , and ſo very unfit ts be made contradiſtiagniſhing. members; un- leſſe Animal. and Homo may be membra _ condividentia , . or Qualitas and Virtus,. V.G. C You plainly miſcite onr- words, making us ſay thus, viz. We diſtingaih (ſay you) voluntary. (4 main ingreatent into your atfi- nition) into two Claſſes, &c. Now we: ſay not ſo, but thus, To what yer ſay of the - word woluntary , we diſtinguiſh into tmo - Claſſes, &c.. Where you omit theſe two Particles the word , and thereby make us - ſpeake of voluntary , . as it is the thing ſignified , without any relation to the - word, as it hatha double fignitication, when we ſpeak of that word onely as capable of that double ſignification. And, your whole Argument againſt 'us proceeds upon this miſcitation,. For though it would be wholly inartificiall : and illogicall, to diſtinguiſha free A# in. to two Claſſes, viz, into an AR which proceeds from free will, and an AR which : Cc.5; pro-:- 586 A A Recapitulation. proceeds imprudently and ſinfully from | free-will, far the reaſon which you give here; becauſe in this inſtance the word _ free aft ſignifies not expreſly both theſe : yet it will be moſt conform to the rules of Logick, to diſtinguiſh the acceptions of the word voluntary into theſe two , be- cauſe it ſignifies both the Gerzs , and the- Species, that is, both A&s under the. ge- zcricall notion of free AFs , and under _ the ſpecifical/ notion of precipitous , im- . prudent, and "+. Ats. And this being. ly true, that you could not Ceny it, how can it be illogicall to affirm ſo notoriou it? Your inſtances therefore of Qxalitas and Virtus, &Cc. are of no concern here: for there is not one word nominated by.. | 28,524 |
https://github.com/hanswenzel/opticks/blob/master/sysrap/SRand.hh | Github Open Source | Open Source | Apache-2.0 | 2,022 | opticks | hanswenzel | C++ | Code | 22 | 77 | #pragma once
#include <cstddef>
#include "SYSRAP_API_EXPORT.hh"
class SYSRAP_API SRand
{
public:
static unsigned pick_random_category(unsigned num_cat); // randomly returns value : 0,..,num_cat-1
};
| 2,817 |
bpt6k477373w_1 | French-PD-Newspapers | Open Culture | Public Domain | null | La Presse | None | French | Spoken | 6,647 | 12,949 | ~e NMJi~~jaiUt~~PMS~ M~mBMr~BHie~im~t ~M~ME. G!L BLM' S~MMEÎATE~EStmmMBEM~ Bëdigës d'après ses Notes et Manuscrits pAn .BP~'ajJEL :jF.JBL< z` paris, mardt soir i~ juiHet. BULLETIN DU JOUR. Le ~ont<6M)' publie le tableau des revenus indirects s~mestrieis. Nous le reproduisons ci-après. Le débat sur l'Italie a eu lieu hier dans les deux Chambres du 'Parlement anglais; mais, si nousnoas en rapportons aux dépêches fétég''aphiques qui Je résument, nous .devons reconnaître que lord John Russell et lord Lyndhurst se sont contentés de bien faibles éclaircissemens. Lord Palmerston s'est, paraît-il, borné à dire que l'Angleterre n'abandonnerait pas l'Italie, en ajoutant que la discrétion lui faisait uaaevoir de n'entrer dans aucun détail lord John Russell s'est déclaré satisfait et a retiré sa motion .qui tendait à la production de la correspondance. Les choses se sont passées de la même maBière à la Chambre d€&iords. En même temps que le gouvernement anglais plaçait à la tète de l'armée le duc de Cambridge, il apportait d'importans changemens à l'organisation des forces militaires. Ceschangemens touchent à la fois la milice~ et l'armée. La première devra désormais se réunir chaque année, au moins en partie, pour se soumettre aux exercices. Eue conservera un état-major permanent. Le gouvernement espère, de cette façon, être à même d'é-* tendre et de développer rapidement, sans trop de trais, ses moyens de défense en cas de guerre. Quant à l'armée, eile va être dotée de deux fonctions importantes. Pour la première fois, l'infanterie aura un mspecteur général, et les gardes seront placés sous la surveiliance et le commandement d'un ofacierdistingt! lordRokeby. Des Bomiaations importantes, faites pour la plupart an profit d'oiticiers supérieurs qui ont fait leurs preuves en Crimée, complètentcës mesures. De son côté, l'amirauté vient de présenter un projet de loi ayant pour objet d'assurer une meilleure défense des côtes, et une meilleure organisation de l'administration de la marine. Il est aussi question de fortiner Liverpool. Kousavoas reçu nos correspondances de Constantinop!e du 4 juHiat. Oa y trouvera, avec des détails sur les d~rmëres opérations de l'évacuation ~t sur les deux procès qui &e jugent en ce moment a Coastaminople,' des documens mtéressass concernant l'état des esprits dans les Pri&cipau'és danubiennes. Le tclégraphe mentionne l'arrivée du Stnaï avec des nuuveUes Au 7. L'Assemblée fédérale suisse ()es deux Chambres réucies) aprncé3é, dans sa séauce du H juiUet, à la nomination du président et d:: vice-président t de la Confédération pour l'année 1857. Lle choix de-l'Assemblée fédérale pour la présidence s'est porté sur le vice-président actue!, M. Fornerod, du canton deVaud, lequel a été élu, au premier tour de scrutin, par 89 voix sur 422 votans. M. Forn~rod, qui est un des plus jeunes membres du gouvernement central et.quiappartient-au camp radical, avait remplacé, il y une année, M Druey.. La vice-présidence du gouvernement fédéral, plus disputée, a été dévolue à M. Furrér, de Zurich, qui a déjà été à deux reprises président de la Confédération, et qui a occupé ce poste éminent à la satisfaction de tous les partis. Il a obtenu 65 -voix: ses principaux compétiteurs ont été M. Nsef de Saint-GaIi, Kausel, deLucerne,ei. FreiHérosé.d'Argovie. On écrit de Sâist-Pétersbonrg '~ne le cabinet FEUILLETON DE LA PRESSE j DU MARDI SOml5JUJHETl856. GMmURSMM~MMES~. I~IE~R DE BOISBHYm. CHAPITRE XXXI. ° B.a ~eMe tma~ame ~onsuseMn Maigre sa réintégration dans son poste, Jousselin était toujours triste, et ses camarades de bureau lisaient sur ses traita l'état! où se trouvait Suzanne qu'on'avait ramenée presque mourante dans la n'aison de sa mère; mais le docteur Richard ne pouvait aller tous les jours M~gny suivre les.progrès de cette maladie qui tramait depuis un an. Cependant un'malin Jousselin entra au'bureau avec -âne telle Sgure. animée que chacun se dit M" Suzanne est sauvée. Les soins de M. Richard avaient triomphé de la maladie, Suzanne entrait en convalescence. Depuis qu&'M;~ Le Peiktier était de retour a Bayeux, JcusgeHn avait accès chez elle tous les jours les g'ens d,e ravine ne furent pas étonnés de rencontrer sur la promenade l'employé donnant le bras h Suzanne et .la. promenant doucement. Ainsi l'avait voulu lu docteur qui fatigua les mauvaises langues de Bayeux par la publici'té des promeB.s.des de Suzanne en compagnie de Jou~selin a de certains rfgrets, a-des inquiétudes que M~e Le Pelletier ne 'savait dissimuler, M. Richard comprit combien il était pénible a. la veuve de quitter Bayeux. Il est un La reproduction est interdite..Voir la .P~Me du 2? mai a.~l4juiUet. '7~7-c russe s'occupe~i~nent, et aIaM?;de"Ih rëjfôrm~'du'sy&teme Ënanciér, d~'révisioa des tarUs' et 'dé ta réorganisation de l'armée et de la uôtte. En ce qui touche cedernier point, on assure que le système des colonies militaires sera étendu aux frontières d'Asie, et qu'il sera fait un service de Cosaques de la Sibérie auDanube. Parle paquebot ~tHenca, 'arrivé à Liverpool, nous recevons les journaux de New-York du 2 juillet. Les nouvelles des Etats-Unis sont insigninactes; la Californie seule fait parler d'elle. Le conflit entre l'autorité légale du gouverneur et l'autorité iltéga~e du comité de vigitance subsiste Sàn-FraBcisco est en état de siège, et on ne sait comment h situation se dénouera. Au Pérou, le général Castilta, président actuel, a promulgué une, amnistie générale, sans conditions. Le Chili a conclu un traité de paix et de commerce avec la Confédération argentine, et s'apprête à en conclure un autre avec la Nouvelle~ Grenade. Dps troubles ont éc!até dans le Venezuela. La nèvre jaune sévit àla. Havane, et le choléra dans l'Amérique Centrale. La guerre a complètement cessé entre Gosta-Risa et Nicaragua, tous les partis se trouvant réduits,à'i'impuissance par la maladie. A. NEFFTZER. L'agence Mayaa noua transmet les dépêches suivantes:* a Londres, .mardi .15. j~jjUpt~ "Ï)'a'us~a sëaace dé la Qhambredes Commune6,loTd JohnRusselI, faisant sa motion pour'Ia production de la. correspondance italienne, insiste, non pas pour l'intervention étrangère, mais, au'contraire, pour que l'on prévienne l'intervention .étrangère. Il presse le gouvernement de soutenir la Sardaigne, tout en évitant de nourrir, en Italie, de dangereuses espérances. s Lord Palmerston, approuvant vaguement la pen.sée de lord John Russe!], promet l'appui de l'Angleterre à l'Italie, mais il s'abstient d'en'indiquer la nature. B M. Disraeli pense que l'intervention de l'Angleterre en rfaUe n'aurai da justice et d'enet que si elle était concertée avec l'Autriche et la Russie. Autrement, l'Angleterre ne pourrait que soutenir les so-ciutes secrètes que la France ne peut pas appuyer. Quant à la Strdaigne, c'est elle qui attaquera l'Autriche plutôt-que d'être attaquée par cette puissance. B M. Bo~yer exprime l'espoir que la France et l'Autriche retireront leurs troupes d'occupation. mPOTSETREVENUSMDïRECTS.–ÉTATS COMPARATIFS DES RECETTESDE L'ANNÉE 1856AVEC CELLES D~SANNÉESi8METi855.. ( ~IIIFOTS ET REYE~US I~DIRECTS.°ÉTATS C~~iPARATIFS DBS RECETTES DE L'AllITI~II 98Sf AVEC'CELLES D~S A~lfi$ES ~854 ET ~8~ v DES REC~TTES DE .S. f CoE)pafaIsont!niMgcBiest:'et!ei856aTiee te Btême semestre de 1854. ComparaïsaMdtt 1er semestre ~eMSS avec !e même semestre do ISSg. t PROMIT NFFEREKCES "FRODMT -~D1FFBKENCES des impôts indirects sur' 'desimpOtsindirscts sur DÉSIGNATION DES IMPOTS. dul<-r semestre. le l~emestreje~856. DÉSIGNATION DES IMPOTS,. du~em~re. le 1er semestre de 1856. lg~: 9ugmèntat: Dimin,ution. · ~~g~ ~S;ï~. Augmentat, Dimlnutian. Drolis d'enregistrement, de g-reffe,d'hypothèq., etc. 145,532,000 1J:2,93&,000 3~593,000 x Droits d'enregistrement, de greffe, d'hypothèque, etc. 145,538,000 128,680,000 16,852,000 )) Droitdetimbre.2~0,000 24,235,000 3,235,000 ? Droitdetim~-e. 27~70,000 25,631,OCO 1,'789,000 ?' Droits /Qéréales. 1,123,000 969,000 154,000 B Droits Céréaies. 1,123,000 221,000 902,000 ? » -Droits ~éréales 1,123,000 969,000, 154,00t' » Droits '1 Céréales.. 1,123,000 221,000 902,000 » dédouanes Marchandises diverses. 54.9'78,000 41,441,000 13,537,000 ? 'dédouanes Marchandisesdiverses. 54,978,000 55,924,000 )) 946,000 'a il ~Sucres des colonies françaises. 19,m,000 14,480,800 4,697,000 )) à Sucres des-colonies françaises. 19,177,000 17,457,000 1,720,000 )) l'importation. (Sucres étrangers. 9,877,000 lld27,COO s 1,250,000 l'importation. Sucres étrangers. 9;877,000 14,925,000 .)) >, 5,048,000 Droits de douanesarexportation. 762,000 620,000 142,000 B Droits de douanes à l'exportation. 762,000 585,000 177,000 ? » Droits da navi ~ation. 1,682 000 1,420;000 262,G00 n Drcit d navi ~tio p I 682;000 1;392,000 290 000 c Droitsdenavigation. 1,682,000 1,420,000 262,000' 0 D Il Droits denavigation. 1,682,000 1,392,000 290,000 B Droitsetproduitsdivërs dédouanes. 1,104,000 J,297,000 Il 193,000 Droitsetproduitsdiversdedouanes. 1,1C4;COO 1,251,000 )) l47,OCD Taxe de consommation des sels perçue dans le rayon des in~ Taxe de consommation des sels perçue dan~ le rayon des douanes. 11,726,000 10,337,000 1,389.000 -B douanes. i 11,726,000 11,418,000 308,OCO » Droits sur les boissons. 67,219,000 51,222,000 15,997,000 B .Droits sur les boissons.67,219,000 50,603,000 16,616,000 » Taxe de consommation des sels perçue hors dn. rayon des 3,266,000 Taxe de consommation des sels perçue hors du rayon des 3,256,000 douanes. 3,266,000 3,074,000 192,000 )' douanes. 3,266,000 3,256,000 10,000 ), douanes 3,266,000 3,074,000 8.58,000 » douanes 3,266000 3,256,000 .10,000 » .1' Droitdefabricationsurlessucresindigënes. 23,341,000 15,483,000 7,858,000 a Droitdefabrieationsnriessncresindigène's. 23,341,000 12,522,000 10,819,000 B DroitsdiYersetrecettesH.différens titres. 23,057,000 16,715,000 6,34~000 t Droits diversetrecettesadinersnstitres 23,057,000.16.789,000 6,268,00~ B Produit de laYonte.destaba.cs. 79,011,000 71.110,0')0 7,901,000 )) Produit do ia vente des tabacs. 79,011,000 74,083,000 4,928,000 » Broduitdelaventedes poudres. 4,397,000 3,189.000 1,208,000 B' Produit delà ventedespoudres. 4,397,000 3,346,000 1,051,000 )) Produitdelataxedes lettres. 25,017,00024.135,000 882,000 » Produit delataxe des lettres. 25,017,00023,812,000 1.205,000 a n .Droitde20/0surlesenvois d'argent. 868.000' 722,000 146,000 B Droitde20/0surlesenvois d'argent 868,000 852,000 16,000 Produit des places dans les malles-postes. 88,000 224,000 » 136,000 Produit des places dans les malles-postes. 88,000 139,000 )) 51000 Produitdesplacesdanslespaquebots. e 22,000 22,000 Produitdeaplaces dans lespaquebots. 8,000 )) 8000 Droit de transit des correspondances étrangères. ? 11,000 s. 0 11,000 Droit de transit des correspondances étrangères. » ?' Recettes accidentelles. 37,000 12,000 23,000 0 ? Recettesaccidentelles. 37,000 18,000 19,000 ?'/ d > 499,732,000 404,784,000. 96,560,000 1,612,0,00 499,732,000 442,962,000 62,970,000 6,200,000 Augmentation. C'est a~sique l'employé fut ~présenté a. Suzanne pour la première fois. Pendant la convalescence do la jeune 611e, M. Richard e't Mme Le Pelletier n'eurent qu'un nom à la bouche Jousselin. Un autre nom répondait dans ie cœur'de Suzanne -mais elle unit par montrer quelque curiosité po~ir cet Inconnu qui l'aimuit avec un dévoû~nent si silencieux depuis trois ans. Un jour le docteur racontait le redoublement d'amour de remployé quand il crut qus la ngurc de Suzanne était brù~e; le lendemain, MaM Le_PeUetierpIaignaitJiusselin, d'avoir ëtô destitué a c~usede 'Suzanne, ear elle cacha, la réintégration de l'employé dans les bureaux. M. Richarl s'enthousiasmait pour la demande en.mariag'e de Suzanne à s.onlitde mort. Il est'do certaines natures discrètes et timides auxquelles le~ femmes prêtent peu d'attention; renfermés en eux-mêmes, émua profondément en présence des ~.L B'Bnan,ord'John Rassell, cohQa.nt dans les assurances de'l~rd'Ta.lmenMbn,rètH'ë,sa inption~ ~L'incident n'a pas d'autres suites. B Dansia séance delaChambrë des lords, lord Lynd'hurst a parlé sur l'Italie d'ans le même sens que lord John Russell, et la réponse du comte de Clarendon a été identique celle de lord Palmerston. x «Marseille, mardi ISjuillet. D De nombreux arrivages do céréales ont.lieu dans notrepert. B Le paquebot des Messageries-Impériales le Stnaï Tient d'arriver, apportant des nouYelIes de Constantinopledu'7juiUet. < Le coDtre'&miral Tréhouart était arrivé. jB Les Turcs espèrent que l'évacuation sera compote avantleSIdëcentois. 0 Les baachl-bozoucks de SchumJa ont été licenciés. )) Le général Smith est retourné à Cohstantinople. e Les Russes doivent donner un banquet aux généraux Codrington et Pélissier. s Les nouvelles de Salat~ du 28 juin portent que la commission a fait trois tracés pour la délimitation de la frontière, lesquels devront être soumis au Congrès, e <'Athenes,9juillet. D Le ministre Christopoulos a pris l'initiative d'une souscription en Grèce pour venir au secours des inondés do France. S. M-. la. reine a souscrit pour 10,000 francs. B La récolte du raisin de Corinthe ë~ m&gninque. B L'agence LejoHvet-PeytraI aoù3 transmet les dépêches suifMtes: n'' .K.I.onnres,mMdi matin IS juillet. ? Dans la. séance de la. Chambre des communes de cette nuit, lord John RusseUa présenté sa motion sur l'Italie. En développant sa motion, "il. a dit que son intention n'était pas d'encourager les libéraux italiens, si les gouvernemens ne sont pas disposés à intervenir en leur faveur. B II ne désire pas que l'Angleterre intervienne en ce pays, mais il voudrait qu'il fût mis un terme a son occupation par de3 armées étrangères. Il désire savoir ce que l'on est disposé à faire pour la Sardaigne.et quels sont les plans du gouvernement à cet égard. )t Lord Patmarston assure que l'Angleterre n'abandonnera pas l'Italie; mais il ajoute que la discrétion lui défend de donner d'autres explications sur ce sujet. M. Bowyer dit que la France et l'Autriche doivent évacuer .prochainement les Etats pontincaux. x M. Disraeli considère l'intervention anglaise com <85<B. <65~ Augmenta.t. Diminution. '85S. i85S. Augmentât. Diminution. femmes, émus de leur voix, de leurs gestes, de leurs ) regarda/ces esprits délicats sont comme'les pierres unes, qui ont besoin d'être montées par un joailler habile pour répandre leur éclat. Quand iigsont compris et mis .en lumière, ces hommes devenus tout expansion dans l'intimité, sont aimés avec une passion qui étonne les êtres vulgaires. J~. Richard, qui connaissait les moindres nuances de l'a~ection, aidé de Mme Le Pelletier, voulut qu'une sorte-d'amitié s'établît entre Suzanne et Jousselin. La première entrevue eut lieu h Isigny, pendant la convalescence de la jeune nile, qui demanda elle-même a voir l'employé. Quand Jousselin apprit cette nouvelle,,il devint extrêmement pâle et le docteur crut qu'il allait refuser de l'accompagner, Il pouvait peine marcher; le même homme, qui avait soulevé .des pierres énormes pour atteindre unebraRche du jardin on sa promenait Suzanne, était écrasé par l'idëe de se trouver en présence de celle qui n'avait pas quitté sa pensée depuis trois ans. Son corps était aussi, faible et chancelant que le corps d'un condamne qu'on mène au supplice. Quand le docteur lui parlait, il pouvait L a peine se faire comprendre, des moitiés de mots entrecoupés sortaient péniblement de son gosier. Du courage, mon cher Jousselin, remettezvous! Oui, oui, vous avez raison, monsieur Richard. Songez que vous m'avez promis d'aller jusqu'au bout. M"~ Le Pelletier a besoin de vous, il faut que vous rameniez Suzanne a Bayeux. Je ferai tout ce que vous désirez, monsieur Richard. De votre visite d'aujourd'hui dépend te sort de Mms Le Pelletier, qui h ésiie toujours à rester à Bayeux .ou à quitter la vil)e. Oh monsieur Richard, qu'elle reste, je vou§ en supplie, Pendant la route, le docteur recomforta.le pauvre me inutile, parce que, dans ce cas,Ies sociétés secrètes seraient victorieuses en Italie, ce que l'Autriche et la Francenepermettraientpas. Lord J. Russell se déclare satisfait de la réponse .do lord Palmerstpn et retire sa motion, qui demandait la production de la correspondance étrangère échangée au sr'jet des affaires d'Italie. B Dans la Chambre haute, lord Lyndhurst a fait également une motion sur les affaires d'Italie. Lord Clarendon a répondu, comme lord Palmerston, que l'intention de l'Angleterre n'était pas d'abandonner l'Italie, mais que les négociations, encore pendantes, ne permettaient pas de donner des détails sur ce sujet. B Lord Lyndhurst n'a pas persista dans sa motion.!) Le tableau des revenus indirects pour les six premiers mois de cette année est publié ce matin au ~foM~eMf. Les résultats sont très satisfaisans. Ce premier semestre a produit 499,752,000 fr. C'est une augmentation de 36,770,000 fr.sur 1855,etde94,948,OOOSHrl854. L'augmentation sur l'année dernière s'é)eve à 31,085,008 fr. pour le premier trimestre~ et à 25,685,000 fr, pour le deuxième trimestre.' Les recettes pour le premier trimestre avaient été de. 242,191,000 celles dn 2* trimestre Se divisent delamanièrësuivante: Avril. 85,561,000 j Avril. 257~541,000 Mfai: h ~4,f' ~57,â.t;<,008 ,j~~ TotaÏjusqu'au 50 juin 1856 499.752,000 Les droits d'enregistrement ont produit à eux seuls 145 millions et demi, et près de 17 millions de plus 'que l'année dernière. Les droits sur les boissons se sont élevés à 67 millions, avec 16 millions et demi d'augmentation. Il y a aussi un accroissement de 10 millions sur le droit de fabrication des sucres indigènes, et de près de 5 millions sur la vente des tabacs, qui a produit, pour six mois, 79 millions. Nous ne remarquons une forte, diminution que sur les droits de douanes à l'importation des sucres étrangers. Elle n'est pas moindre de 5 millions. La rareté des sucres de provenances étrangères à engagé cette année nos fabriques indigènes à augmenter leur production dans une proportion coBsidérable. Du reste, les nouveaux impôts ont contribué pour un chiffre coasidérable à l'augmentation des amoureux, qui montra dès lors plus de résolution. -Suzanne était encore d'une pâleur mortelle, les yeux agrandis, les mains allongées; Jousselin sentit ses yeux sé mouiller en vo~nt la malade qui portait tant de EOuSrances à l'inférieur. Ses lèvres pâles remuèrent sans laisser passer de sou, mais l'employé crut remarquer à leur mouvement .que Suzaune avait essayé de formuler son nom. IL se précipita sur la main do Suzanne, qui était tiède et privée de mouvement. Ce n'étaient pas seulement des souBrances physiques qui étaient inscrites sur la physionomie de Suzanne': cette pression demain lui nt froid au'cceur, en lui rappelant les douces étreintes de Cyprien, ça premier serrement de main la smte de l'accident de la Fête-Dieu. Mme Le Pelletier, qui épiait la physionomie de sa'nllo,'s'adressa. amicalement à Jousselin, et lui parla quelque temps, a&n de le distraire de son embarras. Le docteur mit la conversation sur un terrain galment amical,' pour chasser les souvenirs de Suzanne et la timidité de l'employé. Cotte première visite laissa Jousselin dans une douée quiétude d'esprit. Il ne s'était pas senti gêné comme il le craignait. L'habileté de convérsation du docteur et de M"~ Le Pelletier Jul avait permis de s'habituer peu peu à la vue de Suzanne. Il rayonnait en contemplant dans son cerveau la petite chambre d'auberge où était couchée la malade. Il avait été frappé particulièrement d'une grande armoire de chêne qui occupait une place considérabla dans la chambre. Cette armcire/'particulière a la Normandie, o.Sre sur chacun de ses panneaux des attributs soulptéa que. Jousselin ne pouvait s'empêcher de regarder comme un symbole. Dans le médaillon du panneau de gauche, deux calQmbsa se becquetaient agitaient leurs ailes entrelacées de rubans qui les attachaient l'une à l'autre. Un tambourin, une musette, posés sur ua cahier de musique, avaient été sculptés sur le revenus car sur ce chiffre de 56,770,000 fr. d'augmentation comparativement a l'année dernière, les nouveaux impôts ne figurent pas pour moins de 41,100,000 Jr., ce qui réduit l'augmentation sur les autres droits a 15,669,000 fr. Le ministre des anances. fait connaître en on-. trela situation des recouvremens effectues pendant le i" semestre de d856. Le montant des rôles s'élevait pour 4856 à 445,609,000 fr.; sur ce chiffre, il a déjà été recouvre 215,146,000 fr. Cette somme représente S do~ëmes 74 centièmes de douzième du montait des rôles, et dépasse de 27,476,000 fr. les 5 douzièmes exigibles. À la même époque de 1855, les recouvremeas ne s'élevaient qu'a 5 douzièmes 68 centièmes de douzième du montant des rôles, et l'avance sur les termes échus n'était que de 24,785,000 fr. Les frais de poursuite faits eh 1856 sont avec les recouvremens dans la proportion de 1 fr. 00/00. L'année dernière, cette proportion était de 1 fr. 1.5 e~ 00/00. (Voir le tableau ci-dès-~ sous.) AM. LACVRAY. AFFAIRES D'ORIENT. {Correspondance particulière de la .Pr~M.). aConstantlDGple,4juIlIet. B Les nouvelles de la Crimée'touchent a leur terme~ Un ordre du marchai Pélissier prévient le général commandant a Constantinople qn'il n'y a. plus lieu expédier les dépêches de l'armée en Crimée.. a Les arrivages de troupes ont a peu près cessé nous ne voyons débarquer que des chevaux ou passer du matériel. Dix mille hommes environ, surtout du train et des divers services administratifs, sont encore en Crimée ils arriveront tous avec le maréchal, qui ne'prend pas passage sur la Bre~ayMg, vaisseau a vapeur de l'amir&l Tréhouart, mais sur le Bo~M~ qui a porté le prince Napoléon. B L'arrivée du maréchal Pélissier sera l'occasion de grandes fêtes a. Constantinople. Les 18,000 hommes qui restent ici, a Masiaq~ Daoud-Pacaa, aux Eaus;Douces et à Gulhané. et les 10,000 hommes qui arriveront dans cinq ou six jours, seront passas en revue ,e par le sultan. Toute l'armée turque, qui se trouve & Constantinople, 40,000 hommes environ, Rgureront a. cette fête militaire. De plus, il y aura grand dîner de 150 couverts au palais. L'étiquette ne. permet pas au sultan d'y assister; mais S. M. viendra au dessert. L'ambassadeur de France se propose aussi de donner une fête son palais de Thêrapia. C'est un connseur panneau de droite. C'es la fameuse armoire da ma~. riage que la jeune ~aileonro asonépoux lejour des noces. Les colombes représentent .l'ameur dans l'u.nion, les instrumons de musique, l'allégresse Qui couronne le mariage. Sur les noeuds sculptés, dont le tailleur d'armoires enveloppe les colombes, il ea6 d'habitude do graver le nom de baptême de la RUe et du garçon, après la. cérémonie nuptiale.. Jousselin tressaillit en remarquant que l'annoi-'re était neuve et montrait des B-~euds d'amour intacts qui attendaient des ip~criptiocs 1 A sa seconda visite, huit jours apr~a, Suzanne entrait en pleina convalescence. L'employé osa a peine la regarder, il ,n'avait des yeux que pour l'armoire. Les ta.mb&Qrins et les, muset'es sculptés faisaient entendre la plus joyeuse des musiques. Suzanne se leva, marcha par la chambreappuyéa sur sa. mère Suzanne resta quelques heures dans un fauteuil Sasanne s'accouda à la fenêtre, Suzanne était sauvée.. Jousselin ne rêvait qu'a l'armoire frappé du symbole sc~pté qui répondait a. ses secrets sentimens, il s'imaginait queSuzan ne avait dû le remarquer; et il épiait ses regards ann de reconnaître s'ils se dirigeaient da,ns la. directioo. des médaillons symboliques. Un jour il frémit 6e ]oie Suzanne se dirigeait vers l'armoirô R semblait impossible qu'eUe ne reniarquâ.t pas ces rubans vierges qui attendaient des noms unis mais Suzanne Ba paraissait prêter aucune attention a ce meuble, qui se~ trouve dans toutes lés maisons de paysans. Désesnéré Jousselin s'en ouvrit au docteur, qui écouta en souriant cette confidence. D~bs un an ou daux, lui dit-il, nous e&sai~oM de parler de l'armoire. C'était un délai bien éloigné, una pï'amesseva-~ gué; mais Jousselin' l'accueillit ~veo joie. Désormais-reçu dans l'intimité des dames Le PeHetier, traité amicalement par'Suzanne, qui faisait de grands efforts pour cacher samiélaneolie, l'employé, passé sous &Mer européen, le Tortoid de Péra, VaUoury, qui 1 est charge de préparer le dîner du palaig. B Le retour d'AaU-Pacha sert de thème mille prol pos divers. On s'accorde a dire que les projets ~laborpa-en son sbsence seront prochainement l'objet de décrets impériaux et mis & exécution. Tous' ceux qui cat approché du grand-vizir depuis son retour ont pu cofstttter enlui un changement notable. Un des caractères dominans de la. pei-sbrna.Uté d'Aa'd-Pacha é~ait une extrême timidité, qui contrastait singutiëroinent avec sa 'haute capacité. Au contact de tous les hommes politiques dont il s'est trouvé le collègue au qu'il a vua dans son voyage a Paris, Londres et Vienne, AaU-Pacha a pris plus d'aplomb, plus de décision cn~DO saurait trop se féliciter s'il apporte dans l'exercice de ses hautes fonctions une énergie que contrariait jusqu'ici sa timidité et sa bonté. )'Le grand-vizir a repris depuis trois jours les renés des anoures des mains de KuprizIi-MehemmedPaoha, qui rentre au poste important de président du conseil du Tanzunat. Le sultaa a voulu récompenser Aali-Pacha pour le zèle avec lequel il a défendu les intérêts de la Porte dans le Congrès de Paris: une pension viagère de 100,000piastres par mois (20,000 fr. ( lui a été accordée. K II y a eu cette sema'më à la 'Porte ou su ïalé de Aali-Pacba, a leni-Keu'i, une procession d'ambassadeurs, ministres et fonctionnaires de tout rang. Hier, j'ai rencontré Ma Porte le généralParizetetle général Bousquet avec leur état-major, allant féliciter le gra.n'i-~izir sur son retour. )) Ces jours derniers, on a beaucoup parlé d'un M'<!<M du sultan relatif la nomination decaïfnaoamsde Moldavie et de~Valacbie. Toutes informations prises, le bruit est inexact. Ça n'est que plus tard qu'on procédera au remplacement des princes, dont les pouvoirs ont été proroges.. Les deux procès de Varna et du Tunisien préoccupent beaucoup l'opinion publique. L'instruction du procea de Vai'Ma a été faite ici. Une commission spéciale jugera les .accusés, parmi lesquels ne figure pointje pacha dont on a tant parlé, SatJk-Pacha. Une séance préparatoire a eu lieu hier pour le réglement de~ débats, qui commenceront demain au ministère .de la poiico. Les séances seront publiques c'est là une innovation en matière criminelle. On veilt donner satis'&stion à l'opinion publique en Europe. Le procès du Tunisien se poursuit, a l'Arsenal, sans incident nouveau Fofacier général tunisien qui avait insulté l'interprète'hellène a été mis aux arrêts. H paraît avéré que les deux accusés sont les vrais coupables. y Riza-Bey, ministre de la Porte à Athènes, quitte décidément ce poste, dans lequel'ii n'a passé que fort peu de temps; sa démission a été acceptée. Il est remplacé .par Ali-N~had-ECfendi, un jeune fonctionnaire qu'on cite pour son intelligence et sa probité. C'est à lui que la ville de Smyrne doit son cadastre. C'est un bon choix mais la Porte eût beaucoup mieux fait encore de confier a. AU-Effendi le gouvernement d'une province il y eût été beaucoup plus utile qu'à Athè nes. ;f Deux ingénieurs des ponts-et-chaussées français sont arrivés ici pour préparer de grandea études de route et de pavage. I)s ont été demandés par le gouvernement, qui leur assure des émolumens magniB ques, M. Thouvenel n'ira pas en congé/comme on l'avait pensé. Lord Redclin'e ne profite pas non plu:, de celui qui lui a été accordé. M. Thouvenel a fait aujourd'hui'une vi&ite à Riza-Pacha et dîne ce soir chez Mouatafa-Pàcha, tous deux membres des anciens ministères. D Oti annonce la prochaine apparition d'un journal polyglotte entièrement consacré au commerce, comme l'indiquera, son titre .0;ërt<t-M/ar~.B «Constantinople, 4 juillet. ? On continue activement, a l'Arsenal l'examen du procès relatif au crime commit par un. ou deux ofncierstunisieEB sur un Hellène. e Les détails que vous connaissez déj& gont exacts. Has=an-Pacba, le général tunisien qui a si gravesteat insulté et l&tribuual et M. Barozzi, premier drogm&n de la. légation hellénique, indiquait par ses o'estes ou des dami-mota la réponse aux accusés. Les ~usies plaints du drog-mah hatlene excitèrent !a cogère d'Rassau-Pacha qui injuria tous les assistacs, frappa, du po'Eg' sur la table et port& plusieurs fois la main à son jsabre. La sé~nca fut lavée, comme je vous l'ai dit, et M. Ba.rozzi~sj-eti:-a en protestant. a D. faut noter que.Ja présence d'Rassau-Pacha et a'Osman-Pacha; un autre général qui s'est fort convenab'.ement conduit, n'atait que pure tol~rauce, et au'~s n'avaient rien voir aux débats. Deux jours plus tard, convoqué, pour une nouvelle séance, le droo-ma~ereo. sur les ordres du ministre, M,.Condurîotti.1'~uaado se-l'elidras.l'Ârsena.I.Ua mot de Mousta~-Pacha.' contre-amirai, préeidsst le couEei! ~egufrre.lui promit une entière satisfaction, et M. Barozzi se rendit au conEpi!. Hassan-Pacha seTp's=nta. comme auparavant. Mais Moustafa-Pacha lui déciM'a q'ie, vu sa conduite inconyenanie, le ministre de la "narre et le ministre de la marias avaient décide qu'il Da serait plus admis aux débats. -a Le général tunisien céda furieux, mais il ne sa ï&tù'a. pas sans éclater en injures jusqu'à Eon caïq. Mous~a-fa-pacha. a e~ la faiblesse de ne pas le fsire arrêter, ce oui aurait dû être faH déjà à là séance prédenté. Cependant, par ordre du capitan.-p.acha, Hasga.n-Pacha.futmi3a.ux arrêts pourdjx jours a bord dn vaisseau amiral turc le .9f<~moMdM< ` ~hef, se regardait comme le plus heureux des hommes. D'accord avec Mma Le Pelletier, le docteur Richard avait répandu dans Bayeux l'annonce d'une u'mon futurs de Jousselin'et de Suzanne. Les mauvais propos s'étaient arrêtés; chacun complimentait le .sous-chef de cetta unioB, qui reculait sans cesse; mais M. Riehaid, pour ne pas inspirer de dénance aux curieux, arguait les secousses maladives qui avaient mis les jours.ae Suzanne en danger, et on le croyait. Trois sns après ~9 départ de Cyprien, M. de Boisdhyver fut nommé ëvêqua de Marseille il partit de Bayeux emportant les regrets d'un peuple, dont les R13 parient encore avec respect du prél&t remarquable par son caractère et ses actes charitables. Le doc~eur Richard soundt vivement de es départ, malgré jes consolations affectueuses de M~s Le Pelletier. Prenez garde, lui dit-il un jour, que je ne parte SUSS1. Sa.paro~etenaitdelaTail~orie, mais l'événement hi justiSa à pea ds temps de là. Non seulement j'y pense, mais j'y ai longtemps .pen''é et j'y penserai toujours. Ce pau~ra garçon pense a Suzanne encore plus que moi; il sèche, il devient maigre, tandis que Suzanne semble ôeurir de son chagrin. Le vieux Giboreau n'ira pas loin, je vous eu réponds, foi de médecin. Jousselin sera nommé chef de bureaa. N'est-ce pas ce que yous demandiez jadis )) Depuis, 11 y a eu deux sëancea noùrelles. Il tessort à peu près clairement des débats que les deux frères qui comparaissent devant la commission sont les deux coupables. Tous deux sont d'origine grecque, comme l'indique leur préi-om .~e MoraU [de Morée), parms du g~ral en f.hef tunisien Réchid-Pacha, et petits-fils, dit-on, d'un amirattunisiien. D Ce procès a démontré combien il est difficile ici, pour la, justice, d'arriver a la constatation de la vérité. Ptus d'une fois. sans doute, destémoinaontou a souffrir d'avoir déposé contre des musulmans, surtout contre des hommes d'un certain rang. Les témoins appelés arrivent à la commission tremblana de tous leurs membres, si bien qu'on est souvent forcé do les faire asseoir. Puis ceux qui ont des renseignemens a w donner, qui savent certaiues particularités de l'affaire ou même qui ont vu commettre le crime et qui, dans un premier mouvement; ont été dépose? qui à la Porte, qui au ministère de police, viennent déclarer aujourd'hui qu'ils ne savent absolument rien; on a toutes les peines du monde a les amener a reconnaître la véracité d.e leurs premières dée!ar&tions. B Le procès des trois-individus'aecusés du Clime de Varna va probablement présenter lésiné mes inci'dens. C'est demain que commencent les débats. Le gouvernement veut leur donner le plus d'éclat possible une vaste salle a été préparée au ministère da la police les dispositions sont telles qu'une centaine de personnes pourront assister a. l'audience. C'est un progrès, et il mérite d'être constaté. )f Les membres de la commission a~Aoc nommés pour juger les accusés sont d'une honorabitité qui présente des garanties sérieuses d'équité. Le président est Ahmed-Vénk-Enendi., ancien ambassadeur en Perse et membre du grand-conseil; les membres sont Cabouli-Enendi, le premier intfrprète du Divan; Nedjib-Eo'endi, mollah, membres du grand-conseil, dont vous avez longuement parié-déja il y a deux mois; un. général de brigade nommé Omer-Pacha, HassanTahcin-Bey, du conseil da la police, .où il remplit des fonctions analogues a celles de juge d'instruction, et" .un chrétien, M. Gabriel. B Cette affaire sera tout une révolution dans la justice ottomane. On a voulu innover, et on conçoit que cela ait pris du temps. L'instruction première, faite à Varna et aux environs, avait été trè~ sommaire il a, fallu la reprendre a-nouveau, la compléter, la rectifier, appeler des témdtns importans qui n'avaient pas été entendus, en chercher d'autres non moiasimportans qu'on n'a pas encore trouvés, et qui probablement manqueront aux débats. Tous ces renseignemeus' étaient indispensables pour formuler un acte d'accusation. D Voici la voie qui sera suivie elta se rapproche jusqu'à un certain point de la législation française. Un acte d'accusation a été dressé il est fort concis. Après cette lecture, les accusés seront interrogés, les témoins a charge seront entendus; puis suivra l'audition des témoins a. décharge. Ensuite le membre chrétien de la commission, M. Gabriel, résumera l'affaire et fera ressortir toutes les circonstances qui peuventservir a constater la culpabitité'des accusés. C'est, en quelque sorte, lui qui remplira la mission du ministère public. Les principaux membres de la commission interrogeront tour à tour, l'un aujourd'hui, l'autre demain. Après ce résumé, la commission rendra son jugement. B Ainsi que vous le voyez, les accusés n'auront pas toutes les garanties précieuses que leur donnent la plupart des législations européennes; ils n'ont pas de défenseurs, i!s sont abandonnés a leurs propres forces. Cela est regrettable, mais on ne peut pas exiger quelque chose de complet pour le premier essai. Il e~t prpbabte qu'il s6 présentera a.i'audience quelque fait inattendu, quelques difncultês de détail auxqueUes on n'aura pas songé. J'assisterai attentivement aux débats, et je -t&"herai de vous en rendre un comptendèie. Ce sera une étude curieuse a plus d'un point de vue. e Pour compléter cette préface, quelques renseigne-' mens. Trois accusés comparaissent aux débats. SalikPacha. n'y.aguro pas ce sont Busseih-Aga, son intendant Moustafa, un caporal attaché, au service du Pacha, etVacii (un-chrétien), aide-cuisinier de la maison du Pacha. Moustafa a commis le crime, il ne le nie pas, mais il déclare qu'il a agi d'après les ordres d'Hussein. Celui-ci affirme qu'il a dit Renvoie cette nHe(~i?'M"~M<'M/t~)'), ou débarrasse-nous (~OMf<sr) de cette ulle, mais non paa Tuez cette Rl!e. Entre eux f'st le débat. e Quoi qu'il en soit, qu'Hussein ait dit ces deux mots ou qu'fl ait di,t Tue, il n'en est pas moins monstrueux de panser qu'il n~en a pas fallu davantage pour que 'Moustafa se soit rendu a. la campagne, sous un prétexte quelconque, avec la n'Ie Hédéla, l'ait étranglée et frappée de plusieurs coups de baïonnette. Et cependant cela s'est fait ainsi. Vp.ci). est'aecusé dé complicité. ge'on Mousta.fa, il aurait tire la corde et aidé ainsi âperpétr.er ce .crime, Vacil nie énergiquement. Selon lui, il a été emmené par Moustafa pour une par'!ie de GaDip~g'ne avec Néd~la; il a rpçu en'tremblant la communication du 'projet de Moustafa, mais il n'a pas aidé au crime. S'il ne l'a pas revête, c'pat.qu'il a craint une vengeance. L'accusation prétend qu'il pouvait parier une fois rentre a Varna, faij'e sa, déposition .a l'autorité ou a son évêque, et que son silence prouve sa .complicité. C'.est .dang ces termes que l'accusation est placée. ;o Salik-Pacha. Be comparaîtra peut-eiye pas même comme témoin, mais it est encore arrêté et emprisonné au séraskiérat. pour notre chëre enfant? Une position tranquille, assurée. Ma pauvre Suzanne ne l'aime pas. Convenez qu'elle a de l'amitié pour lui. –Elle s'est habituée 18 voir; j'ai essayé de le faire aimer, je n'ai pas réussi. -Eh bien! elle le connaît, elle sait qu'elle aura pour mari un galant homme, qui se jetterait dans le feu pour elle, que peut-on désirer de mieux ? Il l'aime, vous le savez. –Mais elle ne l'aime pas. –~Qu'importe? N'en est-il pas toujours ainsi, un quisounre pour unee~f, ou une e~e pour un M. Vous n'avez pas la prétention de cha.ng'er l'humanité? Une certaine confiance en ménage, une habitude doucement amicale ne valent-elles pas mieux que les grandes passions qui s'éteignent plus tristement qu'un feu de la Saint-Jean? Je ne désire plus qu'une joie dans ce monde, c'est d'embrasser-Mme Jousselin le jour de ses noces. Après ç~ je peux m'en aller. Ne dites-pas ces choses-la, docteur. Avez-vous quelquefois songé aux reproches qua M. Jousselin pourrait un jour faire à sa femme? Ah ] que vous le connaissez peu. Pourquoi vous chagriner encore d'un événement qu'il faut chasser comme un.mauvajs rêve. Eh bien! puisque vous me 6 remettez sur/ce cruel chapitre, je ne vous d~rai qu'un mot Jousselin, pas plus que vous, n'a voulu connaîtra le nom du. Assez, mon ami. vous avez raison. Ainsi, Suzanne sera M'na Jousselin ? –'Je ferai tous mes enbrts. Adiverses reprises, M"M Le Pelletier avait essayé de sonder sa nilo sur ce sujet; mais Suzanne-.fondit en larmes et déclara qu'elle no voulait pas sajmarier; elle paraissait si décidée, que la veuve, craignant de raviver dea souSrancea saignantes, gar.Ja.Ie~sHence. H f Quoique ce M soit 1~ qù'uM~aîfë d'un intérêt restreint, eUe a pri~de teDes proportiona morales, on en a tant parlé en Europe,, que je crois bon de vous tenir au courant des divra innidms du p'oces. "Puisque je pnr!e justice, j'ajoute')<i qu'un s.sscz h&ut employé, M'ihdad-En'c:~ii,H. 6té arrêté pur ordre de Kuprizli-MRhemmed-Pacha,pour avoir reçu une somme de 20,000 piastres destinée a"hàter'la concision d'une ajBTaire engagée Ma Porte. On parle d'autres fonctionnaires menacés des mêmes rigueurs. Ce serait d'un excellent exemple, x e Constantinople, 4. B Le JoMftM~ de CoM.!<an<tKop!e continue ~a croisière contre les Principautés. Aujourd'hui, il s'en prend au ~ord, et il s'étale de la Ca~eMe d'~M~s~oM~. 11 n'y a pas à discuter avec les argumens mis en jeu et que .déjà j'ai relevés. Ce journal donne aussi une prétendue correspondance de Jassy, qui tend a faire croire quête vote du'divan (~ Aoc favorable à la réunion ne représente' pas l'qpioion nationale. Une pareille prétention est inadmissible. A part quelques ambitieux, toutes les classes confondent leurs espérances sur ce point. Je suis heureux de pouvoir vous communiquer la lettre suivante d'un grand boyard, qui a été publiée, et qui a produit une sensation notable dans le pays: eDoleesci,28ma.n836. ~Croyez que je me suis réjoui de tout mon coeur B pour le progrès que vous faites dans l'esprit de la B réunion des Principautés sous un prince étranger. )) Insistez avec l'esprit ;et le coeur a réaliser ces belles e espérances; aujourd'hui, c'est la crise de notre ave'onir. Si nous laissons échapper maintenant l'occa? sion qui ne peut venir que tous les cent ans, ce f ne serait que notre propre faute, et nos descenB dans auront le droit de nous blasphémer, d'autant N plus que les moyens ne nous ont pas manqué, ces s moyens étant fournis par les grandes puissances. Il a no nous reste a. faire qu'à repousser loin de nous le ? vil intérêt personnel, qui, sans raison, aveugle les uns, et de nous réunir tous dans le saint intérêt de notre patrie. B Le Roumain qui,.en ce moment, resterait a penDser encore a'l'intérêt particulier devrait être mauD dit, et traité d'homme sans conscience et mépriB sable 1 < Je suis malheureux qu'étant absent, jen'ai pu siB gner l'acte concernant la réunion; mais je vous au]" torise a user de cette déclaration. BLelogothète.G.STOCRZA.x » )) Co n'est pas tout. Le.clerg6 du pays, jusque-lh retarda taire, placé' qu'il était directement sous Finnuence russe, se réveille et renaît à la vie politique. Fort de son. aucien droit, il vient de se prononcer pour la réunion des Principautés par 'l'intermédiaire du vénérable archimandrite N.Scriban. B Voici la motion de cet ecclésiastique < Voici la question du temps actuel pour toutRoua main qui n'est pas dég-énéré La réunion, que les plus B grands princes moldo-valaqu.es et héros ont désirée e autrefois, Etienne-le-&rand et Michet-le-Brave. ce B qu'ils ne purent, eux, obtenir, ce qui .nnus a laissés x le jouet des circonstances et des destinées décrétées B par la Providence pour tous ces peuples et nour tous B ces hommes; ceux-qui s'écartent dû-principe de Ja.. B réunion et de l'harmonie qui fortine et sauve, ceuxB là ne aspirent que de l'esprit de division et d'ini. D mitiô et de l'horreur des ténèbres. ? Patriotes roumains n!s de la chrétienté jusqu'à » ce jour, vous avez été ouMiés par le monde, par les )f autres nations La Providence divine vous envoie B aujourd'hui la demanda de vie ou de mort. L'Eu]" l'ope vous demande, comme Roumains et comme f chrétiens Voulfz-vous la mort ou la vie? Répone dez Répondez comme Roumains, aQn que le mont de sache que dans vos veines coule du même sang B illustre qui fut jadis la gloire du monde entier! 1 D Répondez comme chrétiens, irnn que le monda saD che que vous êtes chrétiens et non point païens :e Mais il ne faut pas agir aveuglément comme on D a agi jusqu'à cette heure-çi, ce qui fait le sujet de f notre repentir. Il faut nous rappeler la sentence du B philosophe qui dit ()Mt'~MM agis, pt'M~ter agas )) f~ptee ~~em pour qu'a la nn le malheur qui préB sidea notre destinée depuis des siècles ne triomphe Bà nous enchaîner par nos propres mains, et que les B nations croient que nous avons été nous-mêmes B les auteurs de nos maux; et nous le sommes encore s aujourd'hui, comme nos ennemis l'ont déjà dit. II ans faut pas nous suicider. x Pour mieux nous éclairer sur ce sujet de vie ou B de mort, nous allons examiner sans passion et.sans B partialité la question ds réunion, s f Ici l'archimandrite Scriban montre, dans le cas de npn-réuDion, les désavantages qui ~en résulteraient, ainsi quelles avantages que la réunion produirait. Nous reproduisons, entre .autres, le point concernant les intérêts politiques Se la Turquie.. e Par noire réunion, dit rari-bimàndrite, nous ofefroDS le p'us grand servieepourlaTtirquieelIeB même, en )a rassuraBt du côté dn nord par la posic tipn nouvelle jd'avant-garde de l'empire contre tout s ennemi. B B Voil~ des documens qu'on peut sérieusement opposer au JoMrMa<<2eCoK~aK~'?!Op~. | 34,809 |
https://stackoverflow.com/questions/54838522 | StackExchange | Open Web | CC-By-SA | 2,019 | Stack Exchange | Ken White, https://stackoverflow.com/users/62576 | Maltese | Spoken | 295 | 758 | Use SUM with UNION ALL in one line
I have the following query:
SELECT SUM(totalCantidad) AS totalCantidad,
SUM(totalPrecio) AS totalPrecio
FROM(
SELECT SUM(dt1.cantidad) AS totalCantidad,
SUM(dt1.cantidad*dt1.precio) AS totalPrecio
FROM Det_materiales dt1
INNER JOIN Materiales ma ON ma.factura=dt1.factura
WHERE ma.factura='1848'
UNION ALL
SELECT SUM(dt2.cantidad) AS totalCantidad,
SUM(dt2.cantidad*p.precio) AS totalPrecio
FROM Det_mate2 dt2
INNER JOIN Materiales ma ON ma.factura=dt2.factura
INNER JOIN Partes p ON p.cod_parte=dt2.cod_parte
WHERE ma.factura='1848'
)x GROUP BY totalCantidad
it returns me this:
Is there a way to generate both SUM () in a single line, like this:
totalCantidad-----totalPrecio
16909 63550,169
Also I need to print data from FROM but I don't know how to display it, in other words I need like this:
factura-----other data-----totalCantidad-----totalPrecio
1848 xxxxxx 16909 63550,169
Any idea to do this?
When you added the SQL tag, there was a large hint that you should also add a tag for the specific DBMS you're using, as syntax and functionality between them differs greatly. It's a waste of both your time and ours for you not to do so, as either you'll get answers you can't use because they're for a different database or we'll waste our time answering your question only to find out it won't work for you. Please [edit] your post to add that DBMS-specific tag. Use only the tag for the actual DBMS you're using.
You can try below - be removing GROUP BY totalCantidad
SELECT factura,SUM(totalCantidad) AS totalCantidad,
SUM(totalPrecio) AS totalPrecio
FROM(
SELECT ma.factura,SUM(dt1.cantidad) AS totalCantidad,
SUM(dt1.cantidad*dt1.precio) AS totalPrecio
FROM Det_materiales dt1
INNER JOIN Materiales ma ON ma.factura=dt1.factura
WHERE ma.factura='1848' group by ma.factura
UNION ALL
SELECT ma.factura, SUM(dt2.cantidad) AS totalCantidad,
SUM(dt2.cantidad*p.precio) AS totalPrecio
FROM Det_mate2 dt2
INNER JOIN Materiales ma ON ma.factura=dt2.factura
INNER JOIN Partes p ON p.cod_parte=dt2.cod_parte
WHERE ma.factura='1848' group by ma.factura
)x group by factura
| 22,581 |
https://github.com/gigios/Test/blob/master/AutoVer/AutoVerUI/Forms/AppSettings.vb | Github Open Source | Open Source | MIT | 2,021 | Test | gigios | Visual Basic | Code | 1,065 | 4,349 |
Public Class AppSettings
'Private InitSettings As String
'Private ReportStopWatch As New System.Diagnostics.Stopwatch()
'Private OperationCount As Integer
Public Config As ConfigEngine
Public Sub New(ByRef ConfigInstance As ConfigEngine)
InitializeComponent()
Config = ConfigInstance
End Sub
Private Sub AppSettings_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
'defaults usually get set in the Config engine during the AutoVer.ini read
Dim pfx86 As String = Environment.GetEnvironmentVariable("ProgramFiles(x86)")
If String.IsNullOrEmpty(pfx86) Then pfx86 = Environment.GetFolderPath(Environment.SpecialFolder.ProgramFiles)
txtApp.Text = Config.AppConfigDefault("CompareApp", pfx86 & "\WinMerge\WinMergeU.exe ""{0}"" ""{1}""")
txtTextViewer.Text = Config.AppConfigDefault("TextViewer", "Notepad.exe")
txtImageViewer.Text = Config.AppConfigDefault("ImageViewer", "MSPaint.exe")
Select Case Config.AppConfigDefault("ConfigFolder", "COMMON")
Case "COMMON"
rbConfigCommon.Checked = True
Case "USER"
rbConfigUser.Checked = True
Case "LOCAL"
rbConfigLocal.Checked = True
End Select
chkAutoElevate.Checked = Config.AppConfigDefault("AutoElevate", "1") = "1"
chkWMI.Checked = Config.AppConfigDefault("WMI", "1") = "1"
chkDebug.Checked = Config.AppConfigDefault("LogLevel", "INFO") = "DEBUG"
chkRecycleBin.Checked = Config.AppConfigDefault("RecycleBin", "0") = "1"
'AppConfig("ServicePort") = "9090"
Try
If Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Run", "AutoVer", String.Empty) = String.Empty Then chkStartup.Checked = False
' If Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\AutoVer", "CompareApp", String.Empty) = String.Empty Then
' txtApp.Text = Environment.GetFolderPath(Environment.SpecialFolder.ProgramFiles) & "\WinMerge\WinMerge.exe ""{0}"" ""{1}"""
' Else
' txtApp.Text = Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\AutoVer", "CompareApp", String.Empty)
' End If
' txtTextViewer.Text = Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\AutoVer", "TextViewer", "Notepad.exe")
' txtImageViewer.Text = Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\AutoVer", "ImageViewer", "MSPaint.exe")
' If Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\AutoVer", "WMI", 1) = 0 Then chkWMI.Checked = False
' If Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\AutoVer", "Debug", 0) = 1 Then chkDebug.Checked = True
' If Microsoft.Win32.Registry.GetValue("HKEY_CURRENT_USER\Software\AutoVer", "RecycleBin", 0) = 1 Then chkRecycleBin.Checked = True
Catch ex As Exception
Dim Log As New Logger
Log.Error(ex.Message, "Can not get CKCU\..\Run in registry:")
End Try
'Try
' If Not IsNothing(System.Configuration.ConfigurationManager.AppSettings("CompareApp")) Then txtApp.Text = System.Configuration.ConfigurationManager.AppSettings("CompareApp")
' If Not IsNothing(System.Configuration.ConfigurationManager.AppSettings("TextViewer")) Then txtTextViewer.Text = System.Configuration.ConfigurationManager.AppSettings("TextViewer")
' If Not IsNothing(System.Configuration.ConfigurationManager.AppSettings("ImageViewer")) Then txtImageViewer.Text = System.Configuration.ConfigurationManager.AppSettings("ImageViewer")
' If Not IsNothing(System.Configuration.ConfigurationManager.AppSettings("WMI")) Then chkWMI.Checked = System.Configuration.ConfigurationManager.AppSettings("WMI")
' If Not IsNothing(System.Configuration.ConfigurationManager.AppSettings("Debug")) Then chkDebug.Checked = System.Configuration.ConfigurationManager.AppSettings("Debug")
' If Not IsNothing(System.Configuration.ConfigurationManager.AppSettings("RecycleBin")) Then chkRecycleBin.Checked = System.Configuration.ConfigurationManager.AppSettings("RecycleBin")
'Catch
'End Try
'InitSettings = IIf(chkWMI.Checked, "1", "0") & IIf(chkDebug.Checked, "1", "0") & IIf(chkRecycleBin.Checked, "1", "0")
OpenFileDialog1.Filter = "Applications (*.exe)|*.exe"
OpenFileDialog1.CheckFileExists = True
'Config.Lang.ExportControlsToFile(Me, ToolTip1)
End Sub
Private Sub Button3_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnCompApp.Click
'Compare App
Dim strApp As String = txtApp.Text
If strApp.Contains(".exe") Then strApp = strApp.Substring(0, strApp.LastIndexOf(".exe", System.StringComparison.Ordinal) + 4)
Try
Dim fiApp As New System.IO.FileInfo(strApp)
OpenFileDialog1.FileName = fiApp.Name
OpenFileDialog1.InitialDirectory = fiApp.DirectoryName
Catch
OpenFileDialog1.FileName = "WinMergeU.exe"
OpenFileDialog1.InitialDirectory = Environment.GetFolderPath(Environment.SpecialFolder.ProgramFiles)
End Try
If OpenFileDialog1.ShowDialog() = Windows.Forms.DialogResult.OK Then
txtApp.Text = OpenFileDialog1.FileName
End If
End Sub
Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnTextView.Click
'Text Viewer
Try
Dim fiApp As New System.IO.FileInfo(txtTextViewer.Text)
OpenFileDialog1.FileName = fiApp.Name
OpenFileDialog1.InitialDirectory = fiApp.DirectoryName
Catch
OpenFileDialog1.FileName = "Notepad.exe"
OpenFileDialog1.InitialDirectory = Environment.GetFolderPath(Environment.SpecialFolder.ProgramFiles)
End Try
If OpenFileDialog1.ShowDialog() = Windows.Forms.DialogResult.OK Then
txtTextViewer.Text = OpenFileDialog1.FileName
End If
End Sub
Private Sub Button4_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnImageView.Click
'Image Viewer
Try
Dim fiApp As New System.IO.FileInfo(txtImageViewer.Text)
OpenFileDialog1.FileName = fiApp.Name
OpenFileDialog1.InitialDirectory = fiApp.DirectoryName
Catch
OpenFileDialog1.FileName = "MSPaint.exe"
OpenFileDialog1.InitialDirectory = Environment.GetFolderPath(Environment.SpecialFolder.ProgramFiles)
End Try
If OpenFileDialog1.ShowDialog() = Windows.Forms.DialogResult.OK Then
txtImageViewer.Text = OpenFileDialog1.FileName
End If
End Sub
Private Sub btnOK_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnOK.Click
Dim Log As New Logger
Try
If chkStartup.Checked Then
Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Run", "AutoVer", Application.ExecutablePath)
Else
Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Run", "AutoVer", String.Empty)
End If
Catch ex As Exception
Log.Error(ex.Message, "Can not set CKCU\..\Run in registry:")
End Try
If txtApp.Text.Trim <> String.Empty Then
Dim strApp As String = txtApp.Text
If strApp.Contains(".exe") Then strApp = strApp.Substring(0, strApp.LastIndexOf(".exe", System.StringComparison.Ordinal) + 4)
If Not System.IO.File.Exists(strApp) Then
MsgBox("Application not found. Select a valid application to compare your files! (or blank if none)", MsgBoxStyle.Exclamation)
Exit Sub
Else
If Not txtApp.Text.Contains("{0}") Then txtApp.Text &= " {0}"
If Not txtApp.Text.Contains("{1}") Then txtApp.Text &= " {1}"
End If
End If
Me.Cursor = Cursors.WaitCursor
Dim AppSettings As Generic.Dictionary(Of String, String) = Config.AppConfig
If rbConfigCommon.Checked Then
AppSettings("ConfigFolder") = "COMMON"
ElseIf rbConfigUser.Checked Then
AppSettings("ConfigFolder") = "USER"
Else
AppSettings("ConfigFolder") = "LOCAL"
End If
AppSettings("LogLevel") = IIf(chkDebug.Checked, "DEBUG", "INFO")
AppSettings("AutoElevate") = IIf(chkAutoElevate.Checked, "1", "0")
AppSettings("WMI") = IIf(chkWMI.Checked, "1", "0")
AppSettings("CompareApp") = txtApp.Text
AppSettings("TextViewer") = txtTextViewer.Text
AppSettings("ImageViewer") = txtImageViewer.Text
AppSettings("RecycleBin") = IIf(chkRecycleBin.Checked, "1", "0")
Config.AppConfig = AppSettings
'Config.Log.UpdateLogLevel(AppSettings("LogLevel"))
Config.SaveAppConfig() 'Updates the live app too
If Not IO.File.Exists(Config.AppConfigFolder & "AutoVer.ini") Then
MsgBox("Error writing to the config file. Select a different Config Location.", MsgBoxStyle.Exclamation)
Me.Cursor = Cursors.Default
Exit Sub
End If
If Not IO.File.Exists(Config.ConfigFolder & "AutoVer.xml") Then
Config.SaveWatcherConfig()
If Not IO.File.Exists(Config.ConfigFolder & "AutoVer.xml") Then
MsgBox("Error writing to the config file. Select a different Config Location.", MsgBoxStyle.Exclamation)
Me.Cursor = Cursors.Default
Exit Sub
End If
End If
Me.Cursor = Cursors.Default
'Try
' UpdateAppSettings()
'Catch ex As Exception
' Log.Error(ex.Message, "Can not set settings in .config file:")
'End Try
'Try
' 'HKEY_LOCAL_MACHINE
' Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\AutoVer", "CompareApp", txtApp.Text.Trim)
' Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\AutoVer", "TextViewer", txtTextViewer.Text.Trim)
' Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\AutoVer", "ImageViewer", txtImageViewer.Text.Trim)
' Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\AutoVer", "WMI", IIf(chkWMI.Checked, 1, 0))
' Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\AutoVer", "Debug", IIf(chkDebug.Checked, 1, 0))
' Microsoft.Win32.Registry.SetValue("HKEY_CURRENT_USER\Software\AutoVer", "RecycleBin", IIf(chkRecycleBin.Checked, 1, 0))
'Catch ex As Exception
' Log.Error(ex.Message, "Can not set HKCU\Software\AutoVer in registry:")
'End Try
'If InitSettings <> (IIf(chkWMI.Checked, "1", "0") & IIf(chkDebug.Checked, "1", "0") & IIf(chkRecycleBin.Checked, "1", "0")) Then
' MessageBox.Show("You must restart Autover/Service for these changes to take effect", "Restart", MessageBoxButtons.OK, MessageBoxIcon.Information)
'End If
Me.Close()
End Sub
'Private Sub UpdateAppSettings()
' 'Update AutoVer.exe.config
' Dim config As System.Configuration.Configuration = System.Configuration.ConfigurationManager.OpenExeConfiguration(System.Configuration.ConfigurationUserLevel.None)
' If Array.IndexOf(config.AppSettings.Settings.AllKeys, "CompareApp") > -1 Then
' config.AppSettings.Settings("CompareApp").Value = txtApp.Text.Trim
' Else
' config.AppSettings.Settings.Add("CompareApp", txtApp.Text.Trim)
' End If
' If Array.IndexOf(config.AppSettings.Settings.AllKeys, "TextViewer") > -1 Then
' config.AppSettings.Settings("TextViewer").Value = txtTextViewer.Text.Trim
' Else
' config.AppSettings.Settings.Add("TextViewer", txtTextViewer.Text.Trim)
' End If
' If Array.IndexOf(config.AppSettings.Settings.AllKeys, "ImageViewer") > -1 Then
' config.AppSettings.Settings("ImageViewer").Value = txtImageViewer.Text.Trim
' Else
' config.AppSettings.Settings.Add("ImageViewer", txtImageViewer.Text.Trim)
' End If
' If Array.IndexOf(config.AppSettings.Settings.AllKeys, "WMI") > -1 Then
' config.AppSettings.Settings("WMI").Value = chkWMI.Checked
' Else
' config.AppSettings.Settings.Add("WMI", chkWMI.Checked)
' End If
' If Array.IndexOf(config.AppSettings.Settings.AllKeys, "Debug") > -1 Then
' config.AppSettings.Settings("Debug").Value = chkDebug.Checked
' Else
' config.AppSettings.Settings.Add("Debug", chkDebug.Checked)
' End If
' If Array.IndexOf(config.AppSettings.Settings.AllKeys, "RecycleBin") > -1 Then
' config.AppSettings.Settings("RecycleBin").Value = chkRecycleBin.Checked
' Else
' config.AppSettings.Settings.Add("RecycleBin", chkRecycleBin.Checked)
' End If
' config.Save(System.Configuration.ConfigurationSaveMode.Modified)
' System.Configuration.ConfigurationManager.RefreshSection("appSettings")
'End Sub
Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnCancel.Click
Me.Close()
End Sub
Private Sub btnHelp_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnHelp.Click
Help.ShowHelp(Me, "AutoVer.chm", HelpNavigator.TopicId, "4")
'System.Diagnostics.Process.Start(Application.StartupPath & "\AutoVerHelp.htm", "#AppSettings")
End Sub
Private Sub Button5_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnLog.Click
Try
If Config.IsService Then
System.Diagnostics.Process.Start(txtTextViewer.Text.Trim, """" & Config.Log.LogFilePath.Replace("AutoVerService", "AutoVer") & """")
ElseIf IO.File.Exists(Config.Log.LogFilePath.Replace("AutoVer", "AutoVerService")) Then
System.Diagnostics.Process.Start(txtTextViewer.Text.Trim, """" & Config.Log.LogFilePath.Replace("AutoVer", "AutoVerService") & """")
End If
System.Diagnostics.Process.Start(txtTextViewer.Text.Trim, """" & Config.Log.LogFilePath & """")
Catch ex As Exception
System.Diagnostics.Process.Start("""" & Config.Log.LogFilePath & """")
End Try
End Sub
Private Sub btnConfigFolder_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnConfigFolder.Click
Try
System.Diagnostics.Process.Start("""" & Config.AppConfigFolder & """")
If Config.ConfigFolder <> Config.AppConfigFolder Then System.Diagnostics.Process.Start("""" & Config.ConfigFolder & """")
Catch ex As Exception
End Try
End Sub
End Class | 1,649 |
https://github.com/Jackxun123/ArcturusEmulator/blob/master/src/main/java/com/eu/habbo/messages/outgoing/guilds/forums/ThreadUpdatedMessageComposer.java | Github Open Source | Open Source | Apache-2.0 | 2,018 | ArcturusEmulator | Jackxun123 | Java | Code | 155 | 913 | package com.eu.habbo.messages.outgoing.guilds.forums;
import com.eu.habbo.Emulator;
import com.eu.habbo.habbohotel.guilds.Guild;
import com.eu.habbo.habbohotel.guilds.GuildRank;
import com.eu.habbo.habbohotel.guilds.forums.GuildForum;
import com.eu.habbo.habbohotel.guilds.forums.GuildForumThread;
import com.eu.habbo.habbohotel.users.Habbo;
import com.eu.habbo.messages.ServerMessage;
import com.eu.habbo.messages.outgoing.MessageComposer;
import com.eu.habbo.messages.outgoing.Outgoing;
import com.eu.habbo.messages.outgoing.generic.alerts.BubbleAlertComposer;
import com.eu.habbo.messages.outgoing.generic.alerts.BubbleAlertKeys;
public class ThreadUpdatedMessageComposer extends MessageComposer {
public final GuildForumThread thread;
public final GuildForum forum;
private final Habbo habbo;
private final boolean isPinned;
private final boolean isLocked;
public ThreadUpdatedMessageComposer(GuildForum forum, Integer thread, Habbo habbo, boolean isPinned, boolean isLocked) {
this.forum = forum;
this.habbo = habbo;
this.thread = forum.getThread(thread);
this.isPinned = isPinned;
this.isLocked = isLocked;
}
@Override
public ServerMessage compose() {
Guild guild = Emulator.getGameEnvironment().getGuildManager().getGuild(forum.getGuild());
if (this.thread == null)
return null;
if (isPinned != thread.isPinned()) {
this.habbo.getClient().sendResponse(new BubbleAlertComposer(isPinned ? BubbleAlertKeys.FORUMS_THREAD_PINNED.key : BubbleAlertKeys.FORUMS_THREAD_UNPINNED.key).compose());
}
if (isLocked != thread.isLocked()) {
this.habbo.getClient().sendResponse(new BubbleAlertComposer(isLocked ? BubbleAlertKeys.FORUMS_THREAD_LOCKED.key : BubbleAlertKeys.FORUMS_THREAD_UNLOCKED.key).compose());
}
if (this.habbo.getHabboInfo().getId() != guild.getOwnerId() ||
guild.canModForum().state == 2 && (Emulator.getGameEnvironment().getGuildManager().getGuildMember(guild, habbo).getRank() == GuildRank.ADMIN
|| Emulator.getGameEnvironment().getGuildManager().getGuildMember(guild, habbo).getRank() == GuildRank.MOD)
|| this.habbo.hasPermission("acc_modtool_ticket_q")) {
this.thread.setPinned(isPinned);
this.thread.setLocked(isLocked);
this.response.init(Outgoing.ThreadUpdateMessageComposer);
this.response.appendInt(this.thread.getGuildId());
this.thread.serialize(this.response);
guild.needsUpdate = true;
Emulator.getThreading().run(this.thread);
Emulator.getThreading().run(guild);
return this.response;
}
return null;
}
} | 43,086 |
US-201113009494-A_1 | USPTO | Open Government | Public Domain | 2,011 | None | None | English | Spoken | 5,333 | 6,279 | System and method for accumulating social relation information for social network services
ABSTRACT
A system for accumulating social relation information for social network services, includes a user location profile management unit for collecting at preset periods location profile information of a user; a user profile management unit for collecting and storing user profiles preset by the user; and a social activity tracking unit for collecting profiles from social activities of the user. Further, the system for accumulating the social relation information for the social network services includes a social relation information generation unit for collecting pieces of information received from the user location profile management unit, the user profile management unit, the email tracking unit, the chatting tracking unit and the Internet phone call tracking unit, and extracting new social relation information based on correlations between the pieces of collected information to generate a social relation ontology.
CROSS-REFERENCE TO RELATED APPLICATIONS
The present invention claims priority of Korean Patent Application No. 10-2010-0004781, filed on Jan. 19, 2010, and Korean Patent Application No. 10-2010-0100085, filed on Oct. 14, 2010, which are incorporated herein by references.
FIELD OF THE INVENTION
The present invention relates to a technology for performing social network services; and, more particularly, to a system and method for accumulating social relation-information for social network services, which is suitable for a scheme for automatically extracting relations formed during a process of transmitting information among members based on social activities in a social network service, and collecting and managing information about social relations among digital members based on the extracted relations.
BACKGROUND OF THE INVENTION
In general, an information exchange service based on social relations, such as a social network service (SNS), is provided such that information about relations among digital members is personally entered by a user or is determined by mutual negotiation among the members. In most cases, such a method primarily forms social relations using specific categories such as friend/family/coworker, and thus a procedure for determining information about a relation with a specific user at each time is required to determine a new relation formed based on a social activity.
Most users use information exchange methods such as email/chatting/phone call when performing social activities. Objects that are mainly managed using such a method are grouped and managed using an address book, and are very rarely used when performing other information exchange methods. In particular, there is a need to actively use the experience/information of members having social relations as user-centered social relation information because of better reliability in a process of collecting information required to solve the problems (needs) of a specific user using a social network service.
However, from the standpoint of a user, methods that are merely used as the means of most social activities, such as email/chatting/phone call, are managed differently from the aspect of services in reality. In order to be interoperable with services such as a social network service, it is required to have additional information about the user and to make an effort to know various items required for relations to be formed.
In order to form a user-centered social relation information required for the conventional social network service implemented as described above, information needs to be collected in compliance with a social relation formation method required by a specific service provider so that services related to the specific service provider can be provided. However, this method described above is problematic in that each service provider has its own unique information system, so the relation information, as well as repetitive information, must be newly input for each service provider.
Further, even if social relation information changes, there is no method for simultaneously changing the information in all related service providers, and thus there is a limitation in that services are provided based on different pieces of information.
SUMMARY OF THE INVENTION
In view of the above, the present invention provides a system and method for accumulating social relation information for social network services, which can automatically extract relations formed during a process of transmitting information among members based on social activities (email/chatting/phone call) in a social network service, and can collect and manage social relation information among digital members based on the extracted relations.
Further, the present invention provides a system and method for accumulating social relation information for social network services, which is capable of collecting information about social relations with a user formed from the social activities of a specific user (email/chatting/Internet phone call), and storing and managing the social relation information using a normalized expression method, thus allowing social network service providers to provide services using a common interface, and to provide the services so that the same social relation information can be maintained even for other services.
In accordance with a first aspect of the present invention, there is provided a system for accumulating social relation information for social network services, including: a user location profile management unit for collecting at preset periods location profile information of a user; a user profile management unit for collecting and storing user profiles preset by the user; a social activity tracking unit for collecting profiles from social activities of the user; and a social relation information generation unit for collecting pieces of information and extracting new social relation information based on correlations between the pieces of collected information to generate a social relation ontology, wherein the pieces of information are received from the user location profile management unit, the user profile management unit and the social activity tracking unit.
In accordance with a second aspect of the present invention, there is provided a method for accumulating social relation information for social network services, including: collecting location profile information of a user at preset periods; collecting and storing user profiles preset by the user; collecting profiles by tracking social activities of the user; receiving and collecting pieces of information about individual profiles to generate a new social relation using comparison and investigation of correlations between the pieces of profile information; and generating a social relation ontology from information about the generated social relation.
In accordance with a third aspect of the present invention, there is provided a method for accumulating social relation information for social network services, including: receiving and collecting information about user profiles preset by a user, location profiles of the user and profiles collected from social activities of the user; determining whether a change has occurred in correlations with existing profiles by comparing and investigating correlations between the social activities; combining a correlation, which has been changed, with the existing profiles or updating the existing profiles, thus collecting social relation profiles; extracting relation information from the combined or updated information according to a preset classification for social relation formation; and converting the extracted relation information into a social relation Ontology Web Language (OWL).
In accordance with an embodiment of the present invention, the system and method for accumulating social relation information for social network services provides a method of collecting social relation information accumulated from the social activities of a user using a general storage method that can be commonly used in typical social network services and utilizing the social relation information. As a result, it is possible to implement a more efficient social relation information accumulation method.
Further, various types of information required to form a social relation ontology based on information collected from the Internet-based social activities of a user, e.g., email, messenger, Internet phone call, and the like are shared, so that a method of searching for a user-centered social relation map can be provided. Accordingly, efficient information management time and convenience can be provided so that more reliable information can be universally used for other social network services.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram showing the construction of a system for accumulating social relation information for social network services;
FIG. 2 is a block diagram showing the construction of a social relation information generation engine unit in accordance with an embodiment of the present invention;
FIGS. 3A to 3C are diagrams showing information about profiles for respective services that can be obtained by a user from social activities in accordance with an embodiment of the present invention;
FIG. 4 is a diagram showing correlations between the results of social activities for accumulating social relation information in accordance with an embodiment of the present invention;
FIG. 5 is a diagram showing user profiles required to form social relations in accordance with an embodiment of the present invention;
FIG. 6 is a diagram showing the classification system of social relation formation in social relation information management configuration schemes in accordance with an embodiment of the present invention;
FIG. 7 is a diagram showing the structure of an ontology for managing social relation information in accordance with an embodiment of the present invention; and
FIG. 8 is a flow chart showing the operating procedure of the social relation information generation engine unit for social network services in accordance with an embodiment of the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings which form a part hereof.
FIG. 1 is a diagram showing the construction of a system for accumulating social relation information for social network services.
Referring to FIG. 1, a social relation information accumulation system 100 is a system for extracting social relations with other persons from the social activities of a user (email, chatting, Internet phone call and the like) and forming a new social relation based on the extracted social relations. The system 100 includes a social-relation information generation unit 102, a user location profile management unit 104, a user profile management unit 106, an email tracking unit 108, a chatting tracking unit 110, an Internet phone call (VoIP: Voice over Internet Protocol) tracking unit 112, a social relation ontology database (DB) 114.
The social relation information generation unit 102 collects pieces of information received from the user location profile management unit 104, the user profile management unit 106, the email tracking unit 108, the chatting tracking unit 110, and the Internet phone call tracking unit 112, extracts new social relation information based on correlations between the pieces of collected information, and then generate a social relation ontology. Further, the social relation information generation unit 102 converts the generated social relation ontology into an Ontology Web Language (OWL) that can be universally used in various types of social network services, and stores resulting data in the social relation ontology DB 114.
The user location profile management unit 104 collects, at preset periods, information about a location at which the user is located, to determine whether the current location of the user is in an office, a home or other place. In this case, collecting the location information of the user is performed in such a way that information is received either from a mobile computing device which receives a location signal from a Global Positioning System (GPS) satellite, or from a Radio Frequency Identification (RFID) reader which receives location information at a time at which an RFID tag attached to the user is read.
The user profile management unit 106 collects and stores profiles that can be preset by each user, detects profiles collected from the social activities based on the current location information of the user which can be identified either using the user profiles or in connection with the user location profile management unit 104, and stores and manages the detected information.
The email tracking unit 108 detects data profile information generated while the user exchanges emails with another party, and thus enables the data profile information to be used as information required to form social relations depending on new or past stored emails.
The chatting tracking unit 110 tracks information about data profiles related to instant messengers because most instant messengers for performing a Short Message Service (SMS) as a social network service retain information grouped for contacts.
The Internet phone call tracking unit 112 cannot extract social relation information using a typical Public Switched Data Network (PSDN) wired phone. Therefore, data profiles that can be tracked using the Internet phone based on the Internet are extracted to form relation information.
As described above, a social activity tracking unit of the user, which includes the email tracking unit 108, the chatting tracking unit 110, and the Internet phone call tracking unit 112 collects profiles from social activities of the user. Further, the data profiles respectively generated by the social activity tracking unit of the user are transferred to the social relation information generation unit 102.
FIG. 2 is a block diagram showing the construction of the social relation information generation engine unit according to an embodiment of the present invention.
Referring to FIG. 2, the social relation information generation unit 102 includes a profile collection unit 200, a correlation comparison investigation unit 202, a social relation profile collection unit 204, a social relation information generation unit 206 and a normalization unit 208.
The profile collection unit 200 collects information received from the user location profile management unit 104, the user profile management unit 106, the email tracking unit 108, the chatting tracking unit 110 and the Internet phone call tracking unit 112. In this way, the profile collection unit 200 monitors information collected by social activities in real time, to check information that has been accumulated and additionally collected for each unit.
The correlation comparison investigation unit 202 tracks common data required to find correlations between pieces of data based on the collected information, to compare and investigate correlations between the results of the social activities required to accumulate social relation information. Further, the correlation comparison investigation unit 202 checks whether the collected information has changed to determine whether the status of the relation information included in the existing data has changed.
The social relation profile collection unit 204 collects and manages profile information about subjects, e.g., users the social relations of which are to be registered based on various types of data collected from the social activities. Further, when a new data profile is received using the results of a social activity which have been compared and analyzed by the correlation comparison investigation unit 202, the social relation profile collection unit 204 combines the received information with the existing profile information and updates to store the combined profile information.
Further, when a new social relation is formed as a result of a new social activity which has been collected and stored by the social relation profile collection unit 204, the social relation information generation unit 206 generates relation information suitable for a preset classification system from the new social relation.
Further, the new social relation information classified by the social relation information generation unit 206 is updated to be in the structure of an OWL file required for the construction of an ontology by the normalization unit 208. That is, the social relation ontology OWL file is provided as a structurized file so that the same can be universally used for other social network services.
FIGS. 3A to 3C are diagrams showing information about profiles for respective services obtained by the user from social activities in accordance with an embodiment of the present invention. Information about profiles for respective services is transferred to and collected by the social relation information generation unit 102, and a new social relation model can be generated using the information about profiles for the respective services.
FIG. 3A shows information collected by the email tracking unit 108 from the history of emails sent or received via an email service and email address-related profiles.
A primary classification system can be formed using the address extensions of each receiver and each sender. For example, classification can be performed using extensions such as ‘co’ (commercial organizations) for businesses, ‘ac’ (academic organizations) for educational organizations, and ‘go’ (government organizations) for public institutions. Further, keyword categories are classified using the titles of emails sent or received, and words frequently used are classified into, e.g., office, friend, family and the like. Further, the similarities between the words are compared and investigated, so that related words are designated as secondary category items.
Furthermore, whether a relevant email is an officially sent file (document) or a file sent from a friend is determined according to the type of file attached to the email, and weights are added according to the type of file, so that the number of accumulations of weights is counted. As a result, a social relation model can be designated using comparison and investigation subsequently performed by the correlation comparison investigation unit 202.
Further, the name of the other party, the date and time of sending/reception, the existence of an attached file, etc. may be collected.
FIG. 3B shows a data profile generated by the Internet phone call tracking unit 112, and illustrates relation information tracked using the call history of Internet phone calls. For example, information about at least one of a full name, a subject-related profile, an email address, a phone number, and originating/terminating call time bands can be collected.
Most telephone directories are configured using such profiles, and email accounts (correlations with other profiles), the area codes of telephone numbers in Republic Of Korea (for example, 02, 031, 032, 042 and the like) and call time bands (working hour/closing hour) may be tracked and used to analyze social relation information.
FIG. 3C shows social relation information extracted from instant messages by the chatting tracking unit 110. For example, the chatting tracking unit 110 collects information about at least one of a group name, a messenger address, connection time, the number of connections, an average logon time band, and an average logout time band.
Most management tools are maintained to group and manage instant messages and to have information required to manage the emails of the other party. Further, the tools may use the time band of the latest connection, the number of connections, and the like as data required to track familiarity.
FIG. 4 is a diagram showing correlations between the results of social activities for accumulating social relation information in accordance with an embodiment of the present invention. When individual profiles are collected from the social activities, as shown in FIGS. 3A to 3C, the correlation comparison investigation unit 202 tracks the common data required to find mutual correlations among the pieces of data in the profiles.
The common elements of profiles collected from fields including the name/age/sex 410 of each user, the email address 412 of the user, and the group type information 414 of the user managed by chatting applications such as a messenger are tracked based on the information profiles of email 400 and chatting 402.
Further, a comparison operation for tracking the relation information between the pieces of data from name/age/sex 420, home/office address 422, and telephone number 424 is performed based on the information profiles of email 400 and Internet phone call 404.
Whether pieces of information collected from the services of chatting 402 and Internet phone call 404 are identical to each other can be determined using similarity and identicalness therebetween based on pieces of information compared using name/sex/age 434, email address 432, and group type information 430. In the comparison and investigation of correlations, as the number of pieces of information collected from the results of social activities increases, more reliable information results can be extracted.
FIG. 5 is a diagram showing user profiles required to form social relations in accordance with an embodiment of the present invention.
Referring to FIG. 5, the social relation profile collection unit 204 is configured to manage profile information about a subject, the social relations of which are to be registered based on various types of data collected from social activities. The social relation profile collection unit 204 collects and stores new data profiles using the results of the social activities compared and analyzed by the correlation comparison investigation unit 202. A plurality of pieces of data collected from the social activities, e.g., email, chatting, Internet phone call and the like are maintained such that they are correlated with social relation information to be used as instances of the subject. Each profile of the subject is used as a social relation information index configured as an ontology based on an ID.
FIG. 6 is a diagram showing the classification system of social relation formation in social relation information management configuration schemes in accordance with an embodiment of the present invention.
When a new social relation is finally formed by the social relation profile collection unit 204, the social relation information generation unit 206 generates social relation information in compliance with a social relation classification system.
As shown in FIG. 6, when a middle category is the family 100, lower category is categorized into spouse 101, child 102, parent 103, sibling 104, and kin 105. When a middle category is friend 200, the lower category is categorized into friend 201, schoolmate 202, and acquaintance 203. Further, when a middle category is coworker 300, the lower category is categorized into coworker 301 and colleague 302, and when a middle category is the opposite sex (in a romantic meaning) 400, the lower category is categorized into boyfriend 401, girlfriend 402 and date 403. Further, when a middle category is neighbor (in a locational meaning) 500, the lower category is categorized into co-resident 501 and neighbor 502.
FIG. 7 is a diagram showing the structure of an ontology for managing social relation information in accordance with an embodiment of the present invention.
The normalization unit 208 updates relation information, classified by the social relation information generation unit 206, to be in the structure of an OWL file required to construct an ontology, as shown in FIG. 7. The social relation ontology OWL file is a file which is structurized to be universally used for other social network services, and by which a social relation with a new subject or a new user is established and is maintained. Consequently, the social relation ontology OWL file can be used to provide a new service.
FIG. 8 is a flow chart showing the operating procedure of the social relation information generation unit for social network services in accordance with an embodiment of the present invention.
Referring to FIG. 8, the profile collection unit 200 of the social relation information generation unit 102 monitors information collected from social activities in real time, and then determines whether accumulated information or additionally collected information for each unit is present in step S800.
Further, in step S802, the correlation comparison investigation unit 202 examines whether a changed item has occurred by performing comparison and investigation between existing data and collected data. In step S804, if a changed item has not occurred as a result of the comparison and investigation even if newly collected information is present, the process returns to step S800 and the profile collection unit 200 is switched to a waiting state for collecting and monitoring profiles.
However, in step S804, if a changed item has occurred, i.e., the changed item is a new subject or is data capable of causing a change in the status of the relation information of the existing data as a result of the comparison and investigation, the process proceeds to step S806 and the social relation profile collection unit 204 combines new collected information received from the correlation comparison investigation unit 202 with the existing profile information to update the existing profile information.
Further, the social relation profile collection unit 204 transfers the combined and updated information to the social relation information generation unit 206, and extracts relation information according to the preset classification for social relation formation in step S808. However, when the extracted relation information is identical to the existing social relation, i.e., a new social relation is not present in step S810, the process proceeds to step S812 and only the updated information is stored, and returns to step S800 and then the profile collection unit 200 is switched to a collection and waiting state.
However, when the relation information extracted by the social relation profile collection unit 204 is information about a new social relation with the subject, the process proceeds to step S814 and user profile change information is transferred to the profile collection unit 200.
Further, in step S816, changed social relation information is transferred to the social relation profile collection unit 204. Finally, in step S818, an ontology corresponding to a changed portion attributable to the new social relation information is changed, and the changed ontology is stored in the OWL file.
As described above, the system and method for accumulating social relation information for social network services according to embodiments of the present invention is configured to automatically extract relations that are formed during a process of transmitting information among members based on social activities in a social network service, and to collect and manage social relation information among digital members based on the extracted relations.
While the invention has been shown and described with respect to the embodiments, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the scope of the invention as defined in the following claims.
What is claimed is:
1. A system for accumulating social relation information for social network services, comprising: a user location profile management unit for collecting at preset periods location profile information of a user; a user profile management unit for collecting and storing user profiles preset by the user; a social activity tracking unit for collecting profiles from social activities of the user; a social relation information generation unit for collecting pieces of information and extracting new social relation information based on correlations between the pieces of collected information to generate a social relation ontology, wherein the pieces of information are received from the user location profile management unit, the user profile management unit and the social activity tracking unit; wherein the social relation information generation unit comprises: a profile collection unit for receiving and collecting information about the individual profiles; a correlation comparison investigation unit for determining whether a change has occurred in correlations with existing profiles by comparing and investigating correlations between the social activities; a social relation profile collection unit for combining a correlation, which has been changed, with the existing profiles or updating the existing profiles; a social relation information generation unit for extracting relation information from the information collected by the social relation profile collection unit according to a preset classification for social relation formation; and a normalization unit for converting the extracted relation information into a social relation Ontology Web Language (OWL); wherein the social relation information generation unit is configured such that: if a new social relation has been extracted, changed user profiles are transferred to the profile collection unit, and changed social relation information is transferred to the social relation profile collection unit.
2. The system of claim 1, wherein the user location profile management unit collects location information received either from a mobile computing device which receives a location signal from a Global Positioning System (GPS) satellite, or from a Radio Frequency Identification (RFID) reader which collects location information at a time at which an RFID tag attached to the user is read.
3. The system of claim 1, wherein the user profile management unit detects profiles collected from social activities based on current location information in connection with the user location profile management unit.
4. The system of claim 1, wherein the social activity tracking unit comprises: an email tracking unit for collecting history of emails sent or received using an email service and email address-related profiles; a chatting tracking unit for collecting profiles based on instant messages sent or received using a chatting application; and an Internet phone call tracking unit for collecting profiles based on a call history of Internet phone calls.
5. The system of claim 4, wherein the email tracking unit collects information about at least one of an extension of an email address, a keyword of an email title, a name of another party, existence and a type of attached file, and a number of accumulations.
6. The system of claim 4, wherein the Internet phone call tracking unit collects information about at least one of a full name of the user, a subject-related profile, an email address, a phone number, and originating/terminating call time bands.
7. The system of claim 4, wherein the chatting tracking unit collects information about at least one of a group name, a messenger address, a connection time, a number of connections, an average logon time band, and an average logout time band.
8. The system of claim 1, wherein the OWL is universally used in different types of social network services.
9. A method for accumulating social relation information for social network services, comprising: collecting location profile information of a user at preset periods; collecting and storing user profiles preset by the user; collecting profiles by tracking social activities of the user; receiving and collecting pieces of information about individual profiles to generate a new social relation using comparison and investigation of correlations between the pieces of profile information; generating a social relation ontology from information about the generated social relation; receiving and collecting information about user profiles preset by a user, location profiles of the user and profiles collected from social activities of the user; determining whether a change has occurred in correlations with existing profiles by comparing and investigating correlations between the social activities; combining a correlation, which has been changed, with the existing profiles or updating the existing profiles, thus collecting social relation profiles; extracting relation information from the combined or updated information according to a preset classification for social relation formation; and converting the extracted relation information into a social relation Ontology Web Language (OWL); wherein said extracting the relation information comprises: if a new social relation has been extracted, changing the user profiles; and changing the social relation profiles.
10. The method of claim 9, wherein the location profile information of the user is obtained by collecting location information received either from a mobile computing device which receives a location signal from a Global Positioning System (GPS) satellite, or from a Radio Frequency Identification (RFID) reader which collects location information at a time at which an RFID tag attached to the user is read.
11. The method of claim 9, wherein said collecting and storing the user profiles further comprises detecting profiles collected from social activities based on current location information detected from the location profile information of the user.
12. The method of claim 9, wherein said tracking the social activities comprises: performing email tracking by collecting history of emails sent or received using an email service and email address-related profiles; performing chatting tracking by collecting profiles based on instant messages sent or received using a chatting application; and performing Internet phone call tracking by collecting profiles based on a call history of Internet phone calls.
13. The method of claim 12, wherein said performing the email tracking further comprises collecting information about at least one of an extension of an email address, a keyword of an email title, a name of another party, existence and a type of attached file, and a number of accumulations.
14. The method of claim 12, wherein said performing the Internet phone call tracking further comprises collecting information about at least one of a full name of the user, a subject-related profile, an email address, a phone number, and originating/terminating call time bands.
15. The method of claim 12, wherein said performing the chatting tracking further comprises collecting information about at least one of a group name, a messenger address, a connection time, a number of connections, an average logon time band, and an average logout time band.
16. The method of claim 9, wherein the OWL is universally used in different types of social network services..
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https://openalex.org/W3007728540 | OpenAlex | Open Science | CC-By | 2,020 | An epigenetic clock for human skeletal muscle | Sarah Voisin | English | Spoken | 10,176 | 17,294 | This may be the author’s version of a work that was submitted/accepted
for publication in the following source: Voisin, Sarah, Harvey, Nicholas R., Haupt, Larisa M., Griffiths, Lyn R., Ash-
ton, Kevin J., Coffey, Vernon G., Doering, Thomas M., Thompson, Jamie
Lee M., Benedict, Christian, Cedernaes, Jonathan, Lindholm, Malene E.,
Craig, Jeffrey M., Rowlands, David S., Sharples, Adam P., Horvath, Steve,
& Eynon, Nir
(2020) An epigenetic clock for human skeletal muscle. ournal of Cachexia, Sarcopenia and Muscle, 11(4), pp. 887-898. Journal of Cachexia, Sarcopenia and Muscle, 11(4), pp. 887-898. This file was downloaded from: https://eprints.qut.edu.au/202281/ © 2020 The Author(s) This work is covered by copyright. Unless the document is being made available under a
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ance. If there is any doubt, please refer to the published source. ORIGINAL ARTICLE ORIGINAL ARTICLE Journal of Cachexia, Sarcopenia and Muscle (2020)
Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/jcsm.12556 Journal of Cachexia, Sarcopenia and Muscle (2020) Journal of Cachexia, Sarcopenia and Muscle (2020)
Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/jcsm.12556 f
,
p
(
)
Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/jcsm.12556 An epigenetic clock for human skeletal muscle Sarah Voisin1*
, Nicholas R. Harvey2,3, Larisa M. Haupt3, Lyn R. Griffiths3, Kevin J. Ashton2, Vernon G. Coffey2, Thomas
M. Doering2,4, Jamie-Lee M. Thompson2, Christian Benedict5, Jonathan Cedernaes6, Malene E. Lindholm7, Jeffrey M. Craig8,9, David S. Rowlands10, Adam P. Sharples11,12, Steve Horvath13 & Nir Eynon1* Sarah Voisin1*
, Nicholas R. Harvey2,3, Larisa M. Haupt3, Lyn R. Griffiths3, Kevin J. Ashton2, Vernon G. Coffey2, Thomas
M. Doering2,4, Jamie-Lee M. Thompson2, Christian Benedict5, Jonathan Cedernaes6, Malene E. Lindholm7, Jeffrey M. Craig8,9, David S. Rowlands10, Adam P. Sharples11,12, Steve Horvath13 & Nir Eynon1* 1Institute for Health and Sport, Victoria University, Melbourne, Australia, 2Faculty of Health Sciences & Medicine, Bond University, Gold Coast, Australia, 3Genomics Research
Centre, Institute of Health and Biomedical Innovation, School of Biomedical Sciences, Queensland University of Technology, Brisbane, Australia, 4School of Health, Medical
and Applied Sciences, Central Queensland University, Rockhampton, Australia, 5Sleep Research Laboratory, Department of Neuroscience, Uppsala University, Uppsala,
Sweden, 6Department of Medical Sciences, Uppsala University, Uppsala, Sweden, 7Department of Medicine, School of Medicine, Stanford University, Stanford, CA, USA,
8Centre for Molecular and Medical Research, Deakin University, Geelong, Australia, 9Epigenetics, Murdoch Children’s Research Institute, Royal Children’s Hospital,
Melbourne, Australia, 10School of Sport, Exercise and Nutrition, Massey University, Wellington, New Zealand, 11Department of Physical Performance, Norwegian School of
Sport Sciences, Oslo, Norway, 12Stem Cells, Ageing and Molecular Physiology Unit, Exercise Metabolism and Adaptation Research Group, Research Institute for Sport and
Exercise Sciences, Liverpool John Moores University, Liverpool, UK, 13Department of Human Genetics and Biostatistics, David Geffen School of Medicine, University of
California Los Angeles, Los Angeles, CA, USA Received: 13 November 2019; Revised: 15 January 2020; Accepted: 30 January 2020
*Correspondence to: Dr Sarah Voisin, Institute for Health and Sport, Victoria University, Melbourne 8001, Australia. Phone: +61 466469673, Email: [email protected].
Associate Professor Nir Eynon, Institute for Health and Sport, Victoria University, Melbourne 8001, Australia. Phone: +61 399195615, Fax: +61 399199185,
Email: nir eynon@vu edu au © 2020 The Authors. Journal of Cachexia, Sarcopenia and Muscle published by John Wiley & Sons Ltd on behalf of Society on Sarcopenia, Cachexia and Wasting Disorders
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the
original work is properly cited. 1Institute for Health and Sport, Victoria University, Melbourne, Australia, 2Faculty of Health Sciences & Medicine, Bond University, Gold Coast, Australia, 3Genomics Research
Centre, Institute of Health and Biomedical Innovation, School of Biomedical Sciences, Queensland University of Technology, Brisbane, Australia, 4School of Health, Medical
and Applied Sciences, Central Queensland University, Rockhampton, Australia, 5Sleep Research Laboratory, Department of Neuroscience, Uppsala University, Uppsala,
Sweden, 6Department of Medical Sciences, Uppsala University, Uppsala, Sweden, 7Department of Medicine, School of Medicine, Stanford University, Stanford, CA, USA,
8Centre for Molecular and Medical Research, Deakin University, Geelong, Australia, 9Epigenetics, Murdoch Children’s Research Institute, Royal Children’s Hospital,
Melbourne, Australia, 10School of Sport, Exercise and Nutrition, Massey University, Wellington, New Zealand, 11Department of Physical Performance, Norwegian School of
Sport Sciences, Oslo, Norway, 12Stem Cells, Ageing and Molecular Physiology Unit, Exercise Metabolism and Adaptation Research Group, Research Institute for Sport and
Exercise Sciences, Liverpool John Moores University, Liverpool, UK, 13Department of Human Genetics and Biostatistics, David Geffen School of Medicine, University of
California Los Angeles, Los Angeles, CA, USA Received: 13 November 2019; Revised: 15 January 2020; Accepted: 30 January 2020 Introduction exercise) on epigenetic ageing of this tissue
and the relationship with health and disease processes.21 In
general, skeletal muscle tissue is of great interest to ageing
researchers and clinicians because skeletal muscle mass is
lost at a rate of 0.5–1% per year after age 50.22 This mus-
cle loss (sarcopenia) leads to a host of age-related compli-
cations including frailty, as well as increased morbidity
and mortality.23 At the same time, skeletal muscle loses mi-
tochondrial function and becomes increasingly resistant to
insulin with age.24 However, skeletal muscle is remarkably
plastic, which makes it a highly responsive target tissue
for lifestyle.24 For example, changes in DNA methylation
that occur with a healthy diet25 and exercise5,6 may be
mechanistically
involved
in
slowing
down
the
ageing
process.1 The first DNA methylation-based estimator of chronolog-
ical age (known as the pan-tissue epigenetic clock) was de-
veloped using a wide spectrum of tissues and nucleated cell
types.7 The resulting regression model could then be used
to estimate the chronological age of tissue samples based
on the DNA methylation levels of 353 cytosine-phos-
phate–guanine dinucleotides (CpGs). The difference be-
tween estimated DNA methylation age and chronological
age reflects not only technical noise but also biologically
meaningful variation seen in epidemiological studies linking
epigenetic ageing rates to mortality risk, Alzheimer’s dis-
ease, and many age-related conditions.10,11 Age-related
conditions are often associated with tissue-specific effects. For example, obesity is associated with strong epigenetic
age acceleration in human liver samples but negligible ef-
fects in muscle tissue when assessed by the pan-tissue
clock.12 In the current study, we aimed to address the poor per-
formance of the pan-tissue clock in muscle by developing a
muscle-specific
epigenetic
clock. We
hypothesise
that
by using a large number of human skeletal muscle DNA
methylation profiles, we can develop a muscle-specific
epigenetic clock that outperforms the pan-tissue clock and
that
can
estimate
chronological
age
with
high
accuracy. We utilised DNA methylation data to estimate
epigenetic age in a total of 682 male and female skeletal
muscle
samples
aged
18–89. We
also
conducted
an
epigenome-wide
association
study
(EWAS)
to
discover
genes whose methylation change with age in skeletal mus-
cle. We have made the muscle clock freely available in an R
package called MEAT (Muscle Epigenetic Age Test) on
BIOCONDUCTOR. Most tissues exhibit similar epigenetic ages according to
the pan-tissue clock, but there are a few exceptions. Introduction no epigenetic clock that performs well in skeletal muscle. While the pan-tissue clock has many applications, tissue-
specific clocks developed exclusively in a given tissue, pro-
vide higher accuracy and specific application to specific
tissues. In particular, blood tissue provides the opportunity
to
develop
accurate
predictors
of
lifespan
and
healthspan,17,18 which is particularly useful as blood sam-
ples are little invasive. Specific epigenetic clocks have been
developed for fibroblasts, keratinocytes, buccal swabs,19
and for cord blood samples.20 However, to the best of
our knowledge, no study to date has tackled the challenge
of developing an epigenetic clock that is specific to human
skeletal muscle. Ageing is the normal, progressive decline of function occur-
ring at the cellular, tissue and organismal levels over the
lifespan.1 Ageing increases susceptibility to a wide range
of diseases, including cardiovascular and neurodegenerative
diseases, metabolic disorders, and many cancers.1 It is
therefore important to identify early and potentially modifi-
able molecular mechanisms that occur with advancing age. Changes in epigenetic patterns constitute a primary hall-
mark of ageing in all tissues of the human body.2 Epige-
netic marks are cellular properties conferring the ability to
remember a previous biological event,3 and some of these
marks are sensitive to environmental stimuli such as diet,
sleep,4 and exercise training.5,6 Epigenetic changes with
age are particularly well characterised at the DNA methyla-
tion level,7,8 including skeletal muscle.9 An epigenetic clock well calibrated in skeletal muscle
could prove useful for studying the impact of environmen-
tal factors (e.g. Abstract Background
Ageing is associated with DNA methylation changes in all human tissues, and epigenetic markers can estimate
chronological age based on DNA methylation patterns across tissues. However, the construction of the original pan-tissue epi-
genetic clock did not include skeletal muscle samples and hence exhibited a strong deviation between DNA methylation and
chronological age in this tissue. Methods
To address this, we developed a more accurate, muscle-specific epigenetic clock based on the genome-wide DNA
methylation data of 682 skeletal muscle samples from 12 independent datasets (18–89 years old, 22% women, 99% Cauca-
sian), all generated with Illumina HumanMethylation (HM) arrays (HM27, HM450, or HMEPIC). We also took advantage of
the large number of samples to conduct an epigenome-wide association study of age-associated DNA methylation patterns
in skeletal muscle. Results
The newly developed clock uses 200 cytosine-phosphate–guanine dinucleotides to estimate chronological age in
skeletal muscle, 16 of which are in common with the 353 cytosine-phosphate–guanine dinucleotides of the pan-tissue clock. The muscle clock outperformed the pan-tissue clock, with a median error of only 4.6 years across datasets (vs. 13.1 years for
the pan-tissue clock, P < 0.0001) and an average correlation of ρ = 0.62 between actual and predicted age across datasets (vs. ρ = 0.51 for the pan-tissue clock). Lastly, we identified 180 differentially methylated regions with age in skeletal muscle at a
false discovery rate < 0.005. However, gene set enrichment analysis did not reveal any enrichment for gene ontologies. Conclusions
We have developed a muscle-specific epigenetic clock that predicts age with better accuracy than the pan-
tissue clock. We implemented the muscle clock in an R package called Muscle Epigenetic Age Test available on BIOCONDUCTOR
to estimate epigenetic age in skeletal muscle samples. This clock may prove valuable in assessing the impact of environmental
factors, such as exercise and diet, on muscle-specific biological ageing processes. Conclusions
We have developed a muscle-specific epigenetic clock that predicts age with better accuracy than the pan-
tissue clock. We implemented the muscle clock in an R package called Muscle Epigenetic Age Test available on BIOCONDUCTOR
to estimate epigenetic age in skeletal muscle samples. This clock may prove valuable in assessing the impact of environmental
factors, such as exercise and diet, on muscle-specific biological ageing processes. Keywords
Skeletal muscle; Epigenetic clock; Ageing; DNA methylation; Epigenetic age; Biological age S. Voisin et al. 2 Introduction For
example, the cerebellum has been found to age more
slowly.13 Conversely, female breast tissue exhibits an in-
creased
epigenetic
ageing
rate,
especially
in
younger
women.7,14 The construction of the original pan-tissue clock
did not include any skeletal muscle samples. The only two
skeletal muscle datasets included in the original study7
(GSE38291 and GSE36166) were not used as training but
as test sets. Both datasets contained DNA methylation pro-
files
generated
with
the
Illumina
HumanMethylation
(HM)27
array
on
vastus
lateralis
muscle
samples;
GSE38291 included 11 pairs of monozygotic twins aged
53–80 years old and discordant for type 2 diabetes,15 while
GSE36166 included 21 paired samples of young, healthy
men (24.6 years old) whose biopsies were taken after a
control diet and following a high-fat diet.16 When the
pan-tissue clock was tested on these few skeletal muscle
samples (n = 66), half of the samples’ predicted age was
off by more than 18 years.7 Therefore, there is currently Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 Description of datasets used We combined three datasets of DNA methylation in skele-
tal muscle [the Gene Skeletal Muscle Adaptive Response Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 An epigenetic clock for human skeletal muscle 3 to Training,26 the E-MTAB-6908 study,4 and the Bond
University Limb Immobilisation and Transcriptional/Epige-
netic Responses (LITER) study (unpublished)], with human
skeletal muscle DNA methylation data from the open-
access Gene Expression Omnibus (GEO) platform and the
database of Genotypes and Phenotypes. We excluded
datasets with <3 samples, missing information on age
(i.e. no age information on the GEO and corresponding au-
thor unresponsive), and datasets from primary cell culture
experiments. Overall, we identified eight datasets on the
GEO and one dataset on database of Genotypes and Phe-
notypes (Supporting Information Data S1), with sample
sizes ranging from n = 3 to n = 282. Eight datasets were
paired designs (e.g. monozygotic twins discordant for dis-
ease or pre-/post-interventions) and four cross-sectional. We described each dataset in details in the Supporting
Information. Then, a β-mixture quantile normalisation method was ap-
plied to adjust for the Type I and Type II probe designs for
methylation profiles generated from the HM450 and HMEPIC
arrays. To identify technical and biological sources of varia-
tion in each individual dataset, singular value decomposition
was performed. In all pre-processed datasets, both the plate
and the position on the plate were identified as significant
technical effects. Thus, all β-values were converted to M-
values, and the ComBat function from the sva package used
to adjust directly for these technical artefacts. Only 19 401 CpGs were identified to be in common be-
tween the 12 datasets after pre-processing, and all probes
found on the HM27, HM450, and HMEPIC arrays (Data S3). To obtain DNA methylation profiles that were comparable be-
tween datasets, we adopted Horvath’s calibration method. We calibrated 11 or the 12 datasets to a gold standard, using
the adapted version of the β-mixture quantile normalisation
algorithm.7 We used GSE50498 as the gold standard because
it was a large dataset (n = 48 samples) with the broadest age
range (18–89 years old). Pre-processing Whenever possible (i.e. when we had information on P
value detection for each probe, raw methylated and
unmethylated signals or IDAT files, and batch/position
information for each sample), we downloaded and pre-
processed the raw data. If we did not have enough infor-
mation on a given dataset (e.g. missing batch information),
we utilised the processed data available on the GEO. In
datasets that we did not pre-process, missing data was im-
puted using the champ.impute function of the ChAMP
package,27 with default parameters. As quality control, we
ensured all datasets had a mean inter-correlation >0.97
and a maximum beta-value >0.99. For each individual
dataset we pre-processed, we applied the following pre-
processing steps using the R statistical software (www.r-
project.org) together with the ChAMP analysis pipeline27
(for a full description of pre-processing steps on each
dataset, see Data S2): β value ¼
intensity of the methylated allele
intensity of the unmethylated allele þ intensity of the methylated allele þ 100 Muscle clock development Predicted and actual age
ated using Pearson’s correlation coefficient (unless all individuals had the same age or the dataset was too small). We also calculated the AA
fference between predicted and actual age. We then calculated the median of the absolute values of AAdiff to estimate how well calibrate
was to this particular test set, and we calculated the mean of AAdiff to see whether the test set as a whole was younger (or older) than expe
y, we calculated the residuals from a linear regression of predicted age against actual age (AAresid) to obtain accuracy measures insensitive t
age of the dataset and to pre-processing techniques. S. Voisin S. Voisin et al. 4 Figure 1 Methodology for leave-one dataset-out cross-validation (LOOCV) and measures of age prediction accuracy. In the LOOCV, one dataset is lef
out (test set) and all other datasets (training sets) are used to develop the age predictor. The DNA methylation profiles of the training sets are inpu
into an elastic net regression model (glmnet package in R), and this model is then used to estimate age in the test set. Predicted and actual age wer
correlated using Pearson’s correlation coefficient (unless all individuals had the same age or the dataset was too small). We also calculated the AAdiff a
the difference between predicted and actual age. We then calculated the median of the absolute values of AAdiff to estimate how well calibrated th
clock was to this particular test set, and we calculated the mean of AAdiff to see whether the test set as a whole was younger (or older) than expected
Finally, we calculated the residuals from a linear regression of predicted age against actual age (AAresid) to obtain accuracy measures insensitive to th
mean age of the dataset and to pre-processing techniques. Figure 1 Methodology for leave-one dataset-out cross-validation (LOOCV) and measures of age prediction accuracy. In the LOOCV, one dataset is left
out (test set) and all other datasets (training sets) are used to develop the age predictor. The DNA methylation profiles of the training sets are input
into an elastic net regression model (glmnet package in R), and this model is then used to estimate age in the test set. Predicted and actual age were
correlated using Pearson’s correlation coefficient (unless all individuals had the same age or the dataset was too small). Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 Muscle clock development We analysed 12 DNA methylation datasets from human skel-
etal muscle for which chronological age was available. We de-
veloped the muscle clock using an elastic net regression
model identical to Horvath’s where a transformed version
of chronological age was regressed on the 19 401 CpGs.7
We first performed 10-fold cross-validation to select the opti-
mal regularisation parameter λ, using the elastic-net mixing
parameter α = 0.5. Given the limited number of datasets and the biased age
distribution in each dataset, we adopted a leave-one-
dataset-out cross-validation procedure to obtain an unbiased
estimate of the muscle clock accuracy. We then calculated
the prediction error as the age acceleration (AA), using two
definitions that have been previously described7,29: the dif-
ference between predicted and actual age (AAdiff) and the re-
sidual from a linear regression of predicted age against actual
age (AAresid) (Figure 1). While AAdiff is a straightforward way
of calculating the error in age prediction, it is sensitive to
the mean age of the dataset7 and to the pre-processing of
the DNA methylation dataset29; AAdiff can be biased upwards
or downwards depending on how the dataset was normalised
and depending on the mean age and age variance of the
dataset. In contrast, AAresid is insensitive to the mean age of
the dataset and is robust against different pre-processing Any sample with >10% of probes with detection P value
>0.01 was removed (default parameter of the champ.load
function). All probes with missing β-values, with a detection
P value >0.01, probes with a bead count <3 in at least 5%
of samples, and non-CG probes and probes aligning to mul-
tiple locations were removed, and for datasets containing
men and women, probes located on the sex chromosomes
were
removed. SNP-related
probes
(“EUR”
population
probes in Zhou et al.28) were also removed. β-values were
obtained and defined as Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 e 1 Methodology for leave-one dataset-out cross-validation (LOOCV) and measures of age prediction accuracy. In the LOOCV, one dataset
est set) and all other datasets (training sets) are used to develop the age predictor. The DNA methylation profiles of the training sets are
n elastic net regression model (glmnet package in R), and this model is then used to estimate age in the test set. Statistics We used a paired t-test on the absolute AA (AAdiff or AAresid)
to compare the accuracy of the muscle clock with that of the
pan-tissue clock. As recently suggested to improve replicabil-
ity in science,30 a P value <0.005 was deemed significant. To identify age-associated methylation positions (DMPs),
we used linear models and moderated Bayesian statistics as
implemented in the limma package.31 The DNA methylation
levels at 19 401 CpGs from the n = 682 muscle samples were
regressed against age, sex, and dataset ID. We used the block
design as implemented in LMFIT to account for the paired de-
signs of some datasets. DMPs associated with age at a false
discovery rate (FDR) < 0.005 were deemed significant.30,32
To identify differentially methylated regions (DMRs, i.e. clus-
ters of DMPs with consistent DNA methylation change with
age), we used the dmrcate package.33 The 682 samples had a bimodal distribution of age, with an
under-representation of 30–50 year olds (n = 242 aged 18–
30, n = 105 aged 30–50, n = 275 aged 50–70, n = 60 aged
70-90, Figure 2). More importantly, datasets greatly differed
in their mean age and age range (Figure 2, Data S1). For ex-
ample, dataset GSE50498 contained younger (21.3 ± 2.4
years old) and older (73.2 ± 4.6 years old) but no middle-aged
individuals; GSE36166 and GSE40798 had no variability in age,
as all individuals were 24–25 years old. To identify age-associated GO terms, we conducted a gene
set enrichment analysis as implemented in the gometh func-
tion of the missMethyl package,34 using our own improved
annotation of the epigenome and largely based on Zhou
et al.’s annotation.28 This function accounts for the biased
distribution of CpGs in genes. All GO terms pathways at FDR
< 0.005 were deemed significant.30,32 Muscle clock development We also calculated the AAdiff as
the difference between predicted and actual age. We then calculated the median of the absolute values of AAdiff to estimate how well calibrated the
clock was to this particular test set, and we calculated the mean of AAdiff to see whether the test set as a whole was younger (or older) than expected. Finally, we calculated the residuals from a linear regression of predicted age against actual age (AAresid) to obtain accuracy measures insensitive to the
mean age of the dataset and to pre-processing techniques. Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 An epigenetic clock for human skeletal muscle 5 methods.29 Finally, we also calculated the Pearson correlation
between predicted and actual age of the sample cohorts. and the more recent HMEPIC, totalling n = 682 samples
(Figure 2, Data S1). Three datasets came from our own lab
or collaborators, and the other nine were publicly available
on the GEO platform or the database of Genotypes and Phe-
notypes. Only three datasets included women, and only two
datasets included non-Caucasian individuals. Eight of the 12
datasets were paired designs (e.g. monozygotic twins discor-
dant for disease or pre-/post-interventions, Data S1), mean-
ing that some of the 682 muscle samples were taken from
healthy individuals at baseline or after a control diet, while
other samples were taken after an exercise intervention, a
high-fat diet, sleep deprivation, insulin stimulation, or were
from individuals with type 2 diabetes. We chose to keep all
samples in the development of the muscle clock, as none of
these factors were associated with drastic changes in age ac-
celeration. For details on each individual dataset such as sam-
ple collection and DNA methylation assay, see Data S2. Development of a highly accurate skeletal muscle
epigenetic clock To develop the muscle clock, we adopted the same approach
as Horvath.7 Briefly, we restricted our analysis to the 19 401
CpGs that were present in all 12 datasets. Then, we used
dataset GSE50498 that had a large sample size (n = 48), and
the broadest age range (18–89 years old), as a gold standard
to calibrate all other datasets. Although it does not entirely
remove variability from different labs and platforms, this step
allows for a harmonisation of DNA methylation profiles be-
tween datasets. Then, a transformed version of chronological
age was regressed on the 19 401 CpGs using a penalised re-
gression model (elastic net). To test whether the clock CpGs showed any enrichment in-
side or outside CpG islands, or enrichment for specific chro-
matin states, we compared the distribution of the clock
CpGs with that of all other CpGs in different CpG island do-
mains (open sea, CpG island, CpG island shore, and CpG is-
land shelf) or chromatin states in male skeletal muscle from
the Roadmap Epigenomics Project with a Fisher’s exact test. As there are four different positions with respect to CpG
islands and 15 different chromatin states, we only considered
positions with respect to CpG islands and chromatin states
significant if FDR < 0.005. The elastic net model automatically selected 200 CpGs; with
increasing
age,
109
were
hypomethylated
and
91
hypermethylated (Data S4). Sixteen were in common with
the 353 CpGs used in the pan-tissue clock (Figure 3a). This is
more than expected by chance, as none of the 1 000 000 ran-
domly drawn samples of 200 CpGs from our dataset had more
than 14 CpGs in common with the 353 CpGs of the pan-tissue
clock. In addition, the effect of age on the methylation levels of
15/16 of these common CpGs was the same in both clocks. This shows that the muscle clock includes some CpGs whose
methylation changes with age in all human tissues. We then
tested for enrichment of the 200 muscle clock CpGs in CpG Pan-tissue clock We used the online epigenetic age calculator (https://
dnamage.genetics.ucla.edu/home) selecting the option “Nor-
malized Data” to implement the original pan-tissue clock.7 Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 Description of the 12 skeletal muscle DNA
methylation datasets We gathered skeletal muscle methylomes from 12 datasets
generated with three different platforms: HM27, HM450 Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 S. Voisin et al. 6 Figure 2 Age distribution in the 12 datasets used to develop the muscle clock. (A) Waffle chart of the 12 datasets, split by database. Each cell repre-
sents 1 percentage point summing up to the total number of samples (n = 682); dbGAP, database of Genotypes and Phenotypes; FUSION, Finland-
United States Investigation of NIDDM Genetics; GEO, Gene Expression Omnibus; LITER, Limb Immobilisation and Transcriptional/Epigenetic Responses;
Gene SMART, Gene Skeletal Muscle Adaptive Response to Training. (B) Age distribution in all 12 datasets pooled together (n = 682). (C) Age distribution
in each individual dataset. Datasets were colour-coded as in the waffle chart (A). Figure 2 Age distribution in the 12 datasets used to develop the muscle clock. (A) Waffle chart of the 12 datasets, split by database. Each cell repre-
sents 1 percentage point summing up to the total number of samples (n = 682); dbGAP, database of Genotypes and Phenotypes; FUSION, Finland-
United States Investigation of NIDDM Genetics; GEO, Gene Expression Omnibus; LITER, Limb Immobilisation and Transcriptional/Epigenetic Responses;
Gene SMART, Gene Skeletal Muscle Adaptive Response to Training. (B) Age distribution in all 12 datasets pooled together (n = 682). (C) Age distribution
in each individual dataset. Datasets were colour-coded as in the waffle chart (A). Figure 2 Age distribution in the 12 datasets used to develop the muscle clock. (A) Waffle chart of the 12 datasets, split by database. Each cell repre-
sents 1 percentage point summing up to the total number of samples (n = 682); dbGAP, database of Genotypes and Phenotypes; FUSION, Finland-
United States Investigation of NIDDM Genetics; GEO, Gene Expression Omnibus; LITER, Limb Immobilisation and Transcriptional/Epigenetic Responses;
Gene SMART, Gene Skeletal Muscle Adaptive Response to Training. (B) Age distribution in all 12 datasets pooled together (n = 682). (C) Age distribution
in each individual dataset. Datasets were colour-coded as in the waffle chart (A). the pan-tissue clock), we adopted a leave-one dataset-out-
cross-validation (LOOCV) procedure to obtain unbiased esti-
mates of the muscle clock accuracy.7 LOOCV is performed by
removing one dataset and developing the clock on the 11 re-
maining datasets; the omitted dataset is then used as a test
set (Figure 1). Description of the 12 skeletal muscle DNA
methylation datasets Because we had 12 available datasets, we per-
formed 12 LOOCVs (one for each dataset); this is better than
performing a leave-one sample-out cross-validation procedure
where the samples used to develop the clock contain samples
from the same dataset as the omitted sample. This could lead
to overly accurate age estimation, and would not apply well to
new datasets. We then calculated three measures of accuracy:
the correlation between predicted and actual age, the differ- islands and in skeletal muscle chromatin states. These chroma-
tin states were determined by the Roadmap Epigenomics Pro-
ject and provide a powerful, accurate mapping of gene and
enhancer activity in human skeletal muscle at individual geno-
mic positions. While we did not find any enrichment in CpG
islands, shores, or shelves, the muscle clock CpGs that were
hypomethylated with age showed depletion in regions
flanking active promoters (FDR = 0.00085, Figure 3B). Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 Epigenome-wide association study of age ence between predicted and actual age (AAdiff), and the resid-
ual from a linear regression of predicted age against actual age
(AAresid) (Figure 1). We took advantage of the large number of samples to ex-
plore DNA methylation patterns associated with age in skel-
etal muscle. We found 1,975 age-associated Differentially
Methylated
Positions
(DMPs),
corresponding
to
180
Differentially Methylated Regions (DMRs) at FDR < 0.005
(Figure 6A, Data S6). The direction of DNA methylation
with age was balanced, with 51% of DMRs hypomethylated
and 49% hypermethylated with advancing age (Data S6). 60% of the muscle clock CpGs were among the age-
associated
DMPs;
one
of
these
DMPs,
located
in
Pipecolic Acid And Sarcosine Oxidase (PIPOX), was both in
the muscle and pan-tissue clocks and showed one of the
largest effect sizes (DNA methylation increased by 2.8%
per decade of age, Fig 6b, Data S6). Both hypo- and
hypermethylated DMPs were depleted in CpG islands and
active TSS while simultaneously enriched in CpG island
shelves, open sea, actively transcribed regions and en-
hancers (Figure 6C). However, while hypomethylated DMPs
were enriched in regions flanking active TSS and depleted
in bivalent/poised TSS and in regions flanking bivalent
TSS/enhancers,
hypermethylated
DMPs
showed
the
opposite pattern (Figure 6C). We then conducted a gene
set enrichment analysis that takes into account the biased
distribution of CpGs in genes, but found no enrichment of
the DMPs for particular gene ontologies (GO) at FDR <
0.005. The skeletal muscle clock significantly outperformed the
pan-tissue clock on the correlation between predicted and
actual age (average ρ = 0.62 vs. ρ = 0.51 across datasets,
Figure 4A, Data S5), and on the absolute AAdiff by 7.0 years
(paired t-test P < 0.0001, Figure 4B left panel, Data S5); how-
ever, the muscle clock was as accurate as the pan-tissue clock
on the absolute AAresid (paired t-test P = 0.16, Figure 4B right
panel, Data S5). We also estimated the accuracy of the mus-
cle clock by calculating the median absolute error and the av-
erage difference between predicted age and chronological
age for each dataset.7 While the median absolute error is a
robust measure of prediction error, the average difference in-
dicates whether the predicted age of a given dataset is con-
sistently higher (or lower) than expected7 (Figure 1). An epigenetic clock for human skeletal muscle 7 Figure 3 The 200 muscle clock CpGs. (A) Overlap between the 353 CpGs of the pan-tissue clock and the 200 CpGs of the muscle clock. The 16 CpGs in
common between the two clocks are displayed as table, with the annotated gene(s), and the direction of methylation with age in each of the two
clocks. (B) Enrichment of the 200 muscle clock CpGs in positions with respect to CpG islands (top) and in chromatin (bottom). Enrichment was tested
with a Fisher’s exact test, adjusted for multiple testing. *False discovery rate< 0.005. CpG, cytosine-phosphate–guanine dinucleotide; TSS, TssAFlnk;
ZNF, zinc-finger proteins. Figure 3 The 200 muscle clock CpGs. (A) Overlap between the 353 CpGs of the pan-tissue clock and the 200 CpGs of the muscle clock. The 16 CpGs in
common between the two clocks are displayed as table, with the annotated gene(s), and the direction of methylation with age in each of the two
clocks. (B) Enrichment of the 200 muscle clock CpGs in positions with respect to CpG islands (top) and in chromatin (bottom). Enrichment was tested
with a Fisher’s exact test, adjusted for multiple testing. *False discovery rate< 0.005. CpG, cytosine-phosphate–guanine dinucleotide; TSS, TssAFlnk;
ZNF, zinc-finger proteins. Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 The muscle clock outperforms the pan-tissue clock As the number of datasets and samples were rather limited
(around six times fewer samples than those used to develop Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 7 An epigenetic clock for human skeletal muscle Muscle Epigenetic Age Test: an R package to
determine the epigenetic age of skeletal muscle but also age acceleration (AAdiff and AAresid). Users can also
ask MEAT to fit standard or robust linear models to test asso-
ciations between phenotypes of interest (e.g. sex) and age ac-
celeration in their datasets. As part of the current investigation, we developed an open-
access R package called MEAT, available on GitHub (https://
github.com/sarah-voisin/MEAT). MEAT uses DNA methyla-
tion profiles generated in skeletal muscle the with Illumina
HM technology (HM27, HM450, and HMEPIC) to infer epige-
netic age of the samples. MEAT uses R code adapted from
Horvath7 to calibrate skeletal muscle DNA methylation pro-
files to the GSE50498 gold standard. MEAT then calculates
the epigenetic age of the calibrated samples using the muscle
clock (elastic net model as implemented in glmnet). Users
should provide a pre-processed β-value matrix generated
with the Illumina HumanMethylation platform, as well as an
optional phenotype table containing information such as
age, sex, health/disease status, and so forth. If age is pro-
vided, the package will not only estimate epigenetic age, Epigenome-wide association study of age Across
the 12 datasets, the muscle clock performed very well, with
a median absolute AAdiff of only 4.6 years on average (range
2.4–10.6 years) vs. 12.0 years for the pan-tissue clock, and a
median absolute AAresid of 3.4 years on average vs. 2.7 years
for the pan-tissue clock (Data S5). Unsurprisingly, considering
the biased age distribution between and within datasets
(Figure 2, Data S1), both the muscle and pan-tissue clocks
tended to predict younger ages for older individuals using AA-
diff (Figure 5). However, this bias was significantly reduced in
the muscle clock and was inexistent for AAresid because by
definition, AAresid is unrelated to age. Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 S. Voisin et al. 8 Figure 4 Predicted vs. actual age and errors in age prediction in the LOOCV procedure. Each point corresponds to one of the 682 samples, coloured by
datasets to which they belong. (A) Predicted vs. actual age. Note that to obtain truly unbiased estimates of age prediction accuracy, the age predicted
by the muscle clock is from the leave-one-out cross-validation procedure. (B) Error in age prediction either as the difference between predicted and
actual age (left panel) or as the residuals from a linear model of predicted against actual age (right panel). Note that both panels are on different scales. FUSION, Finland-United States Investigation of NIDDM Genetics; LITER, Limb Immobilisation and Transcriptional/Epigenetic Responses; Gene SMART,
Gene Skeletal Muscle Adaptive Response to Training. Figure 4 Predicted vs. actual age and errors in age prediction in the LOOCV procedure. Each point corresponds to one of the 682 samples, coloured by
datasets to which they belong. (A) Predicted vs. actual age. Note that to obtain truly unbiased estimates of age prediction accuracy, the age predicted
by the muscle clock is from the leave-one-out cross-validation procedure. (B) Error in age prediction either as the difference between predicted and
actual age (left panel) or as the residuals from a linear model of predicted against actual age (right panel). Note that both panels are on different scales. FUSION, Finland-United States Investigation of NIDDM Genetics; LITER, Limb Immobilisation and Transcriptional/Epigenetic Responses; Gene SMART,
Gene Skeletal Muscle Adaptive Response to Training. Muscle Epigenetic Age Test: an R package to
determine the epigenetic age of skeletal muscle Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 An epigenetic clock for human skeletal muscle Figure 5 Age acceleration as a function of age in the muscle and the pan-tissue clocks. Here, we show the bias in age prediction depending on the age
of the individual. Using the difference between predicted and actual age (AAdiff), younger individuals show systematically epigenetic ages than their
real age, while older individuals show systematically older epigenetic ages than their real age. However, this bias is less pronounced in the muscle clock
and inexistent when using AAresid. FUSION, Finland-United States Investigation of NIDDM Genetics; LITER, Limb Immobilisation and Transcriptional/Epi-
genetic Responses; Gene SMART, Gene Skeletal Muscle Adaptive Response to Training. Figure 5 Age acceleration as a function of age in the muscle and the pan-tissue clocks. Here, we show the bias in age prediction depending on the age
of the individual. Using the difference between predicted and actual age (AAdiff), younger individuals show systematically epigenetic ages than their
real age, while older individuals show systematically older epigenetic ages than their real age. However, this bias is less pronounced in the muscle clock
and inexistent when using AAresid. FUSION, Finland-United States Investigation of NIDDM Genetics; LITER, Limb Immobilisation and Transcriptional/Epi-
genetic Responses; Gene SMART, Gene Skeletal Muscle Adaptive Response to Training. CpGs that are less sensitive to differences in cohorts, labs,
and platforms because it is trained on datasets from various
cohorts, labs, and platforms. Fourth, the relatively large num-
ber of datasets helps average out spurious results and arte-
facts. Lastly, age affects DNA methylation levels of tens of
thousands of CpGs.9 profiles assessed with the Illumina Infinium technology as in-
put and outputs predicted age. This tool allows researchers to
study the impact of environmental factors (e.g., exercise
training, bed rest/immobilisation, diet, etc.) on the rate of
ageing in skeletal muscle samples. It could also be used to
test
whether
diseased
populations
exhibit
accelerated
muscle-specific age acceleration compared with a matched
healthy population, as was previously done using the pan-
tissue clock.12,35–37 We found that there were more CpGs in common between
the muscle- and pan-tissue clock7 than what would be ex-
pected by chance (as determined by our random sampling
test). This suggests that the ageing process, despite being as-
sociated with many tissue-specific DNA methylation changes,
is also associated with DNA methylation changes ubiquitous
to all human cell types. The epigenome-wide association study
of age in skeletal muscle uncovered many genes whose meth-
ylation change with age. Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 Discussion In the present study, we developed an accurate epigenetic
clock, specific to skeletal muscle, which outperformed the
pan-tissue clock by an average of ~7 years across 682 sam-
ples, in 12 independent datasets. This clock uses DNA meth-
ylation levels at 200 CpGs to predict chronological age, with
a median absolute error of only 4.6 years, a significant im-
provement compared with the pan-tissue clock (12.0 years). We have made this clock available as an open-access R pack-
age called MEAT and available on GitHub (https://github. com/sarah-voisin/MEAT). MEAT
takes
DNA
methylation Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 An epigenetic clock for human skeletal muscle 9 An epigenetic clock for human skeletal muscle It is un-
known whether the muscle clock performs well on samples collected from other muscle groups, such as abdominal
muscle collected during surgery. Uncovering which DNA
methylation patterns change with age in fast-twitch fibres,
slow-twitch fibres, or in both fibres would be the next step
to further enhance precision in the estimate of muscle age
and in understanding how age affects muscle structure and
function. differences in satellite cell number and profiles. Slow- and fast-
twitch fibres have distinct DNA methylation profiles,39 and
older muscle tends to have a greater proportion of slow-
twitch fibres than young muscle.40 In addition, satellite cells
maintain their multipotent state via distinct DNA methylation
profiles,41 and both satellite cell numbers42 and DNA methyl-
ation profile43 change with age. The strength of this study lies
in the utilisation of datasets that contained both young and
older individuals from the general population; thus, it is likely
that the muscle clock captured these DNA methylation
changes because of fibre type changes with age. It was re-
cently
shown
that
controlling
for
heterogeneity
in
tissue/muscle fibre type reduces the number of physiological
trait associations,44 and it may also be the case that the epige-
netic clock developed herein predicts different ages in differ-
ent fibre types of a given individual. This uncertainty
surrounding the influence of different cell types on epigenetic
age does not pertain to skeletal muscle and is also a challenge
for virtually all epigenetic clocks, as highlighted in a recent,
very comprehensive review.45 This matter is further compli-
cated for skeletal muscle, as different muscle groups show var-
ied proportion of fibre types46 (e.g. ~80% of Type I fibres for
the soleus vs. 39% for the biceps brachii). It should be noted
that the muscle clock developed herein used DNA methylation
profiles exclusively from the vastus lateralis muscle. An epigenetic clock for human skeletal muscle However, these genes were mostly
distinct from the genes that are known to be differentially
expressed in muscle with age.38 Our relatively large sample
size and wide age range allowed us to detect small effect sizes
and to uncover a large number of genes differentially methyl-
ated with ageing in skeletal muscle. It is possible that age af-
fects DNA methylation levels at these CpGs in all muscle
cells. However, it is also possible that the DNA methylation dif-
ferences between young and old individuals are because of
differences in fibre type distribution and perhaps also We highlighted some important limitations in age distribu-
tion both within and between datasets that could influence
the accuracy of the muscle clock. Despite these limitations,
the accuracy of the age predictor was excellent. The remark-
able accuracy in prediction can be explained by multiple fac-
tors, most of which previously mentioned by Horvath.7 First,
the largest datasets (GSE50498, GSE49908, Gene Skeletal
Muscle Adaptive Response to Training, and FUSION (Finland-
United States Investigation of NIDDM Genetics)) were also
those with the broadest age range, which limits the confound-
ing effect of age with dataset. Second, measurements from
Illumina DNA methylation arrays are known to be less affected
by normalisation issues compared with those from gene ex-
pression (messenger RNA) arrays. Third, the elastic net model
used to develop the epigenetic clock automatically selects S. Voisin et al. 10 Figure 6 Differential DNA methylation with age in skeletal muscle. (A) Volcano plot of DNA methylation changes with age. Each point represents a
tested CpG (19 401 in total) and those highlighted in red were the differentially methylated positions (DMPs) significant at a false discovery rate
(FDR) < 0.005. The x axis represents effect size, expressed as differential methylation per year of age. The y axis represents statistical significance,
expressed as –log10(P value), so CpGs that are higher on the graph are more significant. (B) DNA methylation level as a function of age, for the
CpG in PIPOX that was in both the muscle and pan-tissue clocks and that showed one of the largest effect size. (C) Enrichment of DMPs in positions
with respect to CpG islands (left), and in chromatin states (right). Enrichment was tested with a Fisher’s exact test, adjusted for multiple testing. *FDR
< 0.005. CpG, cytosine-phosphate–guanine dinucleotide; TSS, TssAFlnk; ZNF, zinc-finger proteins. Figure 6 Differential DNA methylation with age in skeletal muscle. An epigenetic clock for human skeletal muscle (A) Volcano plot of DNA methylation changes with age. Each point represents a
tested CpG (19 401 in total) and those highlighted in red were the differentially methylated positions (DMPs) significant at a false discovery rate
(FDR) < 0.005. The x axis represents effect size, expressed as differential methylation per year of age. The y axis represents statistical significance,
expressed as –log10(P value), so CpGs that are higher on the graph are more significant. (B) DNA methylation level as a function of age, for the
CpG in PIPOX that was in both the muscle and pan-tissue clocks and that showed one of the largest effect size. (C) Enrichment of DMPs in positions
with respect to CpG islands (left), and in chromatin states (right). Enrichment was tested with a Fisher’s exact test, adjusted for multiple testing. *FDR
< 0.005. CpG, cytosine-phosphate–guanine dinucleotide; TSS, TssAFlnk; ZNF, zinc-finger proteins. differences in satellite cell number and profiles. Slow- and fast-
twitch fibres have distinct DNA methylation profiles,39 and
older muscle tends to have a greater proportion of slow-
twitch fibres than young muscle.40 In addition, satellite cells
maintain their multipotent state via distinct DNA methylation
profiles,41 and both satellite cell numbers42 and DNA methyl-
ation profile43 change with age. The strength of this study lies
in the utilisation of datasets that contained both young and
older individuals from the general population; thus, it is likely
that the muscle clock captured these DNA methylation
changes because of fibre type changes with age. It was re-
cently
shown
that
controlling
for
heterogeneity
in
tissue/muscle fibre type reduces the number of physiological
trait associations,44 and it may also be the case that the epige-
netic clock developed herein predicts different ages in differ-
ent fibre types of a given individual. This uncertainty
surrounding the influence of different cell types on epigenetic
age does not pertain to skeletal muscle and is also a challenge
for virtually all epigenetic clocks, as highlighted in a recent,
very comprehensive review.45 This matter is further compli-
cated for skeletal muscle, as different muscle groups show var-
ied proportion of fibre types46 (e.g. ~80% of Type I fibres for
the soleus vs. 39% for the biceps brachii). It should be noted
that the muscle clock developed herein used DNA methylation
profiles exclusively from the vastus lateralis muscle. Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 metabolic fuel utilization in humans. Sci
Adv 2018;4:eaar8590. Conclusions Note, the shaded cells indicate we did not calculate the Pear-
son correlation coefficient for datasets GSE36166 and
GSE40798 as they are invariant in age, nor for dataset
GSE87655 as the sample size was too low (n = 3). Data are
shown as mean ± SD. Data S4. Additional file 4. Detailed information on the 200
CpGs automatically selected by the elastic net model.Coeffi-
cient = coefficient in the elastic net model. Each CpG was an-
notated to one or more genes using the annotation file from
Zhou et al.28 to which we added annotation to long-range in-
teraction promoters using chromatin states in male skeletal
muscle
from
the
Roadmap
Epigenomics
Project
and
GeneHancer information from the Genome Browser (hg38). An epigenetic clock for human skeletal muscle It is un-
known whether the muscle clock performs well on samples Skeletal muscle follows a circadian rhythm whose phase
can be changed by environmental cues such as food, exercise,
and sleep.47 Importantly, epigenetic mechanisms are involved
in circadian rhythms, and some DNA methylation oscillations
were recently shown to happen at the same CpG sites that
show age-related DNA methylation shifts in mice.48 In the
datasets we used to develop the muscle clock, most biopsies
were taken in the morning in a fasted state, following a con-
trol diet for >24 h and exercise restriction for >48 h, which
limits short-term environmental influences on DNA methyla-
tion levels. However, some datasets containing middle-aged
and older individuals (GSE49908 and GSE38291) did not have
information on the conditions surrounding biopsy collection,
so there is the possibility that some of these oscillations in
DNA methylation are confounded with age in these datasets. We foresee that as more DNA methylation profiles in skeletal
muscle are generated under controlled conditions and be-
come publicly available, the muscle clock will be updated
and gain in precision. Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 An epigenetic clock for human skeletal muscle 11 Acknowledgements This work was supported by Sarah Voisin’s National Health
and Medical Research Council Early Career Research Fellow-
ship (APP11577321) and by Nir Eynon’s National Health and
Medical Research Council Career Development Fellowship
(APP1140644). The Gene Skeletal Muscle Adaptive Response
to Training and LITER studies were both supported by the Col-
laborative Research Network for Advancing Exercise and
Sports Science (201202) from the Department of Education
and Training, Australia. Mr Nicholas Harvey was supported
by a PhD stipend also provided by Bond University Collabora-
tive Research Network for Advancing Exercise & Sports Sci-
ence. This research was also supported by infrastructure
purchased with Australian Government Education Investment
Fund Super Science Funds as part of the Therapeutic Innova-
tion Australia—Queensland Node project. We also greatly ac-
knowledge Erika Guzman at the Australian Translational
Genomics
Centre/Institute
for
Health
and
Biomedical
Innovation/Queensland
University
of
Technology
for
performing the HMEPIC assays in the LITER study. We would
also like to acknowledge Matthew McKenzie at Deakin Uni-
versity for coming up with the MEAT acronym. The authors
adhere to the ethical guidelines for publishing in the Journal
of Cachexia, Sarcopenia and Muscle.49 Data S6. Additional file 6. Summary of differentially methyl-
ated positions and regions with age. Effect size = methylation
change per year of age or between men and women. Each
CpG was annotated to one or more genes using the annota-
tion file from Zhou et al.28 Conflict of interest The authors declare that they have no conflict of interest. Journal of Cachexia, Sarcopenia and Muscle 2020
DOI: 10.1002/jcsm.12556 5. Voisin S, Eynon N, Yan X, Bishop DJ.
Exercise training and DNA methylation in
humans. Acta Physiol 2015;213:39–59. 3. Lappalainen T, Greally JM. Associating cel-
lular epigenetic models with human phe-
notypes. Nat Rev Genet 2017;18:441–451.
4. Cedernaes J, Schonke M, Westholm JO, Mi
J, Chibalin A, Voisin S, et al. Acute sleep
loss results in tissue-specific alterations in
genome-wide DNA methylation state and 2. López-Otín C, Blasco MA, Partridge L, Ser-
rano M, Kroemer G. The hallmarks of ag-
ing. Cell 2017;153:1194–1217. Conclusions Additional supporting information may be found online in the
Supporting Information section at the end of the article. In conclusion, we have developed an advanced muscle-
specific epigenetic clock, using all known available datasets. This clock is freely available on GitHub (https://github.com/
sarah-voisin/MEAT) as an R package (MEAT) for the scientific
community to calculate epigenetic age in their samples inter-
rogated with the Illumina HM technology (HM27, HM450,
and HMEPIC). This new clock significantly outperforms the
previous pan-tissue clock and can calculate the epigenetic
age in skeletal muscle with a mean accuracy of 4.9 ± 4.5 years
across 682 samples. This muscle clock will be of interest and
potential use to researchers, clinicians, and forensic scientists
working in the fields of skeletal muscle, chronic diseases, and
ageing. In the future, we intend to evaluate how environmen-
tal factors, such as exercise and diet, could influence ageing
via this newly developed clock. Data S1. Additional file 1. Overview of the 12 datasets of DNA
methylation in skeletal muscle. Data S2. Additional file 2. Detailed description of the 12
datasets of DNA methylation in skeletal muscle. Data S3. Additional file 3. Genomic location and annotated
genes for the 19,401 CpGs in common between all 12
datasets of DNA methylation in skeletal muscle. datasets of DNA methylation in skeletal muscle. Data S4. Additional file 4. Detailed information on the 200
CpGs automatically selected by the elastic net model.Coeffi-
cient = coefficient in the elastic net model. Each CpG was an-
notated to one or more genes using the annotation file from
Zhou et al.28 to which we added annotation to long-range in-
teraction promoters using chromatin states in male skeletal
muscle
from
the
Roadmap
Epigenomics
Project
and
GeneHancer information from the Genome Browser (hg38). Data S5. Additional file 5. Leave-one dataset-out cross-valida-
tion (LOOCV) analysis of the muscle clock and comparison
with the pan-tissue clock.Each row shows accuracy estimates
for a given dataset. The three accuracy measures reported in
this paper include the Pearson correlation coefficient be-
tween predicted and actual age, the difference between pre-
dicted age and actual age (AAdiff), and the residuals from a
linear model of predicted age against actual age (AAresid). 6. Jacques M, Hiam D, Craig J, Barres R, Eynon
N, Voisin S. Epigenetic changes in healthy 4. Cedernaes J, Schonke M, Westholm JO, Mi
J, Chibalin A, Voisin S, et al. Acute sleep
loss results in tissue-specific alterations in
genome-wide DNA methylation state and 3. Lappalainen T, Greally JM. Associating cel-
lular epigenetic models with human phe-
notypes. Nat Rev Genet 2017;18:441–451. metabolic fuel utilization in humans. Sci
Adv 2018;4:eaar8590.
5. Voisin S, Eynon N, Yan X, Bishop DJ.
Exercise training and DNA methylation in
humans. Acta Physiol 2015;213:39–59.
6. Jacques M, Hiam D, Craig J, Barres R, Eynon
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sn83045433_1913-04-10_1_5_1 | US-PD-Newspapers | Open Culture | Public Domain | null | None | None | English | Spoken | 6,104 | 9,439 | SMirMCS"iife- z- mtmrv akij'.ffefGJtv&ri-3-r"&c..r'C'trr. wjw1-'. i rij ;i7tvt n " r r u imt-tt-i r t rr. m -t ti f rr. t j rr.'i n. "irTTTi jh,. v.it.tn'.,".i.r'.,W'(i.wriw ?g5L jxw3'!zzf e j&r&w v it 'Wf ' X v V TEE WASHINGTON HERALD. THURSDAY, APRIL 10, 1913. THE -NEW-YORK Second Floor of the Greater Pitts Royal. AT SOCIAL CIRCLES Mrs. Goodrow Wilson occupied a box at the Belaçon Theater for the matinee performance, her guests being Mrs. Herndon, Miss Eleanor Wilson, Miss Helen Woodrow Bones, and Miss Hagner. Miss Jessie Wilson left Washington yesterday afternoon for Richmond, Va., to attend the national convention of the T. W. C. A., the sessions of which will be held in historic St. Paul's Church. Miss Margaret Wilson, who has been extensively entertained during her stay in Washington, will be the guest of honor. Visit to New York, will return to Washington today or tomorrow. Mrs. Thomas Marshall, wife of the Vice President, kept her day at "home yesterday afternoon, and received many callers informally in the attractively arranged drawing-room of her apartment at the Shoreham. "Cabinet Day" was observed yesterday afternoon, and all the fashionable world went "calling." Mrs. William Jennings Bryan received her many visitors alone in the red drawing-room of the New Willard: Mrs. Garrison, wife of the Secretary of War, also received her friends informally at her apartment in Stoneleigh Court. Mrs. Daniels, wife of the Secretary of the Navy, held her first Wednesday reception yesterday afternoon, and the country residence, "Single Oak," which they have recently leased, was charmingly decorated for the occasion. The many distinguished callers were received with the cordiality and old-fashioned hospitality for which Southern women are famous the world over. Mrs. Daniels was assisted in receiving by Mrs. Franklin D. Rose, wife of the Assistant Secretary of the Navy. Mrs. Lee S. Overman, Mrs. Adelaide Worth Bagley, mother of Mrs. Daniels; Mrs. Templin M. Potts, and Mrs. William Fullam, wives of the aids to the Secretary. The handsomely appointed tea table was presided over by Mrs. Leigh Palmer, Miss Bagley, and Miss Ethel Bagley, sisters of Mrs. Daniels. Another charming hostess of the afternoon was Mrs. Franklin K. Lane, wife of the Secretary of the Interior, who kept her first "Cabinet Day," and was assisted in receiving by Mrs. Joseph McKenna, Mrs. Works, Mrs. George Chamberlain, Mrs. Hugh Wallace, Mrs. Ira Copley, Mrs. Fechler, Miss Chamberlain, and Miss Fechler. Mrs. William B. Wilson, wife of the Secretary of Labor, did not receive yesterday afternoon on account of indisposition, but her daughter, Miss Agnes Wilton, was at home instead, and had a charming party of girls to assist her. Miss Bristow, niece of Representative Stevens of Texas, poured tea, and Miss Ragsdale and the Misses Brodbeck, daughters of the Representative from Pennsylvania, also assisted. The Counselor of the German Embassy and Mme. von Halmhausen were hosts at a charming dinner last night at their residence in H Street. Later in the evening additional guests attended the informal dance which followed the dinner. The Military Attache of the German Embassy and Mme. von Halmhausen were hosts at a charming dinner last night at their residence in H Street. Later in the evening additional guests attended the informal dance which followed the dinner. The Military Attache of the German Embassy and Mme. von Halmhausen were hosts at a charming dinner last night at their residence in H Street. Later in the evening additional guests attended the informal dance which followed the dinner. The Military Attache of the German Embassy and Mme. von Halmhausen were hosts at a charming dinner last night at their residence in H Street. Later in the evening additional guests attended the informal dance which followed the dinner. assy and Mme. von Herwarth entertained at a dinner last night at their residence in Rhode Island Avenue. Their guests were the Italian Ambassador, the Russian Ambassador and Mme. Bakhmeteff. Maj. Gen. and Mrs. Wotherspoon, Senator Henry Lippitti, Col. and Mrs. Charles McCawley, Mrs. Robert Patterson, Mrs. Mabel Boardman, Brig. Gen. William Crozier, U. S. A.: Miss Patten, Mr. and Mrs. Hugh Wallace, Col. and Mrs. Spencer Cosby, Mr. and Mrs. Edson Bradloy, the Austrian charge d'affaires, Baron Sudenhorst, Mrs. Seth Barton French, Mr. and Mrs. Preston Gibson, and the Second Secretary of the German Embassy and Mme. Kienlin. Mr. and Mrs. Thomas Nelson Page gave a large dinner last night at their residence in R Street. Mrs. Saulsbury, wife of Senator Saulsbury of Delaware, will not be at home this afternoon, but will receive the following Thursdays during the spring. Senator and Mrs. Saulsbury have taken an apartment at the Shoreham for this extra session of Congress. Mrs. Bryce, wife of the British Ambassador, has sent out invitations for a farewell tea on Saturday afternoon. One of the first of the spring weddings took place last night at the Church of the Epiphany when Miss Claire Claxon, daughter of Mr. Philander P. Claxon, United States Commissioner of Education, and Mr. Dale Redmond Majo, Health and Health. BY MRS. MAE Ethel: I am glad you like my canthrox shampoo recipe. Bertha: You ask why a woman in the twenties gets crow's feet and wrinkles and what to do to avoid them. Ill health may cause loss of flesh and weakness of the skin which is no longer filled out by flesh, but more often they are caused by worry, deep thought, scowling or the habit of smiling. They can be quickly removed by using this stimulating vegetable jelly cream which can be made at home at very little cost and will, while filling out the wrinkles, purge the skin of muddy spots and pimples. Get from your druggist one ounce almozoin and dissolve it in half-pint of cold water, adding 2 teaspoonfuls of glycerine. Stir and let stand one day. Apply to wrinkled surface or entire face to prevent wrinkles and leave through night. Then wash off and use more of the jelly cream as a massage. This treatment will remove the most obstinate wrinkles or finest crow's feet, while toning the skin to a velvety texture. It is greaseless and does not grow hair. M. W.: Worry will not remove the fuzz from your chin. Get a small, original package of delatone and with water mix into a paste enough of the powder to cover the hairy surface. Apply and after 2 or 3 minutes rub off, wash the skin and the fuzz is gone. This is a harmless method and does not discolor the skin. Be certain it is delatone you get. Myra: Thick, glossy eyebrows add greatly to beauty. Get a small, original package of pyroxin and rub some on eyebrows frequently with forefinger. This produces the desired effect. To make eyebrows Long, silky and curly, apply pyroxin at lash-roots with thumb and forefinger. Be cautious and don't get anywhere near no hair is wanted. Lucile: Face-lotions or washes are to be preferred to ordinary face powders. Your sallow, dark and oily skin can be made white and mere youthful if you will use this recipe: To a half-pint of hot water or witch hazel and 2 teaspoonfuls of glycerine add 4 ounces of spurmax; let stand until cold. Apply to the hands and face with the palm of the hand and continue rubbing the skin where applied hot. This is a beautifier that when on seems part of the skin, and gives it a velvety appearance. Blanch: If your eyes feel tired and are dull and inflamed, you need an eye tonic. Dissolve an ounce of crystals in a pint of water. One or two drops of this in each eye every day is all that is needed to strengthen your eyes and ask them of Knoxville, Tenn., were married in the presence of a large gathering of friends. The Rev. Dr. McKim performed the ceremony, and the church was beautifully decorated for the occasion. The handsome bride wore a gown of white brocaded satin draped with rare lace and a tulle veil which was caught in place by orange blossoms. She carried a shower bouquet of lilies of the valley. Mrs. Max TuJlc -Payne, of Greensboro, N.C., who was matron of honor; wore pink charmeuse and carried Killarney roses. The maid of honor, Miss Rebecca Cushman, of Asheville, N.C. Also wore pink charmeuse and carried Killatney roses. Miss Laura Mayo, of Knoxville, Tenn., sister of the bridegroom, wore a gown of white satin and carried a bouquet of white roses. Misses Helen and Elizabeth Claxton, sisters of the bride, were her flower girls and wore charming dresses of pink crepe de chine, the skirts being pleated. Mr. Warren Converse, of Chattanooga, Tenn., was Mr. Mayo's best man, and the ushers were Representative Joseph W. Byrns, of Tennessee; Representative John H. Small, of North Carolina; Dr. Elmer Brenlzer, a cousin of the bride, of North Carolina; Mr. Ashton Embry, of Tennessee, and Mr. Max Payne, of North Carolina. A small reception at the home of Dr. and Mrs. Claxton, in Connecticut Avenue, followed the church ceremony, the guests being the out-of-town relatives, who came here to attend the wedding, and a few intimate friends. The house was decorated with Easter lilies and white spring blossoms. A buffet supper was served during the evening. Mrs. Claxton, stepmother of the bride, whose marriage to Dr. Claxton was a social event of last year in Knoxville, wore her wedding gown of ivory satin, trimmed with point lace and made with a court train. Later in the evening Mr. and Mrs. Mayo, Jr., left Washington on their wedding trip. The bride's going-away costume was a modish traveling suit of blue serge and a chic gray and blue straw hat. Miss Helen Taft, daughter of former President Taft, came to Washington on Tuesday, and is visiting the Misses Meyer, daughter of Mr. and Mrs. Mrs. George von L. Meyer, at their residence in Scott Circle, Miss Taft will be one of the bridesmaids at the wedding of Miss Alys Meyer and Lieut. Raymond Rodgers, on April 26. Miss Taft was extensively entertained during her stay in Baltimore by her numerous friends. The jeweled and gold mesh bag which she lost in Emmanuel Church on Sunday was found in the church later in the day and returned to her. The bag was presented to Miss Taft by a number of her intimate friends before her departure from Washington, and is one of her most valued possessions. Mr. and Mrs. James R. Garfield have arrived in Washington and are the house guests of Dr. and Mrs. William Holland Wilmer, at their residence in R Street. Mr. Joseph Leiter left Washington yesterday for Chicago, where he will make a brief stay. The wedding of Miss Feroline Perkins, daughter of Mr. and Mrs. Henry Cleveland Perkins, and Capt. Robert Wallach will take place at St. John's Church, the Rev. Dr. Roland Cotton Smith officiating. Mrs. Perkins and Miss Feroline Perkins have just returned to Washington from New York. Capt. Wallach will take his bride to Fort Ethan Allen, where he is at present stationed. Mrs. James Harriman and Miss Alice Harriman will close their Connecticut Avenue residence for the summer shortly and go to New York, whence they will sail for Europe on May 3. Mrs. Charles Boughton Wood will be at home on Friday afternoons during April, at her residence, 1619 Rhode Island Avenue. Mrs. James B. Montgomery, of Portland, Oreg., her house guest, will assist her in receiving. Mrs. William Perkins, of West Virginia, has arrived in Washington and is stopping at the Grafton Hotel. Mrs. Theodore F. Shuey entertained a large luncheon party yesterday, having as guests the Minister of Switzerland and Mme. Ritter, the Minister of Peru and Mme. Pezet: Mrs. Shafroth, wife of the Senator from Colorado; the Counselor of the French Embassy and Counselor de Pérez de la Rocca; Mr. Scholck. Beauty Hints MARTYN, bright and sparkling. This tonic will not smart or burn and is a great aid to those who wear glasses. It makes the eyes appear brilliant and full of expression. A friend of mine, who is on the stage, tells me she keeps her much-admired eyes beautiful by using this tonic. I find it very strengthening to weak, inflamed, dull, and tired eyes and for granulated eyelids. Grace: Yours is only a spring complaint. At the first signs of warm weather, "spring fever," poor appetites, pale, sallow, pimply faces, and that tired, drowsy, overworked feeling remind us of the urgent need of taking preventive measures to ward off sickness and give us energy and good health. No better tonic can be had than the good old-fashioned one made at home at small cost by dissolving an ounce of karden (which you can obtain at any drug store) in one-half pint alcohol, adding one-half cupful sugar and hot water to make a full quart. A tablespoonful before each meal will do wonders for those who feel "all gone" after the strain of winter or who feel sick and yet don't know just what's the matter. Orothy: You can make a fine quinine hair tonic as follows: To 1 ounce of quinine add 1 pint of alcohol and 1 pint of cold water; let stand until the quinine is dissolved. Rub in well until absorbed. This will remove dandruff and stop falling hair, relieve itching scalp, keep the scalp in healthy condition and promote the growth of hair if used once or twice a week. Shampoo the hair twice a month. (See answer to Ada J.) Ada J.: The best and cheapest shampoo I know of is made from pure, plain canthrox. Simply dissolve a teaspoonful of canthrox in a cup of hot water and stir well until all is dissolved; then proceed to shampoo by pouring it on the hair and rubbing well. This makes a fine lather which makes the head feel good, and cleans the scalp, relieves irritation and makes the hair soft and fluffy and such a shampoo costs very little. (See answer to Dorothy for making a good hair tonic.) Mrs. T.: It is true that exercising and dieting have brought about satisfactory results to many who considered themselves too fat, but if you are so situated that you cannot, take exercise and find that dieting weakens you. I would advise you to try a simple mixture of parnotis and hot water. Put 4 ounces of parnotis in 14 pints of hot water and shake well until dissolved. Strain when cold and it is then ready for use. Take a tablespoonful 3 times a day and just before meals. This is B.harmlces flesh reducer, of the Netherlands Legation; Viscount Benolst d'Azy, French naval attaché; the Second Spanish Secretary and Countess de San Esteban; Miss Lacy, Henri Martin, consul general of Switzerland at Montreal; Senorita de Pena, daughter of the Minister of Uruguay and Senor de Pena; Dr. Baumann, secretary of the Swiss Legation; Mr. Racedo, jr., second Argentine secretary; Christopher Smith, secretary of the Norwegian Legation; Mrs. Holbrook Bonney, of New York, and Miss Dorothy Shuey, daughters of the hostess. The College Women's Club will have a benefit at the Columbia Wednesday evening, April 23, as the beginning of a fund for clubrooms. Mrs. Dana Durand, the vice president, is disposing of the boxes, and Mrs. Cella Mayse's Nye has charge of tickets, which may now be exchanged at the bar office. The first secretary of the Legation of Panama and his sister, Miss Ramona Lefevre, entertained a box party at the New National Theater yesterday afternoon, in compliment to their aunt, who is their house guest, Mrs. de Amador, widow of the first President of Panama. The additional guests were Senor and Mme. Remon, of the Legation, and Mr. A. Washington Pezet. Miss Alice Stone entertained an interesting party at luncheon yesterday at Lafayette Arms in compliment to Mrs. Lane, wife of the Secretary of the Interior. Among the additional guests were Mrs. Ira C. Copley and Mrs. Clarence Perley, who were classmates of Mrs. Lane and Miss Stone at St. Mary's Boarding School, at Knoxville, Ill. The Secretary of State and Mrs. Bryan, the Secretary of War and Mrs. Garrison, the Secretary of the Navy and Mrs. Daniels, Secretary of the Interior Lane, and Assistant Secretary of the Navy and Mrs. Roosevelt will attend the Navy League dinner at the New Wharf tomorrow night. Mrs. William F. Dennis was hostess at a card party yesterday afternoon. A number of additional guests were invited to the informal tea which followed. The engagement has been announced of Miss Bessie M. Draper, daughter of Representative and Mrs. William H. Draper, of Troy, N.Y., and Dr. George M. Ruffin, of this city. No date has been set for the wedding. Washingtonians are interested in the engagement, announced on Tuesday in Baltimore, of Miss Olga Smolianoff, daughter of the late Count Smolianoff, of St. Petersburg and Washington, to Mr. Lucian Hill, son of the late Mr. and Mrs. Jerome K. Hill, of St. Louis. The wedding will take place this spring in Washington, from the home of the bride's relatives here. Miss Smolianoff, who is now in Baltimore, made her debut at the first Monday German two seasons ago. Mr. Hill has spent much time in New York and Pittsburgh, but is now living in Baltimore, and is a member of the Baltimore Club and the Baltimore Country Club. Miss Elizabeth Sears, eldest daughter of Herbert M. Sears, and Bayard Warren, son of the late Samuel D. Warren and grandson of the late Thoniaj F. Bayard, of Wilmington, Del., who was Mr. Cleveland's Secretary of State, were married Tuesday in Boston. The bridegroom is a member of the senior class at Harvard and will receive his degree in June. The bride was attended by Miss Phyll's Scars, her sister, while the bridegroom's elder brother, Samuel D. Warren, was his best man. The group of ushers were: Charles P. Curtis, jr., Thomas G. Frothingham, Frederick Parker, Jr., John S. Parker, Daniel Sargent, George C. Cutler, jr., Upton S. Sullivan, Edward D. Morgan, Jr., Percy L. Wendell, Robert S. Potter, Gordon H. Batch, and A. Montgomery Goodale. A gift of the bride's father is a country place at Prides Crossing, adjoining Mr. Scar's own estate, Wood Rock. Mrs. William F. Seatzow announces the marriage of her daughter, Elizabeth Churchill O'Daniel, to Mr. William Taylor Welch, son of Dr. Charles Welch, of Westfield, N.Y., on Monday, December 30. Mr. and Mrs. Welch will be at home after May 15 at 61 South Crown Street, Westfield, N.Y. Gen. and Mrs. Howard Carroll, of New York, arrived in Washington yesterday, and are stopping at the Shoreham Hotel. Capt. Douglas Tennant, of London, England, arrived at the Shoreham yesterday to spend some time. The bazaar which is being held at the Raleigh Hotel for the benefit of the Episcopal Eye, Ear, and Throat Hospital gives the public an opportunity to aid in this worthy charity. The hospital is supported by the Episcopal New Tariff Downs Hobble Declares Society Leader Mrs. Christian Dominique Hemmick Says Reduction in Customs Means Reasonable Prices, and Makers Are Willing to Use More Goods. The reduction of the tariff at the hands of the Democrats will reduce the cost of living, but increase the width of worn-out skirte, according to Mrs. Christian Donlouque Hemmick, one of Washington's society leaders and dictators of style. Mrs. Hemmick arrives at this conclusion through observance of the workings of the modelers of the modes. In discussing the prevailing styles of the day, Mrs. Hemmick said yesterday: "I believe that the manufacturers of dress fabrics largely control the styles. When dress goods generally are at low prices they manage to prevail on the dressmakers to inaugurate the style of wide skirts that the sales of material may be large, and when the prices go up, the styles are allowed to swing over to costumes that require less material. A dress of today, although it contains much less cloth than dresses of some years ago, costs just about as much. "If the tariff is reduced, and cloth becomes less expensive, the styles will probably go back to wider skirts that will require more material." Proceeding a Sensible Dress. Mrs. Hemmick also feels that the extreme in tight skirts has been reached, and that the prevailing fashions are disagreeable, but that trousers would be a sensible dress for working women. "The designers of the fashions," said Mrs. Hemmick, "are favoring the Persian types now. The Balkan styles have been taken up to a certain extent, but they are generally used in the cheaper churches of Washington through their board of lady managers, of which Mrs. Charles E. Buck has been president for many years. The proceeds of the bazaar will be used for the summer expenses of the institution, which is open to people of all creeds. During the present winter the large number of patients treated at the hospital show the The usefulness of the institution. Mrs. John J. Noonan and her daughter, Miss Louise Noonan, who spent the Easter holidays in Paris, have returned to Homburg, Germany, where Miss Noonan is studying music. While in Paris they were extensively entertained by friends, and spent a most enjoyable time in that historic city. Mr. Noonan will sail for Europe in June, to join them, and after an extended trip through Switzerland, Italy, England, and Ireland they will return to Washington about November 4. Mrs. H. H. Coolidge and Miss Coolidge, of Boston, have arrived in Washington and are spending some time at the Shoreham. Mr. and Mrs. David U. Whitmore and Miss Whitmore, of Mount Vernon, have arrived in Washington, and are stopping at the Shoreham Hotel. Rev. J. W. Austin, rector of All Saints' Church, Chevy Chase, assisted by Rev. Fredericks B. Howden, of St. John's Church, Georgetown, officiated at the marriage yesterday of Miss Mary Eva McCubbin, of Chevy Chase, and Mr. William H. Taylor, of Georgetown. The bride wore a tailor-made suit of blue, with hat to match, and carried sweet peas. She was attended by her sister, Miss Elsie McCubbin, as maid of honor. The best man was Mr. Charles Orme, and the ushers were Mr. J. W. Chambers and Mr. L. B. Aldrich. The church was decorated with palms, ferns, and spring flowers. The wedding march was played by Mr. W. H. Freeman, Mr. and Mrs. Taylor left for Atlantic City. Upon their return, they will be at home at the Baltimore. Among the many beautiful gifts were a silver service from the congregation, a silver nut set from the Sunday School, a silver cake tray from the choir of All Saints' Church, and all flat silver from Mr. Taylor's associates in Riggs Bank. A quiet wedding took place yesterday afternoon, when Miss Annie Lind Wilkins and Mr. John Herbert Mears, of New York City, were married by Rev. James H. W. Blake, at the home of the bride's mother. Mrs. Herbert Claiborne Wilkins. The bride's gown was of white crepe de chine, and she carried a shower bouquet of Bride roses and lilies of the valley. Miss Lena Wilkins was her sister's only attendant. Mr. Mears had as best man Mr. James Swett, of North Carolina. Mr. Gaston Otey Wilkins, of Roanoke, Va., gave his sister in marriage. After a short wedding trip, Mr. and Mrs. Mears will return here for a few days before going to their future home in New York. SCOTTISH RITE MASONS IN CONGRESS AT BANQUET Severeign Grand Commander James D. Richardson at a dinner at the Ebbitt last night. Vice President Marshall and thirty-seven members of Congress were seated at the table. Those present were: Sovereign Grand Commander Richard son, Vice President Marshall, Speaker Clark, Senators Kern, Chamberlain, C. D. Clark, Thompson, Fletcher, Johnson, Lee, Pittman, Cummins, Sherman, Owen, Robinson, Clapp, Warren, J. P. Oftark. Representatives Mandell, Stephens, Underwood, Davis, Murray, Jacoway, Morrison, Byrns, Treadway, Sherley, Carlin, Roberts, Hill, Peterson, Moss, Miller, Hayes, Kettner, Murdock, McGuire, and Joseph Thompson and Secretary General Cowlcs. Post Office Official Go to Boston. Carter B. Keene, chief post office inspector, and John C. Koons, superintendent of the division of salaries and allowances of the Post Office Department, left Washington yesterday to represent the department in Boston, Mass., today, at the annual convention of the New England Postmasters' Association. Private Employment. A bill prohibiting members of the Senate and House from accepting private employment from any corporation in interstate commerce was reintroduced by Senator Borah yesterday. For Flanne "Bridal" Carriage phone M. 'J2S5, Downe's Stables, 1620 L. shirt waists and commoner dresses. The Persian is the craze in all of the most fashionable circles of Europe. "I think that the Persian dress is not only pretty, but that the style of wearing trousers as the Persian women do would be a sensible style for all women, especially those of the working class who have to move about a great deal. "The woman of fashion who has a carriage or automobile at her call does not need to desert skirts. It does not matter to her so much if her movements are hampered, but for the working women who have to be about on the streets and walking onto streetcars." Buses trousers would be very practical. "The attempt to inaugurate the fashion of women wearing trousers seems to be dying out, however." Trousers that is to say, wide-divided skirts that were bound tightly about the ankles were worn to some extent some time ago, but they did not prove popular because their wearers were ridiculed so on the streets. A number of society women ordered them, but never wore them for this reason. "The Persians are responsible for the style of women wearing veils," you know. The custom is general with them. The women of the Orient, although many of them are dressed in the most modern of French gowns, continue to wear the veils. It is worn over the nose, just below the eyes. The women of this country are now adopting this manner of wearing veils while playing with them. Thoroughness Illustrated in Hats The new Boys' Shop includes an up-to-date Hat Shop with all the new headwear in season and with experts to wait upon you and properly fit every visitor. Prices are only low when style and quality are considered. Cheap Hats are looked upon by the new Boys' Shop chief as dear. Do they not always prove dear in the end, and do they ever look other than cheap? Senior Boys' Hats... $1.00 Junior Boys' Hats... $1.00 Rah Rah Hats... 50c Golf Caps, &c... 25c THE GREATER PALAIS ROYAL AFFAIRS. Hours: 8:30 to 6. G STREET. CROWDS THRONG CHARLEY BAZAAR Benefit for Episcopal Eye, Ear, and Throat Capital Opeas AuipidMsly. HOME COOKING THE MAGNET Throngs of happy people gathered in the ballroom of the New Ballroom last night to enjoy the bazaar given by the board of lady managers of the Episcopal Eye, Ear, and Throat Hospital. Practically the whole floor had been placed at the disposal of the board, and it was transferred into a series of beauty bowers, the decorations of one room merging into those of the next in a way artistic and restful. All manner of things were on sale at the various booths. Prices were moderate and qualities guaranteed. Visitors divided their time between dances, purchasing articles at the booths, and in the grotto-like ice cream corner. The excitement of buying "sight unseen" drew a continual crush around the "mystery corner." It was piled with packages of all shapes and sizes, suggestive of everything one could think of, and wrapped in such a way as to make further examination alluring. Probably the greatest success of the evening was that which came with the supper hour. Every viand was strictly homemade. The managers had a special kitchen all to themselves on the same floor, and there they constructed the wondrous dishes which appear in their full perfection only from the home kitchen. Bachelors among the guests who were accustomed to receive their only nourishment in the quick lunch and the restaurant ate during the hours from 6 to 8. The dining room was decorated with vines, flags, and ferns. Punch, candy, cake, and flower booths were placed at the end of the room where the dancing was held. Here, too. was the booth of shadow pictures and a hut of straw, in which or with which the "goose of golden egg propensities" had some connection. The bazaar opened at 4 o'clock in the afternoon and closed at 10 o'clock in the evening. It will be open during the same hours today. The Fort Myer Band played the dance music last night. Tonight the Engineers Band will play. The following had charge of the arrangements: Fancy tables were in charge of Mrs. W. T. Glover, Mrs. John McDonald, Mrs. E. M. Talcott, and Miss Semple Pettis. Cake tables were conducted by Miss Fannie Gilliss, Mrs. E. J. Stellwagen, Mrs. William De Vries, Mrs. William H. Fox, and Mrs. William M. Dove. Those in charge of the candy tables were Mrs. Joseph R. Johnson, Mrs. Jesse B. K. Lee, Mrs. E. M. Mix, Mrs. A. C. Fenton, and Mrs. Faber Stevenson. Mrs. Frank Hume and Miss Emma W. Abbott arranged for the sale of flowers. Those in charge of the mystery table were Miss Elizabeth Chew, Mrs. Charles E. Buck, Mrs. James H. Taylor, Miss Henrietta Harding, Mrs. Henry B. Munn, Miss B. Isabel Simonds, and Mrs. William B. Trott. Mrs. W. M. Steuart conducted an apron table. The refreshments were under the supervision of Miss Mary Armstrong Mason, Mrs. J. B. Burnside, Mrs. C. Roome, Mrs. Corbin Birch, and Mrs. Julia H. Tompkins. A novelty in "the goose that lays the golden egg" was conducted by Mrs. W. B. Trott. Miss Gall, and Miss Lane. Mrs. C. B. Hoppin and Miss Phyllis Snyder had charge of the arrangements for the music and dancing. The supper committee consisted of the following: Mrs. Emory J. Bentley, Mrs. E. M. Mix, Mrs. H. Walbridge, Mrs. C. B. Roberts, Mrs. Hacker, Mrs. Harry N. Moss, Mrs. John Paul Earnest, Mrs. William M. Dove, Mrs. J. L. Parsons, jr., Mrs. J. B. Burnside. Mrs. Thomas J. Jones, Mrs. H. W. Offutt, Mrs. Henry, Mrs. B. Ross, Mrs. O. B. Magruder. and Misses Sworm stedt, Soper, Alice E. Edwards, Semple, Pettis, and Glorvina B. Gordon. Mrs. William M. Dove and Mra Faber Steven son have chargeof the tickets and pub licity, respectively. Letter to Uacle Sam. A letter addressed to "Uncle Saml!was received yesterday by Postmaster Gen eral Burleson from a man in Norwich, asking funds to prevent the foreclosure, of a mortgage on his home. He stated! that he had an invalid wife, and was himself a sufferer from heart trouble. New -Solicitor Takes Oath. Francis Gordon Caffey, now solicitor of the Department of Agriculture, was sworn In yesterday by C. C Clark, chief clerk of -the department Mr. Caffey for the last ten years practiced law in New York City, but is a native of Alabama. J EWELIY. OF MEIIT Novelties for personaladora ment and wares for household us, all of guaranteed quality. COLE' & SWAN, SSSiAs- EDUCATIONAL PKorXMIOXAL BDCCATIOH IN ACCOVK racr. FncUesl wattr warmly aon ( mm tort. -ira TtallrtliFcH or iUtm, OkwMt ot trtttos. X. M. a A., m a St, WmUmUm. MRS. BMII.Y FR1CH SARNM MMOIKS. MjOCimOoV ... r to $2.50 to $3.00 to $1.25 to 50c STYLES Straw. In white and colors: Felt and Cloth, to match Suits; Bands, school and club colors, at 25c and 50c. Flowers Arranged for all social functions in the most effective manner possible, j Especially artistic dec orations for weddings. Call on us for sugges tions and estimates. J. E Small & Sons WASHINGTON 15th and H Streets NEW YORK Waldorf-Astoria and 11 53 Broadway. TRADE on This -TRADE-MARK If Your Needs Are Musical This house has built up such a reputation for an HONEST JPOLICY and a SQUARE DEAL That it stands todaythe Leading .Piano and Music House m Wash ington. Prices and terms to suit you. PERCY S. FOSTER PIANO CO.. 1330 G STREET. "See Etz and see better." If Your Eyes ' are bothering-you, bet ter let us examine them right away. Delay may mean irreparable injury. EDWIN H. ETZ Optician, 1003 G St. AMUSEMENTS. TliHIIIT AT 1:15 Mhtm Tlirc. & Sit at 2:15. S,. S. SIRE Aaaeaacea c ,Tae latexvatteaal CameAIeaae, , MAY ROBSON la Her Latest Cssclr Jiccmi, "A NIGHT OUT" IEXTWEEm,'"j;&e.f""0 , COUMIMPUYPS la Grace Gcare' "ftlATIFS" BeatBtttal Cornea TfcWU THE COMPANT WILL INCLUDE: Ertrett Butterfietd. A. 0. van DUTCH. uccu uvwin Dorothy Bernard. Curio Thatcher. 3ei Gleodinnisf, OUi Cooper. Maria Drofnab. Franco Younge. Aiiint PtBttr. Helen Hayes Brown. nearn Butter. burner Jtmes, John M. Kline. WUlait) Robertson. JUihm Hitcblo. Edwte B. Curtis. Charti 8qqlm. FRIDAY. APRIL 11.. 1:3ft. YSAYE-GODOWSKY Jourt ftcdtal. Tickets, ., M, f-.,IM. on at Theater. r WEDNESDAY, APRIL 1TH, 4iSt. f- ROSA. JAfcOSLAV OUTZKA K0CIAN Contralto asd Violinist. Tidati,' .00. J. H.09, T5 ceata, on tale at theater. COLUMBIA THEATER WrtiiftMSimptoivOrcMstii HEINBICH HAUMEB, Ceoductor. ink CiMtTt, Tinfcy, April IS. 80LOIST CHARLES ANTHONY, TIAM8T Ticket. !, '3c. 50c, and 25c now oh sale at T. ! Arthur Smith's, 132TT Street. ARC-ADS, ROLF-R KATTLER WMHRW mmm of oVnVVoW"offoTWoVot Sprinr Housecleaning consult us for these special needs labor-saving devices of practical efficiency: Ching Foo Floor Polish $1.00 Mexican Nickel, Brass and Copper polish, can.. 15c Silver Cream Silver Polish, bottle :...25c Gorham Soap Silver Polish, cake 25c D. & M. Silver Polish......... 25c Solarine Liquid Metal Polish. 20c Roachbane Powder, for insects, can 25c Ching Foo Furniture Polish.. 20c Silicon Silver Polish, box.... 10c Wellington Knife- Polish, can 25c Burnishne Metal Polish, can 20c Butcher's Floor Wax for can 45c Old English Floor Wax, lb. can 40c Butcher's Liquid Floor Polish. can... 20c Black-Lusta Stove Polish.... 25c Donkey Floor Oil and Polish 25c Chemical Insect Destroyer, gallon $2.00 Scrubbing Cloths 7c Brooms, Dusters, &c. Dulin & Martin Co. Perry, Fercelain, Caffeine Glass, Sliver, Ac. 1215 F St. and 1214-18 6 St. AMUSEMENTS. LEGAL SSS"1 AT S. MAT. SAT., 15 to 9.50. ROBERT B. HUTTELL HART FORISH KILG LEAR Monday Night MERCHANT OF VEXICE Batodar Matinee RICHARD III Saturday Night Next Week. Starting Tuesday-Seat Sale. Eva Tanguay AND HER OWN COMPANY. VOLCANIC VAUDEVILLE PRICES: DAILY MATINEE, 35c, 35c, 50c. NIGHTS, 23c TO $1. JU-: NEXT SUNDAY, 35c TO $1. HELEN KELLER SALIS, MR. UKIiXSJii, SUBJECT OF LECTURE. "THE HEART AND THE HAND" OR THE RIGHT PACE OF OUR SENSES. NEXT MONDAY NIGHT ONLY TO COS. THE FAMOUS MUSICAL TRIUMPH THE USUAL TRIUMPH THE OSURT OF LUXEMBOURG "With the Famous Stage Wallis! HE WAS IN THE CITY. Wed. and Sat. CAMBRIDGE Seat Selling. The World's Greatest Dramatic Spectacle THE GARDEN OF ALLAH Reserved seats 75c, $1.50, $1.50, $2.50, $3.50, $5.00. No telegraph orders. The POCUR POU PLATERS in George Broadhurst's Great Success, THEDOLLAR MARKET best quality of prices and in effect. Beautiful photographic coverings of Silver Jewelry away at every matinee to the desired NEXT WEEK - "OLD HEIDBLOCK" MUTUAL ART EXHIBITION MAYSVILLE, THEATER IN THE HISTORY EVERY SEAT, 10 CENTS Elaborate and Attractive Chances in Program Alma Mata. Tues., Thurs., ACADEMIC and Sat All Seats. 3c. Elegant, Best Seat. 25c. 35c. 50c Return Engagement of BUD FISHER'S ORIGINAL CREATION, MUTUAL and JEFF The Musical Comedy Sensation of the Age. WEEKLY EVENING MATINEE YOU LIKE. IV Y WASHINGTON DAILY. ROSE-BUDS Headed by JOE ADAMS, Jolly Comedian. See the European Sensation. The Slower Ballet. And Buds of Feminine Loveliness. Wrestlissr Tuesday Eve., "Leo Pax. delio vs. Free McKay, the cast. Flats. Msteh. (TRIDAT NIGHT-COUNTRY STORE) Nert Weefc-HBNRT P. DIXON'S BIG REVIEW. GAYETY . Two Ssappy, Gistery Performances Daily By Sam Howe's ii LOVEMAKERS With Mr. Howe Hkaeelt and Florence Bennett. WRBSTLINO WEDNESDAY NIGHT: JOE TURNER VS. MARTIN LORXARD NEXT WEEK.. -."ROBINSON" CRUSOE GIRLS' "MAIL MCCES" IW 2s-1ffll0 kK STEEETECMSMI I- FLAT RACE , Six or More Races Races Dairy; Fenn. Express, with Parlor Car lit. TnIam Ctatlnv 1 n m nhAUnailra Beach. 9:30' a. m. Express 12 noon and 1:40 p. m. Rapid service. Admissions. boo.; 'frjptt-riiic Ci jnvdiSl'Fli'T 'ri5s:s3tT& if.kiiw imjaa.. j.ttt aoin r -,5M -. i tftrA M fz VxjmJq' "t M "V-",. 39 &skfc JL.1.. &&' I ' . Vff 1, J t V, -K? mMd, rJ2a&3&a .a -i-rfV... -Vif. jC J I. w 1 - -J"" , fA"J.l.. STOVES. JLJiri& JUL t A&22& ..J, r t& ZL&gg. KrUjtS lLTX'iZ&Jlg'i..f'rfJlSW,rKr.-', J V tKS"WS. idrS".-fftWS- ",.2.J", frl iMsSmimm. | 22,851 |
https://github.com/ValdiviaDev/Unity-Xarxes-Game/blob/master/Frogger Online/Assets/Scripts/PlayerNameSync.cs | Github Open Source | Open Source | MIT | null | Unity-Xarxes-Game | ValdiviaDev | C# | Code | 58 | 237 | using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.UI;
using Photon.Pun;
using Photon.Realtime;
public class PlayerNameSync : MonoBehaviourPunCallbacks, IPunObservable
{
private Text displayName;
private void Awake()
{
displayName = GetComponent<Text>();
GetComponent<RectTransform>().parent = GameObject.Find("Panel").GetComponent<RectTransform>();
}
#region IPunObservable implementation
public void OnPhotonSerializeView(PhotonStream stream, PhotonMessageInfo info)
{
if (stream.IsWriting)
{
stream.SendNext(displayName.text);
}
else
{
if(!photonView.IsMine)
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reflexionessobr00muragoog_2 | Spanish-PD-Books | Open Culture | Public Domain | 1,782 | Reflexiones sobre el buen gusto en las Ciencias, y en las artes | Lodovico Antonio Muratori | Spanish | Spoken | 7,271 | 9,880 | Ha sobrevivido tantos años como para que los derechos de autor hayan expirado y el libro pase a ser de dominio público. El que un libro sea de dominio público significa que nunca ha estado protegido por derechos de autor, o bien que el período legal de estos derechos ya ha expirado. Es posible que una misma obra sea de dominio público en unos países y, sin embargo, no lo sea en otros. Los libros de dominio público son nuestras puertas hacia el pasado, suponen un patrimonio histórico, cultural y de conocimientos que, a menudo, resulta difícil de descubrir. Todas las anotaciones, marcas y otras señales en los márgenes que estén presentes en el volumen original aparecerán también en este archivo como testimonio del largo viaje que el libro ha recorrido desde el editor hasta la biblioteca y, finalmente, hasta usted. Normas de uso Google se enorgullece de poder colaborar con distintas bibliotecas para digitalizar los materiales de dominio público a fin de hacerlos accesibles a todo el mundo. Los libros de dominio público son patrimonio de todos, nosotros somos sus humildes guardianes. No obstante, se trata de un trabajo caro. Por este motivo, y para poder ofrecer este recurso, hemos tomado medidas para evitar que se produzca un abuso por parte de terceros con fines comerciales, y hemos incluido restricciones técnicas sobre las solicitudes automatizadas. Asimismo, le pedimos que: + Haga un uso exclusivamente no comercial de estos archivos Hemos diseñado la Búsqueda de libros de Google para el uso de particulares; como tal, le pedimos que utilice estos archivos con fines personales, y no comerciales. Ha sobrevivido tantos años como para que los derechos de autor hayan expirado y el libro pase a ser de dominio público. El que un libro sea de dominio público significa que nunca ha estado protegido por derechos de autor, o bien que el período legal de estos derechos ya ha expirado. Es posible que una misma obra sea de dominio público en unos países y, sin embargo, no lo sea en otros. Los libros de dominio público son nuestras puertas hacia el pasado, suponen un patrimonio histórico, cultural y de conocimientos que, a menudo, resulta difícil de descubrir. Todas las anotaciones, marcas y otras señales en los márgenes que estén presentes en el volumen original aparecerán también en este archivo como testimonio del largo viaje que el libro ha recorrido desde el editor hasta la biblioteca y, finalmente, hasta usted. Normas de uso Google se enorgullece de poder colaborar con distintas bibliotecas para digitalizar los materiales de dominio público a fin de hacerlos accesibles a todo el mundo. Los libros de dominio público son patrimonio de todos, nosotros somos sus humildes guardianes. No obstante, se trata de un trabajo caro. Por este motivo, y para poder ofrecer este recurso, hemos tomado medidas para evitar que se produzca un abuso por parte de terceros con fines comerciales, y hemos incluido restricciones técnicas sobre las solicitudes automatizadas. Asimismo, le pedimos que: + Haga un uso exclusivamente no comercial de estos archivos Hemos diseñado la Búsqueda de libros de Google para el uso de particulares; como tal, le pedimos que utilice estos archivos con fines personales, y no comerciales. Ha sobrevivido tantos años como para que los derechos de autor hayan expirado y el libro pase a ser de dominio público. El que un libro sea de dominio público significa que nunca ha estado protegido por derechos de autor, o bien que el período legal de estos derechos ya ha expirado. Es posible que una misma obra sea de dominio público en unos países y, sin embargo, no lo sea en otros. Los libros de dominio público son nuestras puertas hacia el pasado, suponen un patrimonio histórico, cultural y de conocimientos que, a menudo, resulta difícil de descubrir. Todas las anotaciones, marcas y otras señales en los márgenes que estén presentes en el volumen original aparecerán también en este archivo como testimonio del largo viaje que el libro ha recorrido desde el editor hasta la biblioteca y, finalmente, hasta usted. Google se enorgulla de poder colaborar con distintas bibliotecas para digitalizar los materiales de dominio público a fin de hacerlos accesibles a todo el mundo. Los libros de dominio público son patrimonio de todos, nosotros somos sus humildes guardianes. No obstante, se trata de un trabajo caro. Por este motivo, y para poder ofrecer este recurso, hemos tomado medidas para evitar que se produzca un abuso por parte de terceros con fines comerciales, y hemos incluido restricciones técnicas sobre las solicitudes automatizadas. Asimismo, le pedimos que: + Haga un uso exclusivamente no comercial de estos archivos Hemos diseñado la Búsqueda de libros de Google para el uso de particulares; como tal, le pedimos que utilice estos archivos con fines personales, y no comerciales. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. + No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. + Conserva la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. + Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conservar la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. + No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. + Consiga la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. + Mátese siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserva la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conservar la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. + No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. + Consiga la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. + Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La marca de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. + No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. + Consiga la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. + Mántese siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. + No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. + Consérvenla atribuida. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. + Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conservar la atribución. La marca de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. + No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. + Consérvese la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. + Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserva la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserva la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserve la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserva la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. No envíe solicitudes automatizadas. Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. Conserva la atribución. La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. Manténgase siempre dentro de la legalidad. Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. + No envíe solicitudes automatizadas Por favor, no envíe solicitudes automatizadas de ningún tipo al sistema de Google. Si está llevando a cabo una investigación sobre traducción automática, reconocimiento óptico de caracteres u otros campos para los que resulte útil disfrutar de acceso a una gran cantidad de texto, por favor, envíenos un mensaje. Fomentamos el uso de materiales de dominio público con estos propósitos y seguro que podremos ayudarle. + Consiga la atribución La filigrana de Google que verá en todos los archivos es fundamental para informar a los usuarios sobre este proyecto y ayudarles a encontrar materiales adicionales en la Búsqueda de libros de Google. Por favor, no la elimine. + Manténgase siempre dentro de la legalidad Sea cual sea el uso que haga de estos materiales, recuerde que es responsable de asegurarse de que todo lo que hace es legal. No dé por sentado que, por el hecho de que una obra se considere de dominio público para los usuarios de los Estados Unidos, lo será también para los usuarios de otros países. La legislación sobre derechos de autor varía de un país a otro, y no podemos facilitar información sobre si está permitido un uso específico de algún libro. Por favor, no suponga que la aparición de un libro en nuestro programa significa que se puede utilizar de igual manera en todo el mundo. La responsabilidad ante la infracción de los derechos de autor puede ser muy grave. | 25,366 |
https://github.com/ktraunmueller/Computable/blob/master/Computable/Computable/Source/App/ViewControllers/NotebookBrowser/NotebookBrowserLayout.h | Github Open Source | Open Source | MIT | 2,021 | Computable | ktraunmueller | C | Code | 29 | 89 | //
// NotebookBrowserLayout.h
// Computable
//
// Created by Karl Traunmüller on 16.03.14.
// Copyright (c) 2014 microLARGE. All rights reserved.
//
#import <UIKit/UIKit.h>
@interface NotebookBrowserLayout : UICollectionViewFlowLayout
@end
| 23,432 |
https://github.com/refinedmods/refinedstorage/blob/master/src/main/java/com/refinedmods/refinedstorage/apiimpl/util/ItemFilter.java | Github Open Source | Open Source | MIT | 2,023 | refinedstorage | refinedmods | Java | Code | 84 | 241 | package com.refinedmods.refinedstorage.apiimpl.util;
import com.refinedmods.refinedstorage.api.util.IFilter;
import net.minecraft.world.item.ItemStack;
public class ItemFilter implements IFilter {
private final ItemStack stack;
private final int compare;
private final int mode;
private final boolean modFilter;
public ItemFilter(ItemStack stack, int compare, int mode, boolean modFilter) {
this.stack = stack;
this.compare = compare;
this.mode = mode;
this.modFilter = modFilter;
}
@Override
public Object getStack() {
return stack;
}
@Override
public int getCompare() {
return compare;
}
@Override
public int getMode() {
return mode;
}
@Override
public boolean isModFilter() {
return modFilter;
}
}
| 7,138 |
https://my.wikipedia.org/wiki/%E1%80%92%E1%80%AD%E1%80%AF%E1%80%80%E1%80%BA%E1%80%A6%E1%80%B8%E1%80%98%E1%80%B0%E1%80%90%E1%80%AC | Wikipedia | Open Web | CC-By-SA | 2,023 | ဒိုက်ဦးဘူတာ | https://my.wikipedia.org/w/index.php?title=ဒိုက်ဦးဘူတာ&action=history | Burmese | Spoken | 10 | 154 | ဒိုက်ဦးဘူတာ သည် ရန်ကုန်-မန္တလေးမီးရထားလမ်းပိုင်းရှိ ဘူတာရုံတစ်ခု ဖြစ်သည်။ ဒိုက်ဦးမြို့တွင် တည်ရှိသည်။
ကိုးကား
ပဲခူးတိုင်းဒေသကြီးရှိ ဘူတာရုံများ | 23,402 |
https://github.com/Juraldinio/snowplow-objc-tracker/blob/master/Snowplow/Internal/Payload/SPPayload.h | Github Open Source | Open Source | LicenseRef-scancode-warranty-disclaimer, Apache-2.0 | 2,021 | snowplow-objc-tracker | Juraldinio | Objective-C | Code | 686 | 1,326 | //
// SPPayload.h
// Snowplow
//
// Copyright (c) 2013-2021 Snowplow Analytics Ltd. All rights reserved.
//
// This program is licensed to you under the Apache License Version 2.0,
// and you may not use this file except in compliance with the Apache License
// Version 2.0. You may obtain a copy of the Apache License Version 2.0 at
// http://www.apache.org/licenses/LICENSE-2.0.
//
// Unless required by applicable law or agreed to in writing,
// software distributed under the Apache License Version 2.0 is distributed on
// an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
// express or implied. See the Apache License Version 2.0 for the specific
// language governing permissions and limitations there under.
//
// Authors: Jonathan Almeida, Joshua Beemster
// Copyright: Copyright (c) 2013-2021 Snowplow Analytics Ltd
// License: Apache License Version 2.0
//
#import <Foundation/Foundation.h>
NS_SWIFT_NAME(Payload)
@interface SPPayload : NSObject
@property (nonatomic) BOOL allowDiagnostic;
/**
* Initializes a newly allocated SPPayload
* @return A SnowplowPayload.
*/
- (id) init;
/**
* Initializes a newly allocated SPPayload with an existing object of type NSDictionary.
* @param dict An object of NSDictionary.
* @return A SnowplowPayload.
*/
- (id)initWithNSDictionary:(NSDictionary<NSString *, NSObject *> *)dict;
/**
* Adds a simple name-value pair into the SPPayload intance.
* @param value A NSString value
* @param key A key of type NSString
*/
- (void) addValueToPayload:(NSString *)value forKey:(NSString *)key;
/**
* Adds a dictionary of attributes to be appended into the SPPayload instance. It does NOT overwrite the existing data in the object.
* All attribute values must be NSString types to be added; all others are discarded.
* @param dict An object of NSDictionary.
*/
- (void)addDictionaryToPayload:(NSDictionary<NSString *, NSObject *> *)dict;
/**
* Adds a dictionary of attributes to be appended into the SPPayload instance. Gives you the option to Base64 encode the data before adding it into the object.
* @param json NSData of JSON-compatible data to be added.
* @param encode Boolean option to choose whether the JSON data should be encoded.
* @param typeEncoded If the data is to be encoded, the result will be a value of the key in typeEncoded.
* @param typeNotEncoded If the data is NOT going to be encoded, the result will be a value of the key in typeWhenNotEncoded.
*/
- (void) addJsonToPayload:(NSData *)json
base64Encoded:(Boolean)encode
typeWhenEncoded:(NSString *)typeEncoded
typeWhenNotEncoded:(NSString *)typeNotEncoded;
/**
* Adds a JSON string of attributes to be appended into the SPPayload instance. Gives you the option to Base64 encode the data before adding it into the object. This method converts the string to NSData and uses the data with addJsonStringToPayload:base64Encoded:typeWhenEncoded:typeWhenNotEncoded:
* @param json NSData of JSON-compatible data to be added.
* @param encode Boolean option to choose whether the JSON data should be encoded.
* @param typeEncoded If the data is to be encoded, the result will be a value of the key in typeEncoded.
* @param typeNotEncoded If the data is NOT going to be encoded, the result will be a value of the key in typeWhenNotEncoded.
*/
- (void) addJsonStringToPayload:(NSString *)json
base64Encoded:(Boolean)encode
typeWhenEncoded:(NSString *)typeEncoded
typeWhenNotEncoded:(NSString *)typeNotEncoded;
/**
* Adds a dictionary of attributes to be appended into the SPPayload instance. Gives you the option to Base64 encode the data before adding it into the object. This method converts the dictionary to NSData and uses the data with addJsonStringToPayload:base64Encoded:typeWhenEncoded:typeWhenNotEncoded:
* @param json NSDictionary of JSON-compatible data to be added.
* @param encode Boolean option to choose whether the JSON data should be encoded.
* @param typeEncoded If the data is to be encoded, the result will be a value of the key in typeEncoded.
* @param typeNotEncoded If the data is NOT going to be encoded, the result will be a value of the key in typeWhenNotEncoded.
*/
- (void) addDictionaryToPayload:(NSDictionary<NSString *, NSObject *> *)json
base64Encoded:(Boolean)encode
typeWhenEncoded:(NSString *)typeEncoded
typeWhenNotEncoded:(NSString *)typeNotEncoded;
/**
* Returns the payload of that particular SPPayload object.
* @return NSDictionary of data in the object.
*/
- (NSDictionary<NSString *, NSObject *> *) getAsDictionary;
/**
* Returns the byte size of a payload.
* @return A long representing the byte size of the payload.
*/
- (NSUInteger)byteSize;
@end
| 1,888 |
sn82014248_1925-01-17_1_11_1 | US-PD-Newspapers | Open Culture | Public Domain | null | None | None | English | Spoken | 2,945 | 4,974 | All Wool $0.95 Sweaters 0 Here is the greatest sweater value we have ever offered. Made of the very best all-wool yarn, in white, white and red and white and blue. Adult sizes* only. These sweaters have been selling as high as $12. We are overstocked and must close them out. A full line of warm apparel for outdoor sports. J. B. Farrell Co. 237 Water Street Augusta jmU-l* BARGAINS at the MORIN SYSTEM’S Gigantic Shoe Less than Cost Prices on All , t Men s- Women ’s-Children ’s Boots-Oxfords-Straps AND Rubber Footwear MORIN SYSTEM Of Shoe Stores Inc. 182 Water st. janlTdltx AUGUSTA, ME. Stores Ev erywhere Residents of Augusta Will find at this bank complete facilities for the satisfactory handling of their financial transactions—business or personal. Our departments include Commercial, Checking, 4% Savings, Certificates of De posit, Foreign Exchange- Safe Deposit, Trust, and Banking by Mail. All of these facilities are at YOUR com mand. Augusta irust (fiompang ^ADrSON Auqu^ta, JWaitie. — RICHMOND — WINTHROP WISCASSET OAKLAND §Sets Over $10,000.00^00 WE SELL FURNACE OIL LIGHT FUEL OIL The cleanest, most economical fuel, there is no waste. Kennebec Oil Co. AUGUSTA, ME. TEL. 1295 AUGUSTA LOCALS J Mrs. Eugene Garcelon o£ this city ha3 returned to her home after a week’s visit with Mrs. L. H. Cooper of Newark, N. J., and Boston. I Mrs. John Weymouth has returned to her home In Dover-Foxcroft after visiting here with her daughter, Mrs. Maude Pierce. Mrs. Rachel Marson, who has been quite ill at the home of her daugh ter, Mrs. J. A. Folsom, Willow street, is slowly improving. O. B. Fernandez of Bangor, former Penobscot county sheriff, was in the city for two days this week on busi ness. Charles IC. Smith has returned to his home in Newport after passing several days in this city on matters of business. Mr. and Mrs. Edward Bonenfant have returned from Waterville. where they went to attend the fun eral of Mrs. Bonenfant's sister, Mrs. Charles Bushey. Harry Francis Ilorne, juvenile act or. writes Augusta friends that he is visiting with his mother in Portland and with Miss Lillian Foss, who in private life is Mrs. Horne, is playing at the Elm Theatre in Portland. Mrs. A. G. Averlll of Oldtown was in the city this week, visiting with friends She came to attend the fun eraT of the late E. H. Mosher. Mr. and Mrs. Mosher visited in Oldtown many times in the past. There will be a “story hour” at the LIthgow library at 10.30 A. M. Sat urday. It is expected that these story hours, which have proved pop ular in tiie past, will lie held Satur days for a period of several weeks. These are conducted by Miss Lou Buker, supervisor of the primary schools. W. D. Thurber, executive secretary of the Maine Public Health associa tion, leaves today for St. Louis, where he will attend the national conference of the executive otlicers of volunteer health organizations. He will be accompanied as far as Chicago by Mrs. Thurber, who will visit her parents in that city. Mr. Thurber expects ot be away about a week. i ; Hallowell Surgeon Named To Augusta Hospital Staff Dr. Charles E. II. Beane, of Ilallo well, a well known Kennebec surgeon this week received his notification that he had been elected a consulting surgeon on the staff of surgeons at the Augusta general • hospital. Dr. Deane is the son of Judge Fred E. Beane of Hallowell and has prac . ticed medicine in his home city for the last IS -'ears. He is a graduate of Hallowell high school and of the Bowdoin college medical school. Prior to his locating in Hallowell, Dr. Beane was a surgeon at Nor ridgewoek. For a number of years he has been the school physician of Hallowell. Augusta Study Club Record Attendance In spite of the stormy weather of Friday, but one member was absent when the Augusta Study club was delightfully entertained at the home of Mrs. O. L. Sumner at 235 State street. Mrs. W. E. Gage gave a very interesting paper on geopraphlcal conditions of Argentine. Mrs. Fred Hand also read a comprehensive story, describing the Amazon river. Piano solos by Miss Varney were pleasing features, as well, of the aft ernoon's program. The^hostess served dainty refreshments aniPthe members voted the meeting to have been a 1 most enjoyable one. Smith Kindergarten Mothers’ Club A very interesting meeting of the Smith Kindergarten Mothers' club was held Thursday afternoon in the Kindergarten room. Miss L'na Clark, the school nurse, gave an Instructive talk on proper foods for children and suggested several nice recipes for supper dishes. The subject of selling sandwiches to the school children was discussed and the mothers voted to serve sandwiches to the Smith school pupils, each Friday morning at re L°Mrs. Milton O. Dean and Mrs. Al fred Tavernier were appointed as representatives to the women’s joint committee to take the places of those whose terms have expired. Mrs. Ar thur Merrill rendered a very pleas ing solo. Mrs. Alfred Tavernier. Mrs. Henry Patten and Mrs. George Mc Curdy served delicious refreshments. Annual Meeting Kennebec Towage Company Thursday - . _ _ __ „.n n Mnnnpfor) fl A good season was reported at the annual meeting of the Kennebec Towage Co., at the Augusta House, Thursday. L. G. Purinton of Augus ta was elected to the board of direc tos to succeed to the vacancy caused bv the death on Saturday last of his uncle, the late Francis B.,£ur,nt°n These are the directors for the coming year: Fred N. Boston, Gardi ner; Rupert H. Baxter, Bath: Thom as S. Gibbons, Bath; L. G. Purinton, Augusta; L. L. Cooper, Augusta; Rodney E. Ross, Bath; Levi T Will iams, Augusta; Harry G. Dcerlng, Bath; Edward L. Bussell, Gardiner, William S. Newell, Bath; Fred N. Boston was re-elected president, Rupert IT. Baxter vice president and Thomas S. Gibbons treasurer and general manager. Staples Camp, S. of V. To Have Installation Officers Monday Eve. The installation of officers of Henry G Staples Camp. Sons of Veterans, will be helc^Monday evening, Jan. 19. at G. A. R. hall. The installing offi cer will be Past Division Commander I, L Cooper, assisted by Past Camp Commander Phi S. Malloy All the patriotic allied orders of the Grand Army have been invited, fa. of V. Aux lllary, Clara Barton Tent, D. of V, Seth Williams Post. G. A. It.. Seth I Williams Post Independent Relief Corps. Phil Sheridan Circle, and Seth Williams Post National Relief Corps. An old fashioned baked bean sup-< ner with all the trimmings will be served bv the Sons of Veterans Aux iliary members from <>.30 to 7.30. The officers of the S. of V. have secured th-=> services of the Cony High schoo orchestra of 18 pieces and they will render several popular selections. One of the musical numbers of the e\ ening will be a harmonica solo by Lillian McKachern. president of Sta ples Camp Auxiliary. A patriotic ad dress will be given by Judge Robert A Cony, past division commander, and Melvin K. Sawtelle. A good time is assured to ail members who at tend. LOCAL NOTICE “Don't forget the baked bean sup per at G. A. R. hall, given by the Pythian Sisters Home Club, Satur day, Jan. 17, from i to 7 o'clock. ITic« 36 cents.” Janl7dlt CHERNOWSKY’S -Store for Women■ OFFERINGS Here are Values that you should not miss. Our January Dept Sales offer wonderful opportunities to provide for your future needs at real savings. New Spring Dresses Style and Quality s a Surprise Crepe satin frocks Flannel Sport p Frocks ( Georgette Dance Frocks (New Colors) Others at $15.00 up $19.50 Sale of Coats High-Priced coats marked down—and many new coats at January markdown prices—an exceptional lot, unusual in quality of fabric, in workmanship, and in the quality of the furs used for trimming. Beautiful Fur Collars and Collars-and-Culfs SQUIRREL MINK-DYED MARMOT OPOSSUM NATURAL MUSKRAT The materials include suede-tinishcd fabrics and rich, lustrous pile fabrics—the styles slender, buoyant, youthful. All are lined and warmly lined. Wanted Colors—Cranberry Red, Oxblood Penny Brown, Gray. Navy- Black $19.75, $29.50, $39.50 Sale of CORSETS Most every style and size now on sale. All standard brands. 15 Prs. of $1.50 and $2.00 Ferris Waists at $1.00 pr. 20 Prs. of $5.00 Rubber Corsets at. .$2.98 pr. 7 Prs. of $11.85 Madame X Rubber Corsets, color flesh at.$7.50 pr. 6 Prs. of $9.85 Madame X Rubber Corsets, $6.00 pr. 10 Prs. of $3.50 American Lady Corsets, $2.25 pr. 25 Prs. of $3.50 Peerless Corsets.. .$1.50 pr. 1 Lot of Warner’s $3.50 Wrap-around Cor sets, at.$1.50 pr. Nemo Corsets, style 322 and 320, regular $6.50 corsets . *.$3.00 pr. January Clearance Sale of Silk and Muslin Underwear—See Tuesday’s Journal One rack of Children’s Coats at '/z price HOSIERY 300 Prs. Pure Thread Silk full-fashioned hose in all the newest shades. Made by such famous brands as Tripletoe, Onyx, Kayser ,and Van Raalte. Formerly sold from $2.00 up to $2.95 January Clearance Price $1.50 50 Doz. Mercerized Silk Lisle Ribbed Hose, colors, black, mouse, cocoa, cordovan, log cabin and tap. Regular 50c hose. Sizes Sl/o up to 10 January Clearance Price 4 prs. $1.00 Boys’ heavy ribbed, regular 59c stockings, in black only January Clearance Price 39c 50 Doz. $1.00 wool hose, colors, cordovan, black, grey and blue, in broken sizes ' January Clearance Price 50c $2.50 Silk and Wool Hose, full-fashioned. Colors, heather, black and white, fawn, log cabin, cordovan, camel, grey and black January Clearance Price $1.75 $3.50 Wool Embroidered Hose, full-fash ioned, with a hand embroidered clock % January Clearance Price $1.50 Broadcast Bill’s Radiolays , By WM. E. DOUGLAS re.ck.on im going \ TO STAY «N AT NIGHT In the paper printed here in town, | The Pumpkin Center Breeze, almost every time I read it I see headlines such as these. “Pastor Killed on Way to Mission.” “Texas Doctor Slays His Wife,” "Bankers Death From Unknown Causes.” "Noted Bawyer Takes His Bife,” “Twenty Beds Shot ^fter Trial,” "Daylight Holdup on Main Street,” "Officers Fight Whiskey Runners,” “Copper Clancy Killed on Beat." “Handsome Wife Feeds Husband Poison,” “Bride Forsaken Goes Insane,' “Bank Official Shot by Bandit,” "Joy Riders Hit by Train.” Terrible the way they're shootln', bumpin' folks off every day, hope it don't get teal contagious, hate to see it out our way. Reckon I'd stay at home nights, stead of loafin’ down to Si's, can’t toll when somethin' might hap pen. way they’re hillin’ off these guys. Why. in friendly conversa tion, even there I might by chance say I lissened every ev’nin’ to an orchestra in France. One word might bring on another, mebbee thinkin’ 1 wu7. lyin’ some one in the gang might say so. then the fur would start a (lyin'. While I’m gen erally real peaceful nothin' irritates me so as to have my statements doubted when I’m talkin’ Radio; consequences might be serious, then my good friends here would see headlines in the home town paper 'bout a tight er jamboree—“Well Known Man Incites a Riot,’’ “Focal Store is Scene of Fight”; guess I'll stay at home an’ pick up KYW to night.—Copyright, 102H, Westing house Electric & Manufacturing Company. I Radio Programs TODAY, JAN. 17 KDKA—Westinghouse Electric, East Pittsburgh, Fa., 920 Kilocycles, 328 Meters, Wave length, Eastern Btandard Time 6.00 P. M. Dinner concert by the Westinghouse Band, T. J. Vastine, conductor. 7.30 P. M. Children's period. 6.30 P. M. Concert by the Westing house Band, T. J .Vastine, con ductor. 9.55 P. M. Arlington time signals; weather forecast. Hockey scores from the Duquesne Carden at the end of each period. Pittsburgh Hornets vs. Boston A. A. WBZ—Westinghouse, New England, 890 Kilocycles, 337 Meters, Eastern Standard Time. Studios: Hotel Kim ball, Springfield, . Mass.; Boston Herald-Traveler-Westinghouse, Ho tel Brunswick, Boston C.00 P. M. I-eo Beisman Hotel Lenox Ensemble. 7.00 1*. Al. Market report as furnished by the United States department of agriculture at Boston. 7.05 P. M. Bedtime story for the kid dies, from the Hotel Kimball stu dio, Springfield. 7.15 P. M. Sketches from United States Naval history by E .S. K. Brandt, lieutenant commander. United States Navy. 7.30 1’. M. Concert by the Hotel Kim ball Trio, direct from the Hotel Kimball dining room, under the di -rection of Jan Geerts. 8.Of P. M. Broadcast direct from the Boston Arena of the hockey game, Harvard vs. Vale. 9.55 P. M. Arlington time signals; of fieinl United States weather re ports. 11.30 L\ M. Hotel Brunswick Orches tra. WOY—Schenectady, N. Y., General Electric Company, 790 Kilocycles, 380 Meters, Eastern Standard Time 9.30 P. M. Dance music by I’hil Ro mano's Orchestra, from the New Kenmore Hotel, Albany N. Y., and popular songs. WEEI— (Edl3on light of Boston) 303 Meters Silent. SUNDAY, JAN. 18 EDKD—Westlnghouee, East Pitts- j burgh, Pa., 309 Meters, 970 Kilo cycles. “The World's Pioneer Broad caster," E. S. T. 11.00 A. M. Services of the First I’resbvterian church, Pittsburgh, Rev. J .Alvin Orr, pastor. 2.30 P. M. Concert. 4.00 I’. M. Organ recital by Dr. Charles Helnroth, director of music of Carnegie Institute. Pittsburgh, broadcast directly from Carnegie Music hall, Pittsburgh. 4.43 P. M. Vesper services of the Khadvside Presbyterian church. Pittsburgh, Itev. Hugh Tliomson Kerr, pastor. C.13 P. M. Dinner concert by Scalzo's Orchestra, playing at the Pitts burgh Athletic Association, Fitts- j burgh. 7.43 1*. M. Services of the Calvary | Episcopal church. Rev. E. J. Van ; Etten, pastor. i 9.00 P. M. Open forum from the East] End Christian church, Rev. John j Ray Ewers, pastor. WBZ—Westmgnouse, New England, | 337 Meters, 890 Kilocycles. Studios: Hotel Kimball, Springfield, Mass.;; Boston - Herald-Traveler - Westlng Brunswich, Boston, E. S. T. 10.45 P. M. Church services trans mitted from the Church of the Unity, Itev. Charles A. Wing, pas tor: music by the Philharmonic DRY GOODS DEPT. 1 Lot Blankets, values from $3.00 to $3.73. 66xS0 Blanket. $1.98 $2.29 $3.19 .33 .19 .79 81x99 Seamless Sheet, ex- d»| j Q tra special value. 72x90 Pequot Sheets. 72x99 Pequot Sheets. fn 4) ■— * Du 81x90 Pequot Sheets.^ j Extra large size Turkish towel 66x80 Blanket. 42x36 Pillow Cases.. 42x36 Pillow Cases.. 72x90 Seamed Sheet. Large size Turkish towel. .39 .29 • Medium size Turkish towel | Ladies’ gloves, all colors... | Ladies’ gloves, all colors... | Plisse crepe, in fancy and • plain, yd. J 36 in. Percales, fast colors,. : tight and dark patterns, yd j 32 in. “Kalburnie” ging ; nams, yd. .19 59 .98 .21 .15 .19 Bigger etter ARGAINS SAVE MONEY ON DOMESTICS KITCHEN FURNISHING DEPT. Special values in cups and saucers, 6 for.$1.00 4 cup, brown earthen tea pot . .39 6 cup, brown earthen tea pot. -49 8 cup, brown earthen tea pot . 59 Set of 5 brown earthen mixing bowls.59 4 at Aluminum bean pot .89 4 qt. Aluminum convex sauce pan, with cover £9 6 qt. Aluminum preserv ing kettle.89 10 in. Pyrex pie plate .79 HARDWARE DEPT. Guaranteed alarm clock $1.19 5 ft. zig-zag folding rule . .25 6 ft. zig-zag folding rule .29 Wrench set, 6 wrenches with 12 openings.19 CHINA DEPT. Special table of china, val ues up to $2.00, choice . $1.00 Special value* in china pitchers .10c to .39 Dresden style china cake plates and berry dishes .39 GLASSWARE DEPT. Table tumblers, 6 for .25 2 qt. glass pitcher.... .49 Special table of cut glass, values up to $2.50, choice $1.00 Other special values from 10c to .79 jani 7dlt Male Quartet; Raymond C Hodge, first tenor; Howard X. Smith sec ond tenor; William H. Lippmann, baritone; George B. Dowd, bass; Robert W. Field, organist and di rector. 3.23 I*. M Broadcast from the St. .lames Theater of the concert by the 1'copies' Symphony Orchestra. 7.00 1’. M. Concert by the Copley Vlaza Orchestra under the direc tion of W. Edward Boyle. 8.00 ]>. M. rrogram to be announced. 0.13 I\ M. Concert by the Stelnert Quartet broadcast from the Stein ert organ studio. WEEI—(Edison Eight of Boston) 303 Meters 3.45-5.30 P. M. Men's conference In the Bedford Branch, Y. M. C. A., Brooklyn, N. Y. 7.20-10.30 P. M. "Roxv and his Gang.” direct from the Capitol Theatre, New York City. WOY—Schenectady, W. Y., General Electric Company, 790 Kilocycles, 380 Meters, Easten. Standard Time 10.30 A. M. Service of Albany Street Methodist Episcopal church, Schenectady, N. Y. S.35 P. M. Program by WGT Sym phony; Orchestra, Reo Kliwen, conductor; Edward E. St. Louis, baritone, soloist. 5.00 P. M. Organ recital by Dr. Frank SU1 Rogers, assisted by T .Roy Keefer, violinist, from St. Peter’s Episcopal church, Albany, N. Y. 7.30 P. M. Service of Albany Street Methodist Episcopal church, Schen ectady, N. Y. 9.00 P. M. Symphony Orchestra pro gram from Waldorf-Astoria. New York, Joseph Knecht, conductor. Broadcast in co-operation with WJZ. 10.00 1*. M. Selections by the Hamp ton Institute Quartet, also broad cast by WJZ. Attorney Frank A. Morey of Lew. lston was a business visitor Friday In this city. Mrs. Carrie Purlnton of this city has been In Burnham recently, where she visited her mother, Mrs. Dora Ripley. THE BEST “COLD KILLER” An Old Family Doctor’s FavoriteTho Peculiar Penetrating Propertied Prescription 0f janXO.sat.tt Ballard s Golden 03 Makes It most effective for Coughs, Cold, Croup, end all ailments from Inflammation. Reaches the sore spot. Taken Internally 'or rubbed on outs side. Nothing just like It. A houses hold remedy—best In emergencies, liberal bottles 35 cts and 70 cts. AQ drug and general stores. J. | 4,073 |
https://www.wikidata.org/wiki/Q8231855 | Wikidata | Semantic data | CC0 | null | Category:Albums certified quintuple platinum by the Federation of the Italian Music Industry | None | Multilingual | Semantic data | 133 | 229 | Category:Albums certified quintuple platinum by the Federation of the Italian Music Industry
Wikimedia category
Category:Albums certified quintuple platinum by the Federation of the Italian Music Industry instance of Wikimedia category
Category:Albums certified quintuple platinum by the Federation of the Italian Music Industry category contains album
Categoria:Album certificati cinque volte disco di platino in Italia
categoria di un progetto Wikimedia
Categoria:Album certificati cinque volte disco di platino in Italia istanza di categoria di un progetto Wikimedia
Categoria:Album certificati cinque volte disco di platino in Italia categoria contiene album discografico
Catégorie:Album certifié quintuple disque de platine en Italie
page de catégorie de Wikimédia
Catégorie:Album certifié quintuple disque de platine en Italie nature de l’élément page de catégorie d'un projet Wikimédia
Catégorie:Album certifié quintuple disque de platine en Italie type d'élément contenu dans la catégorie album | 31,600 |
https://github.com/bicheng2008/batch/blob/master/spring-boot-shiro/src/main/java/com/leone/boot/shiro/entity/rbac/Role.java | Github Open Source | Open Source | Apache-2.0 | 2,019 | batch | bicheng2008 | Java | Code | 48 | 143 | package com.leone.boot.shiro.entity.rbac;
import lombok.Data;
import java.util.Date;
import java.util.HashSet;
import java.util.Set;
/**
* 角色信息
*
* @author leone
* @since 2018-04-19
**/
@Data
public class Role {
private Long roleId;
private String roleName;
private String description;
private Boolean deleted;
private Date createTime;
private Set<Permission> permissions = new HashSet<>();
} | 39,844 |
https://blender.stackexchange.com/questions/128235 | StackExchange | Open Web | CC-By-SA | 2,019 | Stack Exchange | DerpyNerd, Michael Ben David, https://blender.stackexchange.com/users/113521, https://blender.stackexchange.com/users/34531, https://blender.stackexchange.com/users/66815, moonboots | English | Spoken | 857 | 1,099 | How i fix this texture rotation in most of the mesh faces in cycles?
the pbr textures when rendered in cycles look rotated differently in some parts of the wall textures for example,this is a testing scene which its very empty because its a test, i am using blender 2.78a (i cannot update it T_T)its this has some thing to do with uv maps or nodes settings?
here is the file https://files.gamebanana.com/bitpit/rendertestenviroment.blend
if we are supposed to see some image textures, we can't, perhaps pack all your image textures in your file so that we can see them
If you have UV unwrapped and your texture looks wrong then usually best to look first at the UV unwrapping (mapping).
Before creating complicated shading node setups its often a good idea to simply check the UV mapping using one of Blenders 2 UV grid textures instead.
To do that, in the UV editor create a new image: Image > New > give it a name (in this example I name the new image Grid ) then from the Generated Type menu choose either UV Grid or Color Grid
Next in the Node editor assign this new checker board image to your mesh.
Now lets look at your perimeter wall when it is mapped to this checker board image :
The Checkerboard texture looks rotated and differently scaled on each wall.
From your PBR node setup it looks like you are wanting to use a seamless red brick texture on this wall.
For that to work you will need to have the scaling even on each section of wall, with minimum distortions and ideally without any rotation.
The Brick texture will be aligned horizontally so you should aim to ave the UV islands of the wall also mapped horizontally.
To achieve this you will need to add few more seams so that with a new UV unwrap the perimeter wall will be broken into 4 UV islands.
Unwrap the perimeter wall again :
The checkerboard texture is looking better but we can see in the UV editor that the uv islands are aligned vertically.
Select them all and rotate 90°.
Now you should be able to use this UV unwrap in your original PBR node setup.
It wont be perfect. I think if I were doing this I would have the tops of the walls as separate UV islands and edit those in the UV editor so that they could be mapped to a part of the red brick texture that looks like the top of a wall but I'm trying to keep this simple.
Here you will find another example of UV unwrapping a wall :
How to unwrap model so its perfectly proportioned?
There are different ways or laying out UV's depending on what you want to do with them.
Don't worry about the perimeter wall now taking up so much more space in the UV square. It shouldn't effect what you seem to be trying to do.
The perimeter wall is using the wall1 texture and now covering 50% of the UV space.
What about all the rest of the model ? The ground (grass001 material) the buildings (wall2 material) etc etc well think of those as different layers on the same UV map.
Each material will be on its own "layer".
The UV unwrapping (mapping) work flow will be:
Select all the mesh which uses material_1 and UV unwrap that, Check the Unwrap using the grid texture and edit those Uv's as required. Laying out the islands so that they are aligned and scaled to the grid.
When you are happy with the layout of the mesh using material_1 repeat for the next material.
When you are finished, if you select all of the mesh the UV's will look a complete mess in the UV space because each material will be stacked (layered) one on top of the other in the UV space. But selecting one material at a time they should look good (understandable).
I recommend you spend a couple of hours watching YouTube videos on the different ways of UV unwrapping depending on how they will be used.
Also...............
Your L shaped building has most of its wall inside out (flipped normals)
Something to think about : I added a 1.80 meter high character to your scene, looks tiny standing beside the well. Unless you have good reason its usually a good idea to model to scale 1:1 .
Awesome question and awesome answer :) Just started using blender myself. I get the feeling after getting the basics down, it's all about tricks, cheats and buckets of gotchas to get it to look the way you want
@DerpyNerd yep thats right i am now an advanced blender user :D, good luck in your journey dude :D
Thanks! It's a bumpy road, but as soon as you find the normals it will really shine a light on the subject :D (badum tss) Anyhow, I'm doing this in my spare time so I'll wait and see how advanced I can get. Congrats on your advancements. It sounds awesome being able to create anything you want
| 25,832 |
https://es.wikipedia.org/wiki/Huerta%20de%20la%20Reina | Wikipedia | Open Web | CC-By-SA | 2,023 | Huerta de la Reina | https://es.wikipedia.org/w/index.php?title=Huerta de la Reina&action=history | Spanish | Spoken | 323 | 522 | Huerta de la Reina es un barrio de la ciudad de Córdoba (España), delimitado por la avenida de la Libertad, la avenida del Tenor Pedro Lavirgen, la avenida del Brillante y la avenida de los Llanos del Pretorio. Limita al este con el barrio de la Huerta de San Rafael, al oeste con el de barrio de las Moreras y al norte con el barrio del Tablero.
La llegada del ferrocarril atrajo a sus proximidades actividades e instalaciones, a cuya sombra surgieron barrios destinados a albergar a los obreros que en ellas tenían su ocupación. Uno de estos barrios fue el de la Huerta de la Reina, llamado así por ocupar parte de los terrenos de esta histórica huerta.
Paradójicamente, el mismo ferrocarril que le dio vida lo tuvo aislado del centro de la ciudad casi un siglo, pues la permeabilidad de las vías era escasa debida al continuo tráfico de trenes incrementado por la proximidad de la estación y, a pesar de que las primeras protestas por esta situación se produjeron tan sólo tres años después de la llegada del primer tren, tuvieron que pasar sesenta y un años para que se construyera el primer viaducto, el del Pretorio, y casi otros cuarenta para que se eliminaran la instalaciones ferroviarias en superficie.
Algunas industrias de las instaladas en este barrio mantuvieron su actividad hasta la década de los ochenta del , en la que la revalorización de los terrenos las fue haciendo desaparecer, algunas definitivamente y otras por traslado a los polígonos industriales de nueva creación en el extrarradio de Córdoba. De este pasado industrial apenas queda como monumento el chimeneón de la fábrica de aceites de Rodríguez Hnos. en un pequeño jardín lindante con las calles Goya y Pasaje del Pintor Mariano Belmonte, rotulado bajo el nombre de Jardines Virgen de la Estrella, en honor a la Hermandad afincada en el barrio.
Referencias
Enlaces externos
Barrios de Córdoba (España)
Distrito Noroeste | 22,743 |
https://www.wikidata.org/wiki/Q21786261 | Wikidata | Semantic data | CC0 | null | Kōh-e Sangar | None | Multilingual | Semantic data | 98 | 271 | Kōh-e Sangar
bungtod sa Apganistan, Wilāyat-e Ghaznī
Kōh-e Sangar (kulle i Ghazni)
Kōh-e Sangar (kulle i Ghazni) Geonames-ID 1447244
Kōh-e Sangar (kulle i Ghazni) instans av berg
Kōh-e Sangar (kulle i Ghazni) geografiska koordinater
Kōh-e Sangar (kulle i Ghazni) land Afghanistan
Kōh-e Sangar (kulle i Ghazni) GNS-ID 6247690
Kōh-e Sangar (kulle i Ghazni) inom det administrativa området Ghazni
Kōh-e Sangar
mountain in Ghazni, Afghanistan
Kōh-e Sangar GeoNames ID 1447244
Kōh-e Sangar instance of mountain
Kōh-e Sangar coordinate location
Kōh-e Sangar country Afghanistan
Kōh-e Sangar GNS Unique Feature ID 6247690
Kōh-e Sangar located in the administrative territorial entity Ghazni | 39,533 |
https://security.stackexchange.com/questions/111308 | StackExchange | Open Web | CC-By-SA | 2,016 | Stack Exchange | Jeroen, https://security.stackexchange.com/users/29704, https://security.stackexchange.com/users/59503, https://security.stackexchange.com/users/6253, ott--, schroeder | English | Spoken | 584 | 859 | How to get an internal network address range during a footprinting stage?
As new to pen testing, I am a bit stuck at finding out a local network address range from external network to perform a pen testing. I will give you a fake scenario with fake IP addresses as below.
Company name: www.testme.com
IP: 125.124.123.122
Name server: main.testme.com
Name server IP: 150.149.148.147
main.testme.com is our main office where all our employees are with our internal network address range is 172.160.0.0/24
During a footprinting stage, how, if possible, do I extract 172.160.0.0/24 address range? Whois, nslookup, dnsenum, Netcraft, or other methods don't seem to get me that far unless I was doing something wrong.
Any help is very much appreciated.
internal network IPs will not be found in external DNS - you need to be inside the network and query the internal DNS
Isn't 172.160.0.0 a typo? Shoukdn't it be 172.16.0.0 instead?
Like most other businesses in the world, this target network is likely using Port Address Translation (PAT aka "overloaded NAT") whereby internal addresses get translated into the public IP (or an IP from the public pool) on egress into the Internet when making connections. This means that the private space (172.160.0.0/24) is used on the local LAN inside the company network, but any communications to/from the Internet use the public IP (125.124.123.122). Usually, you are unable to tell what the internal space is from the outside. Even guessing won't get you anywhere, since the firewall will block unwarranted requests from the Internet to 172.160.0.0/24 on the external interface.
There have been known some information leakage vulnerabilities that expose private internal address space:
I personally found internal address space addresses among HeartBleed audits performed against a friend's external-facing web server. Memory leaks can expose private information like this, especially from servers in a company's DMZ that also talk inbound (many companies allow MS domain traffic to/from DMZ to LAN for management purposes).
Emails from the Exchange server within your target network will stamp each SMTP message with 'message headers' that include the LAN IPs and hostnames of any internal Exchange servers the message was processed by on its way out of the target organization. It's possible for a company to scrub these, but most don't, and RFC 2821 says you shouldn't. More info on that here.
There are common ways to misconfigure DNS to expose private internal addresses. Here is an example.
If you can be on the same network as an asset from the target network elsewhere (Bob from Victim Corp. is on the same WiFi as you in a coffee shop), you can possibly sniff the traffic for RARP, SMB, and other requests that leak this info in hopes that (A) Bob is using a company VPN, and (B) the VPN client is configured for split tunneling, which is relatively common.
If you have physical access to/near the victim network, however, there are far easier ways to obtain this data from plugging into a conference room port, cracking the WiFi, etc. You could even spear phish with malware designed to perform some network reconnaissance and exfiltrate back to your server if you feel someone will open your malicious email attachment (hint: they always do). Otherwise, NAT/PAT prevails and there is no standard or common way to reveal the internal IP range.
I would like to add mis-configured load balancers where cookies can be decoded and reveal the internal IP address of the web server(s). Examples are BigIP F5 and Netscaler LB's.
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https://github.com/ntl-ros-pkg/motoman_path_planning/blob/master/motomini_dynamics_publisher/src/MotoMINI_Model/ssc_sli_e7b327bb.c | Github Open Source | Open Source | Apache-2.0 | null | motoman_path_planning | ntl-ros-pkg | C | Code | 1,639 | 42,511 | #include "pm_std.h"
#include "pm_std.h"
int_T pm_FBD_ZCGRyF9Zix4mvl6Ip0(PmSparsityPattern*pm_Pc8_RQ7nsOlzNUh7aYI680,
size_t pm_JhTijL0ZlABf2EhQiFVX71,size_t pm_qYV3thKugwWwSrIbTfcS10,size_t
pm_8oezoIPNG9LZPP18xVIrw_,PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);
PmSparsityPattern*pm_create_sparsity_pattern(size_t pm_JhTijL0ZlABf2EhQiFVX71,
size_t pm_qYV3thKugwWwSrIbTfcS10,size_t pm_8oezoIPNG9LZPP18xVIrw_,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);void pm_3YYVuJb7mmfC_9_znq5yH2(PmSparsityPattern*
pm_xhS7ip83N1al9vsl9z_jP2,const PmSparsityPattern*pm_7CpwkWeWUw6deoCGAHlcg0);
boolean_T pm_F9dzGbF9bw2QlZyj3V1Gf_(const PmSparsityPattern*
pm_xhS7ip83N1al9vsl9z_jP2,const PmSparsityPattern*pm_7CpwkWeWUw6deoCGAHlcg0);
PmSparsityPattern*pm_9oMk0xBPD28NQC6egedGY2(const PmSparsityPattern*
pm_PJaAk_OAdWPbuizgCm_rK1,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void
pm_s_tA_vyom56bxaGbqlGcb0(PmSparsityPattern*pm_Pc8_RQ7nsOlzNUh7aYI680,
PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);void pm_06dTzOwkhN7oGBM_7J2hK1(
PmSparsityPattern*pm_Pc8_RQ7nsOlzNUh7aYI680,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);PmSparsityPattern*pm_OLpBo6MxIVPIjv0_z_qCc2(size_t
pm_WkDzWdo3HJglufgddrvj_1,size_t pm_Y_WQkyfqLWq4_EV8mXQjt_,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);PmSparsityPattern*pm_8BokEnlj2bsehUZ6VBVqc0(size_t
pm_WkDzWdo3HJglufgddrvj_1,size_t pm_Y_WQkyfqLWq4_EV8mXQjt_,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);PmSparsityPattern*pm_LPeaDYoYWpCMrX0FHDZrj2(size_t
pm_KYlcoOk9rSSGYswizhYqZ2,size_t n,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);
PmSparsityPattern*pm_Fd_reSzeOBuDPZtoIWlnj0(size_t n,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);
#include "pm_std.h"
#include "ne_std.h"
typedef enum ne_60dJMwDMpcTfV2UtxALLx0{ne_8FhBfYGsRrIUJXlFke3CR_= -1,
ne_ewWbiHc7mBlqAowHZTMr92,ne_DW6hUGWU47QqG8_uO7OLs_,ne_3zYRlL05yScaYxY0oYBfa1,
ne_w0vG_grsAjma_Tx6D1RXz0,ne_yC_cAMUEaISNjXH9eUipY_,ne_J_RL4xLnkyZjg6YwIDNQ6_}
ne_CVZ_NKDjnU_uZj1uGIHSK0;
#include "ne_std.h"
typedef unsigned int ne_iKBI88E_MYhQF_LbbI3Jw1;typedef unsigned int
ne_STDOHNX5J8u4JBDN2T_Gx0;typedef struct ne_7ytMg4n4RxPRG6b09fJVc2{const char*
ne_BWIU_EH395KKOl_2ZOi7w0;size_t ne_mvpp3TC9yOLyCyuveTygS0;
ne_iKBI88E_MYhQF_LbbI3Jw1 ne_JtYGiPy3uX25Hx7FtsA8F_;ne_CVZ_NKDjnU_uZj1uGIHSK0
ne_zzMA3NH6vL9VZNbgJalMz2;const char*ne_T8W8CLCjUSDwEzbw_BdaT_;size_t
ne_9gh2n0WL2hIFcizrpyX4x1;size_t ne__jhdLQVnbLnjitrEzs3gl1;boolean_T
ne_CkvlbpH9IGmk7yezOYiNT2;real_T ne_U44ICtR6qL2r1sCfMEClL0;const char*
ne_e8Wq204CZQFlH192aiwOx_;}ne_qLSBCwa6_3RyHGztq1pVf_;typedef struct
ne_RFTlCM8BYTYqzyTLDglb_0{const char*ne_BWIU_EH395KKOl_2ZOi7w0;size_t
ne_mvpp3TC9yOLyCyuveTygS0;ne_STDOHNX5J8u4JBDN2T_Gx0 ne_JtYGiPy3uX25Hx7FtsA8F_;
const char*ne_T8W8CLCjUSDwEzbw_BdaT_;real_T ne_U44ICtR6qL2r1sCfMEClL0;const
char*ne_e8Wq204CZQFlH192aiwOx_;real_T ne_XBN8TkM3HoQJb_b94PBJS_;boolean_T
ne_ZCVcdDJLVysormv7iyj5p1;size_t mM;size_t mN;NeInitMode
ne__bwdH_pRjCQHFnCSFUHvV0;const char*ne_GeViGBsWqtZDGOY_mDwqq2;}
ne_1kVZ9wuGaAMQaZZ1cNS8d0;typedef struct ne_uLKOSPnWPfBY4DsBCt2Rp0{const char*
ne_BWIU_EH395KKOl_2ZOi7w0;const char*ne_T8W8CLCjUSDwEzbw_BdaT_;size_t mM;
size_t mN;const char*ne_e8Wq204CZQFlH192aiwOx_;real_T ne_zO1Dsbqfi1SU_HHSJ9ffM_
;const char*ne_bc_Vin2AV0KYYzObKmOYD_;NeNominalSource ne_hj8CXekjKP4FZ6Wza_Ocf_
;NeInitMode ne__bwdH_pRjCQHFnCSFUHvV0;boolean_T ne_Rf7dRidg_Qmp_11ebn3QK0;
boolean_T ne_ZCVcdDJLVysormv7iyj5p1;NeFreqTimeType ne_UbVb5ZjxHFeJArQxAHPFL1;
boolean_T ne_uKgJESRRUJ8npTlzYbeVV2;boolean_T ne_bQOrieq0Ef3XBgxdp8R1G_;const
char*ne_GeViGBsWqtZDGOY_mDwqq2;}ne_u4R9ZWAN5E_gXTNPDRZme0;typedef struct
ne_pW2WAZPgiJ36ypTtagxL31{const char*ne_BWIU_EH395KKOl_2ZOi7w0;size_t
ne_mvpp3TC9yOLyCyuveTygS0;const char*ne_T8W8CLCjUSDwEzbw_BdaT_;int32_T
ne_XBN8TkM3HoQJb_b94PBJS_;const char*ne_GeViGBsWqtZDGOY_mDwqq2;}
ne_YDYdT8nc8p7zreMRVeWIt2;typedef enum ne_DnwLlHswp8FmfrcqOvR1n0{
ne_plEXWwEiGY2WcL_AbJP0H_= -1,ne_NgDTqhsArlS0MZoHCUb9I1,
ne_zkC8DXNLTORgUxvH9zier0,ne_aXT87sYXcYI6unHnoIG2j1,ne__KceJWL3vkb6csWJDBg1L2}
ne_5lgxcXGctVutp5FgAsB6h2;typedef struct ne_P3OUyWJ_fUSFm9m9UJz3i_{const char*
ne_mxKgEck1IS3ocF5r_Rp69_;size_t ne_LujK4Lvw_ptOgIAHbqaQ1_;size_t
ne_b3h3PIqRg_v1rvyQCDTSX1;size_t ne_mT1rEiYvffSgBK1S7zNbt0;size_t
ne_LNwtdMegsRFWZbM9WUBgg0;ne_5lgxcXGctVutp5FgAsB6h2 ne_gd0O0pXJpcT0Jt_NlyJMv2;
}ne_HrBmWAktiH5mz_7V4Jvh5_;typedef enum ne_cko8UegNzboFZ5_N1cG2l2{
ne_jO72Mu1E5NxOBOqDAd5tV1= -1,ne_5PiR_qTnescDR68ln9rRT_,
ne_ehAJYgx4i91TkEzDEOPnG1,ne_dfZ1YJOaaa3m4fhvjS0Da0,ne_2_c9mKrL0QBHb0lZNFyA92}
ne_XLkvETvJV_dVL67qFu8mV0;typedef struct ne_PFHuI2xE35Gv4bAcc5cEq2{const char*
ne_T8W8CLCjUSDwEzbw_BdaT_;size_t ne_9gh2n0WL2hIFcizrpyX4x1;size_t
ne__jhdLQVnbLnjitrEzs3gl1;const char*ne_KN1l_OiCfx97zxW1E4T4__;const char*
ne_B_7df_XkwkD1Fkh4gRTbM1;ne_XLkvETvJV_dVL67qFu8mV0 ne_gd0O0pXJpcT0Jt_NlyJMv2;
}ne_9Y6oesOBOB5o16StpuAgX0;typedef struct ne_8_MFLSMIlui6QONfAd8gM2{const char
*ne_T8W8CLCjUSDwEzbw_BdaT_;size_t ne_9gh2n0WL2hIFcizrpyX4x1;size_t
ne__jhdLQVnbLnjitrEzs3gl1;const char*ne_KN1l_OiCfx97zxW1E4T4__;const char*
ne_B_7df_XkwkD1Fkh4gRTbM1;boolean_T ne_YZ_BWeXYGt7ViKJCzBPWU_;const char*
ne_PKVV2JOcqzqsjka1_Ym0K_;const char*ne_h5QBEuI0RfuzxPz_akP0b2;}
ne_QCTrr7P0IkeBDlp_OlzpM0;typedef struct ne_86_Yg9b4trxig6oyPjQ6f2{const char*
ne_BWIU_EH395KKOl_2ZOi7w0;const char*ne_T8W8CLCjUSDwEzbw_BdaT_;const char*
ne_GeViGBsWqtZDGOY_mDwqq2;size_t ne_mvpp3TC9yOLyCyuveTygS0;size_t mM;}
ne_1QO_Zx1HcrjkiWg8yDFgD0;
#include "pm_inline.h"
typedef enum ne_YLLKdNAU2UcsISBMQ8gPv2{ne_DIbEgZtFBoTa0ZIyMMBR61= -1,
ne_IHedTsscRKrwm2G2aRZJ50,ne_9FFeE7MFQXv45Xg_mftul_,ne_pbIidIn0YnSS1rDfpppKV1}
ne_E9Yq8BzbKK69eMec16mSt1;typedef struct ne_mM4GGj7rvvgQp0dYY2JN02{const char*
ne_YujQ6CNylcyXoQQHnwaki0;size_t mM;size_t mN;const char*
ne_e8Wq204CZQFlH192aiwOx_;const char*ne_GpLDcFtlIuEy7KvaGIQja_;}
ne_X3ev1H0P1wHkmrV6W2HXY2;PMF_DEPLOY_STATIC size_t ne_AYKp7TvbKo_EgCXKC0XEv2(
const ne_X3ev1H0P1wHkmrV6W2HXY2*ne_UsLthn3_uv_kbDJ3knglr0,size_t
ne_OFVGlEe8cj1jmNZ9fmKcg1){size_t mc_SmSSPSQfR1qEYWsVj5ELF0=0,
ne_uIlG_fhxbtnCjGzzCDDva0=0;for(mc_SmSSPSQfR1qEYWsVj5ELF0=0;
mc_SmSSPSQfR1qEYWsVj5ELF0<ne_OFVGlEe8cj1jmNZ9fmKcg1;mc_SmSSPSQfR1qEYWsVj5ELF0
++){ne_uIlG_fhxbtnCjGzzCDDva0+=ne_UsLthn3_uv_kbDJ3knglr0[
mc_SmSSPSQfR1qEYWsVj5ELF0].mM*ne_UsLthn3_uv_kbDJ3knglr0[
mc_SmSSPSQfR1qEYWsVj5ELF0].mN;}return ne_uIlG_fhxbtnCjGzzCDDva0;}typedef struct
ne_lYEdCssyTxF8d67JqDJm01 ne_701aCeEHJLHh_SQNtyzcM0;typedef struct
ne_TpXOhyXCAJNVUXX4piRqV_ ne_LXe3dvLJ2qJnl1RELHHtw0;
#include "pm_inline.h"
enum{ne_IVIPHc_Vjzd9bLF4FitaO2=1<<0,ne_5U95y_WqAHRouIZGBKSo82=1<<1,
ne_xLLn23Bjvo8nZwt0mkePU1=1<<2,ne_Y_1ooDvu_xry9zmSMFQe9_=1<<3,
ne_V7y_Rv3YCjkCR2Dws7ajG_=1<<4,ne_NPUfp0p1DhHCfM_xpIJOE0=1<<5,
ne_wiKZFk1kFcEG4ulwj5sKf_=1<<6,ne_Zm3cmY_iVpzz92zeU7Kku0=0};enum{
ne_zbGfN2_2MtuQMidpFT6wq_=1<<0,ne_3Nqm9N8EIEN7qYHy95z_11=1<<1,
ne_s2oO7TSPT2mKoqW_kfO430=1<<2,ne_57eRgd4njEnjTa1u1xXuG0=1<<3,
ne_0O15eOP2s_j1MwsfR44CZ1=1<<4,ne_bRHOJ8euWp5PrOgXVtUbi2=1<<5,
ne_GCafvy1SpOgQ6_zlDCY4n0=0};typedef union ne_PHT6_NsWHPUa5ojEgu_Cb0{
PmSparsityPattern ne_vnTj47c5MwycPLUULiNMu2;PmRealVector mM;PmBoolVector
ne_jiTQgngVF58dzO_S8Rtbl0;PmSparsityPattern ne_bfYj0VizZSQKWC0HElmog0;
PmRealVector ne_26OPJLNyw4rmtZb_hby151;PmSparsityPattern
ne_FoC7em2DSg_LfI22ni5vD_;PmRealVector ne_Gl0oYCZ97_wo4lQMUINQ50;
PmSparsityPattern ne_XJDXsDeKHXq0pUKqqku_Z2;PmRealVector
ne_JGL1aLlr3Dcx4G5unwS9T_;PmSparsityPattern ne_GihTwLhnqysBSN42V59iA2;
PmRealVector ne_tC_lhrVr7sh_ia6yMUjV21;PmSparsityPattern
ne_aZ4SwJKE5wKrKPNpbWZd80;PmRealVector ne_VV3lJP_Y7CzPjWTG8OYSQ_;
PmSparsityPattern ne__m1W_z8oSg_z0lNrAdFoq2;PmRealVector
ne_35w8s_5UyxgT0lHRPnweR_;PmRealVector ne_BfYFi4NPyADpve42PBJHd2;PmBoolVector
ne_Y_5g5qG6Wx6mDGdq4HmAv2;PmBoolVector ne_y2Yd6uU1mB77n8Md1jO8F_;PmBoolVector
ne_juKI1wDRMc6o6QCm8Sl7G1;PmSparsityPattern ne_GvH1AOgKfDP0k_k4pE3Vk2;
PmRealVector ne_5IlgPYgNwkD1Mc0i34Xk60;PmSparsityPattern
ne_1CI2VvWb6OLbnMPTFrfps_;PmRealVector ne_kT7RvSuleJpJJjGNic37z2;
PmSparsityPattern ne_cDjPB9qhDAt8p3LQE4Y3C_;PmRealVector
ne_v1fOOs2HAwI9Ky1jAtlhB2;PmSparsityPattern ne_r6vd5OsuX5Eh9o7dwfylw2;
PmRealVector ne_wuR9xBJCQZ2AbEbMXLB7C1;PmSparsityPattern
ne_fjiwdI_MGOBkmV2n3GB_P2;PmSparsityPattern ne_Rv8Vy5nMrFLhpQTAVQSjI_;
PmSparsityPattern ne_nmsm8nxrvsNWONx4tTHck2;PmRealVector
ne_j2CUIOitDJYerpIzWvkqN_;PmBoolVector ne_GS_hAW1ipQ9eUea7kRqyD1;PmRealVector
ne_OxhGZZvClV0jxrI8UgPev0;PmRealVector ne_qCk_sWqBG_NyDdM2ETp861;PmIntVector
ne_GjFSBLDtvJJxEl_Ztv9MH0;PmBoolVector ne_9pXOevtU9PBtwLcbwhvB02;PmBoolVector
ne_cY7gUY5ZT9_yb6enOrfLs2;PmRealVector ne_g9P9d3WjklMH1c13ndJy11;
PmSparsityPattern ne__OGdfJfZea7jaCUr0J2lh_;PmSparsityPattern
ne_K26aJG3KrpacZd9U3H9go1;PmSparsityPattern ne_5O2nE_7CuP5XKQjpagXuB1;
PmSparsityPattern ne_EvbVRxUr4DTTjEhYLO4370;PmSparsityPattern
ne_hNnSr1pyfSih4a5GlJZam0;PmSparsityPattern ne_GzYnj_BbRvmgmmznBb1Fq0;
PmRealVector ne_ciAF8KflILRejS46ik8Pd0;PmSparsityPattern
ne_yii95ZY6_DtJOKgJXrHqM_;PmRealVector ne_urkmlxg1VbYfHB0GPPoMk2;
PmSparsityPattern ne_nWn4RCUno7q3_bfXJbNSc2;PmRealVector
ne_Y6tZCfI8JwyVxivxFzAn92;PmSparsityPattern ne_tTJSlGDHz6W6JmcbbQazR1;
PmRealVector ne_dT_gKHnsic2ZZ39ZTa3jI2;PmIntVector ne_hNUH3KATZSw7_CzLo7sA__;
PmRealVector ne_TSE_Wr_e3fWd314lCeU9w2;PmRealVector ne_t07YmG6VxausltcHcKKis0;
PmIntVector ne_Qad3NsTE6Zh4JqVB_h_8x0;PmRealVector ne_0BbCO61LL104YJucJ6XyW2;
PmIntVector ne_QJaYQmwEB4HM9Ik0_pcS31;PmRealVector ne__rKryLgSJBlPJv6xdGo_k2;
PmRealVector ne_xxo9ItpFfXpp3YQv2QTFX2;PmRealVector ne_VVBYc4Wob_TG4vBVhqBRA1;
PmIntVector ne_yESMH5MfRj9nDdZgV2U5r0;PmRealVector ne_t1QcR_t3nlHFMZ_InP6up2;
PmIntVector ne_3UOV9d5T3kWHnqK1FFWrr2;PmIntVector ne_taRArMMRhiEExMyIYed_K0;
PmIntVector ne_WJwa6ECm_0GmdrtcY0yDC1;PmRealVector ne_eauYmySFhyhLr_q4ETIvW1;
PmRealVector ne_0V8kKS519jQ8RoHRPwZQs2;PmRealVector ne_5UgrXqI_HorSbNEuYeG_I_;
PmRealVector ne_WeENHckzTuXKy_KB2B4Fi2;PmSparsityPattern
ne_LkRk67VunPBAlkU2ojV991;PmRealVector ne_CTe_ZMHXjC9RSK7cFfnUM0;
PmSparsityPattern ne__qG2YebyPWu8_FxEtLh9v_;PmRealVector
ne_0a1KBVw8oh7g7ucWfpLKj1;PmSparsityPattern ne_olBcYGdjp_7_fHvz03ZQB2;
PmRealVector ne_Bvke3319p7XQNrXhfUgBd1;PmRealVector ne_0RgwAwOPGtaDZiMmiqxYL2;
PmRealVector ne_D1Xxy_FgFZUQRvxBx1YIw0;PmRealVector ne_Olp3Z4GYg6qluFaB5xJry0;
PmBoolVector ne_LxfpLFEMQyDFIajNuXdQR_;PmIntVector mDP_L;PmIntVector mDP_I;
PmIntVector mDP_J;PmRealVector mDP_R;PmRealVector ne_BF_w1YOzVRzuLMw0AR_zn1;
PmRealVector ne_B2k5_fpr1uP04A1KQf_KB2;PmRealVector ne_kJ3DdQIjqb3JUusqmidvC_;
PmRealVector ne_iL8f1iwIKtqNhAUDE5ks71;PmSparsityPattern
ne_hc65xGsPGyMjYTj1RykeN_;PmSparsityPattern ne_xzYplhABCHsh_8k_zYkla_;
PmSparsityPattern ne_wSTvYFczCargCpP3GPNeI0;PmSparsityPattern
ne_HzHJ34B6sEw2J2FLgUoAH1;PmRealVector ne_9D6l5u7GamUz5OWipzHcD_;PmRealVector
ne_gWkf6rb_219mHVxTjGT9y2;PmBoolVector ne_DKn5_oNqpokj0kyisZpb8_;PmBoolVector
ne_yFZhcYinENkKLMcFNTs8c2;}ne_wINOJNSKIKor4Ml1V4FSJ_;typedef enum
ne_4T0JbBADprNtIqp7FhUMF1{ne_6_krIrjhEzlmd8O14ycqH_= -1,
ne_q9U3YOaW9TtAcemzFO3UJ0,ne_33ZFjMr3ZonrMM_An9t0l1,ne_yUFdJq0Lnr_vHAlsIH4Oz0,
ne_hds3FhhxXBybQ16do4IDo1,ne_RHIyPdz_X9q4DNaJ2z0XI2,ne_hruDA9vKNTqCGOOOk6iC22,
ne_HDpswwXV8T6RIQcKwfA19_,ne_jqoVA8XAXclk1S_e9Zjo02,ne_L5YWijXn_GnSNu2vWkH0_1,
ne_wrgX0QQD6ZqEopHeoFoRV_,ne_8H0Comn4Vj2pubvdK1lpt1,ne_EUvmAyAp2bUQ0wbOHXX112,
ne__Bbqvz9U8ylaOM22flKef2,ne_lWJGWpLnFwYQEVnld5l4N1,ne_HZ7fvuPTo5qo_o7zFSJio0,
ne_wk34mgq4fyOq2XFidCL5L1,ne_IyNN1_tf0rcMus4hgPoKI2,ne_Bbt1LC3VrlDhp4FeYDlai1,
ne_9Gb2F7jsrpzi5bz2y2NFL2,ne_XKNH30xgvPUJoDMuBIkt_0,ne_GI8_dBWmjH67nMFRMa6W4_,
ne__fq25q3daU3PpoJVEMDV20,ne_cXqkAbnpokDsGdPj5n4um1,ne_uVafL6Pq2WaRazbBumVPq2,
ne_OOYIqXufxPBdtttKoJkMN0,ne_WtGBxwIhwTtSXRAb7Xeb62,ne_NuAUdxcYA2KdFbtHAGPP32,
ne_l2YU2D705ABxhcYFTVMyN0,ne_0ypex0z_jwTVdFPeZm_361,ne__51bMnmMzsUqd2ySeUE_h0,
ne_drDG2s0VE_hAxbPW7_itC0,ne_sKAsznlddBnqg_MKgjSdD2,ne_18FITKdTLqNjkvP7Ae_Le2,
ne_Yj_COycH2fDX9qEnsVQzv1,ne_60rVqQ3_dwASXMnff6563_,ne_7RHtRQ8_l8efmbO9xtTQA1,
ne_lkYt4l8QbfcxidWaKKRwF1,ne_yRutIU0qzeKvT5QHmY_Ko0,ne_6mxKB5_bsgXX5JbIGStkv_,
ne_WpdNwlBdXYaB5NZu8U6Sv_,ne_ygGzVxzMqwLIunnARhFjP_,ne_sb3o83WcY_JGnvQ0nTPf32,
ne_8xMbgxicMFybps52KOxAB1,ne_Pe6VYlOIe5_H1S0Shscxk2,ne_UUks2pJUvKXY6eRi9PUcI_,
ne_Fm8wdKvRff74c1oGtLoPQ1,ne_Wn7w30ndI8_VcQ8Hu5n100,ne_NgdHoKKlJmdwEK0EcHTPL_,
ne_J0Zt07t19VAP6Keph09oX_,ne_OdctdytzNyEqy20mqeEbi1,ne_4FW8KyMEMbmfJXie6lUpg2,
ne_n29dYMP_HtqgrJViaBqwy0,ne_wTAu1LkNMValmLtmZM8C62,ne_wZIJdqiICC_ipuOLZO37h1,
ne_K367p9E_jovwx_Z92lp46_,ne_erb_XdrnZelATK7S1I2fW0,ne_Wl4W6bYeU8TY05_KpT6CY1,
ne_2ohebm979cSAsGSYFXFcD2,ne_lmiOLc_H2e2Z1UQF1Ij2_0,ne_9itSfVD4ZJ_FiyLmZ4Hkz_,
ne_TVI_J7AnI7zeeSjrKd3CP1,ne_Dp6_bpSFyOJzJT0a5IR8D_,ne_x86zEvo9fu9woy44GoqBj_,
ne_zqDkTv1NBE8u7gHg6fA1_0,ne_6GpoGKV36aVyHJTqN4REu_,ne_5pfdNYL1uNrdvy2wdgjc31,
ne_U0_wMwABO47zp8mQ72PtZ0,ne_q3BCuqbOIIVSZ2qhO_SRp1,ne_a19Jzf4I8ECFVqm_fTeXJ2,
ne_wU7W7leOz2R_io9669fpW0,ne_CZxTZRy1H516Za6zS3l4M2,ne_x97hgTgaUVwIytQP_JDW50,
ne_Jd_vOqlXPyo_cJJdTMP7l1,ne_rxWaTwflrMMJVoYi5kFJ90,ne_c9_vKFUIaltRGEilBvnF31,
ne_Boyq2zSrBBoQrUDAEMkSp0,ne_1r_yDLPsE42c42KYGN_3s0,ne_7kstlrZkVP7Vehu21EKzy0,
ne_8j3aoSlgyEBnomaFfoYRR0,ne__fHFbOct_UfhxIKziuiIP0,ne_78sTWrWT07M_8Z4Umk8jX_,
ne_XsE_rVpNed0H4jXxU647i_,ne_qCiHVbgkmp9pHwpYWFQJF2,ne_X775_zAXNB0dDVmAallWg1,
ne_1xCW7DyIBC03l9_UPiVu_0,ne_RjGnI_DRUKOSaQ0wqDwd21,ne_K_haEJlkncmN40wtlLlDk1,
ne_2921eM__LO890PC_4cEi61,ne_o9yfD3SsL4N6u3NhnrQvT1,ne_EuKVVsRMTKv4SE_JEsxGL2,
ne_ELE8K_iXqcrvFns7_hlp_0,ne_2vrb53E0PzzmE86_ERi4b0,ne_sKJnc_Q50aw5HxheVO5wU1,
ne_fpdGVECQpbglnK61dsvaH1,ne_AFlIfgRx6j_clquPN_fZA_,ne_QJxKYqZqGFSY7XE4LKDH91}
ne_KfZZ2JIGuNbcaoAgE34iJ2;typedef int32_T(*ne_Zurag3tHYnffIePv3JD7X2)(const
NeDynamicSystem*,const NeDynamicSystemInput*,ne_wINOJNSKIKor4Ml1V4FSJ_*);
typedef ne_wINOJNSKIKor4Ml1V4FSJ_*(*ne_7ZF_zyd3sEQQw0S5CHWJL1)(const
NeDynamicSystem*,PmAllocator*);typedef void(*ne_aAyKitU9ainv2aGHvVLQg2)(
NeDynamicSystem*);typedef void(*ne_IoAzQt4zNWlu4GU_8QA0k2)(const
NeDynamicSystem*,const ne_701aCeEHJLHh_SQNtyzcM0*,ne_LXe3dvLJ2qJnl1RELHHtw0*);
typedef void(*ne_ILc9YR2pZhNmjSFW63wu_2)(const NeDynamicSystem*,
NeLoggerBuilder*);typedef NeDynamicSystem*(*ne_kn3zpEsTA8hq6vxdRrtvH0)(const
NeDynamicSystem*);typedef void(*ne_HAm579P9cLhy_lt9UD53_2)(const
NeDynamicSystem*,const NeDynamicSystemInput*,PmRealVector*);struct
NeDynamicSystemTag{size_t ne_wozi2nP33kXu6dxby3pMl1[ne_pbIidIn0YnSS1rDfpppKV1]
;const ne_X3ev1H0P1wHkmrV6W2HXY2*ne_TkcCvcd0oXh9_FPPid6cc2[
ne_pbIidIn0YnSS1rDfpppKV1];size_t ne_82WZvfa288htRQylHsvg2_;size_t
ne_b2vL_uvzP3R92shI_7LuG2;size_t ne_NPkoE1C5booJr6JuHcmoL2;size_t
ne_qiYYIL3MEY_e8TjHQGO880;size_t ne_hclzR16vB2b9ykMyKvWfP1;size_t
mc_kn66IxdrCw_XrKK95TGqP0;size_t ne_eQ2aFEW9wQ03_7Wzb411N0;size_t
ne_WHZ36uCvU0YDrajyPngKS0;size_t ne_GIMpfEj8OKHkmtjICFx3u0;size_t
ne_0hPPJ5bLht5_ffJd9ynSr0;size_t ne_BmRJQmnc31b7nkfX2dk1x0;size_t
ne_bB5bSbGLfmTwhIPLe8UOi1;size_t ne_XwWarfaNAdz6bX9RJluxX2;size_t
ne_U42lsJjye3n9E57hvz5Cy2;size_t ne_WPlpEIQNVpNqJGWNjPWUo1;size_t
ne_NYXyaYwlk0RnUZFlskpOt1;size_t ne__tZjTLepn7TMtnolp73aX0;size_t
ne_Y9Rz2vFe4dTicEAN0p_n91;size_t ne_9gh2n0WL2hIFcizrpyX4x1;size_t
ne_LCig6HdaARtnObdtoC_UF2;size_t ne_Dnl7nCa5_9aVbWNRFgi9C_;size_t
ne_OxRRer7bmNPlVeIu0vzB02;size_t ne_J16IK_75e7dSCeiMU_dix_;size_t
ne_3oMt_MeIDMiLfFE2u9XKQ0;size_t ne_Rz6D4AZFqOIIPhECWTyfE1;size_t
ne_wqRmkBecpUBH708BQ_GCA2;size_t ne__jg5ZeSkqr4hXYX1EI68w2;size_t
ne_Vn2bF4NfFHNf842ts1goJ0;size_t ne_1mNS3iFrbqO_U_WExkPak0;size_t
ne_VFdv2THnEbRJJFXdQA9Gb_;boolean_T ne_RUrsvnNu07FkzqRHs4kj41;boolean_T
ne_DnlpAoLJImDhDm3u16plL1;ne_aAyKitU9ainv2aGHvVLQg2 ne_9IQK8gdk6AsNfKADsfXUb1;
ne_aAyKitU9ainv2aGHvVLQg2 ne_eEhsdZoEUrHBLowaQqZcT2;ne_Zurag3tHYnffIePv3JD7X2
ne_BrHR2TJQsneKvekNUZlBW_[ne_QJxKYqZqGFSY7XE4LKDH91];ne_7ZF_zyd3sEQQw0S5CHWJL1
ne_aqh8DGgWFc_tLR4S1zooL2[ne_QJxKYqZqGFSY7XE4LKDH91];ne_ILc9YR2pZhNmjSFW63wu_2
ne_pFxGHbxZ_ak6Ge3uaZQBx1;ne_qLSBCwa6_3RyHGztq1pVf_*ne_Ken_Il34If8A7yHU7540B1;
ne_1kVZ9wuGaAMQaZZ1cNS8d0*ne__JxVXwtHIkySOlG8u0FjF2;ne_1kVZ9wuGaAMQaZZ1cNS8d0*
ne_Zp3MPAyG9bxsd04D_UMJX0;ne_YDYdT8nc8p7zreMRVeWIt2*ne_FDSYv_YTE06tD_vLGMWZV1;
ne_u4R9ZWAN5E_gXTNPDRZme0*ne_dsY_DaElvziyMRXSlapHd1;ne_9Y6oesOBOB5o16StpuAgX0*
ne_wNrnUJ39E8ehcI_zo9UMn2;ne_QCTrr7P0IkeBDlp_OlzpM0*ne_4o55CBb0SBpuJa57SfyL3_;
ne_HrBmWAktiH5mz_7V4Jvh5_*ne_gxkfnhWwZvC4s2v9pTgCC2;ne_QCTrr7P0IkeBDlp_OlzpM0*
ne_mQWrNhLgzW8K_HCqnXLzz_;ne_HrBmWAktiH5mz_7V4Jvh5_*ne_uf5Q4jhaE_uWu3qg31nmR_;
ne_QCTrr7P0IkeBDlp_OlzpM0*ne_05WY2J_z8XYMI16XjrdGH1;ne_HrBmWAktiH5mz_7V4Jvh5_*
ne_WuJuakfSPSmYVqgZU8zn_0;ne_HrBmWAktiH5mz_7V4Jvh5_*ne_H_ZUS2Nah2xEhj_A_z1xp1;
ne_HrBmWAktiH5mz_7V4Jvh5_*ne_Uwm2vz73wm7V1PjsofKz_1;ne_1QO_Zx1HcrjkiWg8yDFgD0*
ne_BGu5vguW_Xrf2bmSHLEMW2;ne_1QO_Zx1HcrjkiWg8yDFgD0*ne_YkF8iBTtuQGaGHPFkywmG2;
ne_1QO_Zx1HcrjkiWg8yDFgD0*ne_k3q1ST1KCecAWJIMnC2ja2;ne_1QO_Zx1HcrjkiWg8yDFgD0*
ne_5_14kS1n1El_hPir9GXFH0;void*ne_uwGbZalh0VR5RIa80FK2e0;
ne_IoAzQt4zNWlu4GU_8QA0k2 ne_Xc9PZPjiAXMq9pQW4zbXh0;ne_kn3zpEsTA8hq6vxdRrtvH0
ne_ZgQHg3Ts7Sy8V2Ku0F6_J0;ne_HAm579P9cLhy_lt9UD53_2 ne_62nilmnWW2rZZv_5wpP2A0;
NeChecksum ne_GRc8FAd1pd5GiAL97uK5P1;};PMF_DEPLOY_STATIC void
ne__d2u6pP8LPXYnA7My_Cnb1(NeDynamicSystem*ne_7U1oK3K970BGrMfFsMzY10){if(
ne_7U1oK3K970BGrMfFsMzY10){ne_7U1oK3K970BGrMfFsMzY10->
ne_9IQK8gdk6AsNfKADsfXUb1(ne_7U1oK3K970BGrMfFsMzY10);}}PMF_DEPLOY_STATIC void
ne_SBa6epNL1FaqJ_DOMK0By1(NeDynamicSystem*ne_7U1oK3K970BGrMfFsMzY10){if(
ne_7U1oK3K970BGrMfFsMzY10){ne_7U1oK3K970BGrMfFsMzY10->
ne_eEhsdZoEUrHBLowaQqZcT2(ne_7U1oK3K970BGrMfFsMzY10);}}PMF_DEPLOY_STATIC
int32_T ne_rAQP4l0rFSZTXXIF66DKB2(const NeDynamicSystem*
ne_7U1oK3K970BGrMfFsMzY10,ne_KfZZ2JIGuNbcaoAgE34iJ2 id,const
NeDynamicSystemInput*mc_w2sbHOBWMTHvn1ViunNc91,ne_wINOJNSKIKor4Ml1V4FSJ_*
mc_ZFjwwXR9oOYOpGudG7a2f1){return ne_7U1oK3K970BGrMfFsMzY10->
ne_BrHR2TJQsneKvekNUZlBW_[id](ne_7U1oK3K970BGrMfFsMzY10,
mc_w2sbHOBWMTHvn1ViunNc91,mc_ZFjwwXR9oOYOpGudG7a2f1);}PMF_DEPLOY_STATIC
ne_wINOJNSKIKor4Ml1V4FSJ_*ne_DAcVsIqx0kVdMCtNn4ham2(const NeDynamicSystem*
ne_7U1oK3K970BGrMfFsMzY10,ne_KfZZ2JIGuNbcaoAgE34iJ2 id,PmAllocator*
pm_an0wiQTjdlKE72zC6FJ0a2){return ne_7U1oK3K970BGrMfFsMzY10->
ne_aqh8DGgWFc_tLR4S1zooL2[id](ne_7U1oK3K970BGrMfFsMzY10,
pm_an0wiQTjdlKE72zC6FJ0a2);}PMF_DEPLOY_STATIC NeDynamicSystemInputSizes
ne_idGaH_HLCIcmclqeeCHYT_(const NeDynamicSystem*ne_OZrqw35MPCL9LMAiY2n5_0){
NeDynamicSystemInputSizes ne_18op92eXGiCTt3cPVSrLy_;ne_18op92eXGiCTt3cPVSrLy_.
mSizes[NE_DYNAMIC_SYSTEM_INPUT_ID_Q]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_eQ2aFEW9wQ03_7Wzb411N0;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_M]=ne_OZrqw35MPCL9LMAiY2n5_0->
mc_kn66IxdrCw_XrKK95TGqP0;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_T]=1;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_U]=ne_AYKp7TvbKo_EgCXKC0XEv2(
ne_OZrqw35MPCL9LMAiY2n5_0->ne_TkcCvcd0oXh9_FPPid6cc2[ne_IHedTsscRKrwm2G2aRZJ50
],ne_OZrqw35MPCL9LMAiY2n5_0->ne_wozi2nP33kXu6dxby3pMl1[
ne_IHedTsscRKrwm2G2aRZJ50]);ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_V]=ne_AYKp7TvbKo_EgCXKC0XEv2(
ne_OZrqw35MPCL9LMAiY2n5_0->ne_TkcCvcd0oXh9_FPPid6cc2[ne_IHedTsscRKrwm2G2aRZJ50
],ne_OZrqw35MPCL9LMAiY2n5_0->ne_wozi2nP33kXu6dxby3pMl1[
ne_IHedTsscRKrwm2G2aRZJ50]);ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_X]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_82WZvfa288htRQylHsvg2_;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_D]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_b2vL_uvzP3R92shI_7LuG2;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_E]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_Dnl7nCa5_9aVbWNRFgi9C_;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_CR]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_WHZ36uCvU0YDrajyPngKS0;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_CI]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_GIMpfEj8OKHkmtjICFx3u0;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_W]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_OxRRer7bmNPlVeIu0vzB02;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_S]=1;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_P_L]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_J16IK_75e7dSCeiMU_dix_;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_P_I]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_3oMt_MeIDMiLfFE2u9XKQ0;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_P_J]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_Rz6D4AZFqOIIPhECWTyfE1;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_P_R]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_wqRmkBecpUBH708BQ_GCA2;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_DP_L]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne__jg5ZeSkqr4hXYX1EI68w2;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_DP_I]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_Vn2bF4NfFHNf842ts1goJ0;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_DP_J]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_1mNS3iFrbqO_U_WExkPak0;ne_18op92eXGiCTt3cPVSrLy_.mSizes[
NE_DYNAMIC_SYSTEM_INPUT_ID_DP_R]=ne_OZrqw35MPCL9LMAiY2n5_0->
ne_VFdv2THnEbRJJFXdQA9Gb_;return ne_18op92eXGiCTt3cPVSrLy_;}PMF_DEPLOY_STATIC
void ne_mM1EDGCsVmNazMt2jBPtl1(const NeDynamicSystem*ne_7U1oK3K970BGrMfFsMzY10
,NeLoggerBuilder*ne_PcL63KQJQ3ZoxRLKDIfzY2){ne_7U1oK3K970BGrMfFsMzY10->
ne_pFxGHbxZ_ak6Ge3uaZQBx1(ne_7U1oK3K970BGrMfFsMzY10,ne_PcL63KQJQ3ZoxRLKDIfzY2)
;}NeSystemInputSizes ne_m89OQc0hz9qDQnRsnDCyE2(void);NeSystemInputSizes
ne_OYjOyGec_Cu_P2TYG7Jwp_(const NeSystemInput*mc_esW17s79xh5U8ICFKPDHe1);
NeSystemInput*ne_04nTccAGGfTttdxxhMsLp_(NeSystemInputSizes
ne_18op92eXGiCTt3cPVSrLy_,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void
ne_296I30o7aJcMtBtmNyw1p0(NeSystemInput*ne_vc4sBL0CiKYFOPBAYvQOG1,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);NeDynamicSystemInputSizes ne_Y_6lPNpUGK52BGRkt0rBo_
(void);NeDynamicSystemInputSizes ne_EFH9i6kjHBTVR6bR1ohlZ2(const
NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1);NeDynamicSystemInput*
ne_gR3bRQOBxSCjR6TMEGTrv0(NeDynamicSystemInputSizes ne_18op92eXGiCTt3cPVSrLy_,
PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void ne_wK6KZjafZpo5jnFki5ykU1(
NeDynamicSystemInput*ne_vc4sBL0CiKYFOPBAYvQOG1,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);void ne_qtVk1IoavdeVD014l534e1(const NeSystemInput*
ne_h0Q0QWmbdeFlk5BxsVuTt1,const NeSystemInput*ne_ZOeIcWqyXF_PJ_lK8Scg__);
NeSystemInput*ne_K7UYeZG0gB_hTqXd_kepN1(const NeSystemInput*
mc_esW17s79xh5U8ICFKPDHe1,PmAllocator*mc_J3BYejxvpAX9ghSFCe0tN1);void
ne_kuH8Z11ko4YbthBt_N5L01(const NeDynamicSystemInput*ne_h0Q0QWmbdeFlk5BxsVuTt1
,const NeDynamicSystemInput*ne_ZOeIcWqyXF_PJ_lK8Scg__);NeDynamicSystemInput*
ne_NWDrMiW9XOMkH3JIw1n_P0(const NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1
,PmAllocator*mc_J3BYejxvpAX9ghSFCe0tN1);boolean_T ne_6T3HyncMpUk8SEKgIaz361(
const NeSystemInput*ne_h0Q0QWmbdeFlk5BxsVuTt1,const NeSystemInput*
ne_ZOeIcWqyXF_PJ_lK8Scg__);boolean_T ne__L2qaG38npPGuE3csQYxh1(const
NeSystemInputSizes mc_Z54JbeVS6g2FaSJpzTnPz_,const NeSystemInputSizes
mc_tXMARIq5F6Jl9Ic2QNtH50);boolean_T ne_tCn6pEvZvwHwrS4Aj_3Wp1(const
NeDynamicSystemInput*ne_h0Q0QWmbdeFlk5BxsVuTt1,const NeDynamicSystemInput*
ne_ZOeIcWqyXF_PJ_lK8Scg__);boolean_T ne_t18koedu3KGwd8SoraEF82(const
NeDynamicSystemInputSizes mc_Z54JbeVS6g2FaSJpzTnPz_,const
NeDynamicSystemInputSizes mc_tXMARIq5F6Jl9Ic2QNtH50);typedef enum{
ssc_sli_8csfyvjgVQpsseA_if0ck1= -1,ssc_sli_tB48L1Tbuxd1GdGMRo3Hb0,
ssc_sli_oFUh45o5J80BPdbGESA_J1,ssc_sli_YranPXYeVSH1emf_9Axo60,
ssc_sli_UgNo3vZOOSlmqRDdtWu12_,ssc_sli_YoUj3DHHIdXD6jvvtQ0Ex1}
ssc_sli_WYzHkNqf_U3u0kTyDb2NJ2;typedef struct ssc_sli_1ZuI2cvAm4kWxSJSChz2g2
ssc_sli_0ooPaUEjaI1kmi1pvnNpK_;typedef struct ssc_sli_wWJasTCfy6LoDnSAmBTzg_
ssc_sli_JxyBqLugZhdrPWTPuXSsO2;struct ssc_sli_wWJasTCfy6LoDnSAmBTzg_{
ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*mPrivateData;const PmSparsityPattern*
mc_t_6NUyOFwEImo4lDjZDMu0;const PmIntVector*ssc_sli_nSr5yP0PdwlgbkYubnvj11;
const PmIntVector*ssc_sli_Dbk8J1EY9sHFWoa1DzCN_1;const PmIntVector*
ssc_sli_GHVZSDbk_6ulKhARjif1T0;const PmIntVector*
ssc_sli_oPCL_qgJ2nL7yvkqzyl6F1;boolean_T ssc_sli_jmUCDP4AIEf4N2jkEywgb1;
ssc_sli_WYzHkNqf_U3u0kTyDb2NJ2 ssc_sli_NPXK4SSgch2LkF1PRgyU80;void(*
ssc_sli_VEdvFj_a23xN5lcB_FULw0)(const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
mc_B3C4xlzGIoRKlgT97lKBi2,const NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1
,PmRealVector*mc_cPpFNNxfnE9grx4hesF5K_);void(*ssc_sli_4CWN5qmcgXJPGllxzY2Z_2)
(const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2,const
PmRealVector*x,const NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1,
PmRealVector*mc_cPpFNNxfnE9grx4hesF5K_);void(*ssc_sli_j6uHHXcO8S1eh8guBChjQ_)(
const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2,const
PmRealVector*x,const NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1,
PmRealVector*mc_cPpFNNxfnE9grx4hesF5K_);void(*mc_imq97x4PVhYPNA5whBmrb1)(const
ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2,const
NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1,PmIntVector*
mc_cPpFNNxfnE9grx4hesF5K_);void(*ssc_sli_sUukcKAxIl_q3uVrEdicz1)(const
ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2,const
NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1,const PmRealVector*
mc_cPpFNNxfnE9grx4hesF5K_);void(*ssc_sli_IfrojsYUlKgpjdF1QcWdW1)(const
ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2,const
NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1,PmRealVector*
mc_cPpFNNxfnE9grx4hesF5K_);void(*mc_YCFci8IAJkK9w_xpRtHta2)(
ssc_sli_JxyBqLugZhdrPWTPuXSsO2*);};
#include "pm_std.h"
#include "ne_std.h"
typedef struct ssc_core_8kmf655VJUB_m_HXQcb_C0{size_t mN;
ne_1QO_Zx1HcrjkiWg8yDFgD0*mX;}ssc_core_BY5GFIZS_YKN7NuU_WCJb1;typedef struct
ssc_core_5oxcP_O7hXZvPbsbbiiIw1{ssc_core_BY5GFIZS_YKN7NuU_WCJb1
ssc_core_hshxezlBZEHy_vyCM66v90;ssc_core_BY5GFIZS_YKN7NuU_WCJb1
ssc_core_B1xu1F2k1E8Fp3pzL8sIG_;ssc_core_BY5GFIZS_YKN7NuU_WCJb1
ssc_core_WFgwh_jLqlYzw77OLTzf_0;ssc_core_BY5GFIZS_YKN7NuU_WCJb1
ssc_core_579jLh2FF7hG_T7aiwctJ_;}ssc_core_nY8h679iepq0hnAO4tfE_1;typedef struct
ssc_core__H1uF_7oS_v_vNvDZfK5H0 ssc_core_TjK_lpGc8GqQoFp6epLKq_;typedef struct
ssc_sli_WYbHX_30PxMspqQvarioY1 ssc_sli_fiRL08QK83_qb6SisPhsC2;typedef union
ssc_sli_qBWxygRkCJl5GwGhcjAOO1{PmIntVector ne_hNUH3KATZSw7_CzLo7sA__;
PmRealVector ne_ciAF8KflILRejS46ik8Pd0;PmRealVector
ssc_sli_0WuhtD93ueGGEO3VCchQF1;PmIntVector ne_3UOV9d5T3kWHnqK1FFWrr2;
PmIntVector ne_WJwa6ECm_0GmdrtcY0yDC1;PmRealVector ne_VVBYc4Wob_TG4vBVhqBRA1;
PmIntVector ne_yESMH5MfRj9nDdZgV2U5r0;PmRealVector ne_t07YmG6VxausltcHcKKis0;
PmIntVector ne_Qad3NsTE6Zh4JqVB_h_8x0;PmRealVector ne_0BbCO61LL104YJucJ6XyW2;
PmIntVector ne_QJaYQmwEB4HM9Ik0_pcS31;PmIntVector mDP_L;PmIntVector mDP_I;
PmIntVector mDP_J;PmRealVector mDP_R;PmRealVector
ssc_sli_VoviGlCeIufu9aECpHtoP2;}ssc_sli_CHpsZ8o2vbxjEbwZGWLDe_;typedef enum
ssc_sli_6SOggBFu0rKux49KRG9qg1{ssc_sli_AUbUQX6Cg5hNelPlrxq2S2= -1,
ssc_sli_3h25DukZkn1mxPAzA4h151,ssc_sli_7yMrhJsk16lCOirxiTZuw0,
ssc_sli_9RwD0iYXz0JfjSkc2oVqW1,ssc_sli_7uOnCiuiQlULBTUx_tWbf_,
ssc_sli_m6oMQZjfvumbCtzOS2oxj1,ssc_sli_YiiGTl0U97Lk7UPCHzIRX1,
ssc_sli_gAgeiFd_ygcLSFNoV3VMj_,ssc_sli_Fsk5YVDgFUHfjrPUgY3bX0,
ssc_sli_y8DnHIgBFV88w5MmpGvOx2,ssc_sli_RHL_p8riXrUSm4BCRiuft0,
ssc_sli_dfW5s5IGeDJtORlmviJbS2,ssc_sli_6tMh7aXziZnVXyASIeL_K1,
ssc_sli_n0Cd_PKhqeXPvi65YyUA92,ssc_sli_2h_dWLazc6nklltQxPAzl1,
ssc_sli_TXPFLpnaSdjMnf8nrbX1f_,ssc_sli_FZM8XUs2ZCcZrAVvFC4cR0,
ssc_sli_KYBLF6D_mjWMHGzCQGpTQ_}ssc_sli_w53SX_e1ipVeRiQoMI_sl0;typedef int32_T(
*ssc_sli_QLUtOX8RjyFrrSOco2A521)(const ssc_sli_fiRL08QK83_qb6SisPhsC2*,const
NeDynamicSystemInput*,ssc_sli_CHpsZ8o2vbxjEbwZGWLDe_*);struct
ssc_sli_WYbHX_30PxMspqQvarioY1{ssc_sli_QLUtOX8RjyFrrSOco2A521
ne_BrHR2TJQsneKvekNUZlBW_[ssc_sli_KYBLF6D_mjWMHGzCQGpTQ_];size_t
ssc_sli_yGmOQXuA3sjSKap_77zs__;size_t ssc_sli_CzKakSsa_WRWbOEPhid4G1;size_t
ne_XwWarfaNAdz6bX9RJluxX2;const ne_QCTrr7P0IkeBDlp_OlzpM0*
ne_4o55CBb0SBpuJa57SfyL3_;size_t ne_U42lsJjye3n9E57hvz5Cy2;const
ne_HrBmWAktiH5mz_7V4Jvh5_*ne_gxkfnhWwZvC4s2v9pTgCC2;size_t
ne__tZjTLepn7TMtnolp73aX0;const ne_QCTrr7P0IkeBDlp_OlzpM0*
ne_05WY2J_z8XYMI16XjrdGH1;size_t ne_Y9Rz2vFe4dTicEAN0p_n91;const
ne_HrBmWAktiH5mz_7V4Jvh5_*ne_WuJuakfSPSmYVqgZU8zn_0;
ssc_core_nY8h679iepq0hnAO4tfE_1 ssc_core_rge2PdEaFE_CJgdubjFoM2;PmIntVector*
ssc_sli_Dbk8J1EY9sHFWoa1DzCN_1;PmIntVector*ssc_sli_3H5YEdYKV4Mx9zMb183JJ_;};
typedef struct ssc_sli_o4ZGwGyfw1CMzZARZGE2J_ ssc_sli_UwlEHBlUhe_2cUqS2euxS0;
typedef union ssc_sli_nQvuoQM36OUThtL5qIUoq1{PmSparsityPattern
ne_vnTj47c5MwycPLUULiNMu2;PmRealVector mM;PmSparsityPattern
ssc_sli_IpggeE9PSCMrmG9UaoSFW_;PmRealVector ssc_sli_rqjxfFNyIkL8csL4eAJwA2;
PmRealVector ssc_sli_3TeB_6m1EHuhdxVLsgg9T_;PmRealVector
ne_BfYFi4NPyADpve42PBJHd2;PmIntVector ne_hNUH3KATZSw7_CzLo7sA__;}
ssc_sli_oGV1XKGd7n0kPF_9v4Cn30;typedef enum ssc_sli_qsnYK4SIDEpjP_BSKIekI2{
ssc_sli_EQ_n6fBERYDt9AF0O_zhR0= -1,ssc_sli_5igZS5uuDCRUrw99orsWF2,
ssc_sli_Nu4hd1IdghmUg2KsjyIcI2,ssc_sli_Mtwsea8wPCx8qBTZdJih__,
ssc_sli_qWpscKJrKZTGEf36crnO40,ssc_sli_B0fPLrq8TA_VSyCU1xN2D2,
ssc_sli_ka0ivi6kqyrK9QLAWk8sV2,ssc_sli_1rHjkXUAC9l20cWbuhfnj_,
ssc_sli_GS6TRGSfr950U4ddREmQ31}ssc_sli_OjXkWUHtNkSDtAA04o87H_;typedef int32_T(
*ssc_sli_aeZhomCgfEKht1CBD5IBY1)(const ssc_sli_UwlEHBlUhe_2cUqS2euxS0*,const
NeDynamicSystemInput*,ssc_sli_oGV1XKGd7n0kPF_9v4Cn30*);struct
ssc_sli_o4ZGwGyfw1CMzZARZGE2J_{ssc_sli_aeZhomCgfEKht1CBD5IBY1
ne_BrHR2TJQsneKvekNUZlBW_[ssc_sli_GS6TRGSfr950U4ddREmQ31];size_t
ssc_sli_VFA4qdIXsgnK4HptNfMVV2;size_t ssc_sli_BLRTxXz2L3F_sozFmeGYt2;
PmIntVector*ssc_sli_nSr5yP0PdwlgbkYubnvj11;PmIntVector*
ssc_sli_Dbk8J1EY9sHFWoa1DzCN_1;PmIntVector*ssc_sli_GHVZSDbk_6ulKhARjif1T0;
PmIntVector*ssc_sli_oPCL_qgJ2nL7yvkqzyl6F1;boolean_T
ssc_sli_jmUCDP4AIEf4N2jkEywgb1;ssc_sli_WYzHkNqf_U3u0kTyDb2NJ2
ssc_sli_NPXK4SSgch2LkF1PRgyU80;};typedef struct ssc_sli_1BjsKuFN7WDxuz__VyYAw2
ssc_sli_YpmpaS8dk_YvcmAZ_PYtX0;typedef union ssc_sli_1Wr20GVJfyPrHlrw92cAe1{
PmSparsityPattern ne_vnTj47c5MwycPLUULiNMu2;PmRealVector mM;PmRealVector
ne_BfYFi4NPyADpve42PBJHd2;}ssc_sli_AUGGKGpbta9IAA4gh9jv_2;typedef enum
ssc_sli_IzfJCVNh89aQt_tvsbKOl2{ssc_sli_O0TKYuswuvDIMencu3cGi2= -1,
ssc_sli_YRiTjcrwSQJMFT5Ec0F_Y2,ssc_sli_ndd_lB53QCcI6YbhBKdB_2,
ssc_sli_ClM9SBB6Kjl4Qw4GXoJVo0,ssc_sli_NsbTzimHer9dB6WmbdVeX2}
ssc_sli_4O_hcZTkG_Yd9my5TR13F0;typedef int32_T(*ssc_sli_GbywFQP6aoamu4CUJpqyc1
)(const ssc_sli_YpmpaS8dk_YvcmAZ_PYtX0*,const NeDynamicSystemInput*,
ssc_sli_AUGGKGpbta9IAA4gh9jv_2*);struct ssc_sli_1BjsKuFN7WDxuz__VyYAw2{
ssc_sli_GbywFQP6aoamu4CUJpqyc1 ne_BrHR2TJQsneKvekNUZlBW_[
ssc_sli_NsbTzimHer9dB6WmbdVeX2];size_t ssc_sli_VFA4qdIXsgnK4HptNfMVV2;
PmIntVector*ssc_sli_nSr5yP0PdwlgbkYubnvj11;PmIntVector*
ssc_sli_GHVZSDbk_6ulKhARjif1T0;PmIntVector*ssc_sli_oPCL_qgJ2nL7yvkqzyl6F1;
ssc_sli_WYzHkNqf_U3u0kTyDb2NJ2 ssc_sli_NPXK4SSgch2LkF1PRgyU80;};typedef struct
ssc_sli_Hck8dQkuAyS_MFId63Pee_ ssc_sli_Vj13PERzmkON00v5QIWDk1;struct
ssc_sli_Hck8dQkuAyS_MFId63Pee_{NeDynamicSystemInputSizes mSizes;PmIntVector*
ssc_sli__UALwQ0FJDLKgbBcWXXPz_;ssc_sli_fiRL08QK83_qb6SisPhsC2*
ssc_sli_NcmJRTYhSXFreX4iieV_12;size_t ssc_sli_kdhY_w88fu0lQa7Q89_9l0;
ssc_sli_UwlEHBlUhe_2cUqS2euxS0**ssc_sli_DW4vT8xcfdox7PhxkspRZ_;
ssc_sli_YpmpaS8dk_YvcmAZ_PYtX0*ssc_sli_qOJOJHsbwpsMbcfE37jGY0;
ssc_core_TjK_lpGc8GqQoFp6epLKq_*ssc_sli_L6WR2xpQMbFC59XpQs1Mc1;void(*
mc_YCFci8IAJkK9w_xpRtHta2)(ssc_sli_Vj13PERzmkON00v5QIWDk1*
ssc_sli_vzQNqPufCy8c9d_rWvxtj1);};ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
ssc_sli_remH9lvf_B6T8Ony_587q2(const ssc_sli_UwlEHBlUhe_2cUqS2euxS0*
ssc_sli_Ca40057FwBO_idgJMt15n1,const NeDynamicSystemInputSizes
ne_18op92eXGiCTt3cPVSrLy_);
#include "pm_std.h"
#include "mc_std.h"
typedef enum{mc_KhnGFEmutK29G1pFMV7eY2= -1,mc_DKQ2NLbquneq0lUPeY6980,
mc_pZ2gSv1PwNXkkpsIRojds1,mc_s3f6TbPTFsg3OoFmSAmw9_,mc_UVVwEZg9VhYkMacmned87_,
mc_We99sVwuHRSx58iJnCFWJ1,mc_l850kaw5_IoBVNaRVt13c0,mc_PlLsh29Os6JPlaG9RqaLj1}
mc_v0sTqkEWafl9TPgVRJyQ40;typedef struct mc_WhDlDj1zmiQx043biolb81
mc_GlmRlYa6s_WkfFpBYMHnW_;struct McRealFunctionTag{mc_GlmRlYa6s_WkfFpBYMHnW_*
mc_2s9vB1TeGePozpYvhr_nm_;mc_v0sTqkEWafl9TPgVRJyQ40(*mc_AkTbmaeNiVf6F7eo9cqvi0
)(const void*mc_w2sbHOBWMTHvn1ViunNc91,const PmRealVector*
mc_ZFjwwXR9oOYOpGudG7a2f1,mc_GlmRlYa6s_WkfFpBYMHnW_*mc_6peHhhgu8wo0Kp3HDh_aI0)
;const void*(*mc_wlcTuDm2p66ascvFToGzq1)(const McRealFunction*
mc_Egr13MRE9IVP5BUwy4rIY1);void(*mc_YCFci8IAJkK9w_xpRtHta2)(McRealFunction*
mc_Egr13MRE9IVP5BUwy4rIY1);};typedef struct mc_Owe6_gHWIwVgeopMGSBKl0
mc_aVw842GhQvd__vlWfLkt11;struct McIntFunctionTag{mc_aVw842GhQvd__vlWfLkt11*
mc_2s9vB1TeGePozpYvhr_nm_;void(*mc_AkTbmaeNiVf6F7eo9cqvi0)(const void*
mc_w2sbHOBWMTHvn1ViunNc91,const PmIntVector*mc_ZFjwwXR9oOYOpGudG7a2f1,
mc_aVw842GhQvd__vlWfLkt11*mc_6peHhhgu8wo0Kp3HDh_aI0);const void*(*
mc_wlcTuDm2p66ascvFToGzq1)(const McIntFunction*mc_Egr13MRE9IVP5BUwy4rIY1);void
(*mc_YCFci8IAJkK9w_xpRtHta2)(McIntFunction*mc_Egr13MRE9IVP5BUwy4rIY1);};
typedef struct mc_yoIGOXVZU4sR6Ok75JMwh0 mc__mq5AHOLTsZs8aGf7Q6ee0;struct
McMatrixFunctionTag{mc__mq5AHOLTsZs8aGf7Q6ee0*mc_2s9vB1TeGePozpYvhr_nm_;const
PmSparsityPattern*mc__iixD59voIPp_QZe1Ziof_;void(*mc_AkTbmaeNiVf6F7eo9cqvi0)(
const void*mc_w2sbHOBWMTHvn1ViunNc91,const PmRealVector*
mc_ZFjwwXR9oOYOpGudG7a2f1,mc__mq5AHOLTsZs8aGf7Q6ee0*mc_6peHhhgu8wo0Kp3HDh_aI0)
;const void*(*mc_wlcTuDm2p66ascvFToGzq1)(const McMatrixFunction*
mc_Egr13MRE9IVP5BUwy4rIY1);void(*mc_YCFci8IAJkK9w_xpRtHta2)(McMatrixFunction*
mc_Egr13MRE9IVP5BUwy4rIY1);};McRealFunction*ssc_sli_hbyRU3woTHehKPUs_sDxQ2(
const ssc_sli_UwlEHBlUhe_2cUqS2euxS0*ssc_sli_Ca40057FwBO_idgJMt15n1,const
NeDynamicSystemInputSizes ne_18op92eXGiCTt3cPVSrLy_,
ssc_sli_OjXkWUHtNkSDtAA04o87H_ ssc_sli_3ZW7rG_V0bSdGFHTRx08o2,PmAllocator*
pm_an0wiQTjdlKE72zC6FJ0a2);McMatrixFunction*ssc_sli_qv6QjsnEP36_VwPgHT2vL0(
const ssc_sli_UwlEHBlUhe_2cUqS2euxS0*ssc_sli_Ca40057FwBO_idgJMt15n1,const
NeDynamicSystemInputSizes ne_18op92eXGiCTt3cPVSrLy_,
ssc_sli_OjXkWUHtNkSDtAA04o87H_ ssc_sli_3ZW7rG_V0bSdGFHTRx08o2,
ssc_sli_OjXkWUHtNkSDtAA04o87H_ ssc_core_Apla2yCMFWO_5xEBJsASl1,PmAllocator*
pm_an0wiQTjdlKE72zC6FJ0a2);
#include "pm_std.h"
PmAllocator*pm_default_allocator(void);void pm_rv_equals_rv(const PmRealVector
*pm_JMQ_js3toioP0_0hj_fm5_,const PmRealVector*pm__UmJPtGaW9C9junx1RpnH_);void
pm_U1h5Sl4yTxoF_YCvN9hBa1(const PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmIntVector*pm__UmJPtGaW9C9junx1RpnH_);void pm_TnPSeUZeYw5Wc8bvD8sl80(const
PmBoolVector*pm_JMQ_js3toioP0_0hj_fm5_,const PmBoolVector*
pm__UmJPtGaW9C9junx1RpnH_);void pm_fKS8kuV7G_WhlO7CcdVnc1(const PmCharVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmCharVector*pm__UmJPtGaW9C9junx1RpnH_);
boolean_T pm___43lXp90F4bzSkAXqYfT1(const PmRealVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmRealVector*pm__UmJPtGaW9C9junx1RpnH_);
boolean_T pm_XDtBnYqrul1zO7ccbIlmV2(const PmIntVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmIntVector*pm__UmJPtGaW9C9junx1RpnH_);
boolean_T pm_9IegWBFmNW3wA_0fRmj9m2(const PmBoolVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmBoolVector*pm__UmJPtGaW9C9junx1RpnH_);int_T
pm_create_real_vector_fields(PmRealVector*pm_VmBquL1cTEkIgP0cS5pM82,size_t size
,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);PmRealVector*pm_create_real_vector(
size_t pm_Z_HH1rAAmOFPWVcI_yamd_,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);
PmRealVector*pm_ZdJ6KB36NX_7JjULh6fi72(const PmRealVector*
pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void
pm_MgDXCYHfYCiNYyF5Ik7dF2(PmRealVector*pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);void pm_destroy_real_vector(PmRealVector*
pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);int_T
pm_create_int_vector_fields(PmIntVector*pm_VmBquL1cTEkIgP0cS5pM82,size_t size,
PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);PmIntVector*pm_create_int_vector(size_t
pm_Z_HH1rAAmOFPWVcI_yamd_,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);PmIntVector*
pm_pLia5sG_NxTeQbxzYtpXx_(const PmIntVector*pm_VmBquL1cTEkIgP0cS5pM82,
PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void pm_Rdk2CZ3CCj5T0d2uDHUZ20(
PmIntVector*pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);
void pm_destroy_int_vector(PmIntVector*pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);int_T pm_create_bool_vector_fields(PmBoolVector*
pm_VmBquL1cTEkIgP0cS5pM82,size_t size,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);
PmBoolVector*pm_YZQHxvtiv5rBT_iBt45HQ_(size_t pm_Z_HH1rAAmOFPWVcI_yamd_,
PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void pm_SK8Vck8jU45BIyJDK11DV_(
PmBoolVector*pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);
void pm_qv4zOCjtiVRVC86eoqx06_(PmBoolVector*pm_VmBquL1cTEkIgP0cS5pM82,
PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);PmBoolVector*pm_Or6MViYTj4_1rM_3pn1UZ0(
const PmBoolVector*pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);int_T pm_create_char_vector_fields(PmCharVector*
pm_VmBquL1cTEkIgP0cS5pM82,size_t size,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);
PmCharVector*pm_VJ_YkZBOp_Ry9yis8LShD1(size_t pm_Z_HH1rAAmOFPWVcI_yamd_,
PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void pm_cn_kUNHZ0hjihWokUKapj_(
PmCharVector*pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);
void pm_ea51z6lAUjevRfjOCHL37_(PmCharVector*pm_VmBquL1cTEkIgP0cS5pM82,
PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);int_T pm_nUREx2_I6_H8Z9q4fW3LX2(
PmSizeVector*pm_VmBquL1cTEkIgP0cS5pM82,size_t size,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);PmSizeVector*pm_P_7OU_rMIBro7VhkR5sYZ0(size_t
pm_Z_HH1rAAmOFPWVcI_yamd_,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void
pm_5sJaU0uW397ggcDhUnm4m0(PmSizeVector*pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*
pm_WFHqm0fOpgfhKZFbY5NWh2);void pm_hU5rOc4ZvyOrVHd_MYDl_2(PmSizeVector*
pm_VmBquL1cTEkIgP0cS5pM82,PmAllocator*pm_WFHqm0fOpgfhKZFbY5NWh2);void
pm_WlKWB9N0DUmpIlj3_4orb_(const PmSizeVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmSizeVector*pm__UmJPtGaW9C9junx1RpnH_);boolean_T pm_IdLJ4aCFEkd1hlk5xl7aY_(
const PmSizeVector*pm_JMQ_js3toioP0_0hj_fm5_,const PmSizeVector*
pm__UmJPtGaW9C9junx1RpnH_);
#include "pm_std.h"
size_t mc_KpKqaZjZ2rh3lSToFa7Oa2(const PmBoolVector*mc_ljExW6hRw43Vg4SLQUAvT1)
;void mc_KLKWK_FbEAF724qPNbehq1(const PmIntVector*mc_ykDPEcD4BuT8SJa7vuxej1,
const PmRealVector*x,const PmRealVector*mc_yS7VvSIKrGg9ddzBqHtUd_);void
mc_uJ_iGAyluQ5NndhonaPXl1(const PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmIntVector*pm__UmJPtGaW9C9junx1RpnH_,const PmIntVector*
mc_kmcnrlTt6IvFH5HSoyHe21);void mc_oT_HwSgZBfR7LPqZomt0Y0(const PmIntVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmIntVector*pm__UmJPtGaW9C9junx1RpnH_,const
PmIntVector*mc_kmcnrlTt6IvFH5HSoyHe21);void mc_mMmDjYPdSIEEQHj__7cd71(const
PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_);void mc_zYvj4jole4TnufsPoZWW_2(const
PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_,const PmIntVector*
pm__UmJPtGaW9C9junx1RpnH_,const PmBoolVector*mc_i34rFP0sHa_dTbFseidcw0);void
mc_TJe2EtJyyhfHpuJYOjxfC0(const PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmIntVector*pm__UmJPtGaW9C9junx1RpnH_,boolean_T mc_7lBL31aWjgSfMHGQtksob2);
void mc_JM1DLKwRGzo9Uyq32V72E_(const PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_,
const PmIntVector*mc_MmlNWCb0Iec292kl7KbkQ1);void mc_si_irLJWyQLY_l4tqebAe_(
const PmIntVector*mc_rxT7_6KqJcx5sNYEWRALX2,int32_T mc_RGllRMvIRPGkpbvuetJlO2)
;void mc_pJmDkwzzX3Iu6_VR_MyvL_(const PmBoolVector*mc_Hf_a_gs1wyoHoosYiGonU0,
const PmBoolVector*mc_AV_LMGONnBUCahwCg3D4y_,const PmIntVector*
mc_YwEOIpm092vI_BA0rQzvJ2);void mc_SKE1EUStKD_KtRTTXrxqv2(const PmBoolVector*
mc_9_yWAFd98YjxIPCHmG5rr0,size_t mc__VPpmCt_TuqLdOtTsmwgk2,const PmBoolVector*
mc_Ds0gTsuf_v_EnBO9LqpvK_,size_t mc_947YwtWZMq1Crv_q1N3191,size_t
mc_QHNSjd8JBrVVYZAcs7Zm32);void mc_OT_v_IC_x9R85Z4eHn1jA0(const PmRealVector*
mc_9_yWAFd98YjxIPCHmG5rr0,size_t mc__VPpmCt_TuqLdOtTsmwgk2,const PmRealVector*
mc_Ds0gTsuf_v_EnBO9LqpvK_,size_t mc_947YwtWZMq1Crv_q1N3191,size_t
mc_QHNSjd8JBrVVYZAcs7Zm32);void mc_J9HotRGeuZtxiip_GSZPb0(PmRealVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmRealVector*pm__UmJPtGaW9C9junx1RpnH_);size_t
mc_lp5J2bZ8EcxnhyI1PKPZd2(const PmBoolVector*mc_G15g52JPQFeDaEm_uJadW_);void
mc__xr97Mh4VU4bdE2CcyEVf_(const PmIntVector*mc_YwEOIpm092vI_BA0rQzvJ2,const
PmBoolVector*mc_AV_LMGONnBUCahwCg3D4y_);size_t mc_pdD80p5I4a4oDKki08oZ50(const
PmIntVector*mc_kI6kqxnpJaUqvLfVbMkdr0);size_t mc_a_dd0x8Rstf0HD74BJt9A2(const
PmRealVector*mc_ZxltZcnt1eSoyJTnrOm7z2);size_t mc_8u8_LRBN9SbcEOkeum7ag0(const
PmBoolVector*mc_ZxltZcnt1eSoyJTnrOm7z2);boolean_T mc_Ukc2BYyTIIZDpb_lFOWTt0(
const PmIntVector*mc_kI6kqxnpJaUqvLfVbMkdr0);boolean_T
mc_l26oJh0UM_xwSgKIeOC5J0(const PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_,int32_T
mc_RGllRMvIRPGkpbvuetJlO2);boolean_T mc_ocDPr6f6C4_v9b5NDj8JH_(const
PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,real_T mc_RGllRMvIRPGkpbvuetJlO2);void
mc_fuQc8C9CyCuf_KkBLV8eb0(const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmRealVector*pm__UmJPtGaW9C9junx1RpnH_);void mc_8BTcsQ6C8h5zrW1ZQRhKf1(const
PmRealVector*x,real_T mc_ljExW6hRw43Vg4SLQUAvT1);void mc_W0fX8K54ez0qAgM9tXjsi_
(const PmRealVector*x,const PmRealVector*mc_ET9_5EAP116KvP5KVqsrD2);void
mc_fjtK_RGCYgp34_TjPN6zv1(const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmRealVector*pm__UmJPtGaW9C9junx1RpnH_);void mc_LlLyVwCApgTvSBfIvzOuk0(const
PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,real_T a,const PmRealVector*
pm__UmJPtGaW9C9junx1RpnH_);void mc_fIL9UyKjuKeUlnGmcXq5r2(const PmRealVector*x
,const PmRealVector*mc_ET9_5EAP116KvP5KVqsrD2,const PmRealVector*
mc_SheEjf_3lOXDmgzkmhMGG2);void mc_v7V5uZPqLRlsEpMCWsoMJ0(const PmRealVector*x
,const real_T a,const PmRealVector*mc_ET9_5EAP116KvP5KVqsrD2);void
mc_DnL_y_DaeSoRsDtnK0hpB1(const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,const
real_T mc_8IKoYx3qsjeiwHerWlCOS1);void mc_I_W_409sg28ysFYlBfPcr_(const
PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,const real_T mc_8IKoYx3qsjeiwHerWlCOS1)
;void mc_MI5F4RaYNQR7pPk1GRkvn_(const PmIntVector*pm_JMQ_js3toioP0_0hj_fm5_,
const PmIntVector*pm__UmJPtGaW9C9junx1RpnH_);void mc_lkC6x3YtrvW6L16S6aM60_(
const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,const PmRealVector*
pm__UmJPtGaW9C9junx1RpnH_);void mc_vfuXLuRk3KtAfbvK_cTrv2(const PmRealVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmRealVector*pm__UmJPtGaW9C9junx1RpnH_);void
mc_tOKZMGNlSqK650YhjgeKv0(const PmRealVector*mc_9JsNfMLIQx0SlNuEaL4I2_,real_T
mc_8IKoYx3qsjeiwHerWlCOS1);void mc_Uy10YSjkY75ViJd9dTdYI1(const PmBoolVector*
mc_9JsNfMLIQx0SlNuEaL4I2_);void mc_Rhhlgu4QH_WTKd_5kpe4I2(const PmRealVector*
mc_9JsNfMLIQx0SlNuEaL4I2_);void mc_WmHTznO_Ih_dJw_MhKtIQ1(const PmIntVector*
mc_9JsNfMLIQx0SlNuEaL4I2_,int32_T mc_RGllRMvIRPGkpbvuetJlO2);void
mc_nLc17gFNFcvBlJrwxJV4w_(const PmIntVector*mc_9JsNfMLIQx0SlNuEaL4I2_);void
mc_W7kR8viSTKC_By0UjXE_A1(const PmIntVector*mc_9JsNfMLIQx0SlNuEaL4I2_);void
mc_AQtCbBjZ792h1_Xaj_dR92(const PmBoolVector*mc_i34rFP0sHa_dTbFseidcw0,const
PmIntVector*mc_YwEOIpm092vI_BA0rQzvJ2,boolean_T mc_8IKoYx3qsjeiwHerWlCOS1);
void mc_tLxHiRii5tbHWjrunaI2i1(const PmBoolVector*mc_9JsNfMLIQx0SlNuEaL4I2_,
boolean_T mc_8IKoYx3qsjeiwHerWlCOS1);void mc_AZRifAjle326aZku91XJU2(const
PmBoolVector*mc_9JsNfMLIQx0SlNuEaL4I2_);void mc_mGD4FL6_MDLg2bdqzdpfx_(const
PmBoolVector*x,size_t mc_SmSSPSQfR1qEYWsVj5ELF0,size_t
mc_QHNSjd8JBrVVYZAcs7Zm32);void mc_x2bRmxKlHWAMEwOZuiA_62(const PmBoolVector*
pm_JMQ_js3toioP0_0hj_fm5_,const PmBoolVector*pm__UmJPtGaW9C9junx1RpnH_);void
mc_eJ9VFRIFMWxO52_BT7X_C_(const PmBoolVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmBoolVector*pm__UmJPtGaW9C9junx1RpnH_);real_T mc_WJAbbKueqClxuItYQx7b61(const
PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_);real_T mc_TuU8NakpY91qxLM4is2wV2(const
PmRealVector*pm_VmBquL1cTEkIgP0cS5pM82);int32_T mc_dLmR9a64iWQBHX4QM5zCr2(
const PmIntVector*pm_VmBquL1cTEkIgP0cS5pM82);int32_T mc_eIjmwucqCUJT1PyCl_z5b_
(const PmIntVector*pm_VmBquL1cTEkIgP0cS5pM82);void mc_loSQGFba0sjWysbLdmqzS1(
PmIntVector*mc_QyVbO3pTvGiccU8Tn2eK2_,const PmIntVector*
mc_kI6kqxnpJaUqvLfVbMkdr0);void mc_O_flPmjeFB4ZmON9Xp2iV_(PmRealVector*
mc_EBUUePJ08d2hXtTa8LU0J_,const PmRealVector*mc_23nxQONnTNHWizowC7lIt0,const
PmSparsityPattern*mc_UYX2aVqEUCl0fW5_qT4Lo1);void mc_K1ezq3TzhoNUE_SEp0Dr12(
const PmRealVector*mc_kvOR3Cr3RdA0t5JHDRjvp1,const PmSparsityPattern*
mc_73ubi6fCtM2UVxkG602gl0,const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_);void
mc_WuGlfcFda9zO01qKeAxMn_(const PmRealVector*pm__UmJPtGaW9C9junx1RpnH_,const
PmRealVector*mc_kvOR3Cr3RdA0t5JHDRjvp1,const PmSparsityPattern*
mc_73ubi6fCtM2UVxkG602gl0,const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_);void
mc_qEYnRq0Ff87lxOQck1Gqi_(const PmRealVector*pm__UmJPtGaW9C9junx1RpnH_,const
PmRealVector*mc_kvOR3Cr3RdA0t5JHDRjvp1,const PmSparsityPattern*
mc_73ubi6fCtM2UVxkG602gl0,const real_T*x);void mc_SZGAWN4U4XTzc5RKGKSk5_(const
PmRealVector*pm__UmJPtGaW9C9junx1RpnH_,const PmRealVector*
mc_kvOR3Cr3RdA0t5JHDRjvp1,const PmSparsityPattern*mc_73ubi6fCtM2UVxkG602gl0,
const PmRealVector*mc_2cVF0Ggof80TSRmRbhE8l1,size_t mc_LMkPrnaKcsYHEp0eExPFH1)
;void mc_FoRQvfcV_dWdjx5L1lyM_0(const PmRealVector*pm__UmJPtGaW9C9junx1RpnH_,
const PmRealVector*mc_kvOR3Cr3RdA0t5JHDRjvp1,const PmSparsityPattern*
mc_73ubi6fCtM2UVxkG602gl0,const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_,const
PmRealVector*mc_5LkYradW8mKeL3fLSt9By1);void mc_lBp5wbXG7AvQ3hxoerNOW_(const
PmRealVector*pm__UmJPtGaW9C9junx1RpnH_,const PmRealVector*
mc_kvOR3Cr3RdA0t5JHDRjvp1,const PmSparsityPattern*mc_73ubi6fCtM2UVxkG602gl0,
const PmRealVector*pm_JMQ_js3toioP0_0hj_fm5_);void mc_z041e_QXd3uR2ef2CH37s1(
const PmRealVector*mc_ET9_5EAP116KvP5KVqsrD2,const PmRealVector*
mc_0R8y9UtrLk3busEbM65xW_,const PmSparsityPattern*mc__aqwF2UeMrHkDfRgGhMkr0,
size_t mc_OUB2pptsvtdGL_LyqpgOa0,real_T mc_8IKoYx3qsjeiwHerWlCOS1);void
mc_6IsBGrycIJELSxeQVWGP02(const PmRealVector*mc_SheEjf_3lOXDmgzkmhMGG2,const
PmRealVector*x,const PmRealVector*mc_ET9_5EAP116KvP5KVqsrD2);void
mc_fDK_uVHGu_qFAztUmYrXG0(const PmRealVector*mc_Hf_a_gs1wyoHoosYiGonU0,const
PmRealVector*mc_AV_LMGONnBUCahwCg3D4y_,const PmIntVector*
mc_Ma839gzucrzsXwGyDhMa82);void mc_Pv5PxBp1nNTpA2nv2TKO50(const PmRealVector*
mc_Hf_a_gs1wyoHoosYiGonU0,const PmIntVector*mc_Ma839gzucrzsXwGyDhMa82,const
PmRealVector*mc_AV_LMGONnBUCahwCg3D4y_);void mc_57l_YQYSoo0Ro6WNuRptH_(const
PmRealVector*a,const PmIntVector*mc_SmSSPSQfR1qEYWsVj5ELF0,const PmRealVector*
b);void mc_rQYUV3yV8oYU8KnRKkDRk1(const PmRealVector*a,const PmRealVector*b,
const PmBoolVector*mc_SmSSPSQfR1qEYWsVj5ELF0);void mc_Xx__kIPwzSZkrHpStVmJF_(
const PmRealVector*a,const PmBoolVector*mc_SmSSPSQfR1qEYWsVj5ELF0,const
PmRealVector*b);void mc__oSPLVBiXeFzzJsThp3Cn_(const PmRealVector*a,const
PmBoolVector*mc_SmSSPSQfR1qEYWsVj5ELF0,real_T x);void mc_BtNbeiWJf_2ScS2FihDGI0
(const PmIntVector*mc_Fgipzm4dZtWjNvleXva_V1,const PmSparsityPattern*
mc_wgw5_klFOULlYUS4qsiDG1);void mc_rxnwynr09yoIhr_7WJOnw2(const PmBoolVector*
mc_Fgipzm4dZtWjNvleXva_V1,const PmSparsityPattern*mc_wgw5_klFOULlYUS4qsiDG1);
void mc_GXd0l4NyYg6UNbaEbfuyY1(const PmBoolVector*mc_Fgipzm4dZtWjNvleXva_V1,
const PmSparsityPattern*mc_wgw5_klFOULlYUS4qsiDG1);void
mc_0IN6lZI7UaPeQvvz13t6Z_(const PmBoolVector*mc_Fgipzm4dZtWjNvleXva_V1,const
PmSparsityPattern*mc_wgw5_klFOULlYUS4qsiDG1);void mc_jk3AE9w8Z153JpwqOK4cP_(
const PmBoolVector*mc_v4k0LG4l9Qk9hEXlOIKML_,const PmSparsityPattern*
mc_3fmwBoA2gfKGlaDfp8GCd1,const PmRealVector*mc_A1lUr3Ax9HoRb_bkcLe_A1);void
mc_PUtu_CUnyMAexj3n9ThPz1(const PmBoolVector*pm__UmJPtGaW9C9junx1RpnH_,const
PmSparsityPattern*mc_73ubi6fCtM2UVxkG602gl0,const PmBoolVector*
pm_JMQ_js3toioP0_0hj_fm5_);void mc_wMbxp0k7MHKEjpdy17fjt_(const PmRealVector*
mc_jJ78FsEfvlTthTdupUhHD2,const PmSparsityPattern*mc_3fmwBoA2gfKGlaDfp8GCd1,
const PmBoolVector*mc_ID3sxM8zmIB_ZiazgNvWq2);void mc_5PAUXWifOqPPHW3wOzFa92(
const PmRealVector*mc_jJ78FsEfvlTthTdupUhHD2,const PmSparsityPattern*
mc_3fmwBoA2gfKGlaDfp8GCd1,const PmBoolVector*pm_gq3kPpO4Hdv_0UBmX5sfB1);
PmRealVector mc_mnPo3YlQdExsVqjHael_W2(const PmRealVector*
mc_ljExW6hRw43Vg4SLQUAvT1,size_t mc_XteRrKcywHWBP4sFymZ6y0,size_t
mc_jcOSsrULtHDGKqSRz3gAT0);McMatrixFunction*mc_msJ_DKVCQj8y5_UgtqNhu2(
McMatrixFunction*mc_Z54JbeVS6g2FaSJpzTnPz_,McMatrixFunction*
mc_tXMARIq5F6Jl9Ic2QNtH50,PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);
McMatrixFunction*mc_aMPI1g4IJzx_se88DNXxp_(const PmSparsityPattern*
mc_3fmwBoA2gfKGlaDfp8GCd1,const PmRealVector*mc_jJ78FsEfvlTthTdupUhHD2,const
void*mc_5ntU4ids4xVuRQ0c6mPAf1,PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);
McMatrixFunction*mc_ojEKe9_35QoXUYpthE8Iy2(PmSparsityPattern*
mc_3fmwBoA2gfKGlaDfp8GCd1,PmRealVector*mc_jJ78FsEfvlTthTdupUhHD2,const void*
mc_5ntU4ids4xVuRQ0c6mPAf1,PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);typedef struct
mc_eHE7stIyZoHCwzx6_E_ly_ mc_H0Bk7D_oz3N7oWgSjiReu_;typedef struct
mc_329HrTFt7TQQT4Mt2CFdE_ mc_AO5JW8mLUBdiYweiHzH_0_;struct
mc_329HrTFt7TQQT4Mt2CFdE_{mc_H0Bk7D_oz3N7oWgSjiReu_*mc_0TyJOxmrCFOwXODumYaSw2;
void(*mc_S8IgzFZ5xYUDYvaq_F3eY1)(const mc_AO5JW8mLUBdiYweiHzH_0_*
mc__WbKiFtr3y_24_2xwlGxv0,const void*mc_w2sbHOBWMTHvn1ViunNc91);
McMatrixFunction*(*mc_TaiRgNRVp_xjrcnpUe8lA1)(const mc_AO5JW8mLUBdiYweiHzH_0_*
mc__WbKiFtr3y_24_2xwlGxv0);void(*mc_YCFci8IAJkK9w_xpRtHta2)(
mc_AO5JW8mLUBdiYweiHzH_0_*mc__WbKiFtr3y_24_2xwlGxv0);};
mc_AO5JW8mLUBdiYweiHzH_0_*mc_cQv_ZCNfIS6i2SMCSWGyn1(McMatrixFunction*
mc_K__VwF1fOaiI5mgPPJMb62,PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);
McMatrixFunction*mc_Zra4dUIxxYK_M2KNCwYsF_(McMatrixFunction*
mc_DpmmNkDZIX2DRKnAC1cC21,PmBoolVector*mc_ID3sxM8zmIB_ZiazgNvWq2,PmBoolVector*
pm_gq3kPpO4Hdv_0UBmX5sfB1,PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);
McMatrixFunction*mc_jyMMGS25w7v9L5LqhaQtd_(McMatrixFunction*
mc_esW17s79xh5U8ICFKPDHe1,PmIntVector*mc_ID3sxM8zmIB_ZiazgNvWq2,PmIntVector*
pm_gq3kPpO4Hdv_0UBmX5sfB1,PmAllocator*pm_an0wiQTjdlKE72zC6FJ0a2);struct
ssc_sli_1ZuI2cvAm4kWxSJSChz2g2{McMatrixFunction*ssc_sli_lIz__5YV25HK5KskMHfTw0
;McMatrixFunction*ssc_sli_cEC_POkIQUWqqNC5AYoMu_;McMatrixFunction*mM;
McRealFunction*ne_BfYFi4NPyADpve42PBJHd2;mc_AO5JW8mLUBdiYweiHzH_0_*
ssc_sli_rqjxfFNyIkL8csL4eAJwA2;PmBoolVector*ssc_sli_uwHfmmJrk7tauDhUsg2pn_;
PmRealVector*ssc_sli_CvmWSvCCvt9vbOdQ4HxqY1;PmRealVector*
ssc_sli_0IjrTcG0jaX5eysnUhiiQ2;PmRealVector*ssc_sli_NObL_NZhJdurqHBapTQBD0;
PmRealVector*ssc_sli_WzPbaLIW390bQlZdKyEHu0;PmRealVector*
ssc_sli_uXbqI8887SUdnXDtK1FmY0;const ssc_sli_UwlEHBlUhe_2cUqS2euxS0*
ssc_sli_dqkT6GER2_9Xj22kWD4cU2;};static void ssc_sli_ESFCktqpOq973Y4H7Ab5q2(
const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2,const
NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1,PmRealVector*
mc_cPpFNNxfnE9grx4hesF5K_){ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*
ssc_core_SKHbY6rGfe_c5uusXTSRI1=mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData;(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_rqjxfFNyIkL8csL4eAJwA2)->
mc_S8IgzFZ5xYUDYvaq_F3eY1((ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_rqjxfFNyIkL8csL4eAJwA2),(mc_esW17s79xh5U8ICFKPDHe1));(*((
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_lIz__5YV25HK5KskMHfTw0)->
mc_AkTbmaeNiVf6F7eo9cqvi0))((mc_esW17s79xh5U8ICFKPDHe1),(
mc_cPpFNNxfnE9grx4hesF5K_),((ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_lIz__5YV25HK5KskMHfTw0)->mc_2s9vB1TeGePozpYvhr_nm_));}static void
ssc_sli_qgsBeeq2FBLYBz9iTR3kh1(const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
mc_B3C4xlzGIoRKlgT97lKBi2,const PmRealVector*x,const NeDynamicSystemInput*
mc_esW17s79xh5U8ICFKPDHe1,PmRealVector*mc_cPpFNNxfnE9grx4hesF5K_){
ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*ssc_core_SKHbY6rGfe_c5uusXTSRI1=
mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData;;(*((ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ne_BfYFi4NPyADpve42PBJHd2)->mc_AkTbmaeNiVf6F7eo9cqvi0))((
mc_esW17s79xh5U8ICFKPDHe1),(mc_cPpFNNxfnE9grx4hesF5K_),((
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ne_BfYFi4NPyADpve42PBJHd2)->
mc_2s9vB1TeGePozpYvhr_nm_));if(((size_t)(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_cEC_POkIQUWqqNC5AYoMu_->mc__iixD59voIPp_QZe1Ziof_)->mJc[(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_cEC_POkIQUWqqNC5AYoMu_->
mc__iixD59voIPp_QZe1Ziof_)->mNumCol])>0){size_t mc_SmSSPSQfR1qEYWsVj5ELF0,
mc_OUB2pptsvtdGL_LyqpgOa0=0;size_t ssc_sli_UcQ91Wou1NlJm_M1J1BSo1=
mc_cPpFNNxfnE9grx4hesF5K_->mN;;;for(mc_SmSSPSQfR1qEYWsVj5ELF0=0;
mc_SmSSPSQfR1qEYWsVj5ELF0<ssc_sli_UcQ91Wou1NlJm_M1J1BSo1;
mc_SmSSPSQfR1qEYWsVj5ELF0++){if(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_uwHfmmJrk7tauDhUsg2pn_->mX[mc_SmSSPSQfR1qEYWsVj5ELF0]){int
ssc_sli_aDrrtF80Ee4a8GHfy2ffP0=mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_nSr5yP0PdwlgbkYubnvj11->mX[mc_SmSSPSQfR1qEYWsVj5ELF0];
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_NObL_NZhJdurqHBapTQBD0->mX[
mc_OUB2pptsvtdGL_LyqpgOa0]=mc_esW17s79xh5U8ICFKPDHe1->mX.mX[
ssc_sli_aDrrtF80Ee4a8GHfy2ffP0];mc_OUB2pptsvtdGL_LyqpgOa0++;}}(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_rqjxfFNyIkL8csL4eAJwA2)->
mc_S8IgzFZ5xYUDYvaq_F3eY1((ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_rqjxfFNyIkL8csL4eAJwA2),(mc_esW17s79xh5U8ICFKPDHe1));(*((
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_cEC_POkIQUWqqNC5AYoMu_)->
mc_AkTbmaeNiVf6F7eo9cqvi0))((mc_esW17s79xh5U8ICFKPDHe1),(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_WzPbaLIW390bQlZdKyEHu0),((
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_cEC_POkIQUWqqNC5AYoMu_)->
mc_2s9vB1TeGePozpYvhr_nm_));mc_WuGlfcFda9zO01qKeAxMn_(
mc_cPpFNNxfnE9grx4hesF5K_,ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_WzPbaLIW390bQlZdKyEHu0,ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_cEC_POkIQUWqqNC5AYoMu_->mc__iixD59voIPp_QZe1Ziof_,
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_NObL_NZhJdurqHBapTQBD0);}}static void
ssc_sli_CKBwmxVZmHpmwLL4Df6_M2(const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
mc_B3C4xlzGIoRKlgT97lKBi2,const PmRealVector*x,const NeDynamicSystemInput*
mc_esW17s79xh5U8ICFKPDHe1,PmRealVector*mc_cPpFNNxfnE9grx4hesF5K_){
ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*ssc_core_SKHbY6rGfe_c5uusXTSRI1=
mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData;size_t ssc_sli_UcQ91Wou1NlJm_M1J1BSo1=
mc_cPpFNNxfnE9grx4hesF5K_->mN;;;ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_dqkT6GER2_9Xj22kWD4cU2->ne_BrHR2TJQsneKvekNUZlBW_[
ssc_sli_B0fPLrq8TA_VSyCU1xN2D2](ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_dqkT6GER2_9Xj22kWD4cU2,mc_esW17s79xh5U8ICFKPDHe1,(
ssc_sli_oGV1XKGd7n0kPF_9v4Cn30*)ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_0IjrTcG0jaX5eysnUhiiQ2);(*((ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ne_BfYFi4NPyADpve42PBJHd2)->mc_AkTbmaeNiVf6F7eo9cqvi0))((
mc_esW17s79xh5U8ICFKPDHe1),(mc_cPpFNNxfnE9grx4hesF5K_),((
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ne_BfYFi4NPyADpve42PBJHd2)->
mc_2s9vB1TeGePozpYvhr_nm_));mc_fuQc8C9CyCuf_KkBLV8eb0(
mc_cPpFNNxfnE9grx4hesF5K_,ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_0IjrTcG0jaX5eysnUhiiQ2);mc_Rhhlgu4QH_WTKd_5kpe4I2(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_CvmWSvCCvt9vbOdQ4HxqY1);(*((
ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM)->mc_AkTbmaeNiVf6F7eo9cqvi0))((
mc_esW17s79xh5U8ICFKPDHe1),(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_uXbqI8887SUdnXDtK1FmY0),((ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM)->
mc_2s9vB1TeGePozpYvhr_nm_));mc_WuGlfcFda9zO01qKeAxMn_(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_CvmWSvCCvt9vbOdQ4HxqY1,
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_uXbqI8887SUdnXDtK1FmY0,
ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM->mc__iixD59voIPp_QZe1Ziof_,x);
mc_fjtK_RGCYgp34_TjPN6zv1(mc_cPpFNNxfnE9grx4hesF5K_,
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_CvmWSvCCvt9vbOdQ4HxqY1);}static void
ssc_sli_I9Yo1MaSG_EPxdiqAkg751(const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
mc_B3C4xlzGIoRKlgT97lKBi2,const NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1
,PmIntVector*mc_cPpFNNxfnE9grx4hesF5K_){ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*
ssc_core_SKHbY6rGfe_c5uusXTSRI1=mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData;;
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_dqkT6GER2_9Xj22kWD4cU2->
ne_BrHR2TJQsneKvekNUZlBW_[ssc_sli_1rHjkXUAC9l20cWbuhfnj_](
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_dqkT6GER2_9Xj22kWD4cU2,
mc_esW17s79xh5U8ICFKPDHe1,(ssc_sli_oGV1XKGd7n0kPF_9v4Cn30*)
mc_cPpFNNxfnE9grx4hesF5K_);}static void ssc_sli_8Jg6SddkBnjcKaZ9KOHlg1(const
ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2,const
NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1,const PmRealVector*
ssc_sli_oDYIANLEFqzbB5TcCGfag1){ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*
ssc_core_SKHbY6rGfe_c5uusXTSRI1=mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData;size_t
mc_SmSSPSQfR1qEYWsVj5ELF0;size_t ssc_sli_UcQ91Wou1NlJm_M1J1BSo1=
ssc_sli_oDYIANLEFqzbB5TcCGfag1->mN;;;for(mc_SmSSPSQfR1qEYWsVj5ELF0=0;
mc_SmSSPSQfR1qEYWsVj5ELF0<ssc_sli_UcQ91Wou1NlJm_M1J1BSo1;
mc_SmSSPSQfR1qEYWsVj5ELF0++){if(!ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_uwHfmmJrk7tauDhUsg2pn_->mX[mc_SmSSPSQfR1qEYWsVj5ELF0]){int
ssc_sli_aDrrtF80Ee4a8GHfy2ffP0=mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_nSr5yP0PdwlgbkYubnvj11->mX[mc_SmSSPSQfR1qEYWsVj5ELF0];
mc_esW17s79xh5U8ICFKPDHe1->mX.mX[ssc_sli_aDrrtF80Ee4a8GHfy2ffP0]=
ssc_sli_oDYIANLEFqzbB5TcCGfag1->mX[mc_SmSSPSQfR1qEYWsVj5ELF0];}}}static void
ssc_sli_MoqcrdGDOn5KQZxLbORS21(const ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
mc_B3C4xlzGIoRKlgT97lKBi2,const NeDynamicSystemInput*mc_esW17s79xh5U8ICFKPDHe1
,PmRealVector*ssc_sli_oDYIANLEFqzbB5TcCGfag1){ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*
ssc_core_SKHbY6rGfe_c5uusXTSRI1=mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData;size_t
mc_SmSSPSQfR1qEYWsVj5ELF0;size_t ssc_sli_UcQ91Wou1NlJm_M1J1BSo1=
ssc_sli_oDYIANLEFqzbB5TcCGfag1->mN;;;for(mc_SmSSPSQfR1qEYWsVj5ELF0=0;
mc_SmSSPSQfR1qEYWsVj5ELF0<ssc_sli_UcQ91Wou1NlJm_M1J1BSo1;
mc_SmSSPSQfR1qEYWsVj5ELF0++){if(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_uwHfmmJrk7tauDhUsg2pn_->mX[mc_SmSSPSQfR1qEYWsVj5ELF0]){
ssc_sli_oDYIANLEFqzbB5TcCGfag1->mX[mc_SmSSPSQfR1qEYWsVj5ELF0]=0.0;}else{int
ssc_sli_aDrrtF80Ee4a8GHfy2ffP0=mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_nSr5yP0PdwlgbkYubnvj11->mX[mc_SmSSPSQfR1qEYWsVj5ELF0];
ssc_sli_oDYIANLEFqzbB5TcCGfag1->mX[mc_SmSSPSQfR1qEYWsVj5ELF0]=
mc_esW17s79xh5U8ICFKPDHe1->mX.mX[ssc_sli_aDrrtF80Ee4a8GHfy2ffP0];}}}static void
ssc_sli_hBBS3_xbgAgT4C9Khe8Kx_(ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
mc_B3C4xlzGIoRKlgT97lKBi2){PmAllocator*a=pm_default_allocator();
ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*ssc_core_SKHbY6rGfe_c5uusXTSRI1=
mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData;(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_lIz__5YV25HK5KskMHfTw0)->mc_YCFci8IAJkK9w_xpRtHta2(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_lIz__5YV25HK5KskMHfTw0);(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_cEC_POkIQUWqqNC5AYoMu_)->
mc_YCFci8IAJkK9w_xpRtHta2(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_cEC_POkIQUWqqNC5AYoMu_);(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ne_BfYFi4NPyADpve42PBJHd2)->mc_YCFci8IAJkK9w_xpRtHta2(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ne_BfYFi4NPyADpve42PBJHd2);(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_rqjxfFNyIkL8csL4eAJwA2)->
mc_YCFci8IAJkK9w_xpRtHta2(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_rqjxfFNyIkL8csL4eAJwA2);pm_qv4zOCjtiVRVC86eoqx06_(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_uwHfmmJrk7tauDhUsg2pn_,a);
pm_destroy_real_vector(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_CvmWSvCCvt9vbOdQ4HxqY1,a);pm_destroy_real_vector(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_0IjrTcG0jaX5eysnUhiiQ2,a);
pm_destroy_real_vector(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_NObL_NZhJdurqHBapTQBD0,a);pm_destroy_real_vector(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_WzPbaLIW390bQlZdKyEHu0,a);
pm_destroy_real_vector(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_uXbqI8887SUdnXDtK1FmY0,a);{void*ssc_sli_GAbHnJspJ6sMhe_Yzxehb_=(
ssc_core_SKHbY6rGfe_c5uusXTSRI1);if(ssc_sli_GAbHnJspJ6sMhe_Yzxehb_!=0){(a)->
mFreeFcn(a,ssc_sli_GAbHnJspJ6sMhe_Yzxehb_);}};{void*
ssc_sli_GAbHnJspJ6sMhe_Yzxehb_=(mc_B3C4xlzGIoRKlgT97lKBi2);if(
ssc_sli_GAbHnJspJ6sMhe_Yzxehb_!=0){(a)->mFreeFcn(a,
ssc_sli_GAbHnJspJ6sMhe_Yzxehb_);}};}ssc_sli_JxyBqLugZhdrPWTPuXSsO2*
ssc_sli_remH9lvf_B6T8Ony_587q2(const ssc_sli_UwlEHBlUhe_2cUqS2euxS0*
ssc_sli_Ca40057FwBO_idgJMt15n1,const NeDynamicSystemInputSizes
ne_18op92eXGiCTt3cPVSrLy_){PmAllocator*a=pm_default_allocator();
ssc_sli_JxyBqLugZhdrPWTPuXSsO2*mc_B3C4xlzGIoRKlgT97lKBi2=(
ssc_sli_JxyBqLugZhdrPWTPuXSsO2*)((a)->mCallocFcn((a),(sizeof(
ssc_sli_JxyBqLugZhdrPWTPuXSsO2)),(1)));ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*
ssc_core_SKHbY6rGfe_c5uusXTSRI1=(ssc_sli_0ooPaUEjaI1kmi1pvnNpK_*)((a)->
mCallocFcn((a),(sizeof(ssc_sli_0ooPaUEjaI1kmi1pvnNpK_)),(1)));size_t
ssc_sli_UcQ91Wou1NlJm_M1J1BSo1=ssc_sli_Ca40057FwBO_idgJMt15n1->
ssc_sli_nSr5yP0PdwlgbkYubnvj11->mN;ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ne_BfYFi4NPyADpve42PBJHd2=ssc_sli_hbyRU3woTHehKPUs_sDxQ2(
ssc_sli_Ca40057FwBO_idgJMt15n1,ne_18op92eXGiCTt3cPVSrLy_,
ssc_sli_ka0ivi6kqyrK9QLAWk8sV2,a);{PmBoolVector*mc_ID3sxM8zmIB_ZiazgNvWq2,*
pm_gq3kPpO4Hdv_0UBmX5sfB1;McMatrixFunction*ssc_sli_4HETDgQWZrSFYff_ic0xK_,*
ssc_sli_HldIHn1amOckPbv9D2RJF2;ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM=
ssc_sli_qv6QjsnEP36_VwPgHT2vL0(ssc_sli_Ca40057FwBO_idgJMt15n1,
ne_18op92eXGiCTt3cPVSrLy_,ssc_sli_Nu4hd1IdghmUg2KsjyIcI2,
ssc_sli_5igZS5uuDCRUrw99orsWF2,a);ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_uXbqI8887SUdnXDtK1FmY0=pm_create_real_vector(((size_t)(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM->mc__iixD59voIPp_QZe1Ziof_)->mJc[(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM->mc__iixD59voIPp_QZe1Ziof_)->mNumCol]),a);
mc_ID3sxM8zmIB_ZiazgNvWq2=pm_YZQHxvtiv5rBT_iBt45HQ_(
ssc_sli_UcQ91Wou1NlJm_M1J1BSo1,a);pm_gq3kPpO4Hdv_0UBmX5sfB1=
pm_YZQHxvtiv5rBT_iBt45HQ_(ssc_sli_UcQ91Wou1NlJm_M1J1BSo1,a);
mc_tLxHiRii5tbHWjrunaI2i1(mc_ID3sxM8zmIB_ZiazgNvWq2,true);
mc_rxnwynr09yoIhr_7WJOnw2(pm_gq3kPpO4Hdv_0UBmX5sfB1,
ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM->mc__iixD59voIPp_QZe1Ziof_);
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_uwHfmmJrk7tauDhUsg2pn_=
pm_Or6MViYTj4_1rM_3pn1UZ0(pm_gq3kPpO4Hdv_0UBmX5sfB1,a);
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_CvmWSvCCvt9vbOdQ4HxqY1=
pm_create_real_vector(ssc_sli_UcQ91Wou1NlJm_M1J1BSo1,a);
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_0IjrTcG0jaX5eysnUhiiQ2=
pm_create_real_vector(ssc_sli_UcQ91Wou1NlJm_M1J1BSo1,a);
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_NObL_NZhJdurqHBapTQBD0=
pm_create_real_vector(mc_8u8_LRBN9SbcEOkeum7ag0(pm_gq3kPpO4Hdv_0UBmX5sfB1),a);
ssc_sli_HldIHn1amOckPbv9D2RJF2=mc_Zra4dUIxxYK_M2KNCwYsF_(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->mM,mc_ID3sxM8zmIB_ZiazgNvWq2,
pm_gq3kPpO4Hdv_0UBmX5sfB1,a);ssc_sli_4HETDgQWZrSFYff_ic0xK_=
ssc_sli_qv6QjsnEP36_VwPgHT2vL0(ssc_sli_Ca40057FwBO_idgJMt15n1,
ne_18op92eXGiCTt3cPVSrLy_,ssc_sli_qWpscKJrKZTGEf36crnO40,
ssc_sli_Mtwsea8wPCx8qBTZdJih__,a);ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_rqjxfFNyIkL8csL4eAJwA2=mc_cQv_ZCNfIS6i2SMCSWGyn1(
ssc_sli_4HETDgQWZrSFYff_ic0xK_,a);{PmBoolVector*ssc_sli_WP_O_XUzQPzvTsPKdwspu2
,*ssc_sli_vk1wq82VK1_tEbTVGncfb1;McMatrixFunction*
ssc_sli_iLXup_JjZ2b4dzxlE_wpQ1=(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_rqjxfFNyIkL8csL4eAJwA2)->mc_TaiRgNRVp_xjrcnpUe8lA1((
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_rqjxfFNyIkL8csL4eAJwA2));
ssc_sli_WP_O_XUzQPzvTsPKdwspu2=pm_Or6MViYTj4_1rM_3pn1UZ0(
mc_ID3sxM8zmIB_ZiazgNvWq2,a);ssc_sli_vk1wq82VK1_tEbTVGncfb1=
pm_Or6MViYTj4_1rM_3pn1UZ0(pm_gq3kPpO4Hdv_0UBmX5sfB1,a);
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_cEC_POkIQUWqqNC5AYoMu_=
mc_Zra4dUIxxYK_M2KNCwYsF_(ssc_sli_iLXup_JjZ2b4dzxlE_wpQ1,
ssc_sli_WP_O_XUzQPzvTsPKdwspu2,ssc_sli_vk1wq82VK1_tEbTVGncfb1,a);
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_WzPbaLIW390bQlZdKyEHu0=
pm_create_real_vector(((size_t)(ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_cEC_POkIQUWqqNC5AYoMu_->mc__iixD59voIPp_QZe1Ziof_)->mJc[(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_cEC_POkIQUWqqNC5AYoMu_->
mc__iixD59voIPp_QZe1Ziof_)->mNumCol]),a);}{PmBoolVector*
ssc_sli_WP_O_XUzQPzvTsPKdwspu2,*ssc_sli_vk1wq82VK1_tEbTVGncfb1;PmIntVector*
ssc_sli_42aqfu_MJFDtn0OaygKZr1,*ssc_sli_0RKlX4t_YMX2gwGptyfF81;
McMatrixFunction*ssc_sli_KEGpTR_darocCD27_1PSm0,*
ssc_sli_cXB_vIGeCpvv0YcW_583N0;McMatrixFunction*ssc_sli_iLXup_JjZ2b4dzxlE_wpQ1
=(ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_rqjxfFNyIkL8csL4eAJwA2)->
mc_TaiRgNRVp_xjrcnpUe8lA1((ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_rqjxfFNyIkL8csL4eAJwA2));int mc_SmSSPSQfR1qEYWsVj5ELF0,
mc_OUB2pptsvtdGL_LyqpgOa0,ssc_core_PIqWtbzrbQqv_KS_31HnE2;
ssc_sli_WP_O_XUzQPzvTsPKdwspu2=pm_Or6MViYTj4_1rM_3pn1UZ0(
mc_ID3sxM8zmIB_ZiazgNvWq2,a);ssc_sli_vk1wq82VK1_tEbTVGncfb1=
pm_Or6MViYTj4_1rM_3pn1UZ0(pm_gq3kPpO4Hdv_0UBmX5sfB1,a);
mc_Uy10YSjkY75ViJd9dTdYI1(ssc_sli_vk1wq82VK1_tEbTVGncfb1);
ssc_sli_KEGpTR_darocCD27_1PSm0=mc_Zra4dUIxxYK_M2KNCwYsF_(
ssc_sli_iLXup_JjZ2b4dzxlE_wpQ1,ssc_sli_WP_O_XUzQPzvTsPKdwspu2,
ssc_sli_vk1wq82VK1_tEbTVGncfb1,a);ssc_sli_cXB_vIGeCpvv0YcW_583N0=
mc_msJ_DKVCQj8y5_UgtqNhu2(ssc_sli_HldIHn1amOckPbv9D2RJF2,
ssc_sli_KEGpTR_darocCD27_1PSm0,a);ssc_sli_42aqfu_MJFDtn0OaygKZr1=
pm_create_int_vector(ssc_sli_UcQ91Wou1NlJm_M1J1BSo1,a);
ssc_sli_0RKlX4t_YMX2gwGptyfF81=pm_create_int_vector(
ssc_sli_UcQ91Wou1NlJm_M1J1BSo1,a);mc_SmSSPSQfR1qEYWsVj5ELF0=0;
mc_OUB2pptsvtdGL_LyqpgOa0=(int)ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_NObL_NZhJdurqHBapTQBD0->mN;for(ssc_core_PIqWtbzrbQqv_KS_31HnE2=0;
ssc_core_PIqWtbzrbQqv_KS_31HnE2<(int)ssc_sli_UcQ91Wou1NlJm_M1J1BSo1;
ssc_core_PIqWtbzrbQqv_KS_31HnE2++){ssc_sli_42aqfu_MJFDtn0OaygKZr1->mX[
ssc_core_PIqWtbzrbQqv_KS_31HnE2]=ssc_core_PIqWtbzrbQqv_KS_31HnE2;if(
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_uwHfmmJrk7tauDhUsg2pn_->mX[
ssc_core_PIqWtbzrbQqv_KS_31HnE2]){ssc_sli_0RKlX4t_YMX2gwGptyfF81->mX[
ssc_core_PIqWtbzrbQqv_KS_31HnE2]=mc_SmSSPSQfR1qEYWsVj5ELF0;
mc_SmSSPSQfR1qEYWsVj5ELF0++;}else{ssc_sli_0RKlX4t_YMX2gwGptyfF81->mX[
ssc_core_PIqWtbzrbQqv_KS_31HnE2]=mc_OUB2pptsvtdGL_LyqpgOa0;
mc_OUB2pptsvtdGL_LyqpgOa0++;}}ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_lIz__5YV25HK5KskMHfTw0=mc_jyMMGS25w7v9L5LqhaQtd_(
ssc_sli_cXB_vIGeCpvv0YcW_583N0,ssc_sli_42aqfu_MJFDtn0OaygKZr1,
ssc_sli_0RKlX4t_YMX2gwGptyfF81,a);}}ssc_core_SKHbY6rGfe_c5uusXTSRI1->
ssc_sli_dqkT6GER2_9Xj22kWD4cU2=ssc_sli_Ca40057FwBO_idgJMt15n1;
mc_B3C4xlzGIoRKlgT97lKBi2->mPrivateData=ssc_core_SKHbY6rGfe_c5uusXTSRI1;
mc_B3C4xlzGIoRKlgT97lKBi2->mc_t_6NUyOFwEImo4lDjZDMu0=
ssc_core_SKHbY6rGfe_c5uusXTSRI1->ssc_sli_lIz__5YV25HK5KskMHfTw0->
mc__iixD59voIPp_QZe1Ziof_;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_nSr5yP0PdwlgbkYubnvj11=ssc_sli_Ca40057FwBO_idgJMt15n1->
ssc_sli_nSr5yP0PdwlgbkYubnvj11;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_Dbk8J1EY9sHFWoa1DzCN_1=ssc_sli_Ca40057FwBO_idgJMt15n1->
ssc_sli_Dbk8J1EY9sHFWoa1DzCN_1;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_GHVZSDbk_6ulKhARjif1T0=ssc_sli_Ca40057FwBO_idgJMt15n1->
ssc_sli_GHVZSDbk_6ulKhARjif1T0;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_oPCL_qgJ2nL7yvkqzyl6F1=ssc_sli_Ca40057FwBO_idgJMt15n1->
ssc_sli_oPCL_qgJ2nL7yvkqzyl6F1;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_jmUCDP4AIEf4N2jkEywgb1=ssc_sli_Ca40057FwBO_idgJMt15n1->
ssc_sli_jmUCDP4AIEf4N2jkEywgb1;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_NPXK4SSgch2LkF1PRgyU80=ssc_sli_Ca40057FwBO_idgJMt15n1->
ssc_sli_NPXK4SSgch2LkF1PRgyU80;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_VEdvFj_a23xN5lcB_FULw0=ssc_sli_ESFCktqpOq973Y4H7Ab5q2;
mc_B3C4xlzGIoRKlgT97lKBi2->ssc_sli_4CWN5qmcgXJPGllxzY2Z_2=
ssc_sli_qgsBeeq2FBLYBz9iTR3kh1;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_j6uHHXcO8S1eh8guBChjQ_=ssc_sli_CKBwmxVZmHpmwLL4Df6_M2;
mc_B3C4xlzGIoRKlgT97lKBi2->mc_imq97x4PVhYPNA5whBmrb1=
ssc_sli_I9Yo1MaSG_EPxdiqAkg751;mc_B3C4xlzGIoRKlgT97lKBi2->
ssc_sli_sUukcKAxIl_q3uVrEdicz1=ssc_sli_8Jg6SddkBnjcKaZ9KOHlg1;
mc_B3C4xlzGIoRKlgT97lKBi2->ssc_sli_IfrojsYUlKgpjdF1QcWdW1=
ssc_sli_MoqcrdGDOn5KQZxLbORS21;mc_B3C4xlzGIoRKlgT97lKBi2->
mc_YCFci8IAJkK9w_xpRtHta2=ssc_sli_hBBS3_xbgAgT4C9Khe8Kx_;return
mc_B3C4xlzGIoRKlgT97lKBi2;}
| 42,963 |
https://github.com/syedwaseemjan/StatsCollector/blob/master/app/main.py | Github Open Source | Open Source | MIT | null | StatsCollector | syedwaseemjan | Python | Code | 205 | 749 | import logging
import socket
import xml.etree.ElementTree as ET
from models import Stats
from app.tasks import upload_collector
logger = logging.getLogger()
class Main(object):
def __init__(self):
logging.basicConfig(level=logging.INFO)
# create a file handler
handler = logging.FileHandler("server.log")
handler.setLevel(logging.INFO)
# create a logging format
formatter = logging.Formatter(
"[%(asctime)s: %(levelname)s/%(name)s] %(message)s"
)
handler.setFormatter(formatter)
# add the handlers to the logger
logger.addHandler(handler)
logging.getLogger("paramiko").addHandler(handler)
def parse_client(self, client):
"""Parse the XML Element object and returns back dictionary.
Attributes:
client (XMLELement): Client information from clients.xml
"""
logger.info(
"IP: %s, Port: %s, Username: %s",
client.get("ip"),
client.get("port"),
client.get("username"),
)
ip = client.get("ip")
port = int(client.get("port"))
email = client.get("mail")
username = client.get("username")
password = client.get("password")
cpu_threshold = client.find("alert[@type='memory']").attrib["limit"]
mem_threshold = client.find("alert[@type='cpu']").attrib["limit"]
return {
"ip": ip,
"port": port,
"username": username,
"password": password,
"cpu_threshold": float(cpu_threshold[:-1]),
"mem_threshold": float(mem_threshold[:-1]),
"email": email,
}
def process_clients(self, file_path):
"""This method is used to parse the clients.xml and provides the IP,
PORT, USERNAME, PASSWORD and EMAIL to upload_collector
Attributes:
file_path (str): path for clients.xml
"""
logger.info(f"Clients file path: {file_path}")
logger.info("Started parsing clients file")
try:
tree = ET.parse(file_path)
except (ET.ParseError, FileNotFoundError) as exe:
logger.exception(exe)
return False
try:
root = tree.getroot()
for client in root.findall("client"):
data = self.parse_client(client)
stats = Stats.get_or_create(**data)
Stats.save(stats)
upload_collector.delay(
data["ip"], data["port"], data["username"], data["password"]
)
except socket.error as e:
logger.exception(f"Rabbitmq is not accessible. {e}")
return False
| 47,468 |
JURITEXT000007007087 | French Open Data | Open Government | Licence ouverte | 1,981 | Cour de Cassation, Chambre commerciale, du 20 janvier 1981, 79-13.665, Publié au bulletin | CASS | French | Spoken | 568 | 1,285 | SUR LE MOYEN UNIQUE, PRIS EN SES DEUX BRANCHES :<br/>
ATTENDU, SELON LE JUGEMENT DEFERE (TRIBUNAL DE GRANDE INSTANCE DE LYON, 6 AVRIL 1979) QUE LA SOCIETE CIVILE COOPERATIVE DE CONSTRUCTION LES PIVES, AUX DROITS DE LAQUELLE SE TROUVE LA SOCIETE SOREGEP (LA SOCIETE), A ACQUIS LE 29 AVRIL 1970 UN TERRAIN ET QU'AYANT PRIS DANS L'ACTE L'ENGAGEMENT DE CONSTRUIRE DANS LE DELAI DE QUATRE ANS SUR CETTE PARCELLE UN ENSEMBLE IMMOBILIER DONT LES 3/4 AU MOINS DE LA SURFACE BATIE SERAIT AFFECTES A L'HABITATION, ELLE A, CONTRE ASSUJETTISSEMENT A LA TAXE SUR LA VALEUR AJOUTEE, ETE EXONEREE DES DROITS D'ENREGISTREMENT EN VERTU DE L'ARTICLE 1371 DU CODE GENERAL DES IMPOTS ALORS EN VIGUEUR; QU'AUCUNE CONSTRUCTION N'AYANT ETE EDIFIEE DANS LE DELAI, L'ADMINISTRATION DES IMPOTS A EMIS LE 10 MARS 1977 UN AVIS DE MISE EN RECOUVREMENT AUX FINS D'OBTENIR PAIEMENT DES DROITS PAR ELLE ESTIMES DUS ET DU DROIT COMPLEMENTAIRE PREVU A L'ARTICLE 1840G TER DUDIT CODE;<br/>
ATTENDU QU'IL EST FAIT GRIEF AU TRIBUNAL D'AVOIR DEBOUTE LA SOCIETE DE SON OPPOSITION A CET AVIS FONDEE SUR LA FORCE MAJEURE ALORS, SELON LE POURVOI, QUE, D'UNE PART, DANS SON ASSIGNATION RESTEE SUR CE POINT SANS REPONSE, LA SOCIETE SOUTENAIT QUE POUR APPRECIER LE BIEN FONDE DE SA DEMANDE, LE TRIBUNAL DEVAIT SE PLACER A LA DATE DE LA SIGNATURE DE L'ACTE SANS TENIR COMPTE D'EVENEMENTS POSTERIEURS INDEPENDANTS DE LA VOLONTE DE L'ACQUEREUR, QU'A CETTE DATE LE MAIRE AVAIT DONNE UN AVIS FAVORABLE AU PROJET DE CONSTRUCTION, A LA SUITE D'UNE DELIBERATION DE SON CONSEIL MUNICIPAL, CE QUI IMPLIQUAIT DE SA PART LA CERTITUDE QUE L'EGOUT ALLAIT ETRE REALISE DANS UN PROCHE DELAI, LA NON REALISATION DE CET OUVRAGE CONSTITUANT DONC, POUR LE PROMOTEUR QUI S'ETAIT FIE AUX DECISIONS DE L'ADMINISTRATION AU MOMENT DE L'ACQUISITION DU TERRAIN, UN CAS EVIDENT DE FORCE MAJEURE SURVENU POSTERIEUREMENT A L'ACQUISITION, ALORS QUE, D'AUTRE PART, IL NE RESULTE PAS DES MOTIFS DU JUGEMENT QUE LE TRIBUNAL AIT RETENU COMME EVENEMENT NON IMPREVISIBLE OU IRRESISTIBLE, LA NON-CONSTRUCTION DE L'EGOUT OU DES OBSTACLES TENANT AU PROJET DE CONSTRUCTION LUI-MEME, LE JUGEMENT NE PRECISANT D'AILLEURS PAS CES OBSTACLES ET CETTE IMPRECISION NE METTANT PAS AINSI LA COUR DE CASSATION EN MESURE D'EXERCER SON CONTROLE SUR LA QUALIFICATION DES FAITS POUR REFUSER DE CONSIDERER QU'IL Y AVAIT, EN L'ESPECE, CAS DE FORCE MAJEURE;<br/>
<br/>
MAIS ATTENDU QUE LE TRIBUNAL RELEVE, D'UNE PART, QU'AU MOMENT DE L'ACQUISITION DU TERRAIN LA SOCIETE POUVAIT PREVOIR LES ALEAS AUXQUELS ETAIT SOUMISE LA DELIVRANCE DU PERMIS DE CONSTRUIRE A TEL POINT QUE CELLE-CI CONSTITUAIT UNE CONDITION SUSPENSIVE DU CONTRAT ET, D'AUTRE PART, QUE DES DIFFICULTES D'ASSAINISSEMENT ETAIENT APPARUES DES L'ACCORD PREALABLE A LA VENTE; QUE LE TRIBUNAL A PU DEDUIRE DE CES ENONCIATIONS, REPONDANT AUX CONCLUSIONS, QUE LA SOCIETE NE POUVAIT SE PREVALOIR D'UN EVENEMENT CONSTITUTIF DE LA FORCE MAJEURE; D'OU IL SUIT QUE LE MOYEN N'EST FONDE EN AUCUNE DE SES DEUX BRANCHES;<br/>
<br/>
PAR CES MOTIFS :<br/>
REJETTE LE POURVOI FORME CONTRE LE JUGEMENT RENDU LE 6 AVRIL 1979 PAR LE TRIBUNAL DE GRANDE INSTANCE DE LYON.<br/>
CF. Cour de Cassation (Chambre commerciale ) 1975-03-10 Bulletin 1975 IV N. 74 p. 60 (REJET). CF. Cour de Cassation (Chambre commerciale ) 1978-10-25 Bulletin 1978 IV N. 242 p. 202 (CASSATION). CF. Cour de Cassation (Chambre commerciale ) 1978-10-30 Bulletin 1978 IV N. 245 (2) p. 205 (REJET). CF. Cour de Cassation (Chambre commerciale ) 1980-05-12 Bulletin 1980 IV N. 191 p. 152 (REJET)<br/> | 39,151 |
https://github.com/DFrye333/Game-Prototype-0/blob/master/source/BD3GE/utility/message.h | Github Open Source | Open Source | MIT | null | Game-Prototype-0 | DFrye333 | C | Code | 124 | 412 | #ifndef BD3GE_MESSAGE_H
#define BD3GE_MESSAGE_H
namespace BD3GE {
template<class T>
class Message {
public:
Message() {
m_data = nullptr;
}
Message(T data) {
m_data = new T(data);
}
Message(const Message& source) {
m_data = source.m_data != nullptr ? new T(*(source.m_data)) : nullptr;
}
~Message() {
delete m_data;
m_data = nullptr;
}
Message& operator=(const Message& source) {
if (this != &source) {
delete m_data;
m_data = nullptr;
m_data = new T(*(source.m_data));
}
return *this;
}
bool operator==(const Message& other) {
return (*m_data == other.m_data);
}
bool operator!=(const Message& other) {
return !(this == other);
}
T* get_data(void) const {
return m_data;
}
void set_data(T data) {
if (!m_data) {
m_data = new T;
}
*m_data = data;
}
private:
T* m_data;
};
}
#endif // BD3GE_MESSAGE_H | 27,942 |
https://stackoverflow.com/questions/43304544 | StackExchange | Open Web | CC-By-SA | 2,017 | Stack Exchange | Ahasanul Haque, RF_956, ffledgling, https://stackoverflow.com/users/1220089, https://stackoverflow.com/users/3001761, https://stackoverflow.com/users/355230, https://stackoverflow.com/users/5019169, https://stackoverflow.com/users/7283579, jonrsharpe, martineau | English | Spoken | 685 | 967 | How to use regular expression as keys in a dictionary, and how do you access using it?
I have a dictionary with a tuple as keys. Inside the tuple is a number and regular expression. The tuple as key correspond to a any value. I wanted to access the value using the tuple (i.e. regular expression) as keys. For example,
import re
t_dict = dict()
t[(1, r"[0-9]+")] = "Hello world!"
t[(2, r"[a-z]+")] = "Hi!"
Am I doing the right thing in putting a regular expression on it? If not, how do you put a regular expression on it?
Next is I want to get the values in the dictionary using the keys. For example, I want to do it this way.
print t[(1, '99')] # this should print "Hello world!"
print t[(2, 'hey')] # this should print "Hi!"
There is no built in support for your use case. As dictionary is simply a key value pair, there doesn't exist such pattern based support. And, this is not looking a decent data structure as well. May be you could tell us your use cases from more higher level, so we might suggest you a different approach.
This doesn't make sense; the point of a dictionary is that it's a hash table, so you can look up value by key in O(1). You could write a data structure that does what you want, but it would have to do a O(n) scan over the regex "keys" to find the matching values.
Sorry, I don't get what you mean, sirs. I found a code that works like this t[(1, 'a')] = "Hello World!", t[(2, 'b')] = "Hi!". So, retrieving the value, "Hello World" is just t[(1, 'a')].
I am trying to simulate a DFA using dictionaries as a list of transitions of my DFA. So, the regular expressions I wrote in there means "any number from 0-infinite" and all strings only with letters from a-z.
In DFA, it is possible to have different regular expression but have the same starting state. For example, t[(1, r"[0-9]+")] and t[(1, r"[^0-9]+")]
To do what you want, you can subclass the builtin dictionary, then overwrite it's __getitem__ method to have the kind of lookup you want.
The problem with this approach is that you will not be able to reproduce the O(1) lookup of an actual dictionary, since Python's inbuilt hash function doesn't understand regexes (and I don't know of any hash that does).
There is no easy way to have an O(1) (constant time) reverse lookup to find which regular expression matches a string. You cannot know which whether a regular expression matches a string unless you've actually tried it.
The lookup time would be very close to O(1) since the only additional overhead is applying the regex to the supplied key. Regardless, I would upvote your answer if it included code showing how to to override the __setitem__() method inherited from its dict baseclass.
@martineau, "The lookup time would be very close to O(1) since the only additional overhead is applying the regex to the supplied key.". Not quite. You'd have to test the input string for the lookup against every regular expression, since any of them could match. There's no guarantee that an input lookup string matches only one of the regular expressions, and even if there were, you have no way of telling without actually checking against each of them.
@martineau, "The lookup time would be very close to O(1) since the only additional overhead is applying the regex to the supplied key.". Not quite. You'd have to test the input string for the lookup against every regular expression, since any of them could match. There's no guarantee that an input lookup string matches only one of the regular expressions, and even if there were, you have no way of telling without actually checking against each of them.
Seems to me from the examples in the OP's question that which single regex to use is being indicated because each key is a tuple whose first value looks like it's which regex to use when checking for a match.
| 38,630 |
https://apple.stackexchange.com/questions/186143 | StackExchange | Open Web | CC-By-SA | 2,015 | Stack Exchange | Pravin, Ruskes, https://apple.stackexchange.com/users/15338, https://apple.stackexchange.com/users/46541 | English | Spoken | 389 | 587 | Unable to connect internet from any browser but chrome
I am on OSX Yosemite 10.10.3 on MacBook Pro (Early 2011) and I am not able to connect to internet from any browser except chrome. I am not even able to ping from terminal as well. Please help.
When I try to use diagnostics Internet and Server shows Red, rest all are Green.
You mean a simple "ping google.com" does not work ? what does it say ?
Nope. Simple "ping google.com" does not work either.
Pravins-MacBook-Pro:~ pravinhmhatre$ ping google.com
ping: cannot resolve google.com: Unknown host
I had to reinstall Yosemite. Able to connect properly now.
Same exact problem happened after I installed El Capitan. I noticed that my root certificate is untrusted, but I'm not sure if that's at all relevant to the problem. Network preferences does not appear to have a "verify IP" option. I'll try harder.
I had to reinstall Yosemite. Able to connect properly now.
Open Network Preferences, and:
verify IP
verify gateway
verify DNS
Your IP address is either static or dynamic. Static: you put in your IP info. Dynamic: your gateway provides the correct IP info.
Open Terminal.app, and type:
ifconfig -a
That will show you what network interfaces you have. One of these is your primary route and your default gateway. You can only have one default gateway. Even though you may have many interfaces (ethernet, wireless and firewire, etc), there's only one default way to go if the request is not local.
So check for default route by typing in Terminal.app:
netstat -nr | more
The top two resulting lines will tell you who's the boss.
Then ping the gateway.
ping <IP address>
If it doesn't work, reboot and try again. You should at a minimum ping your gateway and ping your DNS before it's worth it to troubleshoot individual applications.
all is fine, but does not explain why Chrome is working and the others not!
I am able to ping gateway which is 192.168.0.1 and DNS which is 103.17.159.50
@Pravin that would be your Router. Did you check the settings of your router so it is not blocking stuff.
I tried connecting from different network and even from mobile hotspot. Still same issue.. :(
@Pravin well it looks like some think this is the correct answer! does it work for you?
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americanindianas00fynnrich_1 | English-PD | Open Culture | Public Domain | 1,907 | The American Indian as a product of environment, with special reference to the Pueblos | Fynn, Arthur John, 1857-1930 | English | Spoken | 7,828 | 10,368 | EANCROFT LIBRARY Digitized by the Internet Archive in 2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/americanindianasOOfynnrich The American Indian As a Product of Environment H O P5 The American Indian As a Product of Environment With Special Reference to the Pueblos By A, J, Fynn, Ph. D. Principal of Longfellow School, and Instructor in Ethnology in Saturday Classes, Denver University With Illustrations Boston Little, Brown, and Company 1907 E4^ ^ f^ Copyright 1907, by A. J. Fynn All Rights Reserved Published October, 1907 Printed by COLONIAL PRESS: C. II. Simonds C& Co., Boston, U. 8. A« u. c. ACAOEM mSTORY FA OF COAST Dedicated to My Wife PREFACE THE fundamental thoughts in this volume were offered some time ago as a thesis for a degree from the University of Colo- rado. Changed as to arrangement of subject matter and increased to several times its original length, the material is now presented in book form, with the hope that it may be of some service in helping to keep alive an interest in that race which is so rapidly losing its identity. Written during short and widely separated inter- vals of time, covering more than a half-dozen years of the busy life of a schoolmaster, it is not surprising if the work shows defects naturally resulting from the interruptions. Thoughts begotten and expressed un- der such disadvantages are likely to lack continuity and completeness. In the work there is no attempt at profundity or exhaustiveness. There is only an effort to set forth a few of the more noticeable characteristics of primi- tive life — especially primitive life in the Southwest — relating to environment. Many interesting phases of Pueblo ethnology bearing on the main subject are merely touched upon, others entirely omitted. Since the general reader rather than the student of anthro- pology has been kept in mind during the prepara- tion of the volume, aboriginal terms of a local or technical character have been purposely avoided as far as possible. Fortune has given the writer the privilege of vis- iting the Southwest several times for the purpose of seeing the land and its people, and collecting data at first hand; but he is pleased to acknowledge the helpfulness derived from that eminent group of authors who have written so well concerning this interesting Pueblo branch of the aboriginal race. His indebtedness to them is manifested in the various quotations and foot-notes of the book. Should there be any one to whom acknowledgment is due but who has been overlooked, an apology is here offered in advance. The manuscript has been read by Dr. Francis Kelsey of Michigan University, the honored sec- retary of the Archaeological Institute of America. A. J. Fynn. Denver, Colorado, June, 1907. CONTENTS Chaptkk Page I Plants, Animals, and Man. I II Concerning the Aborigines of i rHE Western Continent in General • 19 III Pueblo Lands and Homes. 53 IV Food and Clothing. 87 V Government and Social Life • 107 VI Education • 129 VII Industries, Arts, and Sciences. 153 VIII Religion . . . ,. 179 IX Dances and Festivals. 203 X Conclusion . . .. »34 LIST OF ILLUSTRATIONS A Typical Scene in the Southwest Ruins of Cliff House, Cliff House CaRon, Colorado Entrances to Cavate Dwellings, Pajarito Park, New Mexico One of Taos Dwellings, New Mexico. Evolution of Pueblo Forms of Pot- tery FROM Indigenous Gourds Navaho Blanket Weaving — Pushing Down the Batten Antelope Altar in Serpent Cere- monial .... Snake Men Handling Serpents at Oa- AiBi Ceremonial Frontispiece Facing Page 54 76 96 158 172 200 224 The American Indian As a Product of Environment CHAPTER I PLANTS, ANIMALS, AND MAN A LL life is radically affected by environment. /\ The vegetable kingdom exemplifies this in jL JL its geographical distribution of plants. The differences in the flora of the several zones accord with the contrast in surroundings. Only simple plants, such as mosses and lichens, grow on the boundless plains of the far north; while endless va- rieties of mighty forests of palms, palmettos, rose- woods, and mahoganies, with trunks enshrouded in gigantic ferns and branches interlaced with climbing vines, flourish at the equatorial south. Tender trees thrive in pleasant valleys and under mild skies, but only the hardy ones are able to withstand the vio- lent blasts of the mountains or the higher latitudes. Species of vegetation gradually borne by transplant- ation from the equator toward the poles, or to more elevated regions, become stunted, changed in color, altered in composition, modified in general structure, and finally reach the boundary beyond which exist- ence is impossible. I 2 THE AMERICAN INDIAN Birches or willows sometimes are found growing in uncongenial northern regions, but they appear only as degenerates. Their roots cannot reach very far down into the frozen soil, and the inclemency of the weather prohibits them from thriving. As a result, instead of expanding into large, beautiful, and sym- metrical trees, as these species do in the temperate zone, they assume the form and character of mere shrubs, rising but a few inches above the surface. Even in the same latitude and on the same iso- thermal line, peculiarities of locality bring out pecul- iarities of organism. In common swamp-lands, plants are distinguished for rapid growth, soft bark, and abundance of branches and foliage ; on the dry plains and sandy deserts, the few varieties that manage to exist are characterized by scantiness of true leaves, abundance of thorns, nauseating or poisonous juices, and coverings of a glazed or pilose nature. In passing from the plant to its product, a glance is sufficient to remind us that kind, quality, and sup- ply of foods vary in accordance with latitudes and elevations. Seeds and bulbs when carried from one continent, or even one country or state, to another, will not endure radical changes. The less hardy perish, the others become modified in shape, size, flavor, and nutritive qualities. To transplant, for instance, the juicy products of the moist Atlantic coast to the arid plains of Arizona and expect them to flourish would be folly. To be sure many fruits and grains can endure PLANTS, ANIMALS, AND MAN 3 considerable variation of environment, but sooner or later results of changes become observable. Take for example Indian corn. It is naturally a sub-tropical grain, or more strictly a cultivated sub-tropical grass. It thrives best in a land of continuous heat; yet it is capable of growing in regions of country of very diverse temperatures. In fact it may be raised on territory so ever-varying as that reaching from Chili to Canada, a distance of several thousand miles. It matures conveniently during any period of time from three to six months, according to the length of the season of the locality in which it happens to be growing; and, in lands of excessive heat, espe- cially in places where the nights as well as the days are warm, it is possible for it to develop from seed to ripened ear in the course of ten weeks. Under very less advantageous conditions, of course a very much longer time is required. The main fact is that while it is a hardy food-plant, capable of enduring many physiographic changes, it cannot resist the in- fluences of climatic laws. When planted at certain distances from a given isothermal line, the stalks vary in height from two to twelve feet, the ears from three to fifteen inches; the kernels become noticeably changed^ in size, shape, and color, and manifest striking differences in nutritive value. Some foods have gained world-wide celebrity for qualities traceable to local characteristics of soil and climate. The cereals of the upper Mississippi Valley are noted for hardiness as well as plenteousness. 4 THE AMERICAN INDIAN Grapes and oranges of California are justly cele- brated throughout the western continent. Even in the markets of the Old World, the melons and the apples of Colorado are favored on account of their saccharine properties, produced as they are in the continuous sunshine of the Rocky Mountain plateau. From remotest antiquity, the dry warm climate of Persia and Arabia has made those regions of the world famous for exquisite perfumes. In a word the effects of soil, light, moisture, and temperature mani- fest themselves on plant life wherever it is found. In the animal kingdom this dependence on cli- matic conditions is equally noticeable. Redistribute in a hit-or-miss fashion the fauna of the earth, and a large percentage must die or undergo radical modi- fications to meet the various changes. Homogeneous types of brute creation exist on latitudinal, not longitudinal circles. The reindeer, polar bear, and arctic fox flourish in the zone of eternal snows, which is also the home of the large water animals, such as whale, walrus, and seal. Flying about in the icy air as fit companions to these, are numerous ptarmigans and wild ducks. Farther south, on other isothermal lines, the bison of the New World and the wild ox, buffalo, and au- rochs of the Old, animals closely related by nature and adapted to a moderate climate, have lived for ages. Here flourishes also the great group of animals that become easily domesticated, and have been the com- panions and helpers of man since the morning of time. PLANTS, ANIMALS, AND MAN 5 The large and lazy pachyderms thrive under skies well suited to them nearer the equator. On a rather wide belt of land and sea, extending from Upper Guinea to the Philippines, may be found the fiercest and most repulsive beasts of prey, the most ven- omous serpents, and the most gaudy and attractive birds. In the thick forests of Hindustan and cen- tral Africa, " The elephant browses, Undaunted and calm." In the swamps of the valley of the Brahmaputra, the huge rhinoceros is found, wallowing in the mud and satiating his appetite on the rank vege- tation abounding in that interesting region. On the banks of the Nile or the Niger, the clumsy hippo- potamus finds a congenial abiding-place. In other large sluggish rivers of the same zone, huge croco- diles live, sleep, and fight for food with kindred brutes. From the dense jungles of this equatorial belt, man-eating tigers and lions steal down upon the poorly protected natives and annually carry away their thousands of victims. A still greater enemy, because far more destructive to human life, is the deadly cobra de capello, perhaps the most venomous reptile of earth. Along the coast and among the islands of these seas of southern Asia, live the beautiful birds of paradise. Permanent modifications of territory, even within very limited areas, have destroyed, driven away, or radically changed the animals within such bounda- 6 THE AMERICAN INDIAN ries. The musk ox and caribou once roamed through the forests of Kentucky, but an alteration of climate drove them northward. The ancient mammoth, rov- ing through the Arctic regions and protected by coarse woolly covering, differed very materially from his progeny, coming down to us in hairless tegument and browsing to-day on the twigs of a tropical forest. The whale of the frigid zone has been forced to develop thick layers of blubber to fit him for enduring the icy waters of that region. The habitat of animals is also largely determined by the character and quantity of the food supply. The grassy plains of the two worlds attract and hold within their boundaries millions of ruminants. The polar bear lives on the ice, scores of miles out from land, where he is able to catch seals and fish. Various winged animals lay eggs on plants, the tender leaves of which become food for the larvae when hatched. The brute creation is noticeably checked in its land migrations by three great barriers, — moun- tains, deserts, and seas. Before man took a hand in the distribution of animals, there were many regions of earth well suited for species, which, by chance, the forces of nature had debarred. Amer- ica, prior to the arrival of the white man, was de- ficient in its variety of animal life. Flocks and herds, which have since been imported from the Old World and have found the climate and soil congenial, have added millions to the wealth of PLANTS, ANIMALS, AND MAN 7 the country. Australia, shut off from the rest of the continents by the sea, possesses a class of wild beasts peculiarly her own. They are of an ancient and inferior kind. Shaler ^ tells us that many marine animals are strictly limited in locality by the temperature of the water, and that a variation of only a few de- grees will often drive out or destroy the prevailing fish. The preponderance of sex in tadpoles is changed by a change of food.^ Weismann ^ asserts that dogs from Europe become hairless under the influence of the heat of India; and he proves by experiment that two forms of one and the same species of butterfly are produced by difference of degrees of warmth during the pupal stage. In fact the brute creation, while possessing some advantages over the vegetable, especially in the matter of locomotion, still finds itself at every turn slavishly dependent upon the decrees of nature. Sun, air, land, and sea are potent mas- ters, stimulating, limiting, or prohibiting animal life everywhere. In turning to man, there is no intention of set- ting up geographical environment as the " be-all and end-all," in shaping human affairs. Race tend- encies, individual predispositions, self -activities, — all these and other attributes have their influence. * Nature and Man in America, p. 19. ' Pedagogical Seminar, January, 1898. ' Effect of External Influence on Development. 8 THE AMERICAN INDIAN It might be interesting to the psychologist or an- thropologist to attempt to trace even such back to their origin to ascertain if they too may not be strictly the results of the influence of external con- ditions; but the subject at hand requires no such examination, and hence the fighting-ground of a much controverted question is cheerfully avoided. Tennyson makes Ulysses say: — " I am a part of all that I have met," and the line is susceptible of a very broad inter- pretation. Environment reaches to the very heart of the life experiences of both the individual and the race. Latitude, soil, oceans, plains, forests, riv- ers, heat, humidity, and a score of other physio- graphical influences, general and local, are ever present to modify human pursuits, progress, and destiny. " Man," says Bryce, " must in every stage be for many purposes dependent upon the circum- stances of his physical environment." ^ Draper writes : " To this doctrine of the control of physical agencies over organic forms I acknowl- edge no exception, not even in the case of man. The varied aspects he presents in different countries are the necessary consequences of those influences."^ Buckle thinks, " that of the two primary causes of civilization, the fertility of the soil is the one which in the ancient world exercised the most influence. * American Commonwealth, vol. ii, p. 450. ' The Intellectual Development of Europe, vol. i, p. 10. PLANTS, ANIMALS, AND MAN 9 But in European civilization, the other great cause, that is to say, cHmate, has been the most powerful."^ Guyot says : " We may, then, expect to see the great facts of the life of the nations connect themselves essentially with these differences of soil and climate, with these contrasts that nature herself presents in the interior of the continents, and whose influence on the social development of man, although vari- able according to the times, is no less evident in all the periods of his history." ^ Among many other writers well worthy of notice in passing are Montes- quieu,^ Bluntschli,* Foster,^ Comte,^ and Spencer,"^ holding also that the quality of mind and intensity of passions are strongly influenced by climate. In the colder countries people are vigorous, quick of motion, inclined to bold enterprises, tainted with fewer vices, frank and sincere in speech, less fickle, not readily moved by passionate appeal, less suscepti- ble to music, calm in reasoning, and on the whole compelled to use much forethought, energy, and skill. In warmer climates there is less inclination to carry out great enterprises. The inhabitants are dis- posed to be like old men — timid and conservative. * History of Civilization in England, vol. i, pp. 36, 37. 'The Earth and Man, p. 259. ' Spirit of Laws, vol. i, bk. xiv. * Theory of the State, bk. iii, chap, i-iii. 'The Mississippi Valley, chap. xi. " Positive Philosophy, vol. ii, bk. vi, chap. vi-xiL ' Principles of Sociology, vol. i, pt. i, chap, ii, iii. lo THE AMERICAN INDIAN Their imaginations are easily stirred, their passions quickly aroused. A life of ease is preferred to one of care and activity. Feeling runs riot over reason. There is little independence of thought. Idleness is the soul of happiness; hence the people of hotter climates cling to old customs, old laws, old beliefs, in preference to making original investigations and laying out plans for new and better things. They are disposed to endure despotism rather than to go to the trouble of arousing themselves to throw it off. Their philosophy is dreamy and mystic. They are content to be simply comfortable, and are easily imposed upon, outwitted, and outclassed, by more vigorous and more keenly thinking people. " Is it not a fact," says Wallace, " that in all ages and in every quarter of the globe the inhabitants of tem- perate have been superior to those of hotter coun- tries? All the great invasions and displacements of races have been from north to south rather than the reverse." ^ It is also worthy of note that in both the eastern hemisphere and the western the more advanced grades of culture first appeared in or near the torrid zone. On the banks of the Euphrates and the Nile, a notable civilization runs back, popularly speak- ing, into the morning of the world. Arts and sci- ences were flourishing in those lands when the rude tribes of the north with their stone weapons were engaged in hand-to-hand conflicts with the wild * Natural Selection and Tropical Nature, chap, viii, p. 177. PLANTS, ANIMALS, AND MAN ii beasts, that, when overpowered, supplied them with flesh for food, and skins for clothing and shelter. In the new hemisphere the same conditions pre- vailed. It was the strip of land between the Tropic of Cancer and the Tropic of Capricorn that con- tained the most advanced aborigines at the time of the discovery of America by Columbus. Here are Mexico, Yucatan, and Peru; and here lived the Aztecs, Mayas, and Incas respectively, the most cul- tured of all the primitive tribes of this continent. It seems, then, that peoples beneath the equatorial sun are inclined to ripen first, especially when living in lands where the environments demand a certain amount of exertion and ingenuity in order to main- tain a livelihood; but yet where a living may be obtained with only moderate exertion. It has also been observed that the peoples that first attained a marked degree of culture, in both the Old World and the New, were those that lived not only in warm but also in dry climates. A very damp atmosphere, especially when accompanied with excessive heat, enervates. Invalids passing from a country of great humidity to one of extreme dry- ness become at once noticeably invigorated. So it is with tribes and nations. There has been a tend- ency on the part of those living on semi-desert lands to develop more rapidly than their neighbors living on those more moist. When men pass into a different climate and re- main permanently, they change in character. The 12 THE AMERICAN INDIAN hardy barbarians that came down from northern Europe and settled on the coast of Africa lost the sturdiness which had characterized them in their early homes. The Hindus in very remote times left their native land, probably somewhere near central Asia, and moved southward into the isolated region beyond the Indus; and the little accomplished by these people in comparison with what has been done by the Greeks, Romans, Celts, and Teutons, other branches of the same family, is very suggestive. " It is a striking fact," says Laurie, " that the fresh and virile spirit of this vigorous race could not sus- tain itself on the plains of India. The Hindus succumbed to the influences of nature, which were too great and overwhelming to admit of the free growth of the self-conscious personality, so con- spicuous in their brethren." ^ Instead of keeping up his energy and ambition, the new-comer became indolent, dreamy, mystic, unambitious, and panthe- istic. He has no history like that of his kindred in the West. His whole national life has become stagnant, through the prevailing idea that bliss is a synonym for death of personality. To this has been added the paralyzing effect of an odious caste system, originating evidently in the differences in color between the swarthy native and the light- complexioned Aryan conqueror. To what has been stated regarding the Hindus, it may be added that the English, who to-day go * Pre-Christian Education, p. i66. PLANTS, ANIMALS, AND MAN 13 to certain parts of India to reside, are reported to grow lazy and sensual, drifting toward one or the other of the two great classes, which sub-tropical or equatorial countries tend to produce, — despots and serfs.* Professor Shaler,^ in a magazinfe article, attributes New England industries and New England ideas to the physical features of the land on which the Puri- tans settled. Those pioneers found the soil thin and covered with forests. After the trees had been removed and an attempt made to cultivate the soil, it was necessary to clear away the stones. The returns for the amount of labor expended were small. As the stream of migration began to pour westward, it became evident to the New Eng- lander that in raising crops he could not compete with the western farmer, settled on more fertile fields. He turned to the rocks for wealth, but found none. Gold, silver, coal, iron, — none of these miner- als to any great extent rewarded his efforts. There were opportunities, however, in other direc- tions. There was the sea swarming with fish. There * " In India the children of English parents must be sent back to Great Britain or they will perish. It is said that in the history of the civil service there has not been a single family which survived three generations. Even the first gen- eration loses the energy which characterizes the parental stock. The whites nowhere in the tropics can undergo con- tinuous physical toil exposed to the sun. They are always found subsisting on the labor of the native races." Brinton: Races and Peoples, p. 279. ' North American Review, vol. clxii, p. 726. 14 THE AMERICAN INDIAN were excellent harbors. So the inhabitants became sailors, fishermen, traders, and lumbermen. There was also another striking feature of the country. Though the land was not fertile, yet it contained scores of fine rushing rivers. Along these, great manufactories were built. The variety of industries that grew up by the side of these water-courses tended to make the people inventive. Their occupa- tions also had a powerful influence in shaping their political views ; for everybody knows that the manu- facturing and shipping interests of New England have been sources of hot controversies in American politics, from the Philadelphia Convention of 1787 down to the present. No one would question that the adaptability of the tier of southern states for raising cotton, and the fitness of the tier of northern states for entirely different agricultural products, along with mining, manufacturing, and commerce, helped greatly to keep the two sections politically divided for the first seventy years of the Republic, and became a prom- inent factor in hastening the Civil War. Other things being equal, countries with extensive seacoasts have a tendency to develop first. The lands about the Mediterranean had made rapid strides in civilization, while the people of more northern and far interior regions were yet in a state of bar- barism. Greece, Italy, Spain, and Portugal, reaching out into deep waters, invited commercial intercourse. The Phoenicians and Carthaginians, stretched along PLANTS, ANIMALS, AND MAN 15 the seashore as they were, could be hardly anything but sailors. For the same reason in later times the Vikings, perhaps the most hardy of all, left their barren rocks to try their fortunes out on the tur- bulent northern ocean. England ^nd Japan, funda- mentally different in a score of essentials such as blood, language, and religion, each lies out in an ocean on an almost directly opposite side of Eura- sia; and this physical fact secures for both similar prestige among the nations of two great continents. Guyot makes this sweeping statement : " Call to- gether your historical recollections, and cast your eyes upon the map of the world, and you will see that all the highly civilized peoples of the earth, with the exception of one or two primitive nations, have lived, or still live, on the margins of seas or oceans." ^ Other features, such as height of mountains, courses of rivers, width of plains, coast indenta- tions, and fertility of soil, have powerfully stimu- lated, checked, or disturbed the growth of national and tribal life. It may be laid down as a rule that, in temperate regions especially, the first settlements are made on low fertile lands. To be sure, back in the in- terior in unattractive regions, weak and isolated tribal life may exist contemporaneously with that of far higher culture down on the better soils; but, after all, the law holds good that great nationali- *The Earth and Man, p. 171. i6 THE AMERICAN INDIAN ties, big cities, and complicated societies first appear in fruitful valleys and on alluvial plains. After- ward, with the advance of civilization, the enlarge- ment of facilities for promoting industries, and the increased means and appliances for protection against objectionable climates, man is attracted to less favor- able regions. Mining interests for example have led him to build towns on lonely, wind-swept, rock- bound mountain tops. Every schoolboy learns among the first of his geography and history lessons, that the long sinuous coast-line of Europe, with its many outlying islands large and small, has invited civilization since very remote times, and that the monotonous, unindented, islandless shore of Africa has repelled it; that the great number of gulfs and bays for harbors on the Atlantic coast of the United States and the scarcity of them on the Pacific have been and always will be an important consideration in the development of industries, and the distribution of population on the two opposite coasts of our continent; that the Alle- ghany Mountains were of great value in contribut- ing to the success of the early English colonies, keeping the settlements within certain limits until they became strong and united, and serving as a wall of protection against the incursions of the hos- tile aborigines of the interior; that from the notable encounter of Champlain with the Iroquois to the surrender of Burgoyne, the country about the head waters of the Hudson was the scene of many bloody PLANTS, ANIMALS, AND MAN 17 conflicts, simply because nature had fashioned a highway through this region, bestowing great ad- vantages upon those who should possess it. It is not surprising that the earliest of great civilizations should spring up in southern Asia and northeastern Africa, with their soils rich and easy to till, their annually overflowing rivers, lands at- tractive for irrigation, and their several climatic and other natural advantages for obtaining abun- dance of food with comparatively little labor. It is no wonder that the country about the Tigris and Euphrates has been overrun, conquered, and re- conquered by nations eager to possess such a coveted prize. Again, what could be more natural than that Hellas, with a coast fringed with natural harbors, should develop into a great maritime country, and what more likely than that her people in days long before the intercommunicating and confederating agencies of steel and electricity should remain po- litically disunited on account of rocky ranges, cut- ting the land into isolated sections? In the words of Cowper : — " Mountains interposed, Make enemies of nations, who had else Like kindred drops been mingled into one." * Other environmental forces may leave deep im- pressions on a people and strongly influence race characteristics. The aggressiveness which the people * The Task, bk. ii, line 17. 2 i8 THE AMERICAN INDIAN of early Rome were obliged to maintain left a marked effect on the race. The little colony on the Tiber was surrounded by hostile tribes. A war- like spirit grew out of these conditions, hence the inhabitants came to be pre-eminently soldiers. A similar example may be found in the history of the small company that settled on the banks of the Eurotas in the little state of Laconia. The set- tlers had to hold supremacy over a surrounding population that far outnumbered themselves. The necessity of the case demanded that practically the entire people should be trained to the use of arms. Thus the state of Sparta grew into a military school, so to speak, destined to become immortalized on account of its rugged, efficient soldiery. The ancient Persians also became a great martial people, because, in the words of Seeley, " Success in defense against the frequent assaults of their sur- rounding enemies stimulated them to become a na- tion of warriors." ^ These examples of the influence of environment offer many suggestions, as we turn to some phases of life connected with the aborigines of the New World, where, to use the applicable words of Hewett : " Fixed environmental conditions compelled men to certain activities, to certain beliefs and customs, equally coercive whether true or false, good or bad." ^ * History of Education, p. 36. ' American Anthropologist, n. s. vol. vii, p. 3. CHAPTER II CONCERNING THE ABORIGINES OF THE WESTERN CONTINENT IN GENERAL THE people that were found on the shores of the western world, when Europeans came to explore and settle it, were a race offering to students of science exceptionally fresh and interesting material for thought. Scattered as they were over an immense area, un- touched by civilization, living in every variety of climate, the aborigines were granted unique oppor- tunities for the spontaneous growth of their peculiar primitive institutions. If the study of anthropology instead of the pursuit of wealth had been the primary object of many of the early adventurers, how rich would have been the harvest gleaned from this undis- turbed field. To-day the conditions are far less favor- able, for numberless treasures of priceless value to the archaeologist have been lost forever, while apathy and waste have done their work far too effectually. Fortunately all is not lost. Of late a spirit of inquiry has been abroad in the land. Sympathetic, truth-seeking, justice-loving, and science-promoting men and women of America and other countries have attempted to rescue from oblivion the story 19 io THE AMERICAN INDIAN of this changed and vanishing race. In the interest of knowledge, attempts have been made to preserve as far as possible what is left; and it is indeed a matter for congratulation to the student of primitive history, that there still remain some fragments of aboriginal life which the influence of the white man has not seriously molested. We are to consider particularly one branch of these people. We are to approach the situation from the standpoint of environment. We shall often refer to the whole race for general characteristics, and to special tribes for distinctive qualities by way of comparison and illustration. As far as possible let us keep before us the type, unfettered and unaltered, as it appeared when first seen by Europeans, rather than the wasted and scattered tribes of later times, fundamentally changed through contact with civ- ilization. For a people to become modified perceptibly as a result of climatic conditions, a considerable amount of time is required. Some questions, then, naturally present themselves at the outset. Has he, whom we call the Indian,^ been on the continent long enough to be essentially affected by it? If he has changed, ^ It is unfortunate that we have no satisfactory name to apply to the natives of the New World. Writer after writer has lamented it, but no one has yet been able to hit upon an unobjectionable term. "Indian" is not definite. "American Indian" is bungling. "Amerind" has merits, but seems ob- jectionable to many on account of its etymology. Other proposed terms have met with enough of opposition to exclude them from current use. CONCERNING THE ABORIGINES 21 what were his characteristics when he first ap- peared? Where did he come from? What time has elapsed since the migration? For centuries the white man has been thrown into contact with this fellow creature, has driven him from place to place, has bargained with him, has fought with him, has tried to proselyte him, has attempted to educate him, — in fact has endeav- ored to acquaint him with all the arts, customs, advantages, and tricks of civilized life. For cen- turies the older inhabitant and the newer have looked into each other's faces, the one a mystery to the other. The original home of both is unknown. It may be that scores of centuries ago the two races stood on opposite banks of some stream in the Old World, possibly on one of the plateaus of prehistoric Asia. Necessity or inclination may have caused the one to face the rising the other the setting sun. Each wanders from region to region, in opposite direc- tions. As generation succeeds generation and century rolls back upon century, those who began the journey pass away and are forgotten. Even the causes of the migrations cease to be remembered. At length here on the opposite side of the world they come together face to face, changed in form, feature, and status, the one a powerful and prosperous people, the other a simple and uncultivated race. Truly there has been no lack of interest nor want of speculation regarding the part of earth from 22 THE AMERICAN INDIAN which these aborigines drifted.^ There has been many a war of words over the question of the place of their possible origin, and their relationship to the people of other lands. Almost every region of the eastern hemisphere, large or small, definite or indefinite, has been claimed for their habitat. Sacred books, mythology, language, government, industries, craniology, physique, weapons, decorative arts, and social life of the people of the known world have been studied, and oftentimes curiously lugged in as evidence, to throw light upon the question of the place of their origin. There is a world-wide difference in the theories presented. To the east, across the Atlantic by way of Iceland, far away over into Scandinavia, one ethnologist has tried to trace back their course. To the west, from island to island, upon the broad Pacific over to far-off Australia, another has thought he has found evidences of their long ocean voyage, extending back through many centuries. Over the ice-bound regions of northwestern America, by way of Bering Strait or the Aleutian Archipelago from China or Japan, others have argued that they came. Some have thought that they were borne over by the equatorial current from western Africa. Argu- ^Brinton: The American Race, Introductory. Fiske: Discovery of America, vol. i, chap. i. • Bancroft: Native Races, vol. i, chap, i; vol. v, chap. i. Shaler: Story of Our Continent, chap iv. Winsor: Narrative and Critical History of America, vol. i, chap. vi. Powell: Shaler's United States of America, vol. i, chap,.iv. CONCERNING THE ABORIGINES 23 merits have been advanced to prove them Carthagin- ians, Greeks, Egyptians, Trojans, Hindus, Chinese, Japanese, Cehs, Scythians, and even the lost tribes of Israel. Some think that they are an amalgamated result of many migrations from many lands, ex- tending back over scores of centuries, and that they have become a distinct type of man through the influences of new conditions. The controversy is still going on. The problem may remain forever unsolved. These disputations, however, have not been in vain. Indeed in several ways much of value has come from them. They have settled beyond question that wher- ever the red man may have originated, he has been on the soil of the western hemisphere for many, many centuries. Back to the period bordering on the great Ice Age, he has been traced fairly well, and it is possible there yet will appear plenty of geological testimony to prove his existence during the great Ice Age itself. In fact Brinton already assures us that the Indian was here during glacial times, and before the lands of northern Asia or the Islands of Polynesia were inhabited.^ Again, it seems well established that the original inhabitants were practically of one race. Shaler,^ Fiske,^ Bancroft (H. H.),* and many other eminent * Eleventh Census Report: Indians, p. 43, et al. "The Story of Our Continent, chap. iv. ' Discovery of America, vol. i, chap. i. * Native Races, vol. i, chap. i. 24 THE AMERICAN INDIAN authorities think so. The Eskimo may possibly be the trivial exception, but even this is disputed. Brinton says : " The closest observers report the physical traits of the Eskimos as thoroughly American and not Asian, as has sometimes been alleged." ^ He also, in connection with this statement, quotes Dall as saying that there is positively no racial distinction between them and the other American Indians. Some years ago the mound-builders were thought to be a distinct and superior people, but later inves- tigations seem to prove them Indian tribes. The Creeks, when discovered by Ferdinand de Soto in 1540, had villages with embankments of earth about them for the purpose of defense. These embank- ments by comparison are found to be similar in size and construction to those of the Ohio Valley. In fact the opinion is now almost universal that the builders of the Ohio earth-works were the ances- tors of the Cherokees and more northern tribes. Fiske says : " As for the mounds, which are scat- tered in such profusion over the country west of the Alleghanies, there are some which have been built by Indians since the arrival of the white men in America, and which contain knives and trinkets of European manufacture." ^ It is also to be noted that the American aborigines differ materially from any people of the Old World. They have race characteristics and individual peculi- *The American Race, p. 61. ' Discovery of America, vol. 1, p. 141. CONCERNING THE ABORIGINES 25 arities which seem exclusively their own. As Fiske states : " The aboriginal American, as we know him, with his language and legends, his physical and mental peculiarities, his social observances and cus- toms, is most emphatically a native and not an imported article. He belongs to the American con- tinent as strictly as its opossums and armadillos, its maize and its golden-rod, or any members of its aboriginal fauna and flora belong to it." ^ These people differ among themselves to be sure, but there is only that dissimilarity which we would naturally find in climates varying from Alaskan cold and barrenness to Brazilian heat and verdure. It may be concluded, then, on eminent authority, that the native home of the American Indian is un- known; that he has been on the western continent for many centuries, so long, in fact, that to all intents and purposes he may be considered an in- digenous product; that there was substantially but one race occupying the territory up to the time of the discovery of the land by Columbus. It has already been noticed that mountain ranges are strikingly important factors in determining the size, shape, and general character of the habitat of civilized nations and groups of nations. Walls of rock, standing out as barriers, have marked for ages the land limits of great European powers, and held in check the ambitions of land-grasping poten- tates. Asiatic races have found desired safety and * Discovery of America, vol. i, p. 20. 26 THE AMERICAN INDIAN isolation behind the massive mountain chains that run through the very heart of the country. In the New World, boundaries of tribes, or of other social organizations of natives, were naturally formed by mountain systems. Communication be- tween extreme eastern and extreme western groups was scanty and unimportant, on account of gigantic mountain systems, running more or less closely on longitudinal lines and forming serious obstructions. On the other hand, intercourse between northern and southern groups was obviously very extensive. Attention has been drawn by Brinton,^ Bancroft,^ and others to the fact that territorial divisions near the oceans, especially along the Pacific, lay, as a rule, in naturally mountain-bound sections of very limited width. Upon a narrow stretch of land, reaching from southern Alaska to the Gulf of "Calif ornia, a distance of two thousand miles, crowded in between the northern Pacific Ocean and the Coast Range, fav- ored by a climate always softened by ocean breezes from equatorial currents, were several tribes that, on account of similarity of surroundings and easy communication, grew to be wonderfully alike in per- sonal appearance and culture. Through a string of inland valleys of the Rocky Mountains, reaching from the head waters of the Columbia River down through Mexico, extending over territory several thousand miles in length, was the Uto-Aztecan stock, * Races and Peoples, lect. ix. ' Native Races, vol. i, chap. i. CONCERNING THE ABORIGINES 27 embracing so noted members as the Bannocks, Utes, Shoshones, Mokis,^ Pimas, Yaquis, Aztecs, and some forty others of more or less prominence. West and south of these, along the middle Pacific coast, the Nahuas, a part of this great parent stock, occupied a fringe of land, extending from northern Mex- ico to the Bay of Panama. Farther down, the Inca natives were strung along the narrow and sharply inclined western coast to the extent of seventeen or eighteen hundred miles. The extreme southern part of South America, consisting of a cold and moun- tainous region deeply cut into from all directions by arms of the sea, has long been occupied by the Fuegians. There is almost no level country, and the small, rocky islands and peninsulas are so covered with forests that the wretched inhabitants stick, as it were, to the shore close to the edge of the water. They spend the larger part of their days in canoes in search of food, for the major portion of their living comes from the ocean. On the Atlantic side the Guaranis have roamed, time out of mind, over a wide territory reaching from the Argentine Re- * It is unfortunate that there is not a uniform method of spelling the names of American tribes. One finds the people above designated as "Moki", "Moqui", "Hopi", also such differences as " Esquimau " and " Eskimo ". In view of this bothersome state of nomenclature and orthography, the spelling of aboriginal names in this book is that sanctioned by eminent writers, without special reference to linguistic affinity. Other things being equal, preference is given to the orthography found in the Reports of the Bureau of Eth- nology and similar scientific productions. 28 THE AMERICAN INDIAN public to the mouth of the Amazon. On the northern coast of South America lived the Arawaks and Caribs. They built strong canoes and used a rude sail in their explorations about the big sea that bears- the name of the latter. They migrated from island to island over the Lesser Antilles, thence out upon the Greater Antilles, and even up among the Bahamas, where many of them were living at the time of the discovery of America by Columbus, and who were the first people of the American race seen by the great navigator. The warm waters that washed the shores of the closely huddled islands of the West Indies could not fail to be a strong attraction to the tribes along the banks of the main- land; hence the Arawaks and Caribs naturally came to be the aboriginal explorers, adventurers, and quasi- colonists of the eastern shore of the western conti- nent. To the northwest of these, in the southeastern corner of the United States, were the tribes of the Maskoki stock, hemmed in rather securely by the Atlantic Ocean, Gulf of Mexico, Mississippi River, Ohio River, and the southern ranges of the Appa- lachian Mountain system. Farther north the Algon- kins, a great and powerful division of the race, extended from North Carolina upward and around to the Hudson Bay; and, with no natural barriers to interfere, wandered about over the northern plains to the Rocky Mountains. At the extreme north, the widely dispersed Polar people lived, nom- adized, and starved, on their inhospitable ice-fields. CONCERNING THE ABORIGINES 29 Inland, on the banks of the Orinoco, Amazon, and Parana, with their affluents, over a surface of coun- try covering milHons of square miles, intercommuni- cation was the rule, isolation the exception. Accord- ing to Brinton,^ tribes have always wandered freely over this vast area and held direct communication — rounds of friendly visits, as well as deadly encoun- ters — with one another. On some portions of this great stretch of territory it would seem that the thick forests must interfere with travel, especially the land travel; but many parts would not be seri- ously disturbed in that way, and none of them would be obstructed by barriers so formidable as those con- fronting the tribes farther west. On the great plains of North America between the Appalachian Mountains and the Rockies, facility of communication among tribes existed in even a more marked degree. Travel from the Gulf of Mexico to the Arctic Ocean was unimpeded. In the Mississippi Valley, which is the very heart of this region, the nature of the country made nomadism irresistible. Here could be found, especially in the western and southwestern portion of it, great expanse of terri- tory, comparatively flat; unobstructed by forests; covered only with short grasses, weeds, and shrubs; visited with but little rain and snow; intersected by water-cut trenches, dry for the most of the year, and by wide rivers, generally shallow and easily forded. On these unfriendly plains, man was offered a living * The American Race, p. 229, et seq. 30 THE AMERICAN INDIAN principally through the capturing of wild animals. | 17,000 |
US-84182810-A_1 | USPTO | Open Government | Public Domain | 2,010 | None | None | English | Spoken | 4,918 | 6,287 | System and method for detection of mobile operating through a repeater
ABSTRACT
A system and method for a network analysis system operating in a wireless communication system with repeaters is disclosed. Embodiments of the system and method enable the network analysis system to determine if signals being received by the network receivers arrive directly from a target mobile appliance or if the signals are passing through a repeater. The repeaters, through an augmentation, measure attributes of a received signal and based on these attributes the system determine whether the signal is served by a repeater or other network device.
CROSS REFERENCES
This non-provisional application is a Continuation in Part and claims priority benefit of co-pending application Ser. No. 10/586,743 filed Jul. 21, 2006, which claims priority benefit of Provisional Patent Application Ser. No. 60/570,067, titled SYSTEM AND METHOD FOR DETECTING A MOBILE STATION OPERATING THROUGH A REPEATER, filed May 12, 2004, provisional application Ser. No. 60/570,082, titled SYSTEM AND METHOD FOR IDENTIFYING THE PATH OR DEVICES ON THE PATH OF A COMMUNICATION SIGNAL, filed May 12, 2004, and provisional application Ser. No. 60/570,081, titled SYSTEM AND METHOD FOR IDENTIFYING THE PATH OR DEVICE ON THE PATH OF A COMMUNICATION SIGNAL USING (1+r(t)) AMPLITUDE MODULATION, filed May 12, 2004, the contents of which are herein incorporated by reference.
This non-provisional application also claims priority benefit of co-pending application Ser. No. 12/246,156 filed Oct. 6, 2008, titled SYSTEM AND METHOD OF UMTS UE LOCATION USING UPLINK DEDICATED PHYSICAL CONTROL CHANNEL AND DOWNLINK SYNCHRONIZATION CHANNEL, the contents of which are herein incorporated by reference. This non-provisional application also claims priority benefit of Provisional Patent Application Ser. No. 61/293,502 filed Jan. 8, 2010, titled MOBILE LOCATION BY PROXIMITY DETECTION, the contents of which are herein incorporated by reference.
BACKGROUND
The subject matter of this disclosure is directed generally towards a wireless communications network for determining whether a signal from a mobile appliance is operated by a repeater or other network device.
The use of wireless communication devices such as telephones, pagers, personal digital assistants, laptop computers, etc., hereinafter referred to collectively as “mobile appliances,” have become prevalent in today's society.
FIG. 1 shows a conventional mobile-appliance communication system having base stations 10 a-c for communicating with a mobile appliance 20. Each base station 10 contains signal processing equipment and an antenna for transmitting to and receiving signals from the mobile appliance 20 as well as other base stations. A Base Station Controller (“BSC”) and/or Mobile Switching Center (“MSC”) 45 typically is connected to each base station 10 through a wire line connection 41.
To meet the ever growing demand for mobile communication, wireless communication systems deploy repeater stations to expand range and concentration of coverage. In FIG. 1, a repeater 50 a, associated with base station 10 a, is located to extend the coverage area to encompass the back side of the mountain 1. The repeater 50 b, associated with base station 10 c, is mounted on a building and is used to provide service within the building 2.
Repeaters typically fall into two categories: (1) non-translating, also known as wideband, and (2) translating, also known as narrowband. As shown in FIG. 2 a, a non-translating repeater 250 simply passes the forward F_(f1) and reverse R_(f1) frequencies from the base station 210 and mobile appliance 220 respectively to and from the repeater coverage location. Often wideband repeaters are “in-building” or serve limited coverage areas. While the description of non-translating repeaters above and translating repeaters below are described in reference to frequency, their operation can equally be described in terms of channels, and the use of the term frequency should not be construed to limit the scope of the present disclosed subject matter.
A translating repeater assigns the mobile to a different traffic channel unbeknownst to the base station, mobile switch, MPC, and the base station controller. As shown in FIG. 2 b, the translating repeater uses the base station traffic channel R_(f1) for repeater 250 to base station 210 communication while the mobile appliance 220 utilizes a separate frequency R_(f2) for mobile to repeater communications. Translating repeaters act similarly in the forward direction using F_(f1) from the base station 210 to the repeater station 250 and F_(f2) from the repeater station 250 to the mobile appliance 220. In both cases, the existence of the repeater is usually transparent to the network.
The function of the repeater station can be assumed to be equivalent to converting all signals in some received bandwidth from a Radio Frequency (RF) to some Intermediate Frequency (IF). The IF signal bandwidth is then up-converted by suitably frequency shifting this bandwidth while concurrently applying both amplification and a fixed delay to the signals.
For example, let the set of signals transmitted by N mobiles in the repeaters' input bandwidth be denoted by
${{S(t)} = {\sum\limits_{k = 1}^{N}{{a(k)}{x\left( {k,t} \right)}{\sin\left( {w\; t} \right)}}}},$ where the signal from a given mobile is denoted by x(k, t). The signal x(k, t) is contained in the repeater bandwidth and w is the angular frequency center of the RF bandwidth. The repeater downshifts the aggregate signal to generate
${{D(t)} = {\sum\limits_{k = 1}^{N}{{a(k)}{x\left( {k,t} \right)}{\sin({vt})}}}},$ in which v is now representative of the center of the IF bandwidth. The entire signal D(t) is now converted back to RF by operations that are equivalent to forming the signal
${{R\left( {t + T} \right)} = {{G{\sum\limits_{k = 1}^{N}{{a(k)}{x\left( {k,t} \right)}{\sin\left( {v\; t} \right)}{\cos\left( {{w\; t} - {v\; t}} \right)}}}} + {G{\sum\limits_{k = 1}^{N}{{a(k)}{x\left( {k,t} \right)}{\cos\left( {v\; t} \right)}{\sin\left( {{w\; t} - {v\; t}} \right)}}}}}},$ in which G is the repeater gain. The last equation can be written in a more convenient, mathematical manner by noting that R(t) can be derived from D(t) by writing it as R(t+T)=Re{G exp(j(w−v)tI/(t))}, where G exp(j(w−v)t) is the complex representation of the multiplicative signal introduced by the repeater on the downshifted signal bandwidth and I(t) is the complex representation of D(t).
Essentially, the function of the repeater is to convert the RF signal to an IF signal, delay and amplify that IF signal, up-convert the signal back to RF, and transmit the signal. This is true for both translating and non-translating repeaters.
Repeaters typically communicate with the host base station via an RF link as shown in FIG. 3 between base station 310 and repeater 350 a. This connection allows remote operation of the repeater without physical ties back to the host base station, which is particularly advantageous in rugged or other areas where laying lines are difficult or costly. Some repeaters, generally non-translating repeaters, use a fiber optic or copper wire “tether” instead of an RF link to communicate with the host base station as shown in FIG. 3, where base station 310 is connected to repeater station 350 b by tether 351. RF signals are placed onto the tether at the repeater and then summed into the normal base station antenna path at the antenna feed interface 311 at the host base station. After integration into the normal base station antenna path, the signal from the repeater is indistinguishable to the base station regarding its origin (e.g., from the base station antennas or from a tether). In this tether architecture as well, the host base station has no knowledge of the repeater's existence or that a call is being served by the repeater.
Neither the base station nor the switch knows that a repeater or other network device is serving a call. For example, a repeater installed as an in-building distribution system would use indoor antennas to communicate with the indoor handsets and an outdoor antenna to communicate with the host base station.
Repeaters are often not equipped with GPS modules as are location measurement units as such the reference clock of the repeater is subject to drift. This drift is detrimental to detection of the uplink signal.
Repeaters are also generally not aware of the mobiles which they are servicing as described above they repeat any signal received within its domain band.
In order to accomplish location determination in an environment with repeaters, there is a need to overcome the deficiencies in the prior art by employing a novel system and method that is capable of identifying when a mobile's signal is being received via a repeater or other network device by determining its proximity to the repeater. In view of this need, it is an object of the disclosed subject matter to present a method for determining whether a signal is received directly from the mobile or from a repeater in the communication network.
It is also an object of the disclosed subject matter to provide a method by which repeaters may actively assist in determining mobiles in its proximity and thus those mobiles likely served.
The ability to discern the difference between direct signals and repeated signals (i.e., signals that arrive via a repeater) allows for the system to be better managed and is thus advantageous.
These objects and other advantages of the disclosed subject matter will be readily apparent to one skilled in the art to which the disclosure pertains from a perusal of the claims, the appended drawings, and the following detailed description of the preferred embodiments.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a prior art wireless communication system.
FIG. 2 a is an illustration of the operation of a prior art non-translating repeater station.
FIG. 2 b is an illustration of the operation of a prior art translating repeater station.
FIG. 3 is an illustration of a prior art wireless communication system with repeater stations connected with an RF link and over a tether.
FIG. 4 is a representative flow chart for the operation of a repeater in an embodiment of the present subject matter.
FIG. 5 is a representative flow chart for the operation of a network analysis system according to an embodiment of the present subject matter.
FIG. 6 is an illustration of a repeater based proximity detection system according to an embodiment of the present subject matter.
FIG. 7 is a representative flow chart for the operation of proximity detection according to an embodiment of the present subject matter.
DETAILED DESCRIPTION
For the purposes of describing the present subject matter, a communication system is the entirety of an information source (e.g., a mobile transmitter), a transmitted signal conveying that information, a communication path or link/channel, devices along the path through which the signal passes (e.g., a repeater), a host network and an intelligent receiver (e.g., scanning receiver) distinct from the host network. Throughout this disclosure, the terms downlink and uplink will be used interchangeable with forward channel and reverse channel respectfully. No particular distinction is to be applied based on the use of the terms.
The current subject matter relates to a method to determine if a mobile station operating in a wireless network utilizing a repeater is communicating with the base station through the repeater or other network devices or directly with the base station. As previously discussed, repeaters are used to “repeat” the RF signal to enhance range, coverage or service quality; and mobile appliances attached to the wireless network and used as terminal devices for voice or data interfacing.
It may be advantageous for a wireless operator to know how a particular mobile appliance is being served in an area to understand how the wireless network is operating or to size and provision repeaters or other network equipment in an area.
The present subject matter discloses an augmentation to the repeater(s) to assist the network in determining which mobile appliances are operating through the repeater(s) and in another embodiment the augmentation may help the repeater determine which mobile appliances are operational in its proximity.
The augmentation is composed of a scanning receiver and a mechanism for interfacing to a data service used to communicate with the manager. The augmentation may be housed in the repeater and may be connected to the repeater-to-mobile antenna of the repeater. Alternatively, the augmentation may have an antenna and receiver independent of the repeater. Moreover, the augmentation may be physically and operably independent of the repeater altogether. The augmentation scans the reverse link channels where a mobile appliance might transmit and measures energy and/or signal characteristics. These channels can be represented as RF frequencies, time slots, spreading codes or any combination thereof. These measurements may be used to determine if a mobile appliance is operating in the proximity of the repeater antenna. If signal strength and/or quality are high (or within a certain band), then it may be assumed that the mobile is operating through the repeater.
The measurements and/or channel indicators for a mobile appliance determined to be operating through the repeater are transmitted to the manager. The measurements may be analyzed at the augmentation or at the manager to arrive at such a determination. The measurements can be analyzed based on signal strength, particular band of received power, or signal characteristics. The band of received power may be mapped to the power management algorithms that a particular air interface will employ to control the power level of a mobile appliance. Decoding of certain signal characteristics (i.e., presence of sync codes) may indicate sufficient power level to measure signal characteristics, and provide positive indication that the signal energy on that channel is from a device connected to the wireless network of interest.
The measurements or analyses are sent over an interface from the augmentation to the manager over a data service. The data service is most conveniently a data transport mechanism supported by the wireless network of interest. For example, in a Global System for Mobile Communication (GSM) network that supports General Packet Radio Service (GPRS), the measurement data from the augmentation or channel results could be transferred to the manager using this data service. Short Message Service (SMS) services available in TDMA and GSM are also candidates. Wireless connections (e.g., T1, modem, frame relay) are also an option. The manager serves as the control and management device for the augmentation(s), and as an interface point for access to the list of mobile appliances operating through certain repeaters. The manager can have data files indicating where repeaters with augmentations are located in the network, and through connections to other wireless network entities, translate channel information to mobile identity information. In a GSM network, this might consist of translating a traffic channel assignment to a Temporary Mobile Station Identifier (TMSI) or Mobile Station International ISDN Number (MSISDN) through access to network data at the Base Station Controller (BSC) or HLR/VLR.
Implementation of the augmentation and manager in the described fashion is convenient and cost effective. The functions incorporated into the augmentation are formed from common building blocks found in commercial handsets. Thus, the augmentation may be added to a repeater for a fraction of the recurring cost of handset components. The manager may be conceived as a new software component executing on an existing computing device in a wireless network, shared with other functions associated with network entities to which it would be easy to interface.
An important aspect of the presently disclosed subject matter is that the communication network can determine when a received signal from a mobile has passed through a repeater or other network devices. Prior art systems do not have this capability and consequently treat all the received signals as having been directly received from the target mobile. The foregoing embodiments are exemplary only and shall not be used to limit the invention. These examples and others are discussed in more detail below.
FIG. 4 is a representation of a network analysis system within a communication system according to an embodiment of the present disclosure. The communication system includes a repeater 401, a base station 404, and a base station controller 402, as well as a plurality of mobiles, 420 and 405. As illustrated, the mobile 420 communicates directly with the base station 404, and the mobile 405 communicates with the base station 404 through the repeater 401. Antennas 408 and 407 are associated with the base station 404 and the repeater 401, respectively. The repeater 401 is augmented with a scanning receiver that communicates with a manager over an interface 450. The interface 450 may take the form of a separate channel within the communication system or a dedicated wireless, wireline or other communication link.
FIG. 5 is a representational flow chart of a method for detecting a mobile operating through a repeater according to an embodiment of the present subject matter. The mobile 501 transmits an information signal. The repeater 510, in normal operation, receives, amplifies and retransmits the signal as shown in Block 511. The scanning receiver 515 associated with the repeater scans for transmitted signals; and, upon acquiring the transmitted signal, either from the repeater or an independent antenna, the scanning receiver measures attributes of the signal as shown in Block 517. In Block 518, the scanning receiver 515 or augmentation sends the measurement of the attribute of the signal to the manager 530 over a communication interface 550. Alternatively, an analysis of the measured attributes can be conducted at the augmentation and the results of the analysis may be forwarded to the manager 530. The base station 520 receives the signal in Block 521 and operates in a normal fashion, with the operation of the augmentation 515 and manager 530 being transparent to the base station. The manager 530, upon receiving the measured attributes or analyses, determines if the mobile's signal is likely operated upon by the repeater 510. This determination is preferably based on proximity of the mobile to the repeater. For example, if the augmentation 515 measures a high transmit power level, as related to a threshold as in the case of mobile 405, then it is likely that mobile 405 is served by the repeater 510. However, if the transmit power level is below a predetermined level or threshold, as is likely for mobile 420, then it is not likely the mobile 420 is served by the repeater 510. The measured attributes may include signal strength, signal to noise ratio (SNR), band of received power, or other signal characteristics. In addition to communication of the measured attributes, the augmentation 515 also preferentially sends a channel or other identifier relating the measured attributes to the signal measured.
A method and system by which an augmented repeater may effectively determine if a mobile device, appliance, transceiver, etc. is operating within the proximity of the repeater, is yet another embodiment.
The augmented repeater embodiment also utilizes the scanning receiver to obtain timing information from downlink (forward link) signals in order to obtain timing on the uplink (reverse link) of the mobile. The timing derived from the downlink enables the receiver to narrow its search window for the mobile's uplink signal. Unlike location measurement units (“LMUs”) which are typically located at known locations, such as at base stations, and are synchronized, the augmented repeater system is not equipped with GPS and thus advantageously relies upon the downlink to compensate for drift in its clock. The augmented repeater system, with the information gathered from the downlink signal, detects a mobile device in proximity to the augmented repeater system. Since every protocol has a defined uplink-downlink timing synchronization relationship, the downlink signal can be detected and used estimate the downlink timing to narrow the search window of the uplink signal. The uplink will be detected by the training sequence, pilot signal, or any known signal transmitted by the mobile. The augmented repeater system may also allow for a determination of the mobile's distance from the augmented system using known techniques such as time of arrival (“TOA”), Signal strength, quality of service (“QoS”), (“AoA”), etc.
FIG. 6 is an illustration of an embodiment of the augmented repeater system. The repeater 601 is shown with a scanning receiver 603. The system also includes a processor, not shown, which may be incorporated in the scanning receiver 603, the repeater may be remote from the repeater, such as in the manager. The repeater 601 receives forward channel signal transmissions 661 from a base station 602. In normal operations the repeater 601 rebroadcasts the forward channel signal 661 and repeated forward channel signal 662. The repeater is typically unaware of the nature of the repeated signal or corresponding channels. If the mobile appliance 605 assigned to the forward channel is operating in the operational range of the repeater 601, it would be expected, although not a hard and fast rule, that the reverse channel, or uplink signal 672 would also be received and repeated as repeated reverse channel 671 by the repeater. The repeater in its operation would repeat any signal in its operational range which would include the additional reverse channels 681 as well as any other forward channels.
The scanning receiver 603 is interfaced to the repeater such that received signals may be obtained. The scanning receiver 603 searches for the forward channels and obtains timing information or other channel information from the received signals. Using the timing information from the forward channel along with information regarding the relationship between the forward and the reverse channel per protocol standards, the processor operably connected to the scanning receiver 603 may determine a search window 680 narrower than the operation domain of the repeater in order to search for a corresponding reverse channel. Any limitation upon the search spectrum reduces the time, complexity and cost associated with locating the reverse channel. Upon a determination of the search window 680, the scanning receiver is adjusted to detect the reverse channel 672. Characteristics of the scanner that may be adjusted to include frequency band, time slot, spiral sequence, hopping sequence, power level, sector assignment, or protocol. If the reverse channel 672 is detected within the search window, measurements regarding it's characteristics may be taken. These characteristics may be attributes that can be compared to predetermined thresholds to determine whether the reverse channel is emanating from a location proximate to the repeater. The determination may be made by comparing signal strength, QoS, timing advance, TOA, AoA, SNR or GPS measurements obtained from the reverse channel 672 with thresholds associated with the repeater and signals. This determination may be made locally at the repeater system or remotely.
FIG. 7 is a illustrative flow chart for a method of determining if a mobile is operating in the proximity of a repeater using information from the forward link. As shown in Block 702 a signal is transmitted over the downlink channel from base station 720. At the repeater 701, the downlink signals are received and it's attributes are measured by the scanning receiver 703 in Block 704. The attribute in the specific illustration being timing information, but frequency band, hopping sequence, time slot, spread code, may also be measured or obtained in Block 706. Using the information gathered from the downlink signal, a search window may be formulated using predetermined relationships between the forward channel and the reverse channel. For instance, the reverse channel may be offset in time a predetermined amount from the transmission of the forward link, or information in the forward link relates to the timing advance by which the reverse channel is determined. In both cases knowledge of the predetermined relationships may be used along with the obtained forward channel information to determine a time window to search for the reverse channel as shown in Block 706.
The scanning receiver 703 of the repeater may then be adjusted or tuned to cover the search window to acquire the reverse signal of the mobile, as shown in Block 708. Upon detection of the reverse signal, signal characteristics may be measured as shown in Block 710. Such characteristics may be used and compared with thresholds to determine the mobiles degree of proximity to the repeater as shown in Block 712. The thresholds may be determined based on network conditions, network topology, wireless protocol, etc. For instance in a sparsely populated network, the detection of the reverse signal itself may be a strong indication of its proximity to the repeater, whereas, in a congested high traffic area, the mere reception of the reverse signal may not be such a strong indication. The relative signal strength may be a stronger factor or the QoS of the signal may indication its service and proximity to the repeater.
The system may maintain a database of currently served mobile appliances and/or a historical list of those mobile appliances served. The database may also include additional information associated with the service, such as time, duration, network characteristics, QoS, signal strength, SNR, etc. Additionally, the repeater may affirmatively report to the manager which mobiles are likely in proximity to and/or served by the repeater, or the repeater system may report only the raw data and allow the manager to make the determination of which mobiles are served.
While preferred embodiments of the present inventive system and method have been described, it is to be understood that the embodiments described are illustrative only and that the scope of the embodiments of the present inventive system and method is to be defined solely by the appended claims when accorded a full range of equivalence, many variations and modifications naturally occurring to those of skill in the art from a perusal hereof.
1. A proximity location system for locating mobile appliances in a wireless communication system, comprising: a repeater; a scanning receiver co-located with the repeater and interfaced to receive signals received at the repeater; and, a processor operably connected to the scanning receiver; wherein the scanning receiver is adapted to obtain a channel attribute of a forward channel of one of the mobile appliances and the processor is configured to determine a search window for a corresponding reverse channel of the mobile appliance based upon at least the channel attribute.
2. The wireless communication system of claim 1, wherein the processor is configured to determine the search window for the corresponding reverse channel of the mobile based upon a predetermined relationship between the forward channel and the reverse channel.
3. The proximity location system of claim 1, wherein the channel attribute is selected from frequency, spread code, time slot, hopping sequence, or a combination thereof.
4. The proximity location system of claim 1, wherein the scanning receiver is connected to an antenna of the at least one repeater.
5. The proximity location system of claim 4, wherein the scanner is configured to measure an attribute of the reverse channel signal.
6. The proximity location system of claim 1, wherein the scanner is configured to detect the reverse link based on the search window.
7. A method of determining if a mobile is operating in the proximity of a repeater wherein the repeater does not have independent timing synchronization, comprising: scanning a forward communication signal at a repeater; obtaining timing information from the forward signal; determining a search window for a reverse channel of the mobile based on the timing information and a predetermined relationship between the forward channel and the reverse channel; scanning the search window to detect the reverse channel mobile signal; measuring an attribute of the mobile reverse channel signal; and, determining the mobile's proximity based on the measured attribute.
8. The method of claim 7, wherein the attribute reflects a proximity to the repeater.
9. The method of claim 8, wherein the attribute is from the group comprising signal strength, signal characteristics, SNR, band of received power, and combinations thereof.
10. A method of determining the proximity of a mobile to a repeater comprising: scanning and receiving a forward channel signal with a scanning receiver co-located with the repeater; obtaining channel information from the received forward channel signal; adjusting a characteristic of the scanning receiver based upon the obtained channel information and a predetermined relationship between the forward channel and a reverse channel; scanning for a reverse channel signal with the scanner, measuring one or more attributes of the scanned reverse channel signal; and, determining the proximity of the mobile to the repeater based at least in part on the measured attribute.
11. The method of claim 10, wherein the channel information comprises frequency, time slot, spread code, hopping sequence, or a combination thereof.
12. The method of claim 11, wherein the attribute comprises signal strength, signal to noise ratio (SNR), band of received power, signal characteristics, or a combination thereof.
13. A method of locating a mobile device at a repeater having a co-located scanning receiver, comprising: monitoring downlink communication at a repeater to obtain timing information associated with the downlink communication; determining a search window based on the timing information and a predetermined timing relationship between the downlink communication and an uplink communication; tuning the scanner to scan the search window for the mobile device's uplink communication; measuring a characteristic of the of the mobile device's uplink communication; determining the mobile device's proximity to the repeater based on the measured characteristic; and, determining the location of the mobile based on its proximity to the repeater.
14. The method of claim 13, wherein the step of determining the location comprises comparing the proximity of the mobile device to the repeater to a threshold.
15. The method of claim 13, wherein the step of determining a search window includes bounding the estimated uplink transmit time.
16. The method of claim 13, wherein the step of determining a search window includes bounding an estimated frequency.
17. The method of claim 13, comprising reporting to a remote processor the mobile identity if it is determined to be proximate to the repeater..
| 48,874 |
https://github.com/phork/phorkit/blob/master/src/compositions/Chip/index.ts | Github Open Source | Open Source | MIT | 2,022 | phorkit | phork | TypeScript | Code | 16 | 35 | export * from './Chip';
export * from './ChipContent';
export * from './StyledChip';
export * from './types';
| 23,869 |
https://github.com/lexus2k/ssd1306/blob/master/src/ssd1306_generic.c | Github Open Source | Open Source | MIT | 2,023 | ssd1306 | lexus2k | C | Code | 1,269 | 4,462 | /*
MIT License
Copyright (c) 2016-2019, Alexey Dynda
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
///////////////////////////////////////////////////////////////////////////////
////// GENERIC FUNCTIONS APPLICABLE FOR ALL DISPLAY TYPES /////////////////////
///////////////////////////////////////////////////////////////////////////////
#include "ssd1306.h"
#include "ssd1306_fonts.h"
#include "lcd/lcd_common.h"
#include "intf/i2c/ssd1306_i2c.h"
#include "intf/spi/ssd1306_spi.h"
#include "intf/ssd1306_interface.h"
#include "ssd1306_hal/io.h"
#include "nano_gfx_types.h"
enum
{
SSD1306_OLD_FIXED_FORMAT = 0x00,
SSD1306_NEW_FIXED_FORMAT = 0x01,
SSD1306_NEW_FORMAT = 0x02,
SSD1306_SQUIX_FORMAT = 0x03,
};
uint16_t ssd1306_color = 0xFFFF;
lcduint_t ssd1306_cursorX = 0;
lcduint_t ssd1306_cursorY = 0;
SFixedFontInfo s_fixedFont = {}; //{ { 0 }, 0 };
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
uint8_t g_ssd1306_unicode = 1;
#endif
static void (*s_ssd1306_getCharBitmap)(uint16_t unicode, SCharInfo *info) = NULL;
static const uint8_t *ssd1306_getCharGlyph(char ch);
static const uint8_t *ssd1306_getU16CharGlyph(uint16_t unicode);
lcduint_t ssd1306_displayHeight()
{
return ssd1306_lcd.height;
}
lcduint_t ssd1306_displayWidth()
{
return ssd1306_lcd.width;
}
void ssd1306_setCursor(lcdint_t x, lcdint_t y)
{
ssd1306_cursorX = x;
ssd1306_cursorY = y;
}
static const uint8_t * ssd1306_readUnicodeRecord(SUnicodeBlockRecord *r, const uint8_t *p)
{
r->start_code =( pgm_read_byte(&p[0]) << 8) | (pgm_read_byte(&p[1]));
r->count = pgm_read_byte(&p[2]);
return (r->count > 0) ? (&p[3]): NULL;
}
void ssd1306_setSecondaryFont(const uint8_t * progmemUnicode)
{
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
s_fixedFont.secondary_table = progmemUnicode;
if (s_fixedFont.secondary_table != NULL)
{
s_fixedFont.secondary_table += sizeof(SFontHeaderRecord);
}
#endif
}
void ssd1306_getCharBitmap(uint16_t unicode, SCharInfo *info)
{
return s_ssd1306_getCharBitmap( unicode, info );
}
uint16_t ssd1306_unicode16FromUtf8(uint8_t ch)
{
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
static uint16_t unicode = 0;
ch &= 0x000000FF;
if (!unicode)
{
if ( ch >= 0xc0 )
{
unicode = ch;
return SSD1306_MORE_CHARS_REQUIRED;
}
return ch;
}
uint16_t code = ((unicode & 0x1f) << 6) | (ch & 0x3f);
unicode = 0;
return code;
#else
return ch;
#endif
}
void ssd1306_enableUtf8Mode(void)
{
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
g_ssd1306_unicode = 1;
#endif
}
void ssd1306_enableAsciiMode(void)
{
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
g_ssd1306_unicode = 0;
#endif
}
//////////////////////////////////////////////////////////////////////////////////////////////////
/// SECTION WITH FONT FORMATS
//////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////
/// OLD FORMAT: 1.7.6 and below
/// OLD FORMAT is supported by old and latest versions of ssd1306 library
static const uint8_t *ssd1306_getCharGlyph(char ch)
{
return &s_fixedFont.primary_table[ (ch - s_fixedFont.h.ascii_offset) *
s_fixedFont.glyph_size +
(s_fixedFont.h.type == 0x01 ? sizeof(SUnicodeBlockRecord) : 0) ];
}
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
static const uint8_t *ssd1306_searchCharGlyph(const uint8_t * unicode_table, uint16_t unicode)
{
SUnicodeBlockRecord r;
const uint8_t *data = unicode_table;
// looking for required unicode table
while (1)
{
ssd1306_readUnicodeRecord( &r, data );
if (r.count == 0)
{
break;
}
data += sizeof(SUnicodeBlockRecord);
if ( ( unicode >= r.start_code) && ( unicode < (r.start_code + r.count) ) )
{
break;
}
data += r.count * s_fixedFont.glyph_size;
}
if (r.count == 0)
{
// Sorry, no glyph found for the specified character
return NULL;
}
return &data[ (unicode - r.start_code) * s_fixedFont.glyph_size ];
}
#endif
static const uint8_t *ssd1306_getU16CharGlyph(uint16_t unicode)
{
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
const uint8_t * glyph = NULL;
if (g_ssd1306_unicode)
{
if ((unicode < 128) && (s_fixedFont.h.type == 0x00) && (s_fixedFont.primary_table != NULL))
{
return ssd1306_getCharGlyph(unicode);
}
if (s_fixedFont.primary_table)
{
glyph = ssd1306_searchCharGlyph( s_fixedFont.primary_table, unicode );
}
if (!glyph && s_fixedFont.secondary_table)
{
glyph = ssd1306_searchCharGlyph( s_fixedFont.secondary_table, unicode );
}
if (!glyph)
{
return ssd1306_getCharGlyph( s_fixedFont.h.ascii_offset );
}
return glyph;
}
else
#endif
{
return ssd1306_getCharGlyph(unicode);
}
}
static void __ssd1306_oldFormatGetBitmap(uint16_t unicode, SCharInfo *info)
{
if (info)
{
info->width = s_fixedFont.h.width;
info->height = s_fixedFont.h.height;
info->spacing = 0;
info->glyph = ssd1306_getU16CharGlyph( unicode );
}
}
void ssd1306_setFixedFont(const uint8_t * progmemFont)
{
s_fixedFont.h.type = pgm_read_byte( &progmemFont[0] );
s_fixedFont.h.width = pgm_read_byte(&progmemFont[1]);
s_fixedFont.h.height = pgm_read_byte(&progmemFont[2]);
s_fixedFont.h.ascii_offset = pgm_read_byte(&progmemFont[3]);
s_fixedFont.primary_table = progmemFont + 4;
s_ssd1306_getCharBitmap = __ssd1306_oldFormatGetBitmap;
s_fixedFont.pages = (s_fixedFont.h.height + 7) >> 3;
s_fixedFont.glyph_size = s_fixedFont.pages * s_fixedFont.h.width;
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
s_fixedFont.secondary_table = NULL;
#endif
}
void ssd1306_setFixedFont_oldStyle(const uint8_t * progmemFont)
{
s_fixedFont.h.type = pgm_read_byte( &progmemFont[0] );
s_fixedFont.h.width = pgm_read_byte(&progmemFont[1]);
s_fixedFont.h.height = pgm_read_byte(&progmemFont[2]);
s_fixedFont.h.ascii_offset = pgm_read_byte(&progmemFont[3]);
s_fixedFont.primary_table = progmemFont + 4;
s_fixedFont.pages = (s_fixedFont.h.height + 7) >> 3;
s_fixedFont.glyph_size = s_fixedFont.pages * s_fixedFont.h.width;
}
//////////////////////////////////////////////////////////////////////////////////////////////////
/// NEW FORMAT: 1.7.8 and later
/// NEW FORMAT is supported only by latest versions of ssd1306 library
static void __ssd1306_newFormatGetBitmap(uint16_t unicode, SCharInfo *info)
{
if (info)
{
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
uint8_t table_index = 0;
#endif
const uint8_t *data = s_fixedFont.primary_table;
while (data)
{
SUnicodeBlockRecord r;
data = ssd1306_readUnicodeRecord( &r, data );
if (!data)
{
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
if ( table_index == 0 )
{
table_index++;
data = s_fixedFont.secondary_table;
continue;
}
#endif
break;
}
/* Check that unicode in the section being processed */
if ( ( unicode < r.start_code) || ( unicode >= (r.start_code + r.count) ) )
{
// skip jump table
data += r.count * 4;
// skip block bitmap data
data += ((pgm_read_byte(&data[0]) << 8) | (pgm_read_byte(&data[1]))) + 2;
continue;
}
/* At this point data points to jump table (offset|offset|bytes|width) */
unicode -= r.start_code;
data += unicode * 4;
uint16_t offset = (pgm_read_byte(&data[0]) << 8) | (pgm_read_byte(&data[1]));
uint8_t glyph_width = pgm_read_byte(&data[2]);
uint8_t glyph_height = pgm_read_byte(&data[3]);
info->width = glyph_width;
info->height = glyph_height;
info->spacing = glyph_width ? 1 : (s_fixedFont.h.width >> 1);
info->glyph = data + (r.count - unicode) * 4 + 2 + offset;
break;
}
if (!info->glyph)
{
info->width = 0;
info->height = 0;
info->spacing = s_fixedFont.h.width >> 1;
info->glyph = s_fixedFont.primary_table;
}
}
}
void ssd1306_setFreeFont(const uint8_t * progmemFont)
{
s_fixedFont.h.type = pgm_read_byte( &progmemFont[0] );
s_fixedFont.h.width = pgm_read_byte(&progmemFont[1]);
s_fixedFont.h.height = pgm_read_byte(&progmemFont[2]);
s_fixedFont.h.ascii_offset = pgm_read_byte(&progmemFont[3]);
s_fixedFont.primary_table = progmemFont + 4;
s_ssd1306_getCharBitmap = __ssd1306_newFormatGetBitmap;
s_fixedFont.pages = (s_fixedFont.h.height + 7) >> 3;
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
s_fixedFont.secondary_table = NULL;
#endif
}
//////////////////////////////////////////////////////////////////////////////////////////////////
/// SQUIX FORMAT: 1.7.8 and later
/// SQUIX FORMAT is not fully supported. Use it at your own risk
static void __ssd1306_squixFormatGetBitmap(uint16_t unicode, SCharInfo *info)
{
if (info)
{
const uint8_t *data = s_fixedFont.primary_table;
/* Check that unicode in the section being processed */
if ( !data || ( unicode < s_fixedFont.h.ascii_offset) || ( unicode >= (s_fixedFont.h.ascii_offset + s_fixedFont.count) ) )
{
info->width = 0;
info->height = 0;
info->spacing = s_fixedFont.h.width >> 1;
info->glyph = s_fixedFont.primary_table;
return;
}
/* At this point data points to jump table (offset|offset|bytes|width) */
const uint8_t * bitmap_data = data + (uint16_t)s_fixedFont.count * 4;
unicode -= s_fixedFont.h.ascii_offset;
data += (unicode * 4);
uint16_t offset = (pgm_read_byte(&data[0]) << 8) | pgm_read_byte(&data[1]);
uint8_t glyph_bytes = pgm_read_byte(&data[2]);
// uint8_t width = pgm_read_byte(&data[3]);
info->width = glyph_bytes; //(glyph_bytes + s_fixedFont.pages - 1) / s_fixedFont.pages;
info->height = s_fixedFont.h.height / 2;
info->spacing = 1;
// uint8_t index=0;
info->glyph = bitmap_data;
if ( offset != 0xFFFF )
{
info->glyph += offset;
}
}
}
void ssd1306_setSquixFont(const uint8_t * progmemFont)
{
s_fixedFont.h.type = SSD1306_SQUIX_FORMAT;
s_fixedFont.h.width = pgm_read_byte(&progmemFont[0]);
s_fixedFont.h.height = pgm_read_byte(&progmemFont[1]);
s_fixedFont.h.ascii_offset = pgm_read_byte(&progmemFont[2]);
s_fixedFont.count = pgm_read_byte(&progmemFont[3]);
s_fixedFont.primary_table = progmemFont + 4;
s_ssd1306_getCharBitmap = __ssd1306_squixFormatGetBitmap;
s_fixedFont.pages = (s_fixedFont.h.height + 7) >> 3;
s_fixedFont.glyph_size = s_fixedFont.pages * s_fixedFont.h.width;
#ifdef CONFIG_SSD1306_UNICODE_ENABLE
s_fixedFont.secondary_table = NULL;
#endif
}
lcduint_t ssd1306_getTextSize(const char *text, lcduint_t *height)
{
lcduint_t width = 0;
while (*text)
{
if (*text == '\r' || *text == '\n')
{
text++;
break;
}
uint16_t unicode = ssd1306_unicode16FromUtf8(*text);
if (unicode == SSD1306_MORE_CHARS_REQUIRED)
{
text++;
continue;
}
SCharInfo char_info;
ssd1306_getCharBitmap(unicode, &char_info);
width += char_info.width + char_info.spacing;
if ( height ) *height = char_info.height;
text++;
}
return width;
}
| 49,851 |
https://github.com/gammam/gifty/blob/master/GiftListView.js | Github Open Source | Open Source | Apache-2.0 | null | gifty | gammam | JavaScript | Code | 273 | 1,186 | // GistListView.js
// componente che descrive nel dettaglio il gruppo regalo, con le varie proposte
import React from 'react'
import { StyleSheet, Text, ScrollView,TextInput, View, Button ,Image,Switch,FlatList} from 'react-native'
import GiftSummary from './GiftSummary'
//import firebase from 'react-native-firebase'
export default class GiftListView extends React.Component {
state = { imageUrl : null , groupId : null ,giftItem:null }
constructor() {
super()
this.ref = firebase.firestore().collection('gifts');
this.unsubscribe = null;
}
onPressAddGift = ()=>{
this.props.navigation.navigate('AddGiftView', {groupId:this.state.groupId})
}
componentDidMount() {
const groupId = this.props.navigation.getParam('groupId', '0');
console.log('groupId:',groupId);
this.setState({groupId:groupId});
//var strPath = 'guests.'+firebase.auth().currentUser.uid.toString();
// this.unsubscribe = this.ref.where('id','==',${groupId}).onSnapshot(this.onCollectionUpdate)
const docId = this.ref.doc(groupId).id;
console.log('doc ID: ',docId);
this.ref.doc(groupId).get()
.then((doc)=>{
const itemList=[];
const items = doc.get('items');
Object.keys(items).forEach(function(k){
console.log(k + ' - ' + items[k]);
itemList.push({
id : k,
title : items[k].title,
agreement : items[k].agreement,
imageURL : items[k].imageURL,
proposedBy : items[k].proposedBy,
});
});
this.setState({giftItems: itemList});
console.log('data items: ',itemList)
})
.catch((err)=>{console.log('err: ',err)}) ;;
//console.log('item: ',items);
// this.unsubscribe = this.ref.doc(groupId).get('items').then((doc)=>{console.log('item: ',doc)}).catch((err)=>{console.log('err: ',err)}) ;
const ref = firebase.storage().ref('warhammer_gift.jpg');
ref.getDownloadURL()
.then((url)=>{
this.setState({imageUrl : url})
})
.catch(function(e){console.log('getDownload error: ',e)})
}
componentWillUnmount() {
// this.unsubscribe();
}
_onPressItem = (id: string) => {
console.log('GiftListView _onPressItem this.state.groupId: ', this.state.groupId)
this.props.navigation.navigate('GiftView',{groupId:this.state.groupId, refId:id} )
}
render() {
return (
<View style={styles.container}>
<View >
<Text> Le tue liste regalo </Text>
</View>
<ScrollView >
<FlatList
data={this.state.giftItems}
renderItem={({ item}) => <GiftSummary onPressItem={this._onPressItem} {...item} />}
/>
</ScrollView>
<View >
<Button
title={'Crea un nuovo gruppo Regalo'}
onPress={this.onPressAddGift}
/>
</View>
</View>
)
}
}
const styles = StyleSheet.create({
header:{
flex:1,
},
container: {
// display: flex;
// flex-direction:column,
// align-items:stretch,
flex: 1,
flexDirection:'column',
// justifyContent: 'center',
//alignItems: 'flex-start',
backgroundColor: "#fff"
},
item:{
backgroundColor: "#00ff00"
},
footer:{
flex:1,
},
textInput: {
height: 40,
width: '90%',
borderColor: 'gray',
borderWidth: 1,
marginTop: 8
}
}) | 9,710 |
bpt6k14150533_1 | French-PD-Books | Open Culture | Public Domain | null | Escarmouches. Au pays romand. Contre les Vandales. Les artistes et le public. Questions religieuses | None | French | Spoken | 9,795 | 15,089 | PAUL SEIPPEL ff ESCARMOUCHES AU PAYS ROMAND CONTRE LES VANDALES. — LES ARTISTES ET LE PUBLIC QUESTIONS RELIGIEUSES. PARIS FONTEMOING & C ie , ÉDITEURS 4, rue Le Goff (Ve) 1910 Tous droits réservés. 'kÉÉâÀAüà» • a.~*c -> " T assa^>6*«*««’ ESCARMOUCHES iolll DU MÊME AUTEUR : Terres lointaines. — Voyage autour du monde. Illustré de 17 planches hors texte et 153 vignettes, avec couverture artistique en couleur. In-4°, 324 pages ; relié, fr. 22.— ; broché Fr. 15.— (Lausanne, Payot.) Les Deux Frances et leurs origines historiques. — In-8°, XXXVI-409 pages. Edition luxe sur papier Hollande, fr. 15.— ; relié tranches dorées, fr. 14.— ; broché Fr. 7.50 (Lausanne, Payot.) La critique des «Deux Frances». — Br. in-8° » 0.60 (Genève, Jullien.) La Suisse au XIX rae siècle, superbe ouvrage publié par un groupe d’écrivains nationaux sous la direction de M. Paul Seippel. Tome I. Histoire politique. Droit public. Armée. Rôle international. — Tome II. Ecole. Eglise. Lettres. Presse. Arts. — Tome III. Agriculture. Industrie et commerce. Economie politique. La vie et les mœurs. Coup d’œil d’ensemble, etc., etc. — Trois superbes volumes gr. in-8°, richement illustrés. Fr. 25.— Chaque volume séparé » 10.— (Lausanne, Payot.) PAUL SEIPPEL /» K '•£ n K • ê ' ", •: 7 242536 ) ESCARMOUCHES AU PAYS ROMAND CONTRE LES VANDALES. LES ARTISTES ET LE PUBLIC QUESTIONS RELIGIEUSES. LAUSANNE LIBRAIRIE PAYOT & C ie 1, Rue de Bourg, 1 1910 Tous droits réservés. LAUSANNE — IMPRIMERIES RÉUNIES. (S. A.) 202 10 TABLE DES MATIÈRES Pages Préface vii I. — Au pays romand. Genève et la tradition de la liberté 3 La langue et la culture françaises en Suisse ... 31 Au carrefour 46 Existe-t-il une littérature romande ? 74 Rousseau jugé par M. Lemaître 89 Rousseau jugé par M. Louis Ducros 102 II. — Contre les Vandales. Cauchemar 117 Contre les Vandales 122 Pour des saules 127 La Tour de l’Ile La ville de tuiles et la ville d’ardoises .... 133 La Tour, prends garde !. 141 Les deux Savoies 146 III. — Les Artistes et le Public. Peinture alpestre. De Calame à Hodler .... Calante 159 Hodler 164 A l’exposition de 1896 Architecture suisse 174 Hodler et la « Kunstpfiege » 178 Un toast rentré 183 Les artistes et le public 188 VI TABLE DES MATIÈRES IV. — Questions religieuses. Optimisme et pessimisme religieux Pages 197 Anticléricalisme et catholicisme. 207 Taine et le christianisme .... 213 La conversion de Nietzsche. 220 Renégat, ou prophète ?. 233 Un descendant des Camisards. 242 Christianisme exotique .... 250 Calvinistes sans le savoir . .. 257 Crois en toi-même ! 264 Le silence de Vinet 272 Science et religion 296 PRÉFACE /<$ ; . L • , A Philippe Monnier. Mon cher ami. Les mémoires du naturaliste Henri-Albert Gosse publiés par M Ue Danielle Plan m'ont fait lier plus ample connaissance avec un mien ancêtre qui fut, à Genève, un fougueux « représentant », et à Gingins un grand chasseur devant VEternel. En ce temps-là, les jours d'émeute, on descendait dans les Rues Basses, le fusil sur l'épaule, comme pour une partie de plaisir. Et l'on était fier de recevoir le titre de citogen de Genève, auquel JeanJacques venait de donner un nouveau lustre. Un jour Antoine Seippel, s’étant réfugié à Nernier à la suite d’une échauffourée, eut maille à partir, dans une auberge, avec des soldats bernois qui avaient mal parlé de Genève. Ses adversaires n'ayant pas d’épée, il défendit l’honneur de la Cité à coups de poings. C’était un digne homme, n’est-il pas vrai, Monnier? Nos mœurs se sont adoucies, et je me sens un descendant dégénéré de cet ancêtre à la main leste. Il faut bien pourtant qu'il m'ait transmis un peu de son humeur batailleuse. Mais elle a changé de cours et s'est portée au jeu passionnant des idées. Quand j'entends sur la place une bagarre d’idées, j’ai peine à rester chez moi, en quoi j'ai grand tort. Le sage devrait laisser dire à ses contemporains toutes les sornettes qu'ils ont dans la tète, sans vouloir à tout prix y opposer celles que, pour l’heure, il peut avoir dans la sienne. Cette sagesse-là est rare à Genève. Abauzit est, avant le poète Biaise, un des rares qui aient su la cueillir en nos jardins où les chardons poussent plus aisément que les roses. Depuis tantôt quatre siècles la controverse est notre sport national. On y trouve du plaisir, sans doute, mais on y perd son temps et on oublie de faire son œuvre. Pour vous et pour nous, vous eûtes raison, mon ami, de faire votre œuvre et de laisser à d'autres les disputes. L'âge aidant, peut-être entrerai-je un jour, à mon tour, dans les voies de la sagesse. Il me plaît tout au moins d'en caresser l'espoir. Si la vie qui nous talonne sans trêve en nous imposant mille besognes tumultuaires, voulait bien me laisser un peu de répit avant de me conduire au calme port du silence éternel, il me plairait de suivre l'exemple de ceux que j'aime entre tous et dont le poète a dit : Rarus sermo illis et magna libido silendi. En attendant cette heure propice, où il me sera accordé de goûter le plaisir de me taire, quelques insidieux amis, dont vous êtes, Monnier, m'incitent à aggraver les torts que j'ai pu avoir en lançant dans la bise qui passait sur la ville tant de paroles ailées. Ils me conseillent d’en rattraper quelques-unes au vol, pour en faire un livre, ou quelque chose d'approchant. Ce livre, me disent-ils, pourrait avoir son intérêt. Il conserverait le souvenir de luttes que nous avons soutenues côte à côte, durant quatre ou cinq lustres; il résumerait quelques-unes des idées qui nous furent ou plutôt nous sont communes— nous ne leur avons point été infidèles — ; il témoignerait des pensées dominantes de notre génération littéraire, partagées par tous ceux qui ont le tenace vouloir que le pays romand conserve une conscience nationale vigilante, que la beauté de son sol soit sauvegardée, qu’un art vraiment autochtone reflète son esprit, que les idées religieuses ne se caillent pas dans ses veines refroidies, comme un sang qui ne circule plus. Nationalité, lutte contre le vandalisme, culture artistique, pensée religieuse, telles seront les divisions de ce volume. Les trois premières parties sont spécialement consacrées au pays romand ; tandis que la quatrième partie, tout en portant, sans doute, une empreinte que nous ne tenterons jamais d'effacer pour complaire à nos juges du dehors, dépasse en sens divers, le cercle de nos étroites frontières. N'est-ce pas, en effet, par l’idée religieuse surtout, qu’hèritiers émancipés de la Réforme calvinienne, nous demeurons citoyens du monde, et que nous pouvons nous sentir proches parents de l’américain William James, du français Emile Boutroux, du « renégat » Lamennais, ou même du communard Louis Rossel. Moins consciencieux que l’auteur des Causeries genevoises — le connaissez-vous bien ? — je n’ai pas remis sur le chantier ces articles de revues ou de journaux. Quelques-uns pourraient bien porter la trace ou de l'heureuse inexpérience de la jeunesse, ou du peu de loisir d’un âge mur asservi à trop de travaux divers. Je me suis borné à supprimer, çà et là, des propos trop vifs, des allusions à certains faits oubliés aujourd'hui, ou des développements dont l’intérêt m’a paru épuisé. Il se peut, Monnier, que je me sois répété; il se peut aussi que je me sois contredit. Vous avez l’àme bienveillante. Si je me suis répété, vous direz que j’ai montré de la suite dans les idées. Si je me suis contredit, vous vous souviendrez de la parole du poète: L’homme absurde est le seul qui ne change jamais vous observerez qu’un écrivain de bonne volonté se doit à lui-même, non de piétiner sur place, mais de suivre une direction constante. En relisant ces pages écrites au gré de l’actualité, j’ai été — je puis le dire entre nous — agréablement surpris de constater que la plupart sont actuelles encore, même datées d’il y a quinze ou vingt ans. Les préoccupations qui les ont dictées hier ne font que s’imposer aujourd’hui plus impérieusement. Forte de sa jeune ardeur, la génération qui nous suit reprend les mêmes débats dont nous fumes enfiévrés. Quelques-uns des derniers venus d’entre nos écrivains, tout en étudiant avec soin un plus lointain passé, ignorent trop ce qui s’est fait et dit dans notre pays depuis un quart de siècle. Peut-être trouveront-ils ici la preuve que, croyant rompre avec ceux qui les ont immédiatement précédés, ils les ont plutôt, sur bien des points, continués en toute indépendance. Il est bon qu’il en soit ainsi. Une œuvre nationale exige la durée et la continuité du travail. Elle ne peut être menée à bien que sur le plan d'une commune pensée, à laquelle se subordonnent, d’âge en âge, des équipes successives de bons ouvriers. Ainsi tra vaillaient, loin de la préoccupation du succès personnel, les inconnus dont les patientes mains ont élevé les cathédrales gothiques. De siècle en siècle, ils suivaient un plan bien établi, enrichissant l'idée première des formes renouvelées que l'esprit de leur temps leur inspirait. Nous pensons qu'une œuvre analogue se poursuit, depuis l’époque de la Réforme, dans ce petit pays pour lequel nous ne voulons pas être trop modestes. Et s’il nous a été donné d’apporter à l’édifice commun quelques pierres taillées comme il fallait et mises à la juste place, nous aurons conscience de n’avoir pas perdu nos peines. Vous êtes, Monnier, au nombre de ces précieux artistes, trop rares en notre pays, capables de ciseler les fines statues du portail, ou les trèfles délicats de la rosace. Mais vous savez aussi ce qu’il faut de simple maçonnerie pour supporter quelques belles fleurs de pierre. Paul Seippel. AU PAYS ROMAND Genève et la tradition de la liberté. A Monsieur le Conseiller fédéral Louis Forrer en témoignage de reconnaissance pour l’intérêt qu’il porte à Genève et à la vie intellectuelle du Pays romand. Aux Bastions de Genève, en face des bâtiments de l’université actuelle, un monument va s’élever, qui sera, pour les passants de demain, une grande leçon d’histoire. Le mur sera restauré, auquel travaillaient les escholiers du seizième siècle, sous la conduite de leurs maîtres. Contre ce mur se dresseront, austères et rigides, quatre hautes effigies : Calvin, le chef, Farel, le précurseur, Théodore de Bèze et Knox, les disciples. Aux côtés des réformateurs, et moins en vue. de fières silhouettes d’hommes d’état et de soldats, la main à lagardede leur épée ; ceuxqui défendirent par les armes la cause calviniste, ceux qui la propagèrent dans le monde entier et jusqu’au delà des océans, qui la firent sortir de l’enceinte des églises et des écoles, pour la répandre à l’air libre, pour en tirerdesconséquences politiques et sociales non prévues par les réformateurs eux-mêmes : Coligny, Guillaume le Taciturne, Frédéric-Guillaume de Brandebourg, Olivier Cromwell, Roger Williams, l’un des fondateurs des colonies de la Nouvelle-Angleterre, Etienne Bocskay, représentant de la Réforme calvinienne en Transylvanie. Ces grands noms, — et on aurait pu en ajouter bien d’autres, — proclament à eux seuls que l’idée qu’on veut affirmer est universelle. Ce n’est pas à un homme qu’on a voulu élever un monument, ni même à une cité, mais bien à l’idée que cet homme et cette cité représentent dans le monde. Quel spectacle passionnant que de suivre à travers les âges la marche d’une idée ! Elle naît à son heure, dans le cerveau d’un homme, de quelques hommes, ou mieux dans leur cœur, puisque les grandes pensées viennent du cœur et ne sont une force qu’à condition d’être une passion. De proche en proche, l’idée se propage. Elle se transforme elle-même, afin de transformer la vie humaine, complexe et multiple, à laquelle elle doit s’adapter. Elle n’était, au début, qu’une graine imperceptible. Par la mystérieuse puissance qui est en elle, elle croît comme un arbre appelé à couvrir de son ombre les générations. Puis elle se reproduit au loin. Le souffle de l’Esprit a passé sur elle, et la petite semence primitive est devenue forêt. le savons, c’est là une hérésie. Un dogme enseigné en France, du haut des chaires officielles, veut que ce soit la Révolution française, — considérée comme une Révélation, — qui ait institué et répandu dans l’univers les principes fondamentaux sur lesquels reposent les sociétés les plus civilisées, «les immortels principes de 89», formulés essentiellement dans la Déclaration des droits de l'homme et énoncés auparavant par la philosophie du dix-huitième siècle. Ce serait donc à cette philosophie et à la Révolution que nousserions redevables des libertés individuelles dont nous jouissons aujourd’hui. Pas plus que beaucoup d’autres dogmes, ce dogmelà ne supporte l’épreuve de la critique historique. Certes, nous ne songeons pas à nier les services immenses rendus par la philosophie du dix-huitième siècle. Mais, en dehors de Rousseau qui, lui, continua la Réforme, il faut reconnaître que cette philosophie a été essentiellement aristocratique, souverainement dédaigneuse des petits et des faibles, et qu’elle n’a pas môme soupçonné ce que c’est que la liberté individuelle. Ce que veulent les encyclopédistes, c’est moins supprimer le pouvoir absolu que l’accaparer à leur profit. Quant à cette «canaille» pour laquelle Voltaire a un si hautain mépris, elle doit être maintenue dans l’ignorance, afin qu’elle demeure impuissante et soumise. Diderot affirme que « la quantité de la canaille est à peu près toujours la même » et que la multitude ignorante et hébétée, étant faite pour servir, « doit être laissée en servitude ». D’Alembert déclare que « la liberté est un bien qui n’est pas fait pour le peuple ; car le peuple est un enfant qui tombe et se brise dès qu’on le laisse marcher seul, et qui ne se relève que pour battre sa gouvernante ». Voltaire est aussi loin que GENÈVE ET LA TRADITION DE LA LIBERTÉ 7 les encyclopédistes de l’idée de la souveraineté du peuple. « Puisqu’il faut servir, dit-il, je pense qu’il vaut mieux le faire sous un lion de bonne race que sous deux cents rats de mon espèce *, » et il ajoute « qu’il ne s’agit pas de faire une révolution comme au temps de Luther et Calvin, mais d’en faire une dans l’esprit de ceux qui sont faits pour gouverner. » L’idéal des encyclopédistes, c’est Frédéric le Grand, c’est Catherine de Russie, c’est le bon despote, assez intelligent pour protéger les philosophes et la philosophie. égalitaire. Et cette passion égalitaire ne tardera pas à noyer dans le sang l’idée de la liberté, dont l’image rayonnante n’est apparue un instant, dans l’élan mystique qui accompagna l’aurore de la Révolution, que pour être bientôt défigurée dans le plus dérisoire des simulacres. Les théoriciens et les apologistes du despotisme spirituel, aussi bien Joseph de Maistre, l’apôtre de l’infaillibilité papale et de la monarchie absolue, que son proche parent Auguste Comte, fondateur et premier grand-prêtre de l’Eglise positiviste, ont su clairement reconnaître d’où est venue au monde moderne l’« hérésie » des libertés individuelles. Au dire de Joseph de Maistre, ces libertés ne sont que des égoïsmes fous. Le grand tort de la Réforme a été d’en reconnaître le principe, en le garantissant par des chartes constitutionnelles. « Démocratie et Réforme, dit l’auteur du Pape, sont la même folie, ayant seulement changé de nom. » Aux yeux d’Auguste Comte également, le vice capital de la Réforme est d’avoir apporté au monde la liberté. « Le protestantisme, dit-il, est une force rétrograde qui aboutit, dans tous les domaines, au principe anarchique de la liberté ». « Aussi, ajoute-t-il, les nations protestantes sont-elles restées en arrière.» (Chacun sait que la très catholique Espagne est à la tête des nations civilisées, et l’Angleterre à l’arrièregarde ! Chacun sait à quel point les Etats-Unis sont en retard sur les républiques sud-américaines !) L’hérésie capitale du protestantisme, selon Comte, est d’avoir institué le libre examen, car le libre examen conduit à la liberté de parler, d’écrire et d’agir conformément à ses convictions personnelles... Or cette souveraineté morale de chacun aboutit à la sou GENÈVE ET LA TRADITION DE LA LIBERTÉ 9 veraineté de la multitude, suprématie qui suppose elle-même l’égalité entre les citoyens. Ces erreurs, toutes plus fatales les unes que les autres, viennent, selon Auguste Comte, de ce que les protestants ont rejeté le principe tutélaire du Pouvoir spirituel absolu. Auguste Comte raisonne fort bien. Il indique avec une clairvoyance parfaite l’origine et la genèse du « tléau» qu’il déplore. C’est bien la Réforme qu’il faut en rendre responsable, pourvu qu’on l’entende comme la restauration du christianisme par l’élément barbare, lequel aapporté au monde, ainsi que Guizot l’a montré, le sentiment de l’indépendance personnelle, « de la spontanéité humaine dans son libre développement». lequel, de proche en proche, s’est imposé à toutes les nations civilisées ou demi-civilisées, même au Japon, même à la Turquie, même à la Perse, même à l’autocratie russe, qui s’est vue contrainte d’en reconnaître tout au moins le simulacre. II L’homme du monde qui connaît le mieux la Genève du seizième siècle et la vie de son réformateur, M. E. Doumergue, a publié une brochure sous le titre : Calvin, fondateur des libertés modernes. Il s’agit de s’entendre. Nous aurions plus de peine encore à admettre un Calvin libéral qu’un Calvin artiste. Pour faire de Calvin personnellement le fondateur des libertés modernes, il faudrait oublier le régime de contrainte qu’il avait imposé à la cité du Refuge. Tout en s’insurgeant contre l’Eglise romaine, Calvin avait conservé, dans une large mesure, la mentalité que cette Eglise lui avait imposée. Son idéal demeure théocratique. En face de la Rome des papes, il élève une Rome protestante. Il conserve l’idée romaine de la Loi. La souveraineté de Dieu s’est exprimée par une loi écrite, infaillible, absolue, immuable : la parole de Dieu. Cette loi ne saurait être discutée. Mais il convient de l’interpréter, de la coordonner, de la ramener à l’unité logique, d’en faire une Somme, un Gode obligatoire pour toutes les intelligences. « Je pense, dit-il au début de son Institution, avoir tellement compris la somme de la religion chrétienne et l’avoir digérée en tel ordre que celui qui aura bien compris la forme de l’enseigne GENÈVE ET LA TRADITION DE LA LIBERTÉ 11 ment que j’ai suivie pourra aisément juger et résoudre ce qu’il doit chercher en l’Ecriture, et à quel but il faut rapporter le contenu d’icelle. » Ainsi tout chrétien, rejetant l’intermédiaire du prêtre et l’autorité papale, doit rechercher la vérité sainte par lui-même, dans sa conscience et dans la Bible. Le principe du libre examen est posé. Seulement, toute conscience éclairée et tout esprit droit doit nécessairement comprendre et interpréter l’Ecriture comme la comprend et l’interprète Calvin. Cette assurance qu’il ne se trompe jamais dans l’interprétation de la Parole de Dieu, qu’il ne peut pas se tromper et que tous ceux qui diffèrent d’avis sont coupables d’erreur, hérétiques et dignes du bûcher, Calvin l’a ^poussée à un degré qui, pour ses descendants dégénérés, est un sujet de continuelle stupéfaction. Nous ne devons pas oublier, toutefois, que c’est une grande preuve d’inculture, de juger un homme du passé d’après les idées du temps présent. Ah ! nous avons beau jeu de faire la leçon à nos ancêtres du seizième siècle, et il nous convient bien de prendre le sac et la cendre pour expier leurs crimes! Nous sommes, nous, parbleu ! très tolérants, parce que nous sommes très sceptiques. Nous ne tenons guère à nos idées parce que nous n’y croyons jamais qu’à demi et, dès lors, il nous est extrêmement facile d’admettre celles des autres. Dans l’ardente mêlée du seizième siècle, il en allait bien autrement. En ces temps héroïques, la vie d’un homme ne pesait pas lourd, quand étaient en jeu les grandes causes qui soulevaient les peuples. Chacun se tenait prêt à sacrifier, sans hésitation, sa propre existence, et s’il le fallait celle de son voisin. Le tragique destin du malheureux Servet fut de tomber dans une lutte qui le dépassait et à laquelle les siècles à venir étaient intéressés. Défendue par une poignée d’hommes, encore à cette heure divisés contre eux-mêmes, Genève était environnée d’innombrables ennemis qui avaient juré sa perte. Elle vivait dans un perpétuel état de siège. Au dedans, l’opposition contre Calvin s’enhardissait. Il s’agissait de savoir qui l’emporterait, de lui ou de ses adversaires. Ceux qui défendaient l’Espagnol visaient plus haut que lui. S’il était absous, c’était Calvin qui se trouvait moralement condamné, et son œuvre détruite. De là l’acharnement de la lutte. Certes, nous ne sommes pas des calvinolâtres. Il se peut qu’à considérer ce tragique passé comme un roman historique, Servet soit pour nous, comme on dit, un personnage plus sympathique que son terrible adversaire. Au temps de Calvin, il y eut des esprits plus voisins de nous et qui nous attirent davantage par leur intelligente mansuétude. Mais la guerre ne se fait qu’avec les lois de la guerre. Si Calvin avait été un Castellion, il n’aurait pas fait l’œuvre qu’il a faite ; nous ne serions pas ce que nous sommes et l’Europe n’eût pas été, comme l’a dit Michelet, sauvée par Genève de l’Inquisition espagnole. 14 ESCARMOUCHES Et qu’on nous permette de citer également ici, parce qu’elles nous paraissent exprimer les sentiments des moins sectaires, des moins fanatiques d’entre les réformés d’aujourd’hui, les belles paroles que peu de temps avant sa mort Jean Réville, professeur au Collège de France, prononçait à Genève dans la chaire de Saint-Gervais 1 : Nous reconnaissons aussi bien que d’autres les erreurs et les fautes commises par Luther, par Calvin, par Zwingli, par tous nos ancêtres spirituels. Ce n’est pas ici que nous prétendrons justifier le bûcher de Servet. Il y a longtemps, suivant la belle parole que j’ai entendue d’un vieux huguenot, il y a longtemps que nous l’avons éteint par nos larmes. Mais alors que nous gardons la pleine liberté de notre jugement pour apprécier les paroles et les actes des réformateurs, il y aurait chez nous une indépendance du cœur qui friserait l’ingratitude si nous n’adressions pas en ce jour et surtout dans cette ville, qui lui doit sa signification historique, le libre et conscient hommage de notre reconnaissance au puissant esprit, à la conscience inflexible, à l’énergique lutteur, dont le nom frémit en ce moment sur toutes vos bouches, à ce Cavin qui, malgré ses duretés, ses intransigeances, et sur bien des points ses étroitesses, a été le libérateur par excellence des consciences et qui, par le seul ascendant de sa parole et de sa plume, sans avoir jamais disposé personnellement d’un pouvoir politique ou d’une force matérielle quelconque, a brisé les chaînes du despotisme clérical pour des centaines de millions d’hommes répartis actuellement sur trois continents. D’autres sont venus ensuite qui ont complété et achevé son œuvre. C’est lui qui l’a commencée d’une main si sûre et d’un cœur si ferme, que jamais plus on n’a pu ramener sous le joug sacer 1 Ce sermon a été publié sous le titre : Principe de la Réforme, Georg, Genève, 1902. GENÈVE ET LA TRADITION DE LA LIBERTÉ 15 dotal les races qu’il avait marquées à son empreinte. Ce sera l’immortel titre de gloire de Genève dans l’histoire d’avoir été le premier foyer de la liberté spirituelle. Oui, l’œuvre de Calvin fut libératrice. Et si l’on ne cesse de lui reprocher le supplice de Servet, n’est-ce pas parce que l’on comprend, parce que l’on reconnaît que ce supplice fut de sa part une inconséquence, et qu’il contredit ce principe de la liberté de conscience qui fut la pierre angulaire de la Réforme ? En affranchissant la conscience, la Réforme a fondé toutes les libertés. Une force est apparue dans l’àme humaine, irréductible, en révolte contre toutes les contraintes extérieures, parce que la loi dont elle procède est, pour elle, au-dessus de toutes les lois. Mais la révolte ne restera pas confinée dans le domaine spirituel. Après avoir brisé les idoles, elle ébranlera les trônes. Libre intérieurement, l’homme voudra que son franc arbitre soit respecté par le pouvoir. A la flamme de la foi religieuse, l’antique esprit d’indépendance se réveillera chez les fils des barbares. Après avoir anéanti le pouvoir absolu dans le domaine de l’esprit, il faudra qu’ils le détruisent aussi dans le domaine politique. Ce sera essentiellement l’œuvre de la Réforme calviniste. Ses instigateurs, eux-mêmes, ignoraient le sens et la portée de leur œuvre. Ils n’avaient qu’un instinct confus de la force qui les poussait et ne devait se déployer entièrement qu’à travers les siècles. De là des contradictions qu’il serait puéril de leur reprocher. En réprimant la liberté dans son église et dans la cité de Genève, Calvin contribua cependant à la répandre dans le monde. Son œuvre a été essentiel lement une œuvre d’éducation. Or l’éducation calviniste, en faisant porter tout son effort sur la conscience morale, a sans cesse tendu à former des individualités fortes. Ces individualités sont encore sous tutelle. Mais elles sont préparées graduellement pour l’émancipation future. Et cette période de transition était indispensable. Pour croire que le passage d’un régime d’oppression à un état de liberté puisse s’accomplir subitement, ou même par les efforts d’une seule génération, il faut avoir les illusions des jacobins de 93 ou des révolutionnaires russes d’aujourd’hui. Si une éducation! morale lente et progressive n’a pas rendu les âmes libres, rien ne sert d’inscrire le mot dans les lois ; il y reste lettre morte. GENÈVE ET LA TRADITION DE LA LIBERTÉ 17 III Aux yeux de Calvin, toute autorité instituée vient de Dieu : « Un mauvais roi, dit-il, est line ire de Dieu sur la terre, et l’obéissance lui est due par ses sujets ; ils doivent lui porter une aussi grande révérence que s’il était un bon roi. » Et si M. Emile Doumergue a pu découvrir dans cette oeuvre quelques passages qui semblent contredire cette maxime, il n’en reconnaît pas moins que, dans le domaine politique, le respect de l’autorité civile établie par Dieu est l’axiome fondamental de Calvin, axiome constamment répété et répété sous les formes les plus diverses. Ce n’est pas à dire, bien entendu, que, dans la pensée de Calvin, la conscience, éclairée par la révélation de Dieu, puisse abdiquer devant la volonté d’un mauvais prince. Pour lui, comme pour les chrétiens de la primitive église, le recours c’est le martyre, et, en vérité, l’histoire l’a prouvé, ce n’est pas le moins efficace. Mais déjà, pour ses disciples immédiats, le recours c’est la révolte, c’est la déposition du prince indigne, et c’est, s’il le faut, sa condamnation à mort. Du vivant même de Calvin, son ami Goodman, collègue de Knox, lançait, sous le titre : Le droit d'obéissance au souverain, un court pamphlet qu’il avait communiqué au grand réformateur. Goodman proclame déjà, au nom de la conscience, le droit à la révolte. Contre les souverains indignes, il en appelle au peuple. « Rois et gouverneurs, dit-il en substance, sont une partie du peuple : s’ils ne remplissent pas leur devoir, le ESCARMOUCHES 2 peuple a le droit de déposer et de punir des souverains rebelles contre Dieu » En 1558 John Knox fait entendre un langage plus clair encore et plus redoutable dans son Admonition aux frères. Enfin en 1573, un an après la St-Barthélemy, le successeur de Calvin, Théodore de Bèze, publie un traité anonyme, Du droit des magistrats sur leurs sujets, dans lequel il pose nettement le principe de la souveraineté populaire et du droit du peuple à l’insurrection. « Les états, dit-il (c’est-à-dire les représentants de la nation), sont au-dessus des rois. Les peuples auxquels il a plu de se laisser gouverner, ou par un prince ou par quelques seigneurs choisis, sont plus anciens que leurs magistrats, et par conséquent le peuple n’est pas créé pour ces magistrats, mais les magistrats pour le peuple. GENÈVE ET LA TRADITION DE LA LIBERTÉ 19 par Buchanan et mise en pratique par d’autres, qu’un tyran est digne de mort. Cette doctrine démocratique et révolutionnaire donne naissance à la théorie du contrat social, développée entre autres par Locke et, à la fin du dixseptième siècle, par Jurieu. En opposition au principe du droit divin, les jurisconsultes huguenots enseignaient qu’un contrat tacite lie les sujets au souverain et que les sujets se trouvent, de plein droit, dégagés de leurs obligations, si le souverain a violé le contrat. Au temps de la jeunesse de Rousseau, Burlamaqui professait des idées analogues à l’université de Genève. Jean-Jacques en fut certainement influencé. C’est par son intermédiaire que la doctrine des juristes réformés fut transmise à la Réformation française. Par ses contradictions mêmes, le Contrat social est un livre essentiellement calviniste h 11 est le Coran à la fois du principe démocratique, issu de la Réforme, et du principe théocratique issu de Calvin. Et il concilie ces principes contraires en divinisant le peuple souverain, en lui donnant le droit d’instituer une religion civile obligatoire et le pouvoir de punir de mort les réfractaires. C’est ainsi que le Genevois Rousseau fut à la fois le plus éloquent apôtre de la liberté et le prophète des énergumènes qui établirent, par la terreur, la pire des tyrannies, celle de la foule inconsciente. 1 Le citoyen de Genève, descendant des premiers réfugiés pour cause de religion, n’a jamais renié ses origines. Il savait ce qu’il devait à la Réforme calvinienne et à son chef, et il s’est plu à rendre un éclatant hommage à la personnalité de Calvin. « Quelque révolution que le temps puisse amener dans notre culte, a-t-il dit, tant que l’amour de la patrie et de la liberté ne sera pas éteint parmi nous, jamais la mémoire de ce grand homme ne cessera d’être en bénédiction. » La doctrine démocratique élaborée par les juristes huguenots ne demeura pas dans le domaine de la théorie pure. Elle eut une action déterminante sur l’histoire générale. Mais son influence alla en sens très divers, suivant les pays qui l’adoptèrent. Les idées valent tout juste ce que valent les hommes qui les mettent en pratique. Tandis que chez les Jacobins qui s’inspirent, non pas de l’ensemble de l’œuvre de Rousseau, mais de quelques-uns de ses aphorismes les plus imprudents, on voit l’idée du Contrat social aboutir à la suppression radicale de la liberté de conscience et au despotisme populaire le plus odieux, dans le monde anglo-saxon cette même idée préside à l’élaboration du droit constitutionnel et fournit aux nations modernes la formule des garanties fondamentales des libertés individuelles. Les Déclarations des droits américaines, modèles de la Déclaration des droits de Vhomme et du citoyen de 1789, ne sont pas autre chose que l’énoncé des clauses de ce contrat social hypothétique. Il y a là une longue évolution historique qui a été étudiée avec beaucoup de soin par M. Charles Borgeaud, et, après lui, par M. Jellineck. Je n’en pourrai donner ici qu’un rapide aperçu. Issue du calvinisme, la Réforme des Puritains eut un caractère essentiellement démocratique. Les nonconformistes commencèrent par organiser démocratiquement leur église en la fondant sur un pacte constitutif {covenant) qui devait être adopté par tous les membres de la communauté. De l’église la démocratie passa à l’état. Persécutés dans leur foi, les Puritains durent, pour pouvoir vivre selon leur conscience, briser la résistance, non seulement de l’église établie, mais du roi, son chef suprême. La royauté fut emportée dans cette lutte, et l’on sait GENÈVE ET LA TRADITION DE LA LIBERTÉ 21 avec quelle terrible logique furent appliquées, sous Cromwell, les doctrines huguenotes sur le droit des sujets de résister au souverain et de le punir s’il a violé la loi de Dieu. Après avoir renversé la royauté, les Puritains voulurent organiser l’état d’après les mêmes principes que leurs églises, en le fondant sur un pacte constitutionnel que le peuple se donnerait à lui-même et auquel il jurerait obéissance. Le droit divin devait être remplacé par un contrat social assurant la stabilité dans le gouvernement de la nation, la liberté de conscience complète et l’égalité de tous les citoyens devant la loi, conséquence de l’égalité de tous les chrétiens devant Dieu. Le pacte proposé par les Indépendants se termine par une Déclaration des droits : «Nous déclarons que ce sont là nos dVoits de naissance, et que nous sommes résolus, d’un commun accord, à les maintenir de toutes nos forces, contre toute opposition, quelle qu’elle soit. » C’est ainsi que les Indépendants, les premiers dans l’Europe moderne, formulent le principe d’une constitution écrite établie par la volonté du peuple et garantissant des droits individuels fondamentaux auxquels aucune loi ni aucun pouvoir ne doivent attenter. En vain, Cromwell tenta de briser la résistance de ces étranges soldats qui, les soirs de bataille, se réunissaient sous la tente pour lire la Bible et chanter des psaumes. Il dut céder au courant pour le faire ensuite dévier. Pourtant, dans la charte qu’il édicta en 1653 comme protecteur, il introduisit plusieurs des principes stipulés dans VAgreement of the People. La république n’eut qu’un jour en Angleterre. Mais la Réforme n’en avait pas moins brisé le pouvoir absolu. Les libertés individuelles, revendiquées par les Indépendants au nom de la conscience religieuse, demeurèrent acquises à l’Angleterre et se répandirent de proche en proche dans le monde entier. En 1620, à bord de la Mayflower, les pères pèlerins qui s’en allaient fonder une nouvelle Angleterre pour y vivre en restant entièrement fidèles à leur foi, établirent le pacte constitutif de leur future colonie. Tous les passagers, y compris les matelots et les domestiques, furent appelés à apposer leur signature au bas de ce vénérable document d’où procèdent toutes les constitutions américaines. A la veille ou au lendemain de la déclaration d’indépendance, les différentes colonies se donnèrent des constitutions qui servirent de modèle à la constitution fédérale de 1787. Elles étaient en général précédées de Déclarations des droits naturels de l’homme et du citoyen. Ces droits ne sont pas considérés comme institués par la loi. Ils émanent de la personnalité humaine, libre et responsable, ils sont ses conditions d’existence. Le peuple les constate et les proclame. Il ne les crée pas. Ils sont préexistants. Il ne dépend de personne de les abolir. Ils doivent garantir à tout individu un domaine réservé que l’autorité soit tenue de respecter. Comme c’est là un postulat de la conscience morale, il est placé hors de toute discussion. Deux conceptions sont en présence, en droit public : la conception autoritaire, venue de l’empire romain, qui veut que l’individu n’ait de droits qu’en vertu d’une concession de l’état; et la conception germanique et réformée, qui veut que la liberté individuelle, antérieure à l’état, soit simplement garantie par lui. C’est ce dernier principe qui, des constitutions américaines, a passé à la Déclaration des droits de Vhomme et du citoyen de 1789. Cette Déclaration dérive directement de la Réforme calviniste. Etabli à Paris, Franklin édita en 1789 un recueil GENÈVE ET LA TRADITION DE LA LIBERTÉ 2o des constitutions de l’Amérique du Nord. Dans sa maison, Lafayette avait affiché le tableau des Déclarations de droits américaines, laissant tout auprès une place vide pour la future Déclaration des droits française. Ses compagnons de la guerre d’indépendance l’aidaient à répandre les «idées américaines». On en discutait partout, dans les salons et les clubs, à la cour et même en province. Ces idées jouent un rôle important dans la rédaction des cahiers de 89. Elles trouveront leur expression dans la Déclaration des droits de l’homme et du citoyen. Au cours de la discussion de l’Assemblée constituante, dans la séance du 27 juillet, l’évêque de Bordeaux s’exprimait comme suit : « Cette noble idée, conçue dans un autre hémisphère, devait de préférence se transplanter parmi nous. Nous avons concouru aux événements qui ont rendu à l’Amérique septentrionale sa liberté; elle nous montre sur quels principes nous devons appuyer la conservation de la nôtre, et c’est le Nouveau-Monde, où nous avions autrefois apporté des fers, qui nous apprend aujourd’hui à nous garantir d’en porter nous-mêmes. » En mettant les textes en regard, M. Jellineck a prouvé que la Déclaration française est empruntée aux Déclarations américaines, non seulement pour le fond, mais encore pour la forme. Le texte français est seulement plus concis et plus précis. Il s’attache à des «définitions» que les Américains jugeaient inutiles. Il porte les caractères de clarté, de netteté et de logique qui sont éminemment ceux de la race française. D’importation étrangère, la liberté qui avait enthousiasmé les Français ne fut bientôt plus pour eux qu’une notion intellectuelle à opposer aux erreurs du passé, un dogme à définir, à codifier, à imposer par le pouvoir. «Il faut contraindre les hommes à être libres», avait dit Rousseau. La Terreur y pourvoira en établissant cette forme d’oppression nouvelle qu’un orateur de la Convention a caractérisée par cette singulière antiphrase : «Le despotisme de la liberté ». Toutefois, grâce au génie généreux et communicatif de la nation française, l’idée de la liberté, qui, dans les révolutions du monde anglo-saxon, était restée localisée, prend une force d’expansion illimitée. IV Telle est, sous son aspect politique, l’idée qu’évoquera le monument international de la Réforme calvinienne, lequel devra être essentiellement, dans la pensée des Genevois d’aujourd’hui, le monument de la liberté. Si l’on a voulu lui donner ce caractère international, c’est que la Genève de Calvin doit être conçue surtout comme un centre de ralliement. Elle fut un groupement humain .constitué, par la force d’une toute puissante volonté, d’éléments choisis entre toutes les nations, cristallisés autour d’une foi en un bloc homogène et résistant. Genève dément l’idée de race, à laquelle on a donné une valeur trop absolue. Elle montre que la race n’est pas tout, que GENÈVE ET LA TRADITION DE LA LIBERTÉ 25 le milieu n’est pas tout, qu’il y a l’idée et que l’idée peut modeler les hommes à son image. Elle peut aussi créer, autour d’une métropole dénuée de toute puissance matérielle, un royaume de l’esprit s’étendant jusqu’aux confins du monde. Au début du seizième siècle, a dit l’illustre théologien Harnack, surgit de Genève un mouvement religieux et politique qui, au milieu du même siècle, s’étendit à la fois sur la France, l’Angleterre, l’Ecosse et la Hollande. Ce mouvement, — le calvinisme, — créa en peu d’années un type non seulement moral et religieux nouveau, mais encore, étroitement lié à lui, un nouveau type politique social et économique du caractère le plus particulier. En lui se fondirent toutes distinctions entre méridionaux, Français du nord, Hollandais, Anglo-Saxons et Ecossais : car il se montra plus fort qu’eux tous. Le calvinisme de l’Europe occidentale et celui des Etats-Unis montrent partout la même empreinte, et ceux qui la portent semblent tous membres d’une race unique, qu’ils soient pasteurs dans les Gévennes ou banquiers dans Wall Street; car, même abstraction faite des éléments spécifiquement religieux, le type demeure identique à lui-même. Cette action géante, qui l’a exercée ? Une individualité : Calvin. Les peuples élevés à l’école de la Réforme calvinienne ont donc une tradition commune, qui est la tradition de la liberté. Dans la Suisse romande, elle est demeurée l’élément premier de notre vie spirituelle. C’est à nous qu’il appartient de conserver et de faire valoir un si précieux héritage. L’histoire nous enseigne que la liberté individuelle est née, au sein de la civilisation chrétienne, d’un état de conscience. Elle a jailli des sources profondes de la vie intérieure pour se répandre au dehors. Sous l’influence de la foi religieuse, l’homme a reconnu en lui-même une force qui, ne pouvant se soumettre à aucune autorité extérieure, rend invincibles les plus humbles. Les véritables fondateurs des libertés modernes ne sont pas les éloquents orateurs de la Constituante et de la Convention, mais bien plutôt les héros obscurs des premiers temps de la Réforme, ceux qui, plutôt que de renier leur foi, allaient en exil ou au martyre. Ce sera, si l’on veut, Marie Durand, la vaillante huguenote sachant à peine écrire et traçant pourtant d’une main qui ne tremblait pas, sur le mur de sa prison, ce simple mot: Récistez! Résistez ! Tout est dans ce mot-là, tout l'affranchissement de la personnalité morale, libérée pour la première fois des contraintes séculaires. Les théologiens, les juristes, les hommes d’Etat de la Réforme n’ont pas fait autre chose que de le commenter. Aujourd’hui une question se pose: s’il est vrai que la liberté ait été une conquête de la conscience morale, fortifiée par la foi religieuse, survivrait-elle à la force intérieure qui l’a suscitée? On nous dit que les peuples chrétiens se déchristianisent ; on nous dit que toute foi s’éteint dans le monde ; on nous dit que la seule force qui puisse encore soulever les masses, est cette passion qui survit à toutes les autres et qu’un grand historien a appelée « la molle passion du bien-être ». Dans l’état social qui se prépare, y aura-t-il encore une place pour la liberté? Elle GENÈVE ET LA TRADITION DE LA LIBERTÉ 27 n’est un bien que pour celui-là seul qui a en luimême un trésor infiniment précieux à préserver. A qui n’a d’autre désir que d’acquérir et de vivre en douceur, une chaîne dorée suffit. Ces fameuses « libertés modernes » — (sont-elles encore « modernes » à cette heure?) — nous prenons la bonne habitude de les considérer comme une conquête définitive. 11 nous semble qu’elles sont dans l’ordre fatal des choses et que nous n’avons qu’à en jouir avec tranquillité, comme d’un bien qui nous est dû et que nul ne saurait nous enlever. Ne nous berçons pas de cette illusion ! La liberté n’est pas le produit nécessaire de je ne sais quelle loi du progrès indéfini. Elle est antinaturelle. De mon penchant naturel, je puis vouloir ma liberté; jène veux pas la liberté des au très. La liberté des autres m’est indifférente quand elle ne me gêne pas; et si elle me gêne, je la bouscule et je la supprime lorsque je puis le faire. Loin de vouloir la liberté des autres, la morale instinctive veut leur asservissement au bon plaisir de l’individu, lequel est à lui-même son but suprême et sa loi. Sachons ouvrir les yeux ! Jamais les conquêtes précaires de la liberté n’ont été plus menacées qu’à l’heure actuelle ; et cela par toutes les forces dominantes de la Société moderne. Elles sont menacées d’en haut, même dans les pays protestants, où l’on voit prévaloir la religion de la Force. Nul n’ignore comment, en Prusse, on interprète en ce qui concerne les Polonais récalcitrants à l’éducation germanique, les articles de la constitution qui garantissent à tous les sujets du roi l’égalité devant la loi et la libre possession de leurs biens. Au reste, citoyens de la libre Helvétie, gardons-nous de donner des leçons à qui que ce soit. Il semble parfois que le sens élé mentaire du droit se perde dans notre pays. Dans certains milieux, on n’y comprend plus le devoir que nous avons de prendre le parti des petites nationalités violentées par les puissances. N’a-t-on pas vu, dans la Suisse allemande, des journaux importants, répandus à l’étranger, ayant qualité pour représenter au dehors l’opinion de notre pays, n’a-t-on pas vu ces organes de la bourgeoisie éclairée et « libérale » soutenir contre les Slaves du Sud la politique brutale de l’Autriche, encourager la Prusse à germaniser de force les petits Polonais et à « exproprier » leurs parents, applaudiraux plus mesquines mesures prises en Alsace contre l’usage de la langue française ? Si, au dehors, nous abandonnons la cause des nationalités opprimées, par un juste retour nous veillons mal à la défense de nos propres libertés. Les beautés de la règlementation à la prussienne exercent une véritable fascination sur ceux de nos confédérés qui tiennent le plus à leur vieille étiquette de freisinnig. On travaille activement à faire de nous des bourgeois aussi soigneusement parqués que nos voisins du nord ou de l’ouest. Prenons garde de justifier, un jour, le mot cruel de Gœthe sur la liberté suisse, cité l’autre jour par René Morax : Ein altes Màrchen in Spiritus aufbewahrt. La liberté est menacée d’en bas par les masses populaires, lesquelles, devenues non seulement indifférentes, mais hostiles à cette déesse vieillie, sont prêtes à déboulonner sa statue. En marge de la société bourgeoise, une société nouvelle s’organise déjà sous des autorités aussi despotiques qu’irresponsables, et qui suppriment toute velléité d’indépendance individuelle. Hors la loi qui résiste ! Nous venons de GENÈVE ET LA TRADITION DE LA LIBERTÉ 29 voir à Zurich, pendant de longues semaines, un singulier spectacle : des ouvriers emprisonnés dans un atelier, assiégés par les grévistes et, s’ils en sortaient, roués de coups comme rebelles au mot d’ordre de chômage des syndicats. Gela se passait ouvertement, avec beaucoup d’ordre et une régularité tout administrative. Et les factionnaires socialistes réclamaient la protection de la police contre les bons bourgeois de Zurich qui se permettaient de les molester dans l’exercice de leurs devoirs militaires ! Léger avant-goùt des douceurs de la société qu’on nous prépare ! Ah ! dans les luttes sociales qui s’annoncent, nos « libertés modernes » ne pèseront pas lourd si nous n’avons pas l’âpre vouloir de les défendre pied-à-pied contre les masses, aussi bien que contre le pouvoir. On a pris parfois la liberté pour un talisman doué de je ne sais quelle vertu magique ; on a cru qu’il suffisait d’inscrire son nom dans les lois pour qu’elle opérât des miracles. Ce n’est pas dans les lois qu’elle a son siège, c’est dans les âmes. Au lendemain de la révolution du 18 décembre 1830, Vinet disait à ses compatriotes: « Vaudois, votre liberté vaudra justement ce que vous vaudrez ! » La liberté n’est que l’espace réclamé par la volonté morale pour s’affirmer et se déployer. Laissez cet espace inoccupé, il retourne au désert. Pour que l’homme réalise ce miracle de demeurer libre, il faut qu’il ait une foi vivante, qui le dépasse tout en le portant. Peu importe la formule intellectuelle par laquelle cette foi s’énonce ; il suffit qu’au for de la conscience elle ait son sanctuaire, qu’aucune autorité spirituelle ni temporelle ne puisse violer. La défense du sanctuaire de la volonté libre ne peut être assurée qu’au prix d’une lutte de tous les instants. La langue et la culture françaises en Suisse 1. De quelle manière avons-nous à régler nos rapports, d’une part avec nos Confédérés de la Suisse allemande, d’autre part avec le pays dont nous parlons la langue ? Pour nous, Suisses romands, il 1 La présente étude a été publiée dans le Journal de Genève en janvier 1908, à propos du projet de fondation d’une Union romande. A deux assemblées convoquées à Neuchâtel, des discussions assez vives s’étaient produites. Les uns désiraient que V Union romande prît en mains la défense de la langue française, menacée, disaient-ils, par le pangermanisme. D’autres, ne voyant pas de péril en la demeure et jugeant inopportun d’introduire dans notre pays des querelles de langue, insistèrent pour que l’on se bornât à favoriser la culture et l’enseignement de la langue française. Ce dernier avis l’emporta. Mais, n'ayant pu faire prévaloir leur manière de voir, les promoteurs de l’entreprise s’en désintéressèrent. Le comité chargé d’élaborer les projets de statuts n’a plus donné signe de vie depuis deux ans. Et il semble bien que V Union romande soit mort-née. Il faut le regretter, car, dans le domaine de l’enseignement, elle aurait eu une œuvre utile à accomplir. Nous avons remanié cette étude pour supprimer des polémiques désormais sans objet. n’est pas de question plus essentielle que celle-là. Et nous devons lui vouer notre plus constante attention, nous efforçant de la résoudre en toute liberté d’esprit, sans nous laisser entraîner hors de notre voie par les propos sans consistance de quelques pangermanistes échauffés, dont les Suisses allemands sont les premiers à se gausser, ni par les intrigues de quelques vagues politiciens de France, désireux de réparer à nos dépens leur popularité détériorée. Les brouillons doivent être tenus pour des quantités négligeables. Chaque peuple a les siens et, malheureusement, ne les garde pas toujours pour lui ; on ne saurait toutefois l’en rendre responsable. Aujourd’hui, comme par le passé, notre ligne de conduite vis-à-vis de la France est toute tracée : participer largement à la culture française, nous souvenant que nous lui devons, pour une grande part, ce que nous sommes, non seulement dans le domaine de l’idée, mais dans nos goûts, dans nos gestes, dans nos vêtements, dans nos meubles, dans tout le détail familier de notre vie coutumière. N’oublions jamais nos devoirs de reconnaissance envers notre grande éducatrice. Après nous avoir, aux temps héroïques de la Réforme, vivifiés de son sang le plus riche et de ses plus hautes pensées, la France nous a sans cesse donné en exemple la clarté de son verbe, l’élégance de ses mœurs et la noble tenue de ses arts. Acceptons ce qu’elle continue de nous prodiguer, jour après jour — aussi bien ne pourrions-nous faire autrement, car nous le faisons d’une manière tout inconsciente — mais acceptons-le à la fois sans servilité et sans méfiance, en nous réservant le droit d’élaguer, avec un soin vigilant, l’ivraie qui peut s’égarer dans le bon blé de France ; restons assez nous-mêmes pour nous assimiler les meilleurs éléments de la culture française sans nous laisser entièrement englober par elle. Réagissons chaque fois que cela est nécessaire ; gardons ce qui est conforme à nos traditions, rejetons ce qui leur est contraire. Sachons, en un mot, demeurer non pas une « province intellectuelle », mais un peuple, un petit peuple qui sait ce qu’il veut. Vis-à-vis de nos confédérés de la Suisse allemande aussi, nous devons savoir, et clairement, ce que nous voulons. Nous gardons conscience de ce que nous devons à leur énergie opiniâtre et calme. Tous les Suisses romands qui habitent la Suisse allemande, tous ceux qui la connaissent d’un peu près, sont d’accord pour reconnaître qu’on n’y nourrit aucun mauvais vouloir à l’égard de la langue française. Au contraire, cette langue y est cultivée avec prédilection. On l’enseigne dans toutes les écoles secondaires de la manière la plus intelligente, et les résultats de cet enseignement sont si brillants que récemment une troupe composée d’anciens élèves du gymnase de Zurich a pu, sous la direction de M. le professeur Nussbaum, jouer le Barbier de Séville correctement et avec beaucoup de verve. Nombre de jeunes Confédérés de Bâle, Zurich ou St-Gall font leur apprentissage dans nos maisons de commerce; nombre de jeunes Confédérées viennent dans nos pensionnats piocher l’accord du participe passé. A en juger par les statistiques de la Société du Muséum, il n’y a pas un seul écrivain allemand qui ait autant de lecteurs à Zurich que Maupassant. Dans les vieilles familles, la culture française est encore en honneur — bien qu’il y ait recul à cet égard depuis 1870 — et la langue française, considérée comme langue auxiliaire, est parlée de préférence môme au bon allemand, lorsque le dialecte n’est pas de mise. Faut-il rappeler l’accueil fait par le Cercle de lecture de Hottingen à M. René Morax ou à M. Philippe Godet, lequel se fit chaleureusement applaudir en parlant avec un enthousiasme communicatif des meilleurs poètes de la LA LANGUE FRANÇAISE EN SUISSE 35 Suisse romande? Est-il nécessaire de citer d’autres faits encore ? On n’aurait que l’embarras du choix. Et nous serions, nous, assez maladroits pour décourager tant de bonne volonté! Et nous irions crier à la persécution... Pourquoi ? Pour quelques vétilles? Pour quelques puérilités? Pour quelques noms de stations? Parce que certains horaires de chemins de fer, après le mot Yverdon, ajoutent entre parenthèses ( Yferten), faute de prononciation imputable à la conformation des gosiers allémaniques? Parce qu’un quidam sans autorité, ayant rencontré dans un village neuchâtelois quelques moutards parlant le Schwitzer Dütsch, a demandé qu’on y créât une école allemande ? Parce qu’on ne sait quel touriste en chemise Jæger, veston caca d’oie et chapeau Louis XI, surmonté d’un blaireau à barbe, a été pris d’un accès de furor teutonicus (comme disait Bismarck), pour avoir entendu un employé parler français au guichet d’une station du Viège-Zermatt? La belle affaire, en vérité? Il y a des nigauds partout, il y en a même, je vous prie de le croire, dans les universités germaniques ; il y a des orateurs qui disent des sottises, il y a des journalistes qui en écrivent. Est-il nécessaire, pour donner la réplique à ces gens-là, de les suivre sur le terrain qu’ils ont choisi et de se mettre au niveau de leur niaiserie ? Ce serait leur faire trop de plaisir et trop d’honneur. Par bonheur, il n’en est pas question. Nous avons à vrai dire, dans la Suisse romande, un petit groupe d’hommes de bonne volonté, toujours prêts à courir aux Thermopyles pour défendre le sol romand contre l’invasion des barbares. Postés en vigie sur les sommets du Jura neuchâtelois, ils voient, avec terreur, s’avancer la marée montante du pangermanisme, dont les flots menacent d’engloutir le monde latin. Et ce péril les empêche de dormir. Avec éloquence, ils nous exhortent à le conjurer. « La Suisse romande, disent-ils, n’a pas le droit de se désintéresser dusort de la civilisation latine, et de repousser la main que nous tendent nos camarades de langue et de race. Elle a même le devoir d’affirmer, vis-à-vis de la France et de la Belgique, aussi bien que de l’Allemagne, son droit à l’existence comme peuple autonome de langue française. » Voilà qui va fort bien. Mais nous sommes d’avis que nos devoirs envers notre patrie suisse sont plus immédiats et plus certains que ceux que nous pouvons avoir envers cette vague entité qu’on appelle la civilisation latine. Serait-ce trop d’affirmer que la langue française, parlée en Suisse par une minorité, est non seulement tolérée, mais qu’elle a, en fait, une situation privilégiée? Etant une, elle a à lutter, à la frontière linguistique, contre des dialectes multiples, qu’on n’apprend pas aisément, à moins d’avoir, dès son jeune âge, soumis son gosier à une gymnastique spéciale. Dans la concurrence vitale entre les langues, la clarté, l’élégance, l’euphonie sont des forces ; et ces forces-là, LA LANGUE FRANÇAISE EN SUISSE 37 nul ne songe à contester qu’elles ne soient, en Suisse, du côté de la langue française. Et puis, nous autres Welches, nous avons un atout majeur dans notre jeu, savoir notre paresse. C’est un fait bien connu que les Allemands font les efforts les plus persistants pour parler correctement la langue des pays où ils vivent, et qu’ils s’assimilent ainsi, avec une facilité extraordinaire, tandis que les Français n’abandonnent aisément ni leur langue, ni leurs mœurs. Car la question de langue se double ici d’une question de mœurs. Nous n’avons pas le loisir d’aborder ici ce grand sujet; il faudrait l’étudier spécialement en Alsace-Lorraine, où les deux cultures, allemande et française, sont en lutte, et où la supériorité de la culture française — dans ce qui touche à la vie de tous les jours — s’affirme par son invincible force de résistance. La lutte entre les langues est un phénomène qui obéit à des lois semblables à celles qui régissent le Struggle for life des espèces organiques. La plus apte l’emporte et survit. Que l’on ne se fasse pas d’illusions sur les petites mesures défensives qui nous sont proposées. Les associations, les protestations, les manifestes ne servent pas ici à grand’chose. Si l’on tient à accroître la force de résistance de la langue française, il faut, avant tout, s’efforcer de la conserver dans toute sa pureté, dans toute sa beauté, dans toute sa santé. A cela nous pouvons, dans notre pays, travailler avec efficacité par la parole, par la presse, par le livre — combien plus que toute une ligue peut faire ici un livre, un seul livre bien écrit! Et nous pouvons agir surtout par l’enseignement. Nous le pouvons et nous le devons. Tl va de soi, d’ailleurs, que les plus pacifiques d’entre nous ne sont nullement d’humeur à supporter que l’on manque d’égardsàla langue de leurs pères. Tels menus incidents peuvent, ça et là, se produire, qui rendent un acte de résistance nécessaire. Une ligue n’est pas indispensable pour cela, l’action individuelle suffit. Qu’on me permette, à ce propos, de raconter ce qui arriva à mon fils Claude. A un moment où ce petit Welche ne faisait entendre encore que des vagissements bruyants, à vrai dire, mais inarticulés, et ressemblant fort à ceux que peuvent pousser ses camarades zurichois, il trouva moyen de provoquer, à propos d’une question de langue, un conflit entre les plus hautes autorités de son pays. LA LANGUE FRANÇAISE EN SUISSE 39 Voici l’affaire. L’usage s’élait établi dans la ville de Zurich de traduire, tant bien que mal — plus souvent mal que bien — les prénoms étrangers des nouveau-nés que l’on venait inscrire à l’état civil. Que l’on traduisît Ernest par Ernst, il n’y avait certes pas grand mal à cela. Mais tous les cas n’étaient pas aussi simples. La sagacité philologique des officiers d’état civil se trouvait parfois mise à une rude épreuve. Jugez-en plutôt. Un de mes collègues romands eut un fils et voulut l’appeler René. Le grattepapier fut perplexe. Comment traduire René en allemand ? Wiedergeboren? Non, ça ne pouvait pas aller! Par bonheur, en vertu d’une tradition qui date sans doute du Saint-Empire romain, et à laquelle Barberousse ne doit pas être étranger, les Allemands considèrent le latin comme une annexe de leur langue. Le fonctionnaire zuricois alla donc puiser à ce réservoir de sûreté, et, après mûre réflexion, il inscrivit de sa plus belle main, le mot : Renata. — Renata ! s’écria le père indigné, mais c’est un nom de fille ! L’administration consentit à reconnaître le bienfondé de cette observation, et Renata fut changé en Renatus, un nom bien germanique ! Pour mon fils Claude, l’employé n’hésita pas. Le cas s’était déjà présenté plusieurs fois. Il écrivit d’un trait : Claudius, et fut stupéfait de m’entendre déclarer que je protestais contre cette traduction et que je ne tolérerais pas que mon fils fût affublé d’un nom que je jugeais ridicule. Je mis en avant des arguments péremptoires. J’invoquai l’article 116 de la Constitution fédérale,et le fait que partout ailleurs, en Suisse, on laisse les parents libres de donner à leurs enfants le nom qu’il leur plaît. L’employé ne put que recourir à ses supérieurs hiérarchiques. Les supérieurs hié rarchiques me donnèrent tort. Ils motivèrent leur sentence par des considérants dont je vous citerai un passage dans la langue originale. A être traduit, il perdrait trop de sa saveur. Die Sitte, oder Unsitte, an Stelle unserer gut deutschen Berufsund Vornamenbezeichnungen fremdsprachige Ausdrüèke anzuwenden, wie charcutier, marchand tailleur, Jacques, Henri, etc., sei personliche Liebhaberei, deren im Interesse einer klaren und verstândlichen Amtssprache entgegengetreten werden sollte... Mit Rechtwerden gegenwârtig von der Schule, von Sprachgelehrten und Behôrden aile Anstrengungen gemacht, die deutsche Sprache von entbehrlichen fremden Namen und Ausdrücken zu reinigen : diesen Bestrebungen sollten die Zivilstandsbeamten nicht entgegentreten. | 36,664 |
https://github.com/MyJetWallet/MarketingBox.AuthApi/blob/master/src/MarketingBox.AuthApi.Domain/Tokens/Role.cs | Github Open Source | Open Source | MIT | null | MarketingBox.AuthApi | MyJetWallet | C# | Code | 13 | 52 | namespace MarketingBox.AuthApi.Domain.Tokens
{
public enum Role
{
Affiliate,
MasterAffiliate,
AffiliateManager,
Admin,
}
} | 30,857 |
https://nl.wikipedia.org/wiki/Sint-Julianakerk%20%28Verviers%29 | Wikipedia | Open Web | CC-By-SA | 2,023 | Sint-Julianakerk (Verviers) | https://nl.wikipedia.org/w/index.php?title=Sint-Julianakerk (Verviers)&action=history | Dutch | Spoken | 135 | 276 | De Sint-Julianakerk (Frans: Église Sainte-Julienne) is een parochiekerk in de Belgische stad Verviers, gelegen aan de Avenue Pelzer.
Geschiedenis
De parochie, gewijd aan Sint-Juliana werd gesticht in 1892, maar de bouw van de kerk, ontworpen door Charles Thirion, begon pas in 1901, in 1906 werd het meubilair geïnstalleerd en in 1907 werd de kerk ingezegend.
Gebouw
Het betreft een groot, bakstenen bouwwerk in neogotische stijl. Het lange schip heeft zes traveeën, zijkapellen en een veelhoekig afgesloten koor. Het schip wordt doorsneden door een transept, waarvan de noordelijke arm geflankeerd wordt door twee vrijwel identieke torens, voorzien van tentdaken, welke doen denken aan de Abdij van Maredsous. De zuidelijke transeptarm wordt driezijdig afgesloten door een apsis.
Het kerkmeubilair stamt vrijwel geheel uit het begin van de 20e eeuw, en is uitgevoerd in neogotische stijl.
Juliana
Juliana | 19,006 |
https://tr.wikipedia.org/wiki/Subatan%2C%20Tuzluk%C3%A7u | Wikipedia | Open Web | CC-By-SA | 2,023 | Subatan, Tuzlukçu | https://tr.wikipedia.org/w/index.php?title=Subatan, Tuzlukçu&action=history | Turkish | Spoken | 34 | 123 | Subatan, Konya ilinin Tuzlukçu ilçesine bağlı bir mahalledir.
Tarihçe
Subatan; idari bölüm olarak daha önceleri köy iken, 2012 yılındaki yasa değişikliğinden sonra mahalle olmuştur.
Nüfus
Kaynakça
Tuzlukçu'nun mahalleleri
Evrifaessa Bot tarafından oluşturulan mahalle maddeleri | 40,270 |
vorlesungenber00bianuoft_22 | German-PD | Open Culture | Public Domain | 1,910 | Vorlesungen über Differentialgeometrie; autorisierte deutsche Übersetzung von Prof. Max Lukat | Bianchi, Luigi, 1856-1928 | German | Spoken | 6,820 | 12,062 | Indem wir zum System (1) zurückkehren, sehen wir, dass es in Involution mit allen Flächen konstanter Krümmung K = j- und nur mit diesen ist, d. h. mit den Lösungen (x, y) der Differential- gleichung zweiter Ordnung: rt - s^ cos^ ff Wir machen nun die einfache Bemerkung, dass das System (1) für jede beliebige Fläche S von der Krümmung K = j stets das gleiche bleibt, d. h. also, wenn mit S eine beliebige Verbiegung vorgenommen wird, bei der an jeder Facette f von S die entsprechenden Facetten f', gekoppelt sind. Sodann stellen wir die folgende allgemeine Frage: Zusammen mit einer Fläche S seien oo^ Flächen S^ gegeben, von denen jede punktweise der Fläche S zugeordnet sei, so dass jeder Facette f von S oo^ Facetten f', eine für jede Fläche S^, entsprechen. Nun werde mit der als biegsam und undehnbar aufgefaßten Fläche S eine beliebige Verbiegung vorgenommen, bei der an jeder Facette f die oo- entsprechenden f', gekoppelt sind. Wann wird bei beliebiger Verbiegung der Fall eintreten, dass die oo- Facetten f' stets zu oo- Flächen S^ angeordnet werden können? § 283. Grundlagen für die Theorie der Transformationen B^. Die soeben gestellte allgemeine Frage werden wir nun nicht erörtern, sondern nur eine bemerkenswerte besondere Lösung derselben angeben, die alle Flächen zweiten Grades betrifft und uns eben auf das hyperbolische Paraboloid abwickelbar. Flächen. Transformationstheorie der Biegungsflächen von Flächen zweiten Grades führen wird. Wir gelangen sozusagen von selbst zu dieser Lösung, wenn wir auf die Bäcklund-Transformationen der pseudosphärischen Flächen zurückgehen und die Lage jeder Facette von S und der transformierten Facetten hinsichtlich der imaginären Kugel, auf welche die S abwickelbar sind, geometrisch besser zu kennzeichnen suchen. Die Fundamentalkugel ist hier die imaginäre Kugel vom Radius i: (a) x^2 + y^2 + z^2 = 0. Der Abstand zwischen den Mitteln der Facetten ist konstant, gleich J2cosθ; wird daher S auf die Kugel (a) abgewickelt, so ordnen sich die Mitteln der S^ zu einer konzentrischen Kugelfläche vom Radius ii^sinθ an: (b) x^2 + y^2 + z^2 = 0. Da ferner die Ebenen der S^ die Mittel der beiden Facetten S, S^ enthalten und gegen die Tangentialebenen der Kugel (a) um den Winkel θ geneigt sind, so sind sie vom Mittelpunkte gerade um iRBmθ entfernt und umhüllen demzufolge dieselbe Kugel (b). Nach diesen Vorbemerkungen setzen wir in diesem Ergebnis an Stelle der Kugel (a) eine beliebige Fläche Q zweiten Grades und an Stelle der konzentrischen Kugel (b) eine zweite, aus der zu Q konfokalen Flächenschar zweiten Grades willkürlich herangesetzte Fläche Q', so erhalten wir die uns interessierende Lösung der im vorausgehenden Paragraphen gestellten Aufgabe. Ferner aber gilt, wie im besonderen Fall der pseudosphärischen Flächen, der für uns sehr wichtige Satz: Die transformierten Flächen S' sind ebenfalls auf dieselbe Fläche zweiten Grades Q abwickelbar. Wir formulieren unsere grundlegende Konstruktion ausführlich in der folgenden Weise: Es sei eine beliebige Fläche Q zweiten Grades gegeben, es werde aus der zu Q konfokalen Flächenschar zweiten Grades eine zweite Fläche Q' willkürlich herausgegriffen, und in jeder Facette f von Q mögen o^ Facetten f^ nach folgenden Gesetzen entsprechen: 1) die Mitten F^ der Facetten f^ sollen auf dem Kegelschnitt C, der Schnittkurve der Ebene n von f mit der konfokalen Fläche Q', liegen; 2) die Ebenen n^ der f^ sollen den vom Mittelpunkte F von f an dieselbe Fläche Q' gelegten Berührungskegel umhüllen. Hiernach können wir den grundlegenden Satz unserer ganzen Theorie folgendermaßen aussprechen: Theorem A) Wird die Fläche Q zweiten Grades beliebig in eine Fläche S Kubenform, wobei an jeder ihrer Facetten f die o^ entsprechenden Facetten f^ der oben beschriebenen Konstruktion gekoppelt sind, so ordnet sich die o^-Gesamtheit dieser Facetten f^ nach der Verbiegung auf eindeutig bestimmte Weise zu Flächen Sj an, die alle, ebenso wie S, auf die Ausgangsfläche Q zweiten Grades abwickelbar sind. Zweck der folgenden Untersuchungen ist nun eben, diesen grundlegenden Satz für alle Gattungen von Flächen zweiten Grades zu beweisen und die Folgerungen für die Theorie der Verbiegung dieser Flächen zu ziehen. Zunächst jedoch dürfte es von Vorteil sein, den Wortlaut des Satzes etwas näher zu erläutern. Das Theorem A) gilt für jede beliebige reelle oder imaginäre Fläche zweiten Grades, und wenn auch unser Hauptinteresse sich naturgemäß auf die reellen Biegungsflächen konzentriert, so müssen wir doch ausdrücklich darauf hinweisen, daß diese sowohl für eine reelle als auch für eine imaginäre Fläche vorhanden sein können; und gerade das erste Beispiel, von dem wir ausgegangen sind und das uns den ersten Ring zur Kette der Transformationstheorie geliefert hat, bezieht sich gerade auf die imaginäre Kugel. Vorläufig jedoch bleiben wir bei dem Fall einer reellen und allgemeinen Fläche Q zweiten Grades: dann haben wir jedenfalls reelle Transformationen der Biegungsflächen, wie aus dem allgemeinen Theorem A) leicht folgt. Es ist nämlich notwendig und hinreichend, daß die angegebene Konstruktion den reellen Facetten f von Q reelle transformierte Facetten f' zuordnet, d. h. daß die Mittelsenkrechte und die Ebenen dieser f' reell sind und somit 1) jede Tangentialebene n von Q die konfokale Fläche Q' in einem reellen Kegelschnitt C schneidet, 2) wenn F der Berührungspunkt von n und F' ein beliebiger Punkt auf C ist, durch die Gerade FF' reelle Tangentialebenen sich an Q' legen lassen. Diese beiden Bedingungen sind zusammen offenbar dann und nur dann erfüllt, wenn die Fläche Q' reell ist und reelle Erzeugende hat; also: Um reelle Transformationen der Biegungsflächen einer reellen Fläche Q zweiten Grades zu erhalten, hat und braucht man die konfokale Fläche Q' nur aus der Gattung der Linienflächen zweiten Grades zu wählen. 1) Ist die Fläche zweiten Grades eine spezielle (eine Rotationsfläche), so können die reellen Transformationen fehlen. Das ist z. B. bei einer reellen Engel der Fall, wo die Bäcklund'schen Transformationen ihrer reellen Biegungsflächen immer mit Notwendigkeit imaginär sind. (Kap. XVIII, S. 492.) Kap. 19. Transformationen von der auf das hyperbolische Paraboloid abwickelbaren Flächen. Zu diesen allgemeinen Ausführungen fügen wir noch die folgenden Bemerkungen hinzu. Es sei f^ {F, tc} eine beliebige Facette von Q und jPj^ ein beliebiger Punkt auf dem Kegelschnitt C, der Schnittkurve von t mit Q', welcher die Mitte einer der Facette f entsprechenden Facette /", ist. Die Ebene ^r^ dieser Facette muss Q' berühren und die Gerade FF^ enthalten; folglich ist sie die eine oder die andere der beiden Ebenen, die sich durch FF^ und die eine oder die andere durch Fj^ gehende Erzeugende von Q' legen lassen. Demnach zerfallen offenbar unsere Transformationen eigentlich in zwei Klassen, von denen jede einer der beiden Scharen von Erzeugenden auf Q' entspricht. Nach dieser kurzgefassten Erläuterung der grundlegenden Prinzipien unserer Transformationstheorie gehen wir nun zur systematischen Entwicklung der Theorie über. Zunächst behandeln wir den Fall einer Linienfläche Q zweiten Grades als Fundamentalfläche und können dann die erhaltenen Ergebnisse ohne Schwierigkeit auf die anderen Gattungen von Flächen zweiten Grades übertragen. § 284. Ableitung einiger Fundamentalformeln. Unseren analytischen Entwicklungen legen wir einige einfache Formeln für eine Fläche S zugrunde, die so verbogen wird, daß an jeder Facette f eine Facette f^ fest gekoppelt bleibt und die Verbindungs-Linie FF^ der Mitten die Fläche S in F berührt. Bei jeder beliebigen Verbiegung von S, wo bei die Tangentenstücke FF^ an S gekoppelt bleiben, ist der Ort der Endpunkte F^ eine gewisse Fläche S^ oder gelegentlich auch eine Kurve, und wir müssen zunächst allgemeine Formeln für die Fundamentalgrößen dieser Fläche S^ ableiten. Unter Zugrundelegung eines beliebigen krummlinigen Parameter-Systems (u, v) hat S die erste Fundamentalform: (4) ds^ = F dxi^ + 2 F dudv + G dv^ die bei Verbiegungen sich nicht ändert, und die zweite Fundamentalform: (4*) 1 du^ + 2 F dudv + G dv^ die für jede spezielle Zwischenform von S eine ganz bestimmte ist und deren Koeffizienten D, D', D" nur der Gaußischen und den Codazzi-schen Gleichungen genügen müssen (Kap. IV). Bezeichnen wir für eine solche spezielle Zwischenform von S die Koordinaten von F, F^ mit x, y, Z; x^, y^, z^, so muss die Determinante: Vx Vx-y ^1- dx dy dz du du du dx dv dy dv dz dv verschwinden; demnach ergeben sich die Koordinaten von F^ aus Gleichungen von der folgenden Beschaffenheit: dx, dz, dz wo l, m bestimmte Funktionen der krummlinigen Koordinaten u, v von F bedeuten. Nun weisen wir auf folgende sehr einfache, aber für das weitere wichtige Tatsache hin: Wird die Fläche S irgendwie verbogen, wobei die Tangentenstücke FF^ an S gekoppelt sind, so bleiben die Funktionen l(u,v), m(u, v) in (5) stets dieselben, und umgekehrt. Davon überzeugen wir uns leicht, wenn wir zunächst beachten, daß die Länge von FF^ wegen (5) durch: d = (x^ - xf + (Vi - yf + 1^1 - zf = El^ + ^Flm + Gm^ gegeben ist, so daß sich dieser Wert von d bei Verbiegungen nicht ändert. Bezeichnen wir ferner mit Oj, tOg die Neigungswinkel von FF^ gegen die positiven Richtungen der Parameterlinien v = Const., n = Const., so haben wir: cos a, = X. - xdx El -\- Fm 2^ dy/E du ~ dy cos CO, = X. - xdx Fl-\- Gm Aus diesen Gleichungen geht eben hervor, daß, da d, Oj, cjj ungeändert bleiben, auch für jedes Wertepaar u, v die Funktionen ?, m ungeändert bleiben. Nachdem wir dies festgestellt haben, berechnen wir aus (5) die Differentialquotienten von x^y^yZ^ nach u und v. Dazu brauchen wir nur die Fundamentalformeln (I), S. 88, zu berücksichtigen. Setzen wir: wo die Christoffelischen Symbole sich auf die Fundamentalform (4) beziehen, so ergeben sich, wie man unschwer einsieht, als gesuchte Gleichungen die folgenden: Kap. 19. Transform. B^ d. auf das hyperbolische Paraboloid abwickelbare Flächen. du dv ^ = p|^ + (^1^ + {B'l + B"m)X, du dv ^1 = Ä^-i-B^+ GX, du dv Y. du dv z. du dv nebst analog für y^, z^, die wir weglassen, wie stets in der Folge. These Gleichungen (7) gelten natürlich in allen Fällen, auch wenn für die gerade vorliegende Zwischenform von S die Fläche S^ sich auf eine Kurve zusammenzieht. Nun fassen wir weiter, wie oben gesagt, F^ als Mitte einer Facette f^ auf, deren Ebene tc^ ebenfalls an die Facette /"^ {x, y,z} X,T,Z) bei Verbiegungen von S gekoppelt sei. Dann können wir die Lage der Ebene n^ mittels der Richtungskosinus ihrer Normalen, X^, Y^, Z^, bestimmen, und diese lassen sich in folgender Weise ausdrücken: (8) wo Ä, B, C passende Funktionen von u, v sind. Aus ganz ähnlichen Überlegungen, wie wir sie vorher bei den Gleichungen (5) angestellt haben, geht hervor, daß unter unserer Voraussetzung die Funktionen Ä, B, C von u, v dieselben bleiben, wie auch immer S verbogen werden mag. Nehmen wir nun an, daß in (5) und (8) die Funktionen l, m; Ä, B, C außer den Veränderlichen u, v noch einen willkürlichen Parameter A enthalten, so können wir jeder Facette f von S oo'-Facetten f^ zuordnen, die bei Verbiegungen von S an die entsprechende Facette f gekoppelt bleiben. Dieser Fall tritt gerade bei unseren Anwendungen ein. § 285. Erste Formelgruppe für das hyperbolische Paraboloid. Wir beginnen die Untersuchungen über die Verbiegungen der Flächen zweiten Grades mit den Linienflächen zweiten Grades und haben also zwei Fälle zu unterscheiden: den des hyperbolischen Paraboloids und den des einschaligen Hyperboloids. Im vorliegenden Kapitel behandeln wir den ersten Fall, in dem die Gleichungen etwas grössere Einfachheit aufweisen. Es sei daran erinnert, daß, wenn die Gleichungen (8) als lineare Gleichungen in Ä,B,C aufgefasst werden, die Determinante der Koeffizienten, y/EG - F*, «4=^ i**, die Fundamentalfläche ist also jetzt ein hyperbolisches Paraboloid Pq, dessen Gleichung wir in der gewöhnlichen Form ansetzen, wo die positiven Konstanten p, q die Parameter der beiden Hauptparabeln bedeuten. Wir beziehen Pq auf seine geradlinigen Erzeugenden (Haupttangentenkurven) mittels des Ansatzes: a^o = √(m + v), yq = yq(u - v), Zq = 2uv. In dem Ausdruck für das Quadrat des Linienelements von Pq: d4 = Edu^+2Fdudv + Gdv^, haben hiernach E, F, G die folgenden Werte: E = p + q + 4v^, F = p-q- 4mv, G = p + q + 4mv. Setzen wir: H = p(u - vy + q)(u + vy + pq, so erhalten wir: EG - F^ = 4H. Als Werte für die Richtungskosinus Xq, Yq, Zq der positiven Normalen von Pq finden wir im schwer: Y = Vg (u + v) Y = v / (u + v) Z = vM demnach für die Koeffizienten Dq, Dq, Dq der zweiten Grundform: Dq = 0, Dq = -1, Dq = 0. Die Totalkrümmung K von Pq ist somit gegeben durch: K = EG - F', so daß wir mittels des üblichen Ansatzes erhalten: Endlich müssen wir noch die wirklichen Werte der Christoffelischen Symbole für unser ds^ berechnen. Dieses geschieht unschwer aus den. Kap. 19. Transform. B^, d. auf das hyperbolische Paraboloid abwickelb. Flächen. Gleichungen (10) oder auch mittels der schon angeführten Gleichungen (I), S. 88, und wir finden auf diese Weise: Nun wählen wir aus der konfokalen Flächenschar: die durch Pq bestimmt ist, ein zweites hyperbolisches Paraboloid. Schlaglichte. Dazu müssen wir dem Parameter k einen beliebigen Wert in dem Intervall: — q < h < p erteilen. Dieses konfokale Paraboloid bezeichnen wir mit P^ und bemerken ausdrücklich, daß wir bei den folgenden Rechnungen zwar den Wert: h == 0, für den P^, mit Pq identisch wäre, keineswegs aber die Endwerte: k = — q, lc = p ausschließen. Für diese Werte artet das Paraboloid P^ in die doppelt überdeckten Ebenen: ?/ = 0 bzw. x = 0 oder, besser ausgedrückt, in diejenigen Gebiete dieser Ebenen, welche außerhalb der Fokalparabeln: ?/ = 0, liegen. Die Tangentialebene an P^, in einem Punkt Fq = {xq, yq, zq} schneidet P^ in einem Kegelschnitt C (für die singulären Werte: k = — q, k = p in einer Geraden), und die Koordinaten eines beliebigen Punktes Fq = {Xq, yq, zq} dieses Kegelschnitts C sind, wegen der Gleichungen (5) von der Form: Xq = yq(u - v - 1 - m), yq = zq(u - v - 1 - m), Zq = 2(uv + vi + um). Die Koeffizienten l, m sind bestimmte Funktionen von w, v und eines Parameters X, der den beweglichen Punkt Fq auf dem Kegelschnitt C festlegt. Als diesem Parameter X wählen wir denjenigen einer veränderlichen Erzeugenden von P^, entweder der ersten oder der zweiten Schar. Bezeichnen wir abkürzend mit p',q' die Parameter der beiden Hauptparabeln von P^,, setzen wir also: p'=p-x, q' = a + x, so sind p', q' positiv, und als Gleichungen der Erzeugenden von P^ erhalten wir: WO das obere Vorzeichen der ersten, das untere der zweiten Schar von Erzeugenden zukommt. Setzen wir in letzteren Gleichungen für x, y, z die Werte (16) von Xq, yq, Zq ein, so erhalten wir zwei lineare Gleichungen zur Bestimmung von l und m. Durch Auflösung derselben finden wir: x=Tr' m=Tr' wo TJ, V, W die folgenden Werte haben: V=2(yq'+yW) >^'^' - 2 (yM + Vy) ^^ - W=2X[ypq-VÖF(yp+vy)l±Ypq'(u - vy)X]. Es sei darauf hingewiesen, daß in allen diesen Gleichungen der Übergang von den oberen Vorzeichen zu den unteren einer Vertauschung von u mit v gleichkommt. § 286. Beweis einiger Identitäten. In der Folge werden wir einige grundlegende Identitäten brauchen, die zwischen den eingeführten Größen bestehen und die wir folgendermaßen finden: Lassen wir in (16) X konstant, so durchläuft der Punkt {x^, y^, z^} eine Erzeugende X des Paraboloids P^. Dann können wir die allgemeinen Gleichungen in § 284 auf den jetzt vorliegenden Fall anwenden, in dem sich die Fläche S, auf diese Erzeugende von P^ zusammenzieht. Wegen der jetzt vorliegenden Werte (14) der Christoffel'schen Symbole und unter Einführung der Bezeichnungen: Z_q, M_q, P^, Q^ für die Werte von L, M, P, Q erhalten wir infolge (6): .„.. j " du ' ^ cv ' ' ^ du * * du ^ ^ p _dl 1 g logg; /) _^'» . 1 ^logP; , 1 Kap. 19. Transformation von der Ebene in das hyperbolische Paraboloid abwickelbare Flächen. und die Gleichungen (7) gehen über in: (22) du 0 du ^ -^0 dv Weil jetzt der Punkt {X_q, y^, Z_q} eine (gerade) Linie beschreibt, so haben wir offenbar die Proportionen: du ' du ' du dv ' dv ' dv ' folglich ist wegen (22): Po Qo l' somit haben wir die Identitäten: (23) IL_q - mP^ = 0, lM_q-mQo==0, also auch: (23*) 1(IM_q - mLo) = mQQ^ - mP^). Setzen wir links die Werte für Lq, Mq, Pq, Qq ein, so erhalten wir: Dl, Dm, Dp, Dq sind nach (20) Funktionen von u und v allein; infolgedessen nehmen, weiter ist nach (20) U eine Funktion von u allein (und X), V eine Funktion von v allein (und Y); infolgedessen nehmen, du dv gesetzt, die obigen Identitäten die folgende Gestalt an: Aus ihnen ergibt sich weiter durch Addition die wichtige Beziehung: Diese Identitäten lassen sich übrigens auch direkt auf Grund der expliziten Werte (20) von U, V, W beweisen. Eine weitere Identität, die für die Folge von grundlegender Bedeutung ist, ergibt sich aus dem Vergleich des Wertes von: TU/T und T 1^^ ^^ mit dem Binom: Dividieren wir den zweiten Ausdruck durch den ersten, so erhalten wir nacheinander: Aber aus den expliziten Werten (20) von U, F, W ergibt sich nach kurzer Rechnung die Identität: die wir wegen der vorausgehenden Rechnungen auch in der folgenden äquivalenten Form schreiben können: Machen wir jetzt mit den eben erwähnten Funktionen L, M, P, Q, die auf die Facette alpha abzielen, und mit den dazu gehörigen Differenzen: Sind nun w, u, v, x, z koordinatenähnliche Variablen, welche die Facette alpha betrachten, so erhalten wir durch Einsetzen: setzen wir nun fü x, z die Werte 1, 0 ein, so erhalten wir: Nachdem wir jetzt auf Grund der Werte (19) von L, M, P, Q die Differenzen ausgerechnet haben, erhalten wir für die Orientierung der Facette alpha die folgende wesentliche Beziehung: Machen wir nun für x, z die Werte 0, 0 ein, so erhalten wir nach (25): Für die Orientierung der Facette alpha auf dem mit X, Y, Z koordinatierte Geradkreuz erhalten wir somit die wesentliche Beziehung: Im Anschluss an unsere allgemeinen Ausführungen in § 283 ordnen wir jetzt jeder Facette /x, y, z; X, Y, Z der Parabel Pqq durch die Gleichungen (16) gegeben sind und deren Mittelpunktskoordinaten Xq, yq, Zq durch die Verbindungslinie der Mittelpunkte (xo, yo, zo) und durch die Erzeugende X des konfokalen Paraboloids hindurchgehen. Bezeichnen wir mit X^, Y^, Zy die Richtungskosinus des Lotes auf der Ebene n^ und setzen wir wie in § 284, S. 524, (8), an: X = A^-^ + B^y + CZo usw., so kommt es darauf an, die Koeffizienten A, B, C zu bestimmen. Nun sind die Richtungskosinus der Verbindungslinie der Facettenmitten proportional den Differenzen: Xf. — X = l-^ + m-: usw. Und diejenigen der Erzeugenden k von Pq, sind proportional z. B. den Größen: du ^ dv Wir brauchen also nur Werte, die A, B, C proportional sind, aus folgenden beiden Bedingungen zu berechnen: aus denen sich mit Benutzung der früheren Gleichungen ergibt: (El + Fm)A + (Fl + Gm)B = 0, Daraus folgt: A.B.C = B^m(El + Fm) - B^m(Fl + Gm)(EG - F^)(lM^-mL^), und da nach S. 525: EG-F^=H^, B' = -^ß3 ist, so haben wir, wenn wir mit B, einen Proportionalitätsfaktor bezeichnen: (26) A = R(Fl + Gm), B = B(El - Fm), C = R^2(lM^-mL,). mypq Für den letzten Wert können wir wegen S. 525 auch schreiben: (26*) C = 2BYH- (IM, - mL,) = 2BVH- (IQ, - mP,). Der Wert von B^ folgt weiter aus der Bedingung: ^X,^=l, welche ergibt: EA^ + 2FAB + GB^ + C^ = 1. Wegen (26) aber ist: EA^ + 2FAB + GB' = B\EG - F')(El' + 2Flm + Gm'), und mit Rücksicht darauf, daß der Ausdruck: El' + 2Flm + Gm' ^^(x^ - x)' das Quadrat der Entfernung d der beiden Facettenmitten, 8 == yEP + 2Flm + Gm', darstellt, folgern wir daraus: (27) B' 4^[^* + |^,(Zilf„-mi„)*] § 287. Orientierung der Facetten f^. 531 Bezeichnen wir endlich mit Sl den Neigungswinkel der beiden Facettenebenen, so haben wir: cos iJi =- C demnach: §288. Grundlegende Differentialgleichungen für die Punktion X{U^V). Nach allen diesen vorbereitenden Schritten gehen wir nun daran, die in § 283 in allgemeinen Zügen vorgezeichnete Untersuchung für die Biegungsflächen des hyperbolischen Paraboloids durchzuführen. Wir setzen also voraus, das Paraboloid nehme durch Biegung eine beliebige Gestalt S an, und bei dieser Biegung seien an jede Facette f die oo' entsprechenden, auf die im vorigen Paragraphen angegebene Weise be- stimmten Facetten f^ fest gekoppelt. Dann müssen wir zunächst nach- weisen, daß sich nach derVerbiegung die oo^ Facetten fj zu oo^ Flächen ä^ anordnen lassen. Die Biegungsfläche S ist (gestaltlich) durch ihre beiden Grundformen bestimmt, von denen die erste mit dem Quadrat des Linienelements des Paraboloids, S. 525, übereinstimmt; die zweite bezeichnen wir mit: Bdu' + 2B'dudv - Bdvd^ Die notwendigen und hinreichenden Bedingungen, denen D, D', D" genügen müssen, um auf diese Weise eine Biegungsfläche S des Paraboloids zu definieren, sind nach S. 90 durch die Gauß-Codazzi'schen Gleichungen gegeben, die wegen der Gleichungen in § 285 jetzt die folgende Form annehmen: (Gaußische Gleichung) (29) D^D" - D'^D' = -D^ = -^ , (Codazzi'schen Gleichungen) (30) Nach den grundlegenden Untersuchungen in § 284 sind nach der Verbiegung des Paraboloids P^ in die Fläche S die Koordinaten x, y, z des Mittelpunktes einer beliebigen Facette f^ durch: (31) X = X_ + 1^ + h w, + usw., ^ •^ ^ * du dv gegeben, wo l, m die durch (19), (20), S. 527, bestimmten Werte haben, und die Richtungskosinus X, Y, Z des Lotens auf der Ebene f^ sind: (32) Z = Z_ + 5|f ZOX + usw., wo A, B, C die Werte (26) haben. Diese fünf Größen: l, m, Ä, B, C sind bekannte Funktionen von u, V, X, und lassen wir u, v, A sich ändern, so erhalten wir auf diese Weise im Raum die oo^ Facetten fy. Aus dieser dreifachen Machtigkeit, sondern wir eine zweifache dadurch aus, dass wir X als eine gewisse Funktion von M, X=^X(u,v), ansetzen, und diese unbekannte Funktion X(u, v) müssen wir so bestimmen, dass für die Ortsfläche S^ des Punktes {x^, y^, z^} die Richtungskosinus der Normale gerade die Werte X^, Y^, Z^ haben, was in den folgenden beiden Gleichungen seinen Ausdruck findet: Wir berechnen zunächst nach der Gleichung (7), S. 524, die Differenzialquotienten von x^, y^, z^. Dabei müssen wir beachten, dass jetzt u, V nicht nur explizit auftreten, sondern auch implizit insofern, als sie in X(u, v) enthalten sind. Vergleichen wir demnach die Werte (6) von L, M, P, Q mit den Werten (21) von Lq, M^, Pq, Q^, so haben wir offenbar: V — V _u?^^. infolgedessen lauten die gesuchten Gleichungen: du "3v ' \dXdu dldv/du dx "Tl dx (dl dx dm dx\dl y dv -n dx (öl dx dmdx\dl ^ Pq^ - Qo^ h Ut^ h ^^ö— ö- + (^ t + -O m)A usw. Als Gleichungen (33) erhalten wir: EÄ + FBfl + (FÄ + eB)|^]fi + [( + [(EÄ + FB)L, + (FÄ + GB)Mo] + (Dl + B'm)C = 0, [{EÄ + FB)'l + (FÄ+aB)'^'f^^ + + l(EÄ + FB)P, + (FÄ -h GB) Q,] + (B'l + D"m) 0 = 0. 1) Hiermit schließen wir die Mächten aus, die sich für fest bleibendes oder vergeben; doch kommen solche für unser Problem gar nicht in Frage. § 288. Differentialgleichungen für X(u, v). Nach (26) ist: EB-FB = -Rm(EG - F^) = -ARHm, FA+GB= Bl(EG-F')== 4RHI, und mit Rücksicht auf (26*) bleibt demnach übrig: {«•^- 4f ).l^ - '^» - '"^« + ^ ('^» - •»■^«)(^' + ^''»)' Wegen der Identitäten (25*), vereinfachen sich diese Gleichungen zu den folgenden beiden: (I) du kB 2kyH^ = ^U+(B'U+B"V), dv kB 2kyH = und dieses sind die charakteristischen Differentialgleichungen unseres Problems. Jeder Lösung X(u, v) dieses Simultansystems entspricht eine Fläche S^, welche von c^ Facetten gebildet wird, die unter den oo* Facetten f\ enthalten sind. Diese Grundgleichungen (I) können wir noch in die folgende äquivalente Form einer einzigen totalen Differentialgleichung bringen: (I*) dk=={Vdu+ Udv)-\—[ (D Ü+B' V)du+(B' Ü^B" V)dvl und da nach (20) C/, V Polynome zweiten Grades in A sind, so ist dies eine Differentialgleichung vom Riccatischen Typus. § 289. Unbeschränkte Integrierbarkeit des Gleichungensystems CO. Wir wollen nun beweisen, dass die simultanen Differentialgleichungen (I) oder die totale Differentialgleichung (I*) eine Lösung A mit einer willkürlichen Konstanten besitzt, d. h. dass das System (I) unbeschränkt integrierbar ist. Zu diesem Zwecke bilden wir den Ausdruck: und müssen nachweisen, dass er wegen der Gleichungen (I) identisch gleich Null ist. Als expliziten Ausdruck für fl erhalten wir durch Ausrechnung zumeist: Kap. 19. Transformation des hyperbolischen Paraboloids abwickelbarer Flächen. Nun ist, nach den Verhältnissen zwischen Gleichungen (30): andererseits ergibt sich aus der Gaußischen Gleichung (29), dass die Determinante: ^n-2 di^ü^^ ^I = (D2)^-1(d+1)(f|?-?7|^) = DÜ + D'V D'U+D"V ist. Nach Einsetzen dieser Werte wird Sl ein ganzer linearer Ausdruck in D, D', D": Sl=aD + ßD' + yD" + d. Nach einigen selbstverständlichen Vereinfachungen ergibt sich: cc = y = 0, und daher ist: TT Ziehen wir aber die Identität (25), S. 529, heran, die wegen q = -^ auch die folgende Form annimmt: dV j^dU Je Y-rrtTv , UdH, VdH- so ergibt sich: r+ v+ Tr+ r'^+^(u^- r',^)=U'+ r+2 w, § 289. Unbeschränkte Integrierbarkeit des Systems (T). 535 Darin dieser Ausdruck ist, nach (24*), S. 528, gleich Null. Somit sind auch die Koeffizienten ß, ö gleich Null, also auch identisch: ü = 0, w. z. b. w. Daraus schließen wir: Die grundlegenden Differentialgleichungen (I) bilden ein vollständig integrierbares System. § 290. Transformationen Bk der Biegungsflächen des hyperbolischen Paraboloids. Die Differentialgleichungen (I) besitzen also eine Lösung Ä mit einer willkürlichen Konstanten, für die man denjenigen Wert wählen kann, den man dem Parameter X in einem vorgegebenen Punkt (xq, yq) von S erteilen will, was geometrisch darauf hinauskommt, dass als Ausgangsfasse /jj von S eine von den cx>^ den /i entsprechenden Fassener wählt. Wird dann eine solche Lösung in (31) für l eingesetzt, so gehören alle o*-Fassern der auf diese Weise als Ort des Punktes (Xq, yq, Zq) definierten Fläche S^ der o*-Mannigfaltigkeit der ^ an. Damit ist für das hyperbolische Paraboloid der ganze erste Teil des grundlegenden Satzes A) in § 283, S. 521. bewiesen, und es bleibt noch die weitere wesentliche Eigenschaft zu beweisen, daß jede so erhaltene Fläche Äj, gleichwie S, auf das Paraboloid abwickelbar ist. Den Beweis dieser wichtigen Eigenschaft behalten wir uns für die nächsten Paragraphen vor; vorerst wollen wir aus den schon erhaltenen Ergebnissen einige fast unmittelbare Folgerungen ziehen. Mittels der Differentialgleichungen (I) werden, wie wir gesehen haben, die OO' Facetten f^, die den f von S entsprechen, in OO' Flächen S^ gesondert. Jede von diesen Flächen S^ mag als aus der Ausgangsfläche S mittels der Transformation Bj^ abgeleitet bezeichnet werden, wodurch wir also den Wert des Parameters k hervorheben, der zu dem konfokalen Paraboloid gehört, welches das Gesetz der Zuordnung zwischen den Facetten von S und den OO' f^ bestimmt. Nun bemerken wir: Die Ausgangsfläche S und jede transformierte Sj von ihr sind die beiden Brennmäntel des Strahlen-Systems, das von den Verbindungslinien entsprechender (Brenn-) Punkte auf ihnen, F und Fj, gebildet wird. Denn die Ebenen der beiden Facetten f, f^ schneiden sich eben längs des Strahles FF. Später (§ 296) werden wir sehen, daß die in Rede stehenden Strahlensysteme sämtlich zur Klasse der T^-Systeme (Kap. XII) gehören, d. h. daß auf den Brennmänteln S, Sj, die Haupttangentenkurven (die konjugierten Systeme) einander entsprechen. Hier leiten wir noch eine andere interessante Eigenschaft der Transformationen Bj^ ab, die sich aus der Ricci'schen Form der totalen Differentialgleichung (I*) ergibt. Sind A^, A2, X^, A^ vier partikuläre Lösungen derselben, so ist das Doppelverhältnis (A^, Ag, A3, A^) konstant. Um die geometrische Bedeutung dieser Eigenschaft zu erkennen, beachte man, dass in jeder Tangentialebene je von S der Ort der Mittelpunkte der entsprechenden Facetten ein Kegelschnitt ist, den wir als den der Transformation B; assoziierten Kegelschnitt bezeichnen. Nun ergeben die Gleichungen für jedes feste Wertepaar M, V die Koordinaten eines beweglichen Punktes (x, y, z) des Kegelschnitts Cf, als gebrochene (gleichnamige) Funktionen zweiten Grades von A; infolgedessen ist das Doppelverhältnis von vier Werten von A (Aj, Ag', A3, A4) gleich dem Doppelverhältnis der vier entsprechenden Punkte des Kegelschnitts Cj. Wir haben somit den Satz: Vier aus der Fläche S mittels einer Transformation B; abgeleitete Flächen schneiden die in den Tangential-Ebenen von S liegenden assoziierten Kegelschnitte Cj in Gruppen von vier Punkten konstanten Doppelverhältnisses oder kürzer gefasst: Die Flächen aus der Fläche S mittels der Transformation B; abgeleiteten Flächen schneiden die assoziierten Kegelschnitte projektivisch. Fall, in dem die Biegungsflächen Linienflächen sind. Wir setzen nun im besonderen voraus, dass die Biegungsfläche S des Paraboloids P; selbst eine Linienfläche R sei. Wenn wir R durch stetige Verbiegung auf P; ausbreiten, so decken sich die Erzeugenden g von P mit derjenigen Schar von Erzeugenden auf Pq, die denselben Drehsinn haben wie die Schar g (rechts- bzw. linksgewunden sind; vgl. § 116, S. 222: Um die Ideen zu fixieren, nehmen wir an, es seien die Geraden v = Const. Da dann auf P die Linien v Gerade, also Haupt-Tangentenkurven sind, so haben wir: D = 0 und wegen der Gaußischen Gleichung: Z' = + Do; doch wird die Doppeldeutigkeit des Vorzeichens durch die Annahme gehoben, dass die beiden Scharen von Geraden v auf P und P gleichgerichtet seien, und es ist dann: Die zweite Codazzi'sche Gleichung (30), S. 531, lautet jetzt einfach: dB" _ 1 glogg T)// du 2 aw § 291. Fall, in dem die Biegungsflächen Linienflächen sind. 537 Ihre Integration ergibt: wo g(v) eine willkürliche Funktion von v allein ist, die von der in Rede stehenden speziellen Biegungslinienfläche R abhängt und sie eindeutig bestimmt. Werden nun die jetzt Vorliegenden Werte: D = 0, x' = _^, x" = 2yH.<p(v) in den Differentialgleichungen (I), S. 533, eingesetzt, so gehen diese unter in: x = 0 x = —^^^. Demnach ist X eine Funktion von v allein und wird durch die folgende Differentialgleichung vom Riccati Typus bestimmt (s. (20), S. 527): (36) 8xr^_^^ ^ '' dv Je k Nun beweisen wir, dass im vorliegenden Falle die Linien v auf den transformierten Flächen S^ ebenfalls Gerade sind. Bringen wir eine beliebige Erzeugende v auf Pq mit der entsprechenden Erzeugenden g auf R in der Weise zur Deckung, dass ihre durch die Abwickelbarkeit einander entsprechenden Punkte aufeinander fallen, und lassen wir ferner in einem Anfangspunkte die beiden Tangentialebenen von P^ und R zusammenfallen, so berühren einander Pq und R längs der ganzen Erzeugenden g). Wird nun in den Gleichungen (§287, S. 529): ^n = ^0 + f CS + m-^ usw. "Der Größe v und somit auch der Funktion X(v) ein bestimmter Wert erteilt, so bestimmen diese Gleichungen einen längs der Erzeugenden auf P^ beweglichen Punkt (xq, yq, Zq), und daher bestimmen die Gleichungen (31), S. 531: X. = X + h h ni w- usw. ' ' du ' ' do für denselben bestimmten Wert von v eine Gerade im Raum, nämlich die Lage, welche die Erzeugende A auf P^ einnimmt, wenn mittels Dieses ergibt sich daraus, dass nach der Charakteristischen Formel, S. 228, bei der Bewegung eines Punktes längs g die zugehörigen Tangentialebenen gleiche und gleichgerichtete Drehungen um g vollführen. Kap. 19. Transform. B^ d. auf das hyperbolische Paraboloid abwickelb. Flächen. einer Bewegung Pq zur Berührung mit der Linienfläche R längs der Erzeugenden v gebracht wird. Demnach sind die Linien v = const. auf den transformierten Flächen S^ ebenfalls Gerade, d. h.: Aus jeder Biegungslinienfläche B des hyperbolischen Paraboloids ergeben sich durch die Transformationen B^ wieder lauter Linienflächen R^. Indem wir die obigen geometrischen Überlegungen fortsetzen, nehmen wir an, dass die verschiedenen Erzeugenden auf Pq mit den entsprechenden Erzeugenden auf R zusammenfallen; dann rollt Pq auf der Linienfläche R, die auf Pq abwickelbar ist. Bei diesem Rollen von Pq auf R denken wir uns das konfokale Paraboloid Pq, mitbewegt; seine Erzeugenden (der einen oder der anderen Schar) beschreiben dann eine Strahlenkongruenz F, in der alle Erzeugenden der transformierten Flächen R enthalten sind. Diese Zerfällung von F in die oo^ Linienflächen R ist durch die Bedingung vollkommen bestimmt, dass jede Fläche R und die Fläche jR die beiden Brennmäntel eines Strahlen-Systems sein sollen. Die Zuordnung zwischen den Punkten F von R und Fq von R, wird durch das, dass jedem Punkt F einer Erzeugenden r von R auf Rq derjenige Punkt entsprechen soll, in welchem die Tangentialebene in JP an R die r entsprechende Erzeugende schneidet. Somit können wir im vorliegenden Falle der Biegungslinienflächen die erhaltenen Ergebnisse in dem folgenden Satz zusammenfassen: Rollt das hyperbolische Paraboloid Pq, an welches das konfokale hyperbolische Paraboloid Pq, gekoppelt ist, auf einer beliebigen Linienfläche R, die auf Pq abwickelbar ist, so beschreiben die Erzeugenden (der einen oder der anderen Schar) von Pq eine Strahlenkongruenz, die auf eine einzige Weise in oo^ Linienflächen R zerfällbar ist. Jede Fläche R ist der erste und die Fläche R der zweite Brennmantel eines Strahlensystems, das von den Verbindungslinien ihrer entsprechenden Punkte gebildet wird. Diese oo^ Linienflächen R sind eben die mittels der Transformation Bq, aus der Ausgangsfläche R abgeleiteten Flächen. Wir fügen noch eine Bemerkung hinzu. Schon in § 285, S. 526, haben wir darauf hingewiesen, dass unsere Ergebnisse auch für die Endwerte von h = -q, l = p gelten, für die sich das Paraboloid auf die außerhalb der Fokalparabeln gelegenen Gebiete der Hauptebenen zusammenzieht. Das Strahlensystem F des obigen Satzes wird dann von den Tangenten des Fokalkegelschnitts gebildet, der an das Paraboloid während des Abrollens gekoppelt ist. § 292. Berechnung des Linienelements der transformierten Flächen Si. Wir nehmen die Untersuchung der Transformation B2 für die allgemeinen Biegungsflächen S des hyperbolischen Paraboloids wieder auf, in der Absicht, die schon erwähnte Haupteigenschaft der transformierten Flächen Si, nämlich ihre Abwickelbarkeit auf das Paraboloid, nachzuweisen. Dazu müssen wir vor allem das Quadrat des Linienelements von Si berechnen und dann nachweisen, dass es in ds2, das Quadrat des Linienelements des Paraboloids Pq, transformierbar ist. Wir gehen auf die Gleichungen (34), S. 532, zurück und berechnen die Koeffizienten E2, F2, G2 im Ausdruck: ds2 = E2du2 + 2F2dndu + G2dv2. Wir erhalten zunächst: E, - ELI + 2FLM, + GMI + 2[(EI, + F21f,)||(FL, + C?-Mo)^] + F., - BL,P, + F(L,Qo + J/P,) + GM,Q, + [(EP, + F(?)|| + {FP, + (FP, + G Qof^P, + H^'+ 'Hl -.? + « (t)10'+ (^^ + ^"'»y- Um die Rechnungen zu vereinfachen, fassen wir in diesen Gleichungen den speziellen Fall ins Auge, dass S mit dem Paraboloid P^, identisch ist. Dann ist also: D = 0, B' = D^, D" = 0, 9(t;) = 0, und aus (36) folgt: infolgedessen ziehen sich jetzt die transformierten Flächen S^ auf die Erzeugenden X von P^ zusammen. Bezeichnen wir mit: ^Of Vai ^oi ^oj -^o ^o't ^01 ^01 Vof ^o'i -^o -^o ^o ^o die jetzt vorliegenden Werte für: X y, z; X, Y, Z; x^, y_, z^-, E^, J^, G^, ^ = 0, also X = Const. Kap. 19. Transformation B,^ d. auf das hyperbolische Paraboloid abwickelbar. Flächen. So haben wir zunächst: \[ du + dv + dw, dv + dw + dx, du + dx + dw, ... \] Dann, nach (37): \[ EL, + 2FL, + GM = E - B^m, EL, + (Xo + yo + Zo) + G^ (yo + Zo) = yo - K'^rn, EL, + 2FL, + G^ = G, - B',H \] Nun erhalten wir, auf dieselbe Weise, wie in § 285, für x^, y^, z^, die Werte: \[ x^ = x^i + y^ + z^, aus ihnen ergibt sich weiter durch Differentiation nach w und v (für konstantes A): y'Za + dyo + dz^, i/-r9:so \[ cu - gt; ^ ^ dv + dv - gt; ^ ^ dv \] Bilden wir nun dv \] so erhalten wir an Stelle der obigen Gleichungen die folgenden: \[ P^ + ^^ = A(^(^ + ) + I^) \] \[ Werden andrerseits die Gleichungen (38) nach X, das auf den rechten Seiten nur in Z, m enthalten ist, differenziert, so ergibt sich: \] \[ dXo dl_ dxO + dm dx^ \] Multiplizieren wir hierauf in jedem Gleichungenpaar (43), (43*) die erste Gleichung mit y, die zweite mit -y, und addieren wir, so folgt daraus: \[ Endlich erhalten wir durch Quadrieren von (44) und Addieren: \] \[ EL, + (FL, -2(t)) + (GM -2(t)) + \] Mittels der vorstehend entwickelten Gleichungen gehen die Werte (37) von E1, F1, G^ über in: \[ F, = F, + IxW + XW + i^ (^l^ + f^l^) + 1 * ' \ -^ \ cv du du dv \] Setzen wir in diesen Gleichungen für x-, y die durch die Differentialgleichungen (I) gegebenen Werte ein, so haben wir alle Größen, die zur Berechnung des Linienelements dSi der transformierten Flächen S^ erforderlich sind. (47) { § 293. Die Ivorysche Verwandtschaft und die Abwicklungsfunktionen. Wir müssen nun beweisen, dass dieses Linienelementquadrat der Fläche S in dasjenige des hyperbolischen Paraboloids transformierbar ist, wobei jedem Punkt (m, v) auf S bei der Abwicklung ein passender Punkt (u1, v1) auf Pq entspricht. Dazu muss auch: dsl = Edu1 + 2Fiduidv + G^dvl sein, wo E, F, G die Werte haben (S. 525): E1 = 1 + u + 4tj, F = p - q - 4ui, G = p + q - 4u. Es kommt also darauf an, i, j, v als Funktionen von m, v so zu bestimmen, dass sich die beiden Linienelemente als identisch ergeben. Kap. 19. Transformation der auf das hyperbolische Paraboloid abwickelbaren Flächen. Wollten wir nun hier die allgemeinen Kriterien für die Äquivalenz zweier Linienelementquadrate anwenden (Kap. VII, § 94), so würden wir sehr bald vor äußerst verwickelten Rechnungen stehen, besonders infolge des Umstandes, dass E, F, G die Größen D, D', D" enthalten, die nur soweit bestimmt sind, als sie den Gauss-Codazzi'schen Gleichungen (29), (30) genügen müssen, und daher noch von zwei willkürlichen Funktionen abhängen. Außerdem sollen wir nicht nur die expliziten Abwicklungsformeln: Mj = u^(u, v), Vj = v^(u, v) ableiten, sondern wir sollen auch eine bemerkenswerte geometrische Bedeutung derselben erkennen, die für unsere Theorie von weittragender Bedeutung ist. Infolgedessen stellen wir zunächst die folgenden geometrischen Überlegungen an. Wir betrachten das Strahlensystem FF, dessen Brennreflektor S und S' sind, und breiten S auf dem Paraboloid P aus; dann ist der Brennstrahl FF, der bei der Verbiegung verschoben wird, in seinem einen Endpunkt Tangente des Paraboloids P, und der andere Endpunkt liegt auf dem konfokalen Paraboloid P. Auf diese Weise liefert jeder Punkt F' auf S' einen Punkt Mq auf P. Ist andererseits S^ auf P^ abwickelbar, wie wir behaupten, so wird beim Ausbreiten von S^ auf Pq derselbe Punkt F^ in einen bestimmten Punkt M^ auf P^ fallen, und wir werden bald die gesuchten Abwicklungsformeln haben, wenn es uns gelingt, das geometrische Gesetz der Zuordnung der Punkte M^ und Mq der beiden konfokalen Flächen Pq und P^ zu erkennen. Nun gibt es für die Punkte zweier konfokaler Flächen zweiten Grades eine sehr einfache, sozusagen natürliche Zuordnung: diejenige nämlich, die auf den beiden Flächen durch die orthogonalen Trajectoren der Schar, zu der sie gehören, gekennzeichnet wird. Diese Zuordnung ist bekanntlich einfach eine Projektivität oder auch Verwandtschaft; wir bezeichnen sie als die Ivorysche Verwandtschaft, weil sich Ivory bei Untersuchungen, die auch wir uns weiterhin zuzustellen haben, zu ihr gewandt hat. Eigentlich ist die Abwicklung von S^ auf P^ nur bis auf eine Abwicklung von P^ auf sich selbst bestimmt. Letztere bilden, wie sofort einleuchtet, eine Vierergruppe, entsprechend den drei Substitutionen: m'=u, v'=u; u'=-v, v'=-v, u'=-v, v'=-w; dazu kommt noch die Identität: u'=v, v'=u. Mit dieser Ivorysche Verwandtschaft kann man im Falle der konfokalen Paraboloide die Formeln für die Abwicklung zwischen den beiden Flächen S, S^ finden. Dieser günstige Umstand, der auch in allen übrigen Fälle der Transformationen für die Biegungsflächen der Flächen zweiten Grades eintritt, ist es eben, der unserer Theorie ein verhältnismäßig einfaches Gefüge verleiht. Indem wir vorerst bei dem vorliegenden Fall bleiben, bezeichnen wir mit x, y, z die Koordinaten von M, mit X, y, z diejenigen von M', dann gelten die Gleichungen (38), (41) des vorigen Paragraphen. Wir bezeichnen nun mit |, r, t, die Koordinaten des Punktes M, auf P, der bei der Ivorysehen Verwandtschaft M entspricht, und haben dann: folglich; Sind nun u, v die Werte der krummlinigen Koordinaten u, v im Punkte M, so haben wir wegen (9), S. 525: also: Setzen wir in diesen Gleichungen für z seinen Wert (16), S. 526, als Funktion von u, v ein, so haben wir noch nachzuweisen, daß dann durch diese Formeln die Abwicklungsbeziehung zwischen dem Paraboloid P und der Fläche S ausgedrückt wird. An dieser Stelle wird es notwendig, die beiden Fälle (§ 283), in denen in allen Gleichungen die oberen oder die unteren Vorzeichen gewählt werden, getrennt zu behandeln. Aber eine einfache Überlegung zeigt, daß wir uns auf den ersten Fall (der oberen Vorzeichen) beschränken können, da ja im anderen Falle in (49) nur u und v miteinander vertauscht werden, und andrerseits haben wir schon am Schluss von § 285 gesehen, daß dieser Übergang zu den anderen Vorzeichen auf eine Vertauschung der Veränderlichen hinauskommt. | 40,241 |
https://uk.wikipedia.org/wiki/%D0%92%D0%BE%D0%B4%D1%8F%D0%BD%D0%B0%20%28%D1%81%D1%82%D0%B0%D0%BD%D1%86%D1%96%D1%8F%29 | Wikipedia | Open Web | CC-By-SA | 2,023 | Водяна (станція) | https://uk.wikipedia.org/w/index.php?title=Водяна (станція)&action=history | Ukrainian | Spoken | 71 | 257 | Водяна — проміжна станція 4 класу Полтавського напрямку. Розташована між платформами Садки та Панасівка. Станція розташована у селі Водяне Краснокутського району. На станції зупиняться усі приміські потяги Полтавського напрямку та деякі пасажирські потяги. Станція відноситься до Сумської дирекції Південної залізниці.
Відстань до станції Харків-Пасажирський — 67,2 км..
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Станції Південної залізниці
Транспорт Краснокутського району
Залізничні станції Харківської області | 4,054 |
https://pt.wikipedia.org/wiki/Shido | Wikipedia | Open Web | CC-By-SA | 2,023 | Shido | https://pt.wikipedia.org/w/index.php?title=Shido&action=history | Portuguese | Spoken | 21 | 39 | O Shido é a penalidade mais fraca do judô. É uma advertência que não gera pontos ao adversário.
Pontuações do judô | 1,787 |
https://github.com/Lucas-Kohorst/realized-strangle/blob/master/tests/test_deploy_strategy.py | Github Open Source | Open Source | Unlicense | 2,022 | realized-strangle | Lucas-Kohorst | Python | Code | 284 | 1,360 | from brownie import reverts
def test_constructor(RealVolStrategy, StrikeSelection, vault, gov, keeper):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 2400, 1200, 500, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
assert strategy.vault() == vault
assert strategy.pool() == vault.pool()
assert strategy.baseThreshold() == 2400
assert strategy.limitThreshold() == 1200
assert strategy.maxTwapDeviation() == 500
assert strategy.twapDuration() == 600
assert strategy.keeper() == keeper
assert strategy.optionsPremiumPricer() == "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc"
def test_constructor_checks(RealVolStrategy, StrikeSelection, vault, gov, keeper):
# base_threshold % tickspacing != 0
with reverts("threshold % tickSpacing"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 2401, 1200, 500, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
# limit_threshold % tickspacing != 0
with reverts("threshold % tickSpacing"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 2400, 1201, 500, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
# base threshold less than 0
with reverts("threshold > 0"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, -1, 1200, 500, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
# limit threshold less than 0
with reverts("threshold > 0"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 2400, -1, 500, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
# base threshold greater than pool threshold
with reverts("threshold too high"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 1000000, 1200, 500, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
# limit threshold greater than pool threshold
with reverts("threshold too high"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 2400, 1000000, 500, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
# max_twap_deviation < 0
with reverts("maxTwapDeviation"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 2400, 1200, 0, 600, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
# twap_duration < 0
with reverts("twapDuration"):
strikeSelection = gov.deploy(
StrikeSelection, "0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", 1000, 50)
strategy = gov.deploy(RealVolStrategy, vault, 2400, 1200, 500, 0, keeper,
"0x966878c047e3e4aDa52Baa93A94bc176FF67b2Dc", strikeSelection.address)
| 26,488 |
bub_gb_-CouAAAAYAAJ_15 | German-PD | Open Culture | Public Domain | 1,888 | Wien, 1848-1888. Denkschrift zum 2. december 1888 | Vienna (Austria). Gemeinderat | Hamerling, Robert, 1830-1889 | Zeissberg, Heinrich, ritter von, 1839-1899 | Wirth, Max, 1822-1900 | Weiss, Karl, 1826-1895 | Radler, Friedrich, edler von, 1847- | Glossy, Karl, 1848-1937 | Hannak, Emanuel, 1841-1899 | Zimmermann, Robert, Edler von, 1824-1898 | Lützow, Karl Friedrich Arnold von, 1832-1897 | Falke, Jacob von, 1825-1897 | Hanslick, Eduard, 1825-1904 | Speidel, Ludwig, 1830-1906 | Richter, Heinrich, ritter von, 1841- | Uhl, Friedrich, 1825-1906 | German | Spoken | 8,322 | 18,019 | Conservatorium für Musik und darstellende Kunst der Gesell- schaft der Musikfreunde. I. Künstlergasse 3. (5. Jänner 1870 Schluss- steinlegung.) A.: Th. Freih. v. Hansen. B.: H. R. v. Förster und Ant. Dietrich. Giebelgruppe von F. Melnitzky. Statuen der Compo- nisten an der Facade von V. Pilz. Deckengemälde des Saales von Eisenmenger. Kosten: fl. 1,040.360. Bildungs- und Fachschule des Wiener Frauen-Erwerb- vereines. VI. Rahlgasse 4. (1 1. October 1874 eröffnet.) A.: Ladislaus v. Mojsisovics. Kosten: fl. 220.000. Technologisches Gewerbemuseum des n.-ö. Gewerbe- vereines. IX. Währingerstrasse 59. (1879.) Das Gebäude war früher ein Bestandtheil der Sigl'schen Maschinenfabrik. Schulhaus der evangelischen Gemeinde. IV. Techniker- strasse. (5. Juni 1862 Schlusssteinlegung.) A.: Th. Freih. v. Hansen. B.: Karl Lütge. Statuen des Portales von V. Pilz. Kosten: fl. 326.140. Oesterr. israel. Taubstummen - Institut. III. Rudolfs- gasse 22. Israel. Blinden-Institut in Heiligenstadt 32. (1. December 1872 Schlusssteinlegung.) A.: \V. Stiassny. B.: A. Schegar. Nebstdem erbauten die evangelische Cultusgemeinde und die israelitische Cultusgemeinde Volksschulen. Theater. Hofoperntheater. I. Opernring. ^25. Mai 1869 Eröffnung.) A.: E. van der Null und A. v. Siccardsburg. B.: J. Hlawka. Grössere Bildhauerarbeiten von V. Pilz, H. Gasser, Bauer und Hähnel. Male- reien von Rahl, Griepenkerl, Bitterlich, Swoboda, Geiger, Dobya- schofsky, Rieser und Zimmermann. Malerei im kaiserl. Foyer von Ed. v. Engerth und jene in der Loggia von M. v. Schwind. Die Kosten bestritt der Stadterweiterungsfond; diese beliefen sich auf fl. 6,117.541. Digitized by Google 3<>4 — Hofburgtheater. I. Franzensring. (24. November 1874 be- gonnen. 14. October 1888 eröffnet.) A.: Kar) Freih. v. Hasenauer. B. : Schieder. Bildhauerarbeiten von: J. Bayer, J. Benk, K. Costenoble, A. Drill, J. Fritsch, E. Hofmann, J. Kalmsteiner, R. Kauffungen, F. Koch, O. König, J. Last, J. Pechan, E. Pendl, J. Silbernagel, V. Tilgner. P. Wagner, Rudolf Weyr. Malereien: von Burghart, H. Charle- mont, J. Fux, K. Eisenmenger, K. Geiger, V. Hynais, K. Karger, Gebrüdern Klimt und Matsch. Die Kosten bestreitet der Stadterweite- rungsfond; dieselben betrugen bis Ende 1887: fl. 6,360.667. Hoftheater-Decorationen-Depöt. VI. Dreihufeisengasse 8. (Begonnen: 5. April 1875. Vollendet: 10. Juli 1877.) A.: K. Freih. v. Hasenauer. Kosten: fl. 689.748. Stadttheater. 1. Seilerstätte. (15. September 1872 eröffnet.) A.: F. Fellner. B.: Ed. Kaiser. Figuren an der Aussenseite von Mel- nitzky. Deckengemälde des Zuschauerraumes von Schwemminger. Das Theater brannte am 16. Mai 1884 ab und wurde von Ronacher in das am 21. April 1888 eröffnete Vergnügungs-Etablissement um- gestaltet. Kosten des neuen Etablissements: fl. 1,400.000. Komische Oper (Ringtheater). I. Schottenring. (17. Jänner 1874 eröffnet.) A. : Emil R. v. P'örster. B. : Wiener Bauverein. Bildhauerarbeiten von E. Hellmer, S. Schönfeld, Schroffl und F. Steger. Malerei des Plafonds von Ig. Schönbrunner. Kosten: fl. 930.000. Das Theater brannte am 8. December 1881 ab. An dessen Stelle erhebt sich heute das vom Kaiser gestiftete Sühnhaus, erbaut von Friedr. Freih. v. Schmidt. Treumann-Theater iprov.). I. Franz Josephs-Quai. Nieder- gebrannt am 8. Juni 1863. Deutsches Volkstheater. VII. Hofstallstrasse. (1888.) A. : Fellner und Helmer. Im Bau. Harmonietheater. IX. Harmoniegasse. (20. Jänner 1866 eröffnet.) A.: Weiss und Dräsche. Wurde im August 1868 in das »Orpheum« umgestaltet. Oeff entliehe Denkmale. * Reiterstatue des Erzherzogs Karl am äusseren Burgplatz. (12. Jänner 1863 enthüllt.) Von Kaiser Franz Joseph I. errichtet. Bildhauer: R. v. Fernkorn. Kosten: fl. 294.378. (Zum Gusse wurden 350 Centner Kanonenmetall aus dem Arsenale unentgeltlich über- lassen.) Digitized by Google 305 Reiterstatue des Prinzen Eugen am äusseren Burgplatz. (13. October 1865 enthüllt.) Vom Kaiser Franz Joseph I. errichtet. Bildhauer: R. v. Fernkorn. Kosten: fl. 310.953. (Zum Gusse wurden 448 Centner Kanonenmetall aus dem Arsenale unentgeltlich über- lassen.) Donauweibchen (Brunnendenkmal). Stadtpark. (30. September 1865 enthüllt.) Von der Gemeinde errichtet. Bildhauer: Hanns Gasser. Kosten: fl. 5690. Brunnen an der Augustiner-Rampe. (24. December 1869 enthüllt.) Aus dem Stadterweiterungsfonde errichtet. A.: M. R. v. Lohr. Bildhauer: J. Meixner. Kosten: fl. 160.262. Reiterstatue des Fürsten Karl Schwarzenberg. I. am Schwarzenbergplatz. (20. October 1867 enthüllt.) Vom Kaiser Franz Joseph I. errichtet. Bildhauer: F. Hähnel. Kosten: fl. 15.000 preuss. Reichsthaler und fl. 67.854 ö. W. (Zum Gusse wurden 200 Centner Kanonenmetall aus dem Arsenale unentgeltlich überlassen.) Schubert-Denkmal im Stadtpark. (15. Mai 1872 enthüllt.) Vom Wiener Männergesang -Vereine errichtet. Bildhauer: K. Kund- mann. Kosten: fl. 26.700. Schiller-Standbild am Schillerplatz. (10. November 1876 enthüllt.) Vom Schiller -Comit^ errichtet. Bildhauer: Schilling in Dresden. Zelinka-Büste. Im Stadtpark. (3. Mai 1877 enthüllt.) Vom Verein der Fortschrittsfreunde der inneren Stadt errichtet. Bildhauer: F. Pönninger. Beethoven-Standbild. I. am Beethovenplatz, (i. Mai 1880 enthüllt.) Von Verehrern des Tondichters errichtet. Bildhauer: K. Zumbusch. Kosten: fl. 95.000. Maria The resien-Denkmal. I. vor den k. Museen. (13. Mai 1888.) Errichtet aus dem Stadterweiterungsfonde. Architektur v. K. Freih. v. Hasenauer. Bildhauer: K. Zumbusch. Kosten: fl. 820.000. Grillparzer-Standbild. I. im Volksgarten. Wird im Jahre 1889 aufgestellt. Von Verehrern des Dichters errichtet. Bildhauer: R. Weyr. Tegetthoff-Denkmal. II. Praterstern. (October 1886.) Von einem hierzu gebildeten Comite' errichtet. Bildhauer: K. Kundmann. Kosten: fl. 248.727. Ressel-Standbild. IV. Technikerstrasse. (18. Jänner 1863.) Von einem hierzu gebildeten Comitö errichtet. Bildhauer: Ritter v. Fernkorn. 1. 20 Digitized by Google 3oö — Gänsemädchen. (Brunnendenkmal.) VI. Kahlstiege. Von der Gemeinde errichtet. Bildhauer: J. Wagner. Das Denkmal wurde im Jahre 1865 für den Brunnen auf der Brandstätte ausgeführt. Nach Verbauung der letzteren kam das Denkmal im Jahre 187g vor die Pfarrkirche in Mariahilf und nach der Aufstellung des Haydn-Denk- males daselbst (18871 au^ seinen gegenwärtigen Standort. Haydn-Standbild. VI. Mariahilferstrasse (31. Mai 1887 ent- hüllt.) Von Verehrern des Tondichters errichtet. Bildhauer: H. Natter. Kosten: fl. 14.000. ■ Brucken. a) Ueber den Hauptstrom der Donau. Eisenbahnbrücke der österr. Staatseisenbahn-Gesell- schaft bei Stadlau. (8. November 1870 eröffnet .» Ing.: C. v. Huppert. Kosten: fl. 2,100.000. Eisenbahnbrücke der Kaiser Ferdinands-Nordbahn. II. (11. Februar 1874 eröffnet.) Eisenbahnbrücke der Nordwestbahn. II. (Mai 1872 er- öffnet.) Ing.: Morawitz. Kosten: fl. 1,671.000. Kaiser Franz Josephsbrücke. II. (18. August 1874 eröffnet. 1 Aus dem Donauregulirungstonde erbaut. Ing.: K.Hornbostel. Zu den Kosten dieser Brücke leistete die Gemeinde einen Beitrag von fl. 217.740, damit auch ein Gehweg hergestellt wurde. Gesammt- kosten: fl. 2,462.000. Kronprinz Kudolfs- (Keichs-i Brü cke. II. (2!. August 1S76 eröffnet.) Vom Staate erbaut. Kosten: tl. 3,482.172. b) Ueber den Donaucanal. Franzenskettenbrücke. (2. September 1860 eröffnet.) Vom Staate erbaut. Ing.: F. Schnirch. Dieselbe wurde im Jahre 1S84 nach einem Plane des A. de Serres umgebaut. Aspernbrücke. (30. November 1864 eröffnet.) Aus dem Stadt- erweiterungsfonde erbaut. Ing.: Fillunger und Schnirch. Figuren der Stützpfeiler von F. Melnitzky. Kosten: fl. 383.563. Brigittabrücke. (Ende December 1871 eröffnet.) Von der Gemeinde erbaut. Ing.: Köstlin und Battig. Kosten: fl. 288.680. Sofienbrücke. (Ende Juli 1872 eröffnet.) Von der Gemeinde erbaut. Ing.: Köstlin und Battig. Kosten: fl. 323.990. Digitized by Google 307 Donaucanalbrücke der Staatseisenbahn. Bei Stadlau. (1870.) Kosten: fl. 184.500. Kaiser Josefsbrücke. (1873 eröffnet.) Von der Gemeinde er- baut. Nach Plänen der Firma Fives Lille. Kosten: fl. 244.450. Augarte n brücke. (6. Juni 1873 eröffnet.) Von der Gemeinde erbaut. Ing. : Baurath: F. Paul. Kosten: fl. 401.930. Stefaniebrücke (15. Mai 1886 eröffnet.) Von der Gemeinde erbaut. A. : Hieser und Liss. Kosten: fl. 568.890. c) Leber den Wienfluss. (Sämmtliche Brücken wurden von der Gemeinde erbaut.) Elisabethbrücke. (23. April 1854 eröffnet.) A.: Ludwig Förster. Kosten: fl. 431.460. Die Brücke wurde vom älteren Wiener Kunstverein mit acht Standbildern geschmückt, deren Ausführung den Bildhauern: Cesar, Fessler, Jos. Gasser. H. Gasser, F. Melnitzky. V. Pilz, Preleuthner und J. Purkartshofer übertragen wurde. Die Auf- stellung der Standbilder erfolgte 19. November 1867. Radetzkybrücke. (16. October 1855 eröffnet.) Ing.: J. H. Mack. Kosten: fl. 406.340. Schwarzenbergbrücke. (11. November 1853 eröffnet.) Ing.: Hornbostel und Kuhn. Kosten: fl. 307.760. Nevillebrüccke. (1856.) Ing.: Neville. Kosten: fl. 173.780. Leopoldsbrücke. (r86o.) Kosten: fl. 69.240. Karo linenbrücke. (29. September 1863 eröffnet.) Kosten: fl. in. 000. Magdalenenbrücke. (8. Juli 1865 eröffnet.) Kosten: fl. 48.810. Pilgrambrücke. ( i 1. Februar 1867 eröffnet.) Kosten: fl. 90.460. Zollamtsbrücke. (4. Februar 1868 eröffnet.) Kosten: fl. 7100. Tegetthoffbrücke. (14. Jänner 1872 eröffnet.) Ing.: Köstlin und Battig. Kosten: fl. 265.780. Viehtriebbrücke. Bei der Gumpendorfer Linie. (1873.) Kosten: fl. 13.390. Die Versicherungs- und Regulirungsbauten an dem Wienflusse kosteten der Gemeinde in den Jahren 1848— 1886 fl. 1,390.670. Eisenbahnhöfe. Kaiserin El i sab et h -West bahn. Vor der Mariahilferlinie. 1858. A.: Moritz Lohr, Patzelt. Bayer und Thienemann, B.: L. Mayr. Statue im Vestibüle von H. Gasser. Kosten: fl. 1,225.000. 20* Digitized by Google J08 Kaiser Ferdinands-Nordbahn. IL Nordbahnstrasse. Umbau des Bahnhofes. (15. October 1865 vollendet.) Pläne und Details der Gebäude von Th. Hofmann, der Personenhalle von Joh. Hermann. — B.: Uebell und Frauenfeld. Figuren-Bildhauerarbeiten von Mitterlechner und Schönthaler. Fresken des Hofsalons von Schwenningen Kosten des Bahnhofes: fl. 1,975.000. Staatseisenbahngesellschaft. Vor der Belvederelinie. Um- bau des Bahnhofes (24. November 1870 vollendet.) A.: K.Schumann. B.: Ferd. Hauser. Figuren über dem Haupteingange von F. Melnitzky. Kosten: fl. 1,290.000. Kaiser Franz Josefsbahn. IX. Aiserbachstrasse. (23. Juni 1870 eröffnet.) Weitere Daten standen nicht zu Gebote. Nordwestbahnhof. II. Taborstrasse. (1. Juni 1872 eröffnet.) A.: W. Bäumer. B. : G. Bucher. Bildhauer: F. Melnitzky und Schön- thaler. Malerarbeiten von Burghart, Isella und Held. Südbahnhof. Vor der Favoritenlinie. (1873 Eröffnung der er- weiterten undtheilweise umgebauten Personenhalle.) A.: Wilh. Flattich. Bildhauerarbeiten von Leimer und Strictius. Die Kosten der Er- weiterungsbauten des bis zum Matzleinsdorfer Viaduct reichenden Bahnhofes betrugen seit der Concessions-Urkunde der Gesellschaft, d. i. seit dem Jahre 1838 bis Ende 1887 fl. 4,838.350. Wien-Aspangbahnhof. III. Canal. (7. August 188 1 eröffnet.» A.: Franz R. v. Gruber und Alois Vielkind. B.: H. Skala. Kosten: fl. 975.7 10. Ausstellungsgebäude. Gebäude der Gartenbaugesellschaft. I. Parkring. (14. De- cember 1864 eröffnet.) A.: Aug. Weber. Basreliefs von Mitterlechner. Künstlerhaus. Lothringerstrasse (1. September 1868 eröffnet.) A.: A. Weber. Erweiterungen des Baues im Jahre 1883 nach Plänen der Architekten Schachner und Streit und im Jahre 1887/88 nach Plänen des Architekten Deininger. Festbauten für das allgem. österr. Bundesschiessen. II. Prater (1868.) A.: M. Hinträger. Weltausstellungsgebäude. II. Prater. (1. Mai 1873 vollendet.) A.: Karl Freih. v. Hasenauer. B.: Ed. Kaiser, Bosch, Stach und Halmschläger. Eisenconstructionen von Harkort auf Harkoten im Kheinpreussen. Die Rotunde mit Benützung einer Idee des englischen Architekten Joh. S. Rüssel erbaut. Kosten des ganzen Weltausstellungs- Digitized by Google 309 palastes: fl. 6,658.470, wovon jene der Rotunde: fl. 1,850.530. der Maschinenhalle (heute städt. Lagerhaus): fl. 1,448.800 und der Amateurpavillons: fl. 544.720 betrugen. Einzelne Bankgebäude, Börse, Geschäfts- und Waarenhäuser, Nationalbank. (Neues Gebäude.) I. Strauchgasse. (3. October 1859 eröffnet.) A.: H. Freih. v. Ferstel. Basreliefs von J. Gasser und F. Melnitzky. Fresken auf der Bazarstiege von K. Geiger. Brunnen von A. Ritter v. Fernkorn. Kosten fl. 1,897.600. Creditanstalt für Handel und Gewerbe. I. Hof. (1858 bis 1860.) A.: Franz Fröhlich. B.: Ant. Oetzelt. Figuren der Facade von Hans Gasser. Kosten: fl. 2,000.000. Neben-Gebäude der Nationalbank. I. Bankgasse. ^876.) A.: Friedr. Freih. v. Schmidt. Kosten: fl. 741.800. Börse. I. Schottenring. (19. März 1877 eröffnet.! A. : Theoph. Freih. v. Hansen. B.: Allgemeine österr. Baugesellschaft. Gruppen an den Facaden von V. Pilz. Figuren von J. Beyer, A. Düll, Th. Friedel, Haag, H. Härdtl, Koch, Purkartshofer, V. Römer, K. Schwerzek. Kosten: fl. 4,000.000. Aziendahof. I. Graben 31. (1867.) A.: K. Freih. v. Hasenauer. B. : Ed. Kaiser. (Erste Facade eines Privathauses mit Marmor- bekleidung und erste Abdeckung des Hofes mit einer Glaskuppel.» Geschäftshaus der Allgemeinen Assecuranzgesell- schaft. I. Bauernmarkt 2. (1880.) A.: O. Thienemann. Bildhau^-- arbeiten von R. Weyr und C. Feldscharek. Kosten: fl. 622.000. Geschäftshaus des Giro- und Cassen Vereines. I. Rock- gasse 4. (188 1.) A.: Emil Ritter v. Förster. B.: A. Schuhmacher. Bildhauerarbeiten von A. Szily. Kosten: fl. 645.038. Geschäftshaus der Länderbank. I. Hohenstaufengasse 3. 11882.) A.: Ö. Wagner. B.: Dehrn und Olbricht. Bildhauerarbeiten von J. Benk. Kosten: fl. 1,005.334. Geschäftshaus der Verkehrsbank. I. verlängerte Wipplinger- strasse 28. (1875.) A.: F. Schachner. B.: A. Schuhmacher. Bildhauer- arbeiten von J. Pokorny. Kosten: 1,259.367. Geschäftshaus der Escomptegesellschaft. (1884.) I. Kärntnerstrasse 7. A.: Gross und Jellinek. Bildhauerarbeiten von A. Szily. Kosten: fl. 460,911. Geschäftshaus der Bodencreditanstalt. I. Teinfaltstrasse 6. A.: E. Ritter v. Förster. B.: Schumacher. Bildhauerarbeiten von A. Szily. Digitized by Google 3io Geschäftshaus der Firma Ph. Haas. I. Stock im Eisen- platz i. (1867.) A.: v. Siccardsburg. B.: Wasserburger. Kosten: fl. 1,050.000. Geschäftshäuser der Firma Gebrüder Thonet. (1881 I.Brandstätte 2 und Kärnthnerstrasse 16 — 18. A.: Helmer & Fellner. Kosten: fl. 745.391 und fl. 729.695. Gesc häftshaus der Firma E. Wah liss. I. Kärnthnerstrasse 17. (1879.) A.: G. Korompay. B.: Joh. Görlich. Bildhauerarbeiten von F. Koch. Kosten: fl. 550.000. Geschäftshaus der Firma Kranner. I. Stefansplatz 10. (1879.) A.: Ferd. Hauser. Geschäftshaus des Freiherrn von Königswarter. I. Kärnthnerstrasse 43. (1882.) A.: W. Stiassny. Kosten: fl. 160.000. Geschäftshaus der Firma Haas & Czizek. I. Kärnthner- strasse 5. (1883.) A.: Clauss & Gross. Bildhauerarbeiten von Hutterer. Malereien von Wild & Weygand. Kosten: fl. 400.000. Geschäftshaus der Firma Rothberger. I. Stefansplatz 9. (1886.) A.: Fellner & Helmer. B.: J. Matasek. Geschäftshaus der Versicherungsgesellschaft >Equi- table«. I. Stock im Eisenplatz. (Im Bau.) A.: Andr. Streit. Trödlerhalle. IX. Hahngasse. Eigenthum der Hallen-Trödler- gesellschaft. (16. October 1864 eröffnet.) Kosten: fl. 243.000. Einzelne Gasthofe. Imperial. I. Kärnthnerring 16. (1864— 1866.) Ursprünglich Palais des Herzogs Philipp v. Württemberg. Von Ing. Zenetti in München erbaut. Innere Decoration und architektonische Ausstattung vom Arch. Heinrich Adam in Wien, (i 864 — 1866.) In den Räumen des ersten Stockwerkes eine der ersten Anwendungen des Stils Ludwig XV. Die Kosten der ersten Anlage des Palais betrugen: fl. 1,600.000. Grand Hötel. I. Kärnthnerring 9. (1866.) A. und B.: Karl Tietz. Deckengemälde von A. Eisenmenger und Wandgemälde von Bitterlich. Metropole. I. Franz Josefs-Quai 19. (1873.) A.: Ed. Kaiser. Kosten: fl. 4.000.000. Sacher. I. Augustinerstrasse 4. (1875.) A.: W. Fränkel. B.: Unionbaugesellschaft. Kosten: fl. 520.000. Royal. I. Singerstrasse 3. (1879.) A. und B.: D. Sturany. Digitized by Google Hotel de France. I. Schottenring. (1873.) A.: A. Fröhlich. B.: Oetzelt. Kosten: fl. 430.000. Tegetthoff. I. Johannesgasse 23. (1872.) A.: L. Tischler. B. : Wiener Baugesellschaft. Kosten: fl. 430.000. Continental. (Goldenes Lamm.) II. Praterstrasse 7. Erweiterung. A. : A. v. Baumgartner, üesammtkosten des alten und neuen Ge- bäudes: fl. 2,864.493. Englischer Hof: VI. Marian ilferstrasse 81. U867.) A. : F. Fröhlich. B.: F. Neumann u. J. Midschke. Kosten: fl. 160.000. Kummer. VI. Mariahilferstrasse 71a. A.: Tischler u. Quidenus. B. : Wiener Baugesellschaft. Kosten : fl. 400.000. Holl er. VII. Burggasse Nr. 2. (1873.) A. und B.: J. Schenk. Kosten: fl. 645.000. Oeffenttiche Gärten der Gemeinde. Garten am Franz Josefs-Quai. I. (1861.) A.: Kosenthai. Kosten: fl. 48.000. Stadtpark. I. Parkring. (21. August 1862 Eröffnung eines Theiles des Parkes.) Nach einer Grundidee des Malers Selleny von dem Stadtgärtner Rudolf Siebeck ausgeführt. Grösse: 18.000 Qua- dratklafter. Den Cursalon daselbst erbaute 1867 A.: J. Garben, die Gemälde des Saales von Maler Otto. Kosten des Parkes und der Anlagen am rechten Wienflussufer fl. 468.390, des Cur- salons: fl. 394.930. Kinderpark. I. Lastenstrasse, nächst dem Stadtparke. (3. Mai 1863.) A.: K. Siebeck. Garten am Rudolfsplatz. I. Rudolfsplatz. (1863.) Reservegarten. III. Lastenstrasse. (1867.) Kosten: fl. 107.390. Garten zwischen der Elisabeth- und Schwarzenberg- brücke. (1869.) A.: R. Siebeck. Kosten: fl. 50.783. Garten am Rathhausplatz. (14. Juni 1873 Eröffnung der Ostseite, 1885 Eröffnung der Südseite. A.: R. Siebeck und Sennholz. Kosten: fl. 238.000. Garten am Schillerplatz. (1874.) A.: R. Siebeck. Kosten: fl. 12.232. Garten am Beethovenplatz. ( 1 879.) A.: Loth. Abel. Garten am Börseplatz. (1879.) A.: Stadtgärtner Maly. Kosten: fl. 8136. Garten am Reichsrathsplatz. 11884.) A.: Seidl. Kosten: fl. 28.480. Digitized by Google 312 Garten vor der Votivkirche. (1876.) A.: L. Abel. Kosten: fl. 87.510. Garten vor dem polytechnischen Institute. IV. Techniker- strasse. (1864.) Kosten: fl. 14.130. Esterhazygarten. (Früher Privatgarten.) VI. Mariahilferstrasse. (11. Mai 1868 eröffnet.) Garten, VII. Hofstallstrasse. (Mai 1866 eröffnet.» Seit 1888 nicht mehr bestehend. An dieser Stelle wird das Deutsche Volks- theater erbaut. Schönborngarten. (Früher Privatgarten.) VIII. Florianigasse. (1863.) Kosten: fl. 11 2.5 10. Ausser den städtischen Gärten kommen noch in Betracht die Erweiterung des kais. Volksgartens ( 1 865,) die Gartenanlagen vor den kais. Hofmuseen (1884), die Umgestaltung des oberen Praters aus den Mitteln des Weltausstellungsfonds (1873) und die Anlage des von einer Privatgesellschaft geschaffenen Thiergarten im Prater, welcher am 25. Mai 1863 eröffnet, am 1. September 1866 geschlossen und am 1. Mai 1868 neuerdings eröffnet wurde. Die Gemeinde errichtete überdies noch zahlreiche Kinderspiel- plätze in den verschiedenen Bezirken. Bäder, a) Der Gemeinde. Städtisches Bad. Rechtes Donau-Ufer, bei der Kronprinz Rudolfsbrücke. (1876.) A.: Baudirector F. Berger. Kosten: fl. 828.830. Städtisches Bad. Linkes Donau-Ufer, bei der Kronprinz Kudolfsbrücke. 11875.) Volksbad. VII. Mondscheingasse (1887.) b) Des Staates. Militär-Schwimmschule. II. Rechtes Donau-Ufer, oberhalb der Stadlauerbrücke. (1876.) A.: Theodor Kadarz. c\ Der Privaten. Concordiabad. I. Franz Josefs-Quai, nächst der Stelanie- brücke. (1876.) Dianabad. II. Obere Donaustrasse. Vergrösserung. (1879). A. : (). Wagner. Kosten : fl. 250.000. Bad zum weissen Wolfen. II. Obere Donaustrasse Nr. 81. <i 867.) d by Google SK\ — Kömisches Bad. II. Kleine Stadtgutgasse 9. (1873.) A.: Clauss und Gross. Holzer'sches Bad. II. Linkes Donau-üfer, unterhalb der Kronprinz Rudolfsbrücke. (1876.) Josefsbad. III. Sofienbrückengasse 12. (1885.) A. und B.: J. Mareck. Kosten: fl. 135.000. Margarethenbad. V. Wildemanngasse 5. {1872.) A.: August Weber. B. : V. Schwerdtner. Kosten: fl. 245.000. Esterhazybad. VI. Gumpendorferstrasse 59. (1851.) Kosten mit Einschluss der späteren Erweiterungen: fl. 280.000. Giselabad. X. Raaberbahngasse 15. (1876.) Marktgebäude und Marktplätze der Gemeinde. Grossmarkthalle. III. Landstrasse, Hauptstrasse. (31. October 1865 eröffnet.» A.: C. Gabriel und F. Stach. Erbaut wurde sie für Zwecke einer Central-Markthalle. Im Jahre 1868 wurde letztere in eine Grossmarkthalle umgewandelt. Kosten: fl. 585.210. Detail- Markthallen: I. Zedlitzgasse. (1. August 1871 eröffnet.) Kosten fl. 320.750. I. Doblhoffgasse. (23. October 1880 eröffnet.) A.: F. Paul. Kosten: fl. 108.950. IV. Phorusplatz. (November 1880.) A.: Friedr. Paul. Kosten: fl. 77.080. VI. Esterhazygasse. (1. December 1877 eröffnet.) Kosten: fl. 52.000. VII. Neustiftgasse. (November 1880 eröffnet.) A.: F. Paul. Kosten: fl. 240.no. IX. Aiserbachstrasse. (23. October 1880 eröffnet.) A.: F. Paul. Kosten: fl. 135.070. Fisch halle. I. Franz Josefs-Quai. (iu. April 1875 eröffnet.) Central-Viehmarkt. III. Nächst der St. Marxerlinie. (31. März i8*S4 eröffnet.) A.: Frey. Kosten: fl. 3,021.940. Lagerhaus. II. Prater. 123. August 1876 eröffnet. Dasselbe war die Maschinenhalle der Weltausstellung, wurde der Gemeinde auf ihr Ansuchen vom Kaiser am 19. Februar 1876 zur Errichtung eines Lagerhauses übergeben. Die Einrichtungskosten betrugen : fl- 737-850. Digitized by Google 3M Marktplätze. Derlei Plätze wurden neu errichtet: Im II. Be- zirke, am Brigittaplatz (1874/ und in der Franzensbrückengasse (1874 : im III. Bezirke, nächst der Cigarrenfabrik am Rennweg. am Paulusplatz und am Radetzkvplatz 11875); im IV. Bezirke, am Karolinenplatz (18691: im V. Bezirke, am Hundsthurm-Schlossplatze 118631, >n de»' Reinprechtsdorferstrasse für Heu, Stroh, Kalk und Kohlen, Körner- Früchte und Kraut 11863» und für den Verkauf von Pferden 11884 am Bacherplatz (1881); im X. Bezirke, am Eugenplatz '1877.1 Armenhäuser, Waisenhäuser, Asyle der Gemeinde. Bürgerversorgungshaus. IX. Währingerstrasse. 11860.1 A.: F. Fellner. Kosten: fl. 726.036. Allgemeines Versorgungshaus. IX. Spitalgasse. Erbauung des rückwärtigen Hauptgebäudes in den Jahren 1848 — 1850 nach Plänen des A.: Florian Schaden. Am 20. Juni 1868 fand die Eröff- nung des vorderen, nach Plänen des Bauamts-Ingenieurs Rudolf Niernsee erbauten Hauses statt. Kosten: fl. 797.560. Waisenhäuser: V. Gassergasse 1. \ 20. Juni 1864.) Kosten: fl. 106.000. VII. Kaiserstrasse 92. 18. October 1862 eröffnet.» Kosten: fl. 120.000. VIII. Josefstädterstrasse 93. Für Knaben und Mädchen. Stiftungen des Ehepaares Sanetti. < 18. März 1884 eröffnet, jenes für Knaben.) fl. 128.000. IX. Galileigasse 8. (October 1874 eröffnet. 1 Kosten: fl. 167.000. X. Keplerplatz 13. <i8. April 1879 eröffnet. 1 Kosten: fl. 116.000. Sämmtliche Waisenhäuser wurden nach Plänen des Stadtbau- amtes ausgeführt. Asyl- und Werkhaus für Männer und Frauen. X. Simme- ringerstrasse 2. Ursprünglich als Fabrik erbaut und von der Ge- meinde für diesen Zweck im Jahre i8S6 angekauft. Eröffnung am 1. Mai 1887. Kosten: fl. 275.000. Ausserdem wurden von der evangelischen Gemeinde im Bezirke Margarethen (Kosten: fl. 70.000 • und der israelitischen Gemeinde d by Google 315 im Bezirke Aisergrund je ein Waisenhaus und von Vereinen Be- schäftigungsanstalten und Asyle für Erwachsene und für Kinder erbaut. Zu letzteren gehören die Radislowitsch-Braun'sche Knaben- beschäftigungsanstalt (4. November 1863 eröffnet* und die Säuglings- bewahranstalt in der Leopoldstadt (11. Mai 1871 eröffnet), das Asyl- haus »Elisabethinum« (13. December 1870 eröffnet;, das israelitische Mädchen -Waisenhaus im Bezirke Aisergrund (14. Juni 1874 eröffnet », die Kleinkinderbewahranstalt (29. October 1883 eröffnet) im Bezirke Favoriten, das Rudolfinum (1. März 1869 eröffnet), das evangelische W'aisenhaus 11872) im Bezirke Mariahilf, das israelitische Blinden- institut 11. December 1872 eröffnet) auf der Hohen Warte in Döbling. Krankenhäuser, ä) Vom Staate erbaut. Kronprinz Rudolf-Stiftung. III. Rudolfsgasse 15. 113. De- cember 1864 Einweihung). A.: S. Horky. B.: Frauenfeld und Ed. Kaiser. Bildhauerarbeiten von Kugler. Aus dem Stadterweiterungs- fonde erbaut. Kosten: fl. 465.000. Krankenhaus auf der Wieden. IV. Favoritenstrasse 30. 1 Jänner 1854 eröffnet.) A.: F. Schaden. B.: F. Prantner. Erweiterungen wurden 1859, 1876 und 1885 vorgenommen. Kosten: fl. 776.305. Niederösterreichische Landes-Irrenantalt. IX. Lazareth- gasse 14. (October 1852). Die Capelle wurde am 22. November 1857 eingeweiht. Die Anstalt, vom Staate erbaut, ging erst nach dem Jahre 1863 in die Verwaltung des Landes über. Krankenhaus, X. Triesterstrasse. (1888..1 Ist noch im Bau. b) Von der Gemeinde erbaut. Epidemiespital. X. Triesterstrasse. 1 I.Mai 1883.1 Erbaut vom Stadtbauamte. c) Von Privat-Corporationen und Privatpersonen erbaut. Kinderspital. II. Obere Augartenstrasse 28. Von der nieder- österreichischen Sparcasse gegründet. u6. Jänner 1873 eröffnet.) A. : K. Freih. v. Hasenauer. B.: Andr. Luckaneder. Kosten: fl. 140.000. Krankenhaus der Barmherzigen Brüder. II. Grosse Mohrengasse 9. Erweiterungsbau. A.: Otto Hofer und A. Schön- mann. (31. Jänner 1855 eröffnet.) Kosten: fl. 478.915. — .i*6 Kronprinz Rudolf-Kinderspital. III. Kleingasse 7. <i. Juli 1875 eröffnet.! A.: Ed. Kuschee. B.: H. Stein. Kosten: fl. 1 10.000. Dr. S wetlin'sche Privat-Heilanstalt. III. Leonhardgasse 3. -3. August 1883 eröffnet. 1 A.: E. Hauser. R.: A. Schuhmacher. Kosten: fl. 180.620. St. Josef-Kinderspital. IV*. Kolschitzkygasse 9. Erweiterungs- bau. (19. März 1870 eröffnet. 1 Krankenhaus der Wiener Kaufmannschaft. V. Sieben- brunngasse 21. (1872 und 1874.1 Kosten: fl. 160.000. Sofienspital. VII. Kaiserstrasse. 128. Mai 1880 eröffnet.' A. und B.: H. E. Weigang. Kosten: fl. 90.623. Dr. Eder'sche Privat-Heilanstalt. VIII. Schmidgasse 14. 27. April 1887 eröffnet.! A.: H. Auer. B.: Sturanv. Kosten: fl. 370.000. Karoline Riedl'sches Kinderspital. IX. Schubertgasse 2. 1. November 1879 eröffnet..) A.: Ferd. Deym. B.: Firma Dehrn & (»bricht. Kosten: fl. 48.000. Kudolfinerhaus in Unter-Döbling, Langegasse 49—52. 19. October 1885 Eröffnung des ersten und zweiten Kranken- Pavillons.) A.: F. R. v. Gruber und K. Völkner. Kosten: fl. 96.100. Haus der Barmherzigkeit in Währing. Für unheilbare Kranke. (25. Juli 1875 eröffnet.) Im Jahre 1879 und 1885 erweitert. A.: R. Jordan. B.: J. Schmalzhofer. Kosten: fl. 350.000. Spital der israelitischen Cultusgemeinde in Währing. 9. März 1873 eröffnet. 1 A.: W. Stiassny. B.: Oberwimmer. Kosten: fl. 700.000. Vcrcinshüuser. Adeliges Casino: I. Kolowratring 5. (1867.) A.: August Ritter v. Schwendenwein. B.: H. Pucher. Häuser des österr. Ingenieur- und Architekten- und Gewerbe-Vereines. I. Eschenbachgasse 9. (16. November 1872 er- öffnet.) A.: Otto Thienemann. Figuren an der Facade von F. Melnitzky. Kosten: fl. 520.000. Kathol. Gescllenhaus: II. Vereinsgasse 4. (27. Juli 1862 eröffnet.) Kathol. Gesellen-Ver^inshaus: VI. Gumpendorferstrasse 39. !i888.> A.: Rieh. Jordan. B: Jos. vSchmalzhofer. Bildh.: J. Baum- gartner. d by Google 317 Einzelne Paläste, Wohnhäuser und Höfe. Wohnhaus des Jonas Freih. v. Königswarter: I. Kärnthner- ring 4. (1859.) A.: J. Ritter v. Romano. B.: P. Wasserburger. Kosten: fl. 300.000. Palast des Freih. v. Sina: I. Hoher Markt. (1860.) Umge- staltung. A.: Th. Fr. v. Hansen. Fresken der Einfahrt von K. Rahl. Palast des Freih. v. Todesco: I. Kärnthnerstrasse 51. (1861 bis 1864.) A.: H. Ritter v. Förster und Th. Freih. v. Hansen. Fresken von K. Rahl, Griepenkerl und G. Gaul. PalastdesFreih.v. Schey (gegenwärtig der Familie Rappaport) : I. Albrechtsgasse 3. (1865— 1866.) A.: Aug. Ritter v. Schwendenwein. B.: Ed. Kaiser. Bildhauerarbeiten von F. Schönthaler. Kosten: fl. 800.000. Spätere Adaptirung und Ausschmückung fl. 900.000. Familienhaus des Freih. v. Mayr-Mölnhofen: I. Opern- gasse 4. (1863.) A.: A. Hefft. B.: Stipperger. Bildhauerarbeiten von K. Preleuthner. Kosten: fl. 240.000. Palast des Erzherzogs Albrecht: I. Albrechtsgasse 1. (1863.) A.: A. Hefft. B.: Oetzelt. Kosten: fl. 1,050.000. Heinrichshof: I. Opernring 1, 3, 5. (1863.) A.: Th. Freih. v. Hansen. B.: Ed. Kaiser und Ed. Frauenfeld. Fresken der Facade nach Entwürfen des K. Rahl. Kosten: fl. 1,200.000. Majoratshaus der Grafen Hovos: I. Kärnthnerring 5. (1863.) A.: Ludwig Förster. Kosten: fl. 523.300. Wohnhaus des F. Freih. v. Leitenberger: I. Parkring 16. A.: L. Zettl. B.: Pokorny, Kugler und Dollischek. Malerarbeiten: Schilcher und Eisenmenger. Palast des Fürsten Colloredo-Mannsfeld: I. Parkring 6. (1865.) A.: A.Ritter v. Romano. B.: H. Ritter v. Förster. Bildhauer- arbeiten von Pokorny. Kosten: fl. 412.700. Palast des Grafen Larisch. I. Johannesgasse 26. (1886.) A.: van der Nüll. Palast des Erzherzogs Ludwig Victor: I. Schwarzenberg- platz. (1866.) A.: Freih. v. Ferstel. Bildhauerarbeiten von Jos. Gasser und F. Melnitzky, F. Schönthaler und Pokorny. Palast des Grafen Eugen Kinsky: I. Schwarzenberg- strasse 9. A.: A. Ritter v. Schwendenwein. B.: H. Pucher. Palais des N. v. Dumba: I. Parkring 4. (1866.) A.: Romano u. Schwendenwein. B.: E. Kaiser. Fig. Malereien der Wohnräume von H. Makart und Schilcher. Kosten: fl. 300.000. Digitized by Google Ji8 Palast des F. Edl. v. Wert heim: I. Schwarzenbergplatz. 11866.) A.: H. Freih. v. Ferstel. Palast des Grossmeisters des deutschen Ordens, Erz- herzogs Wilhelm: I. Parkring. (1867.) A.: Freih. v. Hansen. B.: J. Hlawka. Statuen an der Facade von J. Gasser. Kosten: 11. 1,200.000. Palast des Victor v. Ofenheim: I. Schwarzenbergplatz 4. 11868.) A.: A. v. Romano. B.: Hauser. Bildhauerarbeiten von Pokorny. Palast des Grafen Henckel-Donnersmarck: I. Parkring 14. (1871.) A.: v. Romano. Palast des Wilhelm Ritter v. Gut mann. I. Kantgasse 6. (1871.) A.: K. Titz und H. Claus. B.: J. Schieder. Bildhauer: J. Pokorny und F. Melnitzky. Maler: A. Risenmenger, Bitterlich und Eichmüller. Kosten: fl. 300.000. Palast des Aug. Freiherrn v. Wehli: I. Elisabethstrasse 5. 11871.) A.: L. Ritter v. Zettl. B.: H. R. v. Förster und H. Pucher. Deckengemälde der Innenräume von H. Makart und H. Charlemont. Bildhauerarbeiten von Dollischek. Kosten: fl. 400.000. Palast des R. Ephrussi. I. Franzensring 24. (1872.) A.: Th. Freih. v. Hansen. B.: H. Ritter v. Förster und A. Dietrich. Palast des R. v. Epstein: I. Burgring 13. 11872.) A.: Th. v. Hansen. B.: H. Ritter v. Förster und A. Dietrich. Bildhauerarbeiten von V. Pilz. Deckengemälde der Innenräume von Ed. Bitterlich und Chr. Griepenkerl. Wandgemälde daselbst von J. Hofmann. Kosten: ll. 700.000. Palast des Baron Liebig: Weihburggasse 30. (1873.) A.: W. Stiassny. B.: Ringer. Deckengemälde der Innenräume von Echter und Frank in München. Kosten: fl. 325.000. Grabenhof: I. Graben 14 und 15. (1873.) A.: O. Thienemann. B.: A. Dietrich. Terracotten aus der Wienerberger Fabrik. Kosten: fl. 380.000. * Kärnthnerhof: I. Kärnthnerstrasse 38. (1876.) A.: O. Thiene- mann. B. : Allgemeine österr. Baugesellschaft. Palast des Fürsten Dietrichstein-Mensdorf: I. Minoriten- platz 4. (1877.) A.: V. Rumpelmayer. Wohnhaus des Joh. Sturany: I. Schottenring 21. (1877.) A.: Fellner und Helmer. Fig. Arbeiten am Portal nach Entwürfen von K. Kundmann. Germaniahof: I. Rothenthurmstrasse, Ecke des Lugeck. (1878.) A.: W. Fränkel. Kosten: fl. 520.000. M9 Arkadenhäuser: I. Reichsrathsstrasse n, 13, 15. (iSNo.) A.: Fr. Kitter v. Neumann jun. B.: A. Hofbauer und Joh. Sturany. Bildhauerarbeiten von Th. Friedl, J. Probst, F. Wolfsberger. Decken- gemälde des Vestibüle v. O. Fessler. Kosten: fl. 600.000. Arkadenhäuser: I. Reichsrathsstrasse 17, 19, 21. (1883.) A.: F. Ritter v. Neumann jun. B.: Unionbaugesellschaft. Bildhauer- arbeiten von Th. Friedl, S. A. Probst, A. Schmidgruber, F. Wolfs, berger. Bächer und S. Hutterer. Üeckenbilder des Vestibüle von O. Fessler. Deckenbilder des Saales der Restauration von Groll. Kosten: fl. 1,400.000. Kaiserliches Stiftungshaus: I. Schottenring 7. 11885.) A-: Fried. Freih. v. Schmidt. B.: P. Wasserburger. Fig. Bildhauerarbeiten: A. Düll, F. Erler, J. Probst, J. Dover. Orn. Bildhauerarbeiten: A. Kangl, La Vigne, J. Pokorny. Fig. Malereien von Franz und K. Probst. Kosten: fl. 900.000. Stephanshof: I. Stefansplatz. U887.) A.: O. Thienemann. B.: K. Krombholz. Bildhauerarbeiten von Strictius. Kosten: fl. 325.000. Palast des A. Freih. v. Klein: II. Praterstrasse 42. (1861.) A.: Ludwig Förster. Fig. Arbeiten von Scharf und Petrusen. Palast des Herzogs v. Nassau: III. Reisnerstrasse 35. (1875.) A. : Alois Wurm. B.: K. Burka. Kosten: fl. 360.000. Palast des Fürsten K. Windischgrätz: III. Strohgasse na. A.: F. Kreuter. Palast der Gräfin Wydenbruck: III. Richardgasse 5. U882.) A.: W. Stiassny. B.: A. Schuhmacher. Kosten: fl. 125.000. Familienhaus des Freih. v. Wieser: III. Veithgasse 4. (1884.) • A. : Wieser und Lötz. B.: M. Schwenda. Fig. Bildhaueraibeiten von » R. Weyr. Deckenmalereien von Groll. Kosten: fl. 149.000. Palast Miller v. Aichholz: IV. Heugasse 30. (1879.) A.: A. Streit. B. : Joh. List. Palast des Grafen Nakö: IV. Alleegasse 16. (1872.) A.: F. Schachner. B.: K. Riess. Malereien von Jobst, Aichmüller und Fux. Bildhauerarbeiten von Schönfeld. Kosten: fl. 175.000. Palast des Ph. v. Haas: IV. Waaggasse 6. (1875.) A.: F. Schachner. B.: Hoppe. Malereien von Jobst. Bildhauerarbeiten von Schönfeld und Hellmer. Kosten: fl. 150.000. Palast der Fürstin Hohenlohe-Bartenstein: IV. Hungel- brunngasse 8. (1882.) A.: V. Rumpelmayer. B.: D. Kubelka. Palast des Grafen F. Kinsky: IV. Plöslgasse 8. (1878.) A.: F. Glaser. B.: Dehrn und Olbricht. Digitized by Google 320 Palast des Daniel Ritter v. Gutmann: IV. Schwindgasse 2. (1877.) A.: Clauss und Gross. Malerei des Speisesaales von Canon, der übrigen Räume von Felix und Löffler. Bildhauerarbeiten von Hutterer. Familienhaus des E. Wahliss: IV. Alleegasse 21. (1883.1 A.: H. Adam. B.: J. Görlich. Bildhauerarbeiten von La Vigne. Palast des Nath. Freih. v. Rothschild: IV. Plösslgasse 7. (1880.) A.: Jean Girette. B.: H. Glaser. Bildhauerarbeiten von Guyonnet. Palast des Alb. Freih. v. Rothschild: IV. Heugasse 26. (1886.) A.: Destailleur in Paris. B.: P. Wasserburger und H. Ernst. Gartenpalast des Fürsten F. Liechtenstein: IX. Alser- bachstrasse 16. (1873.) A.: H. Freih. v. Ferstel. Palast des Grafen Chotek: IX. Währingerstrasse 28.(1871.) A.: Ed. Kaiser. B. : Bosch. Kosten: fl. 795.000. Maximilianhof: IX. Währingerstrasse 6 und 8. (1887.) A. : * Emil Ritter v. Förster. B.: Dehrn und Olbricht. Kosten: fl. 370.000. Palast des Herzogs Philipp Württemberg: IX. Strudel- gasse. (187 1.) Innenräume: Fresken von K. Geiger. Maria Theresienhof: IX. Währingerstrasse 2 und 4. (1884.) A.: L. Tischler. B.: Dehrn und Olbricht. Kosten: fl. 1,000.000. IV. GESELLSCHAFTLICHE WOHLTHÄTIGKEITSPFLEGE V..\ FRIEDRICH v. RADLER. 21 Digitized by Google 2I< Digitized by Google 3^4 innewohnt. In scharf charakteristischer Weise bezeichnet er, knapp und treffend, den Motor aller Errungenschaften menschlichen Geistes, menschlichen Flcisses — und wenn dieser Wahlspruch von dem mächtigen Repräsentanten eines achtunggebietenden Reiches, einer europäischen Grossmacht, als Leitstern seiner Erdenmission gewählt ward, so gibt dies das sprechendste Zeugniss einer wahrhaft grossen, erhabenen Seele, die der Erkenntniss Raum gegeben, dass das Gewaltige stets nur das Resultat des harmonischen Zusammen- wirkens Vieler sein könne. Wie wenig vermag der Mensch allein, wie unsagbar viel jedoch durch Vereinigung aller jener Kräfte, welche die Schöpfung dem Einzelnen in die Wiege gelegt. Die Macht der Association hat die kühnsten Erwartungen an das Walten des menschlichen Geistes übertroffen, ja sie hat Probleme von gigantischer Grösse mit Leichtigkeit und eminenter Präcision zur Lösung gebracht. Vereinte Kräfte legten unendliche Schienenstränge, die den Norden mit dem Süden, den Osten mit dem Westen unseres Erd- balles verbinden; vereinte Kräfte bauten die Locomotive, die, mit Blitzesschnelle dahinrollend, unabsehbare Entfernungen in Dimen- sionen wandelt, welche das Auge ohne Mühe zu überblicken ver- mag. Der Mann des rauhen Nordens, der unter dem düster grauen Firmamente der kalten Zone athmet. wird mit allen seinen physi- schen und intellectuellen Interessen durch sie zum Nachbar des heissblütigen Südländers, dem das Geschick die Gnade zu Theil werden Hess, seinen Lebensgang unter dem ewig blauen Himmel der Tropen zu vollenden. Vom Ueberflusse wäre es, all die Errungenschaften auf cul- turellem, industriellem, socialem und geistigem Gebiete taxativ anzu- führen, welche die Gewalt der Association zu Tage gefördert, all die Producte herzuzählen, die mit vereinten Kräften von tausend und abertausend Arbeitselementen hervorgebracht worden sind, denn kaum dürfte es einen denkenden Menschen geben, der der erfolg- reichen Wirksamkeit dieses Machtfactors seine volle Anerkennung versagen wollte. Nach Aussen präsentirt sich die Gesammtthätigkeit in der Eorm des Vereines. Für den weitblickenden Staatsmann muss es von hohem Interesse sein, die Entwickelung. die Ausbreitung und das gedeihliche Aufblühen dieser Art der modernen gesell- schaftlichen Bewegung zu beobachten und den verschiedenen Stadien Digitized by Google - 325 - der Vereinsthätigkeit im Staatstfebilde seine ungetheilte Aufmerksam- keit zuzuwenden. Der Kanzler Fürst Metternich äusserte sich in einem 1845 abgegebenem Votum folgendermassen: *Zu den wichtigsten und zugleich dringendsten Auf- gaben des Tages rechne ich die richtige Auffassung des aller Orten lebendigen Vereins wesens. In seiner Wesenheit aufgefasst, liegt demselben der Hegriff der verstärkten Kraft durch vereinte Mittel zu Grunde. Vereine und sonach der Trieb nach denselben liegen in den Grundbedingungen der Menschheit. Dieser Trieb dient der Gesellschaft zur Grundlage. Er bildet die Basis des Staatslebens. Was sind denn Staaten anderes als Associationen zu vereinten Zwecken durch vereinte K ra f t e? « Je höher die Cultur, je prätentiöser die Anforderungen einer Bevölkerung an die Bedingungen der materiellen Existenz, an die feineren Genüsse des Daseins, an die unzähligen Annehmlichkeiten des Comforts um verhältnissmässig geringe Preise, desto lebhafter tritt das Bedürfniss nach Unternehmungen im grossen Stil, nach Cultur-Effecten hervor, die einzig nur durch das Wirken vereinter Kräfte erzielt werden können. Dem schwachen Einzelwesen greift der kräftige Verein unter die Arme und ein Staat, in dem die freie Gesellung zur Er- reichung ethischer und realistischer Ziele in Blüthe steht, mag sich mit Beruhigung dem befriedigenden Bewusstsein hingeben, eine der wichtigsten Aufgaben seiner Culturarbeit gefördert zu haben. Die sittliche Grundlage der Vereinigung bildet das Streben der Individuen, durch eine Summe von harmonisch wirkenden Kräften das Leistungsvermögen der Societät zu potenziren, die materielle Basis des Vereines ist das schaffende Moment, — die Froduction. Obgleich der dem Einzelnen angeborene Associationstrieb mit dem Menschengeschlechte erstanden, muss doch das Vereinswesen in seiner jetzigen Gestaltung, seinem heutigen Umfange und seiner gegenwärtig dominirenden Bedeutung ein Kind des auf- geklärten neunzehnten Jahrhunderts genannt werden, und sicherlich nicht blos zufälligen Umständen ist es zuzuschreiben, dass in Oester- 326 reich der Wahlspruch unseres edelsinnigen Monarchen — »Viribus unitis' gerade während dessen Regierung, in so überraschen- der Weise alle Schichten und Kreise der Bevölkerung durch- drungen, daselbst Fleisch und Blut geworden und die Realisirung dieser Sentenz, d. i. die Vereinigung zur Erreichung bestimmter Ziele, in den vielfachen Richtungen des socialen und politischen Lebens und Strebens eine ungeahnte Entwickelungshöhe er- reicht hat. Die Anerkennung der Wichtigkeit des Associationsgeistes im Staate gelangt zum Ausdrucke durch eine freisinnige Vereinsgesetz- gebung, durch die liberale Art der Interpretation, der Anwendung und Handhabung derselben, wie eine solche denn auch heute that- sächlich in unserer Monarchie in Übung steht. Die erschütternden staatlichen und socialen Umwälzungen in Frankreich am Ausgange des XVIII. Jahrhunderts hatten sich schon Decennien vorher durch eine unheimliche Gewitterschwüle am politischen Horizonte, durch eine beängstigende äussere Ruhe, — stets das Kennzeichen des bevorstehenden Sturmes, — angekündigt. Europas Boden glich einem Vulcane, dessen leises Beben, dessen kaum vernehmbares Stöhnen den nicht mehr allzufernen, verderben- bringenden Ausbruch befürchten liess. Allerorten entstanden Verbindungen mit freiheitlichen, ja von den damaligen Staatsmännern sogar als revolutionär verdammten Tendenzen, — Verbindungen, deren Mitglieder, influirt von den durch Jean Jacques Rousseau in die Welt geführten Ideen der Volks- Souveränität und allgemeinen Menschenrechte, mit energischem Trotze die Faust erhoben hatten, um die traditionellen, Aufklärung und Fortschritt hindernden »Schranken gewaltsam zu durchbrechen. Allein neben diesen, vom Zeistgeiste erweckten, zielbewussten Ge- sellungen, schössen, betäubt von kraftstrotzenden Phrasen selbst- süchtiger Streber, auch andere, in ihren Endabsichten völlig unklare Vereinigungen wirrer Köpfe empor. Die Apostel derselben predigten den Umsturz der gesellschaftlichen Ordnung, die blinde Anarchie, ohne ihr Gewissen zu der Frage aufzuraffen: was dann? Diese Verbindungen, welche vorzugsweise in den unteren Volksschichten Terrain gewonnen hatten, waren äusserst gefahr- drohend, denn der kleine Gesichtskreis ihrer Anhänger, deren Mangel an Logik und Fernblick, liess sie vor keinem Mittel zurück- Digitized by LaOOQle — 327 ~ schrecken, um sich zu dem Versuche aufzuschwingen, die mühsame Culturarbeit vergangener Jahrtausende zu vernichten. Durch diese sahen sich die Staatsgewalten in ihren vitalsten Interessen bedroht, weshalb sie auch, ohne zu sichten und zu sondern, Massregeln ergriffen, die ihnen geeignet erschienen, der gesammten Be- wegung Einhalt zu thun, wo nicht gar sie gänzlich niederzu- drücken. In diese Zeit fallen auch in Oesterreich die ersten behördlichen Verfügungen hinsichtlich der Vereinsbestrebungen, allerdings ausnahmslos, Prohibitivmassregeln. So verbot der Regierungs-Erlass vom 23. August 1764 direct die Bildung jeder Gesellschaft in den österreichischen Landen, ohne ausdrückliche Erlaubniss des Landesherrn. Der Erlass vom 8. November 1766 untersagte den Eintritt in die Gesellschaft der Freimaurer und in den Orden der Rosenkreuzer, während das Handbillet Josef II. vom 11. December 1785, nach Tolerirung der Freimaurerlogen, den Eintritt in dieselben zwar ge- stattete, ihn jedoch mit grossen Beschränkungen umgab. Die strengsten Anordnungen wegen Ueberwachung der ge- heimen Gesellschaften und deren »bedenklichen« Zusammen- künfte enthielt das Gesetz vom 1. November 1791. Bis zum Ende des vorigen Jahrhunderts trugen alle diese Verfügungen den Charakter des Tastenden, des Zaghaften und es hatte den Anschein, als scheute man vor dem Eclat zurück, den das energische Hemmen dieser dem Staate so missliebigen Bewe- gung hervorrufen könnte. Die Folge davon war die unausgesetzte Beunruhigung und Bedrohung der gesellschaftlichen Ordnung durch neues Entstehen derlei geheimer Verbindungen. Da erschien das Hofdecret vom 27. April 1801, das ausdrück- liche Verbot aller geheimen Gesellschaften überhaupt aussprechend und später, am 3. September 1803, das Strafgesetz, welches unter Anderem auch die Bestimmung enthielt, dass die Theilnahme an geheimen Gesellschaften als schwere Polizei-Uebertretung gegen die Sicherheit des Staatsbandes zu betrachten und zu ahnden sei. Nachdem die Gewitterstürme, welche so lange und so ge- wichtig die Ruhe Europas gefährdet, niedergegangen, der unersättliche Löwe Napoleon I. kraftlos und ohnmächtig, — ein erschreckendes Beispiel irdischer Vergänglichkeit, — in den Staub gesunken, die alte Ordnung wieder hergestellt war und die Staatslenker ihre Aufmerk- samkeit nunmehr den inneren Angelegenheiten zuzuwenden in die Lage gekommen waren, nel auch auf das vorher so heftig und ohne Wahl verfehmte Vereinswesen der erwärmende Sonnenstrahl des Friedens, wenn auch hauptsächlich in Absicht auf wirthschaftliche Vortheile, und damit Vermehrung der Steuerkraft, sowie in Aussicht auf die Befriedigung sol eher öffentlicher Bedürfnisse, für welche sich die Staatsmittel unzureichend erwiesen, aus egoistischen Gründen der Staatsklugheit. Ja, die Vereinsbewegung wurde von den höchsten Verwaltungs- organen jetzt sogar selbst wachgerufen, als wirksames Schutzmittel gegen die auf das Aeusserste gestiegene Nothlage der Bevölkerung. Die allgemeine Missernte des Jahres 1816, nebst anderen Be- schwerden, die die vorangegangenen, verheerenden Kriegsereignisse zweier* Jahrzehnte verschuldeten, hatte, bei den damaligen mangel- haften Communicationsverhältnissen, eine solche Verarmung der unteren Volksclassen hervorgerufen, die Preise der noth wendigsten Lebensmittel so enorm gesteigert, dass man nur mit Besorgniss jedem neu anbrechenden Morgen entgegensehen konnte. Die Zahl der in den Strassen und auf den Glacien vagirenden Bettler ver- grösserte sich von Tag zu Tag. Bei zwanzigtausend Menschen ver- langten von den Behörden mit Ungestüm — Arbeit. Man zog, um Unterstützungen zu gewähren, die öffentlichen Fonds heran, die aber leider für die Dauer nicht Stand halten konnten. Täglich Hess sich der Kaiser einen genauen Rapport über die Lage der Arbeits- losen vorlegen, im Schosse der Regierung wurde Sitzung auf Sitzung abgehalten und ein Vorschlag löste den anderen ab. Man ventilirte die Frage einer allgemeinen Armensteuer, selbst der Versuch, die Luxussteuer in Anregung zu bringen, wurde unternommen, ja man verstieg sich in der Noth des Augenblickes sogar zu der Proposition — einer Hagestolzensteuer! F'ürst Metternich, der, als rechnender Diplomat, dem Associa- tionswesen auf dem Felde der Wohlthätigkeitspflege mehr Gewicht beilegte, als der Staatshilfe, trat mit seinen darauf abzielenden An- trägen mit Entschiedenheit hervor und Hess dem Gedanken rasch die That folgen. In dem Hofkanzlei-Decrete vom 3. Jänner 181 7 erklärte die Regierung: dass die Kräfte des Staates durch vieljährige ausserordentliche Auslagen geschwächt worden seien, dass indessen so manche nützliche Anstalt der Unter- stützung bedürfe, manche neue zum grossen Vortheile des Staates zu errichten wäre, die inländische Industrie im Digitized by Go S29 - weitesten Verstände Ermunterung erwarte, der Kunstfleiss im Fabriks- und Gewerbewesen und im Landbaue zu be- leben sei, nützliche Erfindungen aller Art aufzumuntern kämen und den Wissenschaften wie den Künsten hilfreiche Hand geboten werden müsse: dass es daher ein hohes Verdienst um das Vaterland sei, wenn Private wenigstens zum Theile und allmälig leisten, was der Staat jetzt zu leisten nicht vermag. Metternich selbst stellte sich nach Vorlage eines am 12. Februar 181 7 dem Monarchen erstatteten Berichtes an die Spitze eines Ver- eines zur Unterstützung der Nothleidenden Wiens. Kaiser Franz II. übernahm das Frotectorat und eröffnete sofort die Sub- scription. Zugleich wurde Arbeit im Stadtgraben geschaffen, wofür jeder dabei Betheiligte einen Gulden Taglohn erhielt, während den bedürftigen Arbeitsunfähigen eine Unterstützung von täglich dreissig Kreuzern angewiesen wurde. Leider gerieth die so energisch in Angriff genommene Action sehr bald in's Stocken. Schon nach einigen Monaten war der Verein genöthigt, seine Thätigkeit einzu- stellen und die Regierung musste sich, so gut es eben ging, mit den vorhandenen Verhältnissen abfinden. Aus nahezu denselben Beweggründen, wie aus denen des eben envähnten Hofkanzlei - Decretes vom 3. Jänner 181 7 wurde schon früher, am 8. September 181 2, eine kaiserliche Resolution erlassen, welche für die Behörden die Weisung enthielt, die Bildung von Privat-Wohlthätigkeitsvereinen nach Möglichkeit zu begünstigen. Die weiters folgenden legislativen Enunciationen der Jahre 182 1, 1832, 1838 und 1840 enthielten auf freiester Basis Sonderbestim- mungen für wirthschaftliche Vereine, bis endlich das Hofkanzlei- Decret vom 5. November 1843 die erste umfassende Vorschrift über Privatvereine überhaupt brachte. Dasselbe ergänzend, folgte das kaiserliche Patent vom 17. März 1849. welches die Regelung der politischen Verbindungen im Auge hatte. Am 26. November 1852 erschien das heute noch zum grössten Theile in Kraft stehende Vereinsgesetz, das neben der freien Be- wegung der Associationsbestrebungen vorzüglich auf wirtschaft- lichem Gebiete den Schutz für die öffentliche Ordnung und gesell- schaftliche Rechtssicherheit durch das dem wStaate nothwendig zukommende Aufsichtsrecht zu garantiren bestrebt ist. — 33° — Den Schlussstein der Vereinsgesetzgebung bildet das liberale Gesetz vom 15. November 1867, welches für alle Arten von Ver- bindungen, einschliesslich der politischen, jedoch mit Ausnahme der Vereine und Gesellschaften, die auf Gewinn abzielen, berechnet er- scheint. Nebenher erflossen selbstverständlich Administrations-Ver- ordnungen über die Anlegung von Vereinskatastern, Tabellen, Hand- habung der Controle u. s. w. Aus der Vielseitigkeit, in der das Vereinswesen gegenwärtig zu Tage tritt, sei hier die edelste Richtung freiwilliger Association, das reinste Ziel uneigennütziger Menschenliebe, die gesellschaft- liche Wohl thätigkeitspf lege herausgegriffen und, soweit sie die Stadt Wien mit den angrenzenden Vororten betrifft, des Näheren beleuchtet. Auf diesem Felde tritt die Societät mit ihren organisirten Humanitätsbestrebungen keineswegs in Gegensatz zu Staat und Gemeinde, sondern vielmehr unterstützend, ergänzend, fördernd. Die moderne Weltanschauung erblickt in der juristischen Person des Staates, zumal des constitutionellen. nicht mehr den unduldsamen Vormund aller Unterthanen, die, mit den Händen im Schosse einer beschaulichen Unthätigkeit fröhnend, alles Heil des Leibes und der Seele von ihren Regierungsautoritäten erwarten dürfen. Die Gesellschaft ist mündig, ist grossjährig geworden, aber sie hat mit den Rechten, die sie erobert, auch Pflichten übernommen, ethische und ökonomische, deren Erfüllung eine Grundbedingung ihrer Sou- veränität bildet. Ueberall im civilisirten Ruropa ist dieses Bewusstwerden der gesellschaftlichen Bedeutung zum Durchbruche gekommen, aller- wärts bewegt und regt sich die Menge und mit geschäftigen Händen greift sie erfolgreich zu, um die Hemmnisse der Entwickelung des Staates und des Volkswohles beseitigen zu helfen. Der Gedanke, der dieser Action innewohnt, ist kein neuer, aber er lag im Schutte vergangener Jahrhunderte, — niedergedrückt durch gewaltthätiges Faustrecht, das jedem Lichtstrahl abhold war. in finsterer Geistesnacht begraben, bis die Stunde der Alles durchwühlenden Umwälzungen geschlagen, die die Traditionen von Sclaverei, Dienstbarkeit und Leibeigenschaft über den Haufen ge- worfen. Die Germanen waren es. welche, im Gegensatze zur hellenisch- römischen Auffassung, der gänzlichen Opferung des Individuums zu d by Google Gunsten des Staates, den persönlichen Freiheitstrieb, die Selbst- ständigkeit der aus freien Männern bestehenden Genossen- schaft als Grundvesten jeder gedeihlichen Communität zur Geltung brachten. Was waren denn ihre Waffenbruderschaften, ihre Gilden und Zünfte, jene mittelalterlichen Repräsentanten der städtischen Schutz- bündnisse gegen die UebergrifTe der ringsum auf ihren Burgen hausenden Raubritter, die religiösen Orden und Bruderschaften, der Hansabund und die späteren Handelscompagnien anderes, als das Resultat des dem Menschengeschlechte angeerbten Associations- triebes. Auf keinem Gebiete der staatlichen Institutionen aber stellt sich trotz der fürsorglichsten Intentionen die Nothwendigkeit leb- hafter heraus, den öffentlichen Bestrebungen durch kräftige gesell- schaftliche Unterstützung zu Hilfe zu eilen, als auf dem weitver- zweigten, mannigfaltigen Gebiete der Armen- und Krankenpflege. Der Pauperismus schlägt dem Staatskörper die klagendste Wunde, ohne deren Heilung Volkswohl und Volkskraft unerreichte Ideale bleiben. Des Staates ethischer Beruf ist die Erfüllung seiner Cultur- mission. Diesem Ziele zuzustreben ist seine Pflicht, bildet seine Existenzberechtigung; er kann sich daher nur insoferne den ein- zelnen Theilen seiner Verwaltungszweige zuneigen, als dieselben von solidarischer Bedeutung für das Ganze sind. Folgerichtig ent- behrt daher manche der öffentlichen Einrichtungen des Gepräges der Vollständigkeit und bedarf, wie schon betont, um keine allzu grosse Lücke im Organismus zu hinterlassen, subsidiärer Kräfte. * Ursprünglich war die Obsorge für den durch Verarmung, Krankheit oder Alter in Noth gerathenen Mitmenschen Sache der christlichen Barmherzigkeit, ohne jede weitere Beschränkung. Der Christ sah sich durch Ausspruch und Beispiel des erhabenen Stifters seiner Religion im Gewissen gebunden, dem Bruder, dem Nächsten, sogar dem Feinde, der der Unterstützung bedürftig geworden, mit voller Liebe und Hingebung, ja mit Aufopferung seiner selbst beizustehen und zu helfen. — Der Samaritanerdienst war ein kosmo- politischer, der weder nach Nationalität, noch nach Confession trug. — sondern stets nur den hilfsbedürftigen Mitmenschen vor Augen hatte. Von diesem Standpunkte aus sehen wir auch die ersten Anordnungen und Anstalten erstehen. Selbstverständlich Digitized by Google waren es vor Allen Diejenigen, welche sich im Dienste einer frommen Mission befanden, die dieser Vortheile theilhaftig wurden. — die Pilgrime. Ein gewisser Nimbus umgab das Haupt dieser Fremdlinge, welche »aus Gottesfurcht und zum Heile ihrer Seelen durch das Land wandern«, wie es in einem die Unterstützung der Dürftigen anordnenden Capitulare Karl's des Grossen heisst. Jeder Glaubige schätzte sich glücklich, einen solchen frommen Wanderer in sein Haus aufnehmen zu können, und ihm »Herberge, Herd und Wasser* zu gewähren, um hierdurch ein gottgefälliges Werk zu verrichten und sich eine Stufe in den Himmel zu bauen. Die Anordnungen Karl's des Grossen und seiner Nachfolger zielten, zur Steuerung der Armenplage, darauf ab, einen Theil des den Priestern von der Bevölkerung geleisteten Zehent und ebenso einen Theil der sogenannten Seelengeräthe, — fromme Spenden und Stif- tungen für Messen und Todtenfeier, welche das seelische Leben nach dem Tode sichern sollten, — der Unterstützung Bedürftiger zuzubringen, welche Massnahmen jedoch von Seite der hierbei Ver- kürzten nicht immer das gewünschte Entgegenkommen fanden. — Um aber den dadurch entstandenen Mangel weniger fühlbar zu ge- stalten, gab die Geistlichkeit, die bedeutende Summen zur eigenen Erhaltung, wie zum Baue der damals noch spärlich vorhandenen Kirchen benöthigte, selbst den Anstoss zur Gründung frommer Orden Bruderschaften — als: der Johanniter oder Hospitaliter. der Lazzaristen, der Elisabethinerinnen und so fort, die innerhalb des Klosterverbandes für die Armen- und Krankenpflege Sorge trugen. Mit dem Emporblühen des Städtewesens erschienen neue Fac- toren, die Gilden, Zechen und Zünfte, — auf dem Plan, welche ihre Mildthätigkeit, allerdings mit der Beschränkung der Zugehörig- keit, den Nothleidenden ebenfalls zuwendeten. In Wien, das in der Mitte des XIII. Jahrhunderts an Bedeutung der ersten Stadt Deutschlands, dem alten, ehrwürdigen Köln, wenig nachstand, finden wir zu dieser Zeit bereits einige Anstalten zur Auf- nahme von Armen und Kranken. Sicherlich hatten dieselben ursprüng- lich den Zweck, hilflosen, kranken oder gebrechlich gewordenen Wanderern, besonders wenn sie das Verdienst für sich in Anspruch nehmen konnten, von einem Kreuzzuge heimkehrend, gegen die Ungläubigen im Kampfe um das heilige Grab gestritten zu haben. Herberge und Pflege zu gewähren. So erstanden das heilige Geistspital (auf Anregung des Arztes Meister Gerhard, von Herzog Leopold VI. mittelst Urkunde Digitized by Googl I — 333 — vom 27. Mai 121 1 gestiftet), ferner »der Burg er Spital« (wahr- scheinlich eine Gründung der Gemeinde Wien), später, im Jahre 1266. ein Spital »bei dem Klagbaum auf der Wieden« für Solche, welche mit der Hiobskrankheit, d. i. mit dem Aussatze behaftet waren. — Die Notwendigkeit der Errichtung einer derartigen An- stalt ergab sich durch die grosse Anzahl der an dieser Seuche Leidenden, welche in Folge der Kreuzzüge oder im Wege des Handelsverkehres, vom Oriente kommend, Wien berührten. Bis in unsere Tage sind nun Gründungen einer stattlichen Reihe von Wohlthätigkeits-Anstalten, Spitälern. Armen-, Versorgungs- und Waisenhäusern von Seite des Staates, des Landes und der Gemeinde zu verzeichnen, es ist ferner der Anregung durch die grosse Kaiserin Maria Theresia und der darauffolgenden factischen Durchführung der heute noch wirksamen Reform der Armenpflege durch Kaiser Josef II. zu gedenken, welcher nach dem Muster der Regelung des Armenwesens, wie sie Graf Bouquoy auf seinen Gütern in Böhmen mit grossem Erfolge in Ausführung gebracht, die Einrichtung der Armeninstitute schuf. Alles aber, was Staat, Land und Gemeinde, besonders in unserem Jahrhunderte, für öffentliche Armen- und Krankenpflege Grosses und Schätzenswerthes geschaffen, entzieht sich der näheren Besprechung auf diesen Blättern, welche nur dem Wirken der Privat -Wohlthätigkeit in Wien gewidmet sein sollen. — So viel jedoch sei neuerlich bemerkt, dass diese Armen- und Kranken- Institutionen, so sehr sie auch dem Ideale solcher Anstalten nahe- zukommen bestrebt sind, der Unterstützung durch die gesellschaft- liche Wohlthätigkeitspflege nicht entbehren können. Einer Gesellung ähnlicher Art, die bis in das XIII. Jahrhundert zurückreicht und wenigstens theilweise die Aufgabe zu erfüllen suchte, freiwillige Liebesgaben an leidende, gebrechliche oder ver- armte Mitbrüder zu spenden, sei hier noch erinnert, nämlich der Bruderschaften. Sie verdankten ihre Entstehung dem religiösen Bedürfnisse der frommgläubigen Christen, »mit vereintem Gebete und gottseligen Uebungen die Ehre Gottes zu vermehren und das Seelenheil unter dem Schutze und der Fürbitte eines bestimmten Heiligen zu befördern.« Anfänglich entwickelten diese ziemlich stark verbreiteten Ver- bindungen, wenn auch in mässigem Umfange, eine wirksame huma- nitäre Thätigkeit, indem sie Sammlungen für die Armen veranstalteten und diese sodann, zertheilt in eine Reihe Almosen, an die Dürftigen abgaben. — Später jedoch, als bei den bruderschaftlichen geistlichen Digitized by Google — 334 — Uebungen und den unmittelbar darauffolgenden Zechgelagen Aerger- niss erregende Missbräuche eingerissen waren, die eingelaufenen Sammelgelder, Almosen und Schenkungen, sowie die angefallenen Vermächtnisse für die Armen ihren Widmungen entweder sehr mangelhaft oder gar nicht mehr zugeführt wurden, begannen sowohl die Staatsbehörden, als auch die Functionäre der Kirche gegen diese Verbindungen Stellung zu nehmen. Ja, die gegen die Bruderschaften im Allgemeinen laut gewordenen Klagen veranlassten sogar einige Kirchenfürsten, der 1536 zu Köln abgehaltenen Synode den Antrag vorzulegen, die Bruderschafts -Vereine wegen der zu Tage getretenen argen Missbräuche gänzlich aufzuheben und ihr Vermögen der Armenunterstützung und dem Unterhalte der Pfarrer zuzu- wenden. Von Seite der versammelten Bischöfe wurde diesem An- sinnen jedoch nicht entsprochen, wahrscheinlich im Hinblicke darauf, dass diese ^frommen Vereinigungen« zu sehr in der Bevölkerung W urzel gefasst und Ausbreitung gewonnen hatten. So blieben die Verhältnisse ohne Veränderung unerquicklich, bis die kräftige Hand Kaiser Josefs II. mit einem Schlage der ganzen Misswirthschaft ein jähes Ende bereitete. | 43,828 |
https://github.com/belyokhin/trusteeWallet/blob/master/crypto/blockchains/btc/address/BtcAddressProcessor.js | Github Open Source | Open Source | MIT | 2,022 | trusteeWallet | belyokhin | JavaScript | Code | 124 | 358 | /**
* @version 0.5
*/
const bitcoin = require('bitcoinjs-lib')
const networksConstants = require('../../../common/ext/networks-constants')
export default class BtcAddressProcessor {
constructor(settings) {
if (typeof settings === 'undefined' || !settings) {
throw new Error('BtcAddressProcessor requires settings')
}
if (typeof settings.network === 'undefined') {
throw new Error('BtcAddressProcessor requires settings.network')
}
if (typeof networksConstants[settings.network] === 'undefined') {
throw new Error('while retrieving Bitcoin address - unknown Bitcoin network specified. Got : ' + settings.network)
}
this._currentBitcoinNetwork = networksConstants[settings.network].network
}
setBasicRoot(root) {
}
/**
* @param {string|Buffer} privateKey
* @param {*} data
* @returns {Promise<{privateKey: string, address: string, addedData: *}>}
*/
async getAddress(privateKey, data = {}) {
const keyPair = bitcoin.ECPair.fromPrivateKey(privateKey, { network: this._currentBitcoinNetwork })
const address = bitcoin.payments.p2pkh({ pubkey: keyPair.publicKey, network: this._currentBitcoinNetwork}).address
return { address, privateKey: keyPair.toWIF() }
}
}
| 13,499 |
sn90050307_1910-09-21_1_1_1 | US-PD-Newspapers | Open Culture | Public Domain | 1,910 | None | None | English | Spoken | 1,177 | 1,681 | \t }3rc5cott 0aUn VOkjy-NO 140_PRESCOTT. ARKANSAS WEDNESDAY, SEPTEMBER 21, 1910 PRICE Ki’v'E CENTS Tk, r MeRae, Pres. Thos. C. McRae, Jr., Cashier. I i Jas. G. Clark, V.-Pres. T. R. Wright, Asst Cashier. BANK OF PRESCOTT PRESCOTT, ARKANSAS. ! CAPITAL STOCK, PAID UP, $35,000.00 SURPLUS. $15,000.00. HINTS TO FARHERS: jj Now is the time that you realize on your season’s work. f. | As you sell your grain, stock j hay or cotton, place your money on open account with a reliable bank. Pay your bills by check, | ;: which makes the best kind of a j j receipt, and avoid the worry and ' 1j danger attending the carrying and hiding of large or small sums j sums of money. Our offices are always at the disposal of our customers and , friends. Thos. C. McRae, Jr^^shj Local News J. B. Munn of Laneburg, was in Prescott today. H. B, McKenzie is spending today in Little Rock. j Scott Transfer Co. will call for your trunk. Phone 86. Mrs. F. J. Johnson and chil dren returned last night from a risit to Texarkana. Cotton is coining in slowly and is bringing from 13 to 13 J cents. Cottonseed is selling at 41c lost—A pair of gold-rimmed glasses. Finder will please re , turn to Joe A. Bryan and receive reward. L*- A. Moody, of Bluff City, passed through Prescott today en route to Southern Texas, on a Prospecting tour. Jno. ]). Bright, of Sutton, was m town today, meeting with the Board ol Equalization, which is 111 session this week. The dry weather is getting luite annoying, the dust being *ery disagreeable, and the lack 0 moisture damaging to fall crops. Fresh line of bulk chocolates at Douglas Brooks’ next door to po’stoftice. The Saturday Evening Post for September 24 now on sale at J. Johnson Jr. News Stand. Mrs. Gertrude Moncrief and Mrs. Arthur Westmoreland are spending a few days with friends in Little Rock. The millinery openings today were attended by a large number of ladies who admired with interest the fine displays of fall millinery. Earl Conklin, of Omaha, Neb., has accepted a position in the East Side barber shop of J. W. McKelvey, succeeding John T. Harris, who has gone to Pine Bluff. The two-year-old daughter of Mr. and Mrs. W. L. Britt of Boughton, remains in a critical condition, but the friends of the family hope for an early improvement. B. J. Daniels, J. T. Burns, Will Buchanan, Will Mitchell, and Clint McCuller are attending the National Association of Rural Mail Carriers, leaving only A. E. McGuire of the regular carriers here. The Citizens Bank CAPITAL, $25,000 Our Services Bur equipment for the protection and safeguarding of money and our facilities for the transaction of municipal matters are respectfully offered to the people of this community with the full assurance that any trust given to this bank will be handled in a safe and air-winded manner. We have no Safety Deposit Boxes to rent, but will be Pleased to keep your valuable papers in our fireproof vault of all cost to you. Unquestionably the greatest value ever offered anywhere at your choice of all the newest and best materials. All sizes. High class suits made by the best manufacturing tailors in New York. Right up to the top notch of fashion and finished in a way that would do justice to the finest custom-tailored garments. They are real $15 Suits. But we make a specialty of selling them at $10. We're bound and determined to give suits at $10 that no other store can equal—Hand-tailored, all wool. 9 a. m. to 1 p. m. MEN’S SUITS Four hours only. Choose from any or medium suit that sold for $15.00. $3.00 Trousers Tomorrow at $1.98 New York Store Scott Transfer Co. haul anything. Phone HO. Woman’s Home Companion for October on sale at 7 Johnson, Jr., News Stand. Dr. S. J. Westerly returned last night from a professional trip to Oklahoma. S. E. Mullins, of Wallaceburg, has accepted a position with the Ozan Mercantile Co. Mrs. J. C. Stegar and Miss Opal Warrell left this morning on a few days visit to Texarkana. Fresh grapes, oranges, apples, bananas, and lemons at Douglas Brooks’ next door to post office. Louis C. Bernays, optician of Little Lock, will be at the Hesterly Drug Store Wednesday and Thursday, Sept. 28-29. W. C. Moore has received his commission as postmaster at Emmett, and will assume charge of the October 1st. W. L. Miller left yesterday for Weber Springs, Ark., where he goes to wind up his affairs in the hotel business and will remove to Prescott with his family in a short time. An auto party of boys, composing Morris Montgomery, Floyd Denman, Jim Gee and Frank Grayson were driven by Floyd Hawkins on a pleasure trip to Hope last night. Dr. R. L. Hinton will fit, and furnish spectacles, and eye glasses and do any kind of repairing— Moncrief Drug Store, Prescott, Ark. Satisfaction given, or your money back. Has had over 30 years experience and study of the work. On account of the illness of Ben Auxer, work moving the old depot is delayed, and will commence as soon as he is able to go to work. The structure to be used as a telegraph office while the new building is being erected is nearing completion and is situated in the street west of the present office. Little Rock Population 45,941 Little Rock, Sept. 20.—This announcement of the population of Little Rock is a great disappointment to the people of Little Rock, who had been confidently expecting a much larger figure. It should be considered, of course, that the census of 1900 and that of 1890 included also Argenta, which has since been separated from Little Rock, but still it was believed that the population of Little Rock itself would be greater than the figure given. In the complete census report a footnote will be added about the separation of Argenta, but as the population of Argenta has not been announced it is impossible at this time to give the combined population of the two towns. The population of Argenta is being variously estimated at from 8,000 to 15,000. The official figures are a very considerable reduction from the estimate made last January by the new city directory, which estimated the population of Little Rock at 78,828, and that of Argentina at 14,628, a combined population of 93,456, which now appears greatly exaggerated. IT SAVED HIS LEG “All thought I’d lose my leg,” writes J. A. Swensen, of Watertown, Wis. “Ten years of eczema, that 15 doctors could not cure, had at last laid me up. Then Bucklen’s Arnica Salve cured it sound and well.” Infallible for Skin Eruptions, Eczema, Salt Rheum, Boils, Fever Sores, Burns, Sores, Cuts and Piles. 25c at Hesterly Drug Store. SUITS are guaranteed to give satisfaction. Our new fall line is now in. Bring your boy in and let us fit him out. Ozan Mercantile Co. Prescott, Ariz. | 6,544 |
https://stackoverflow.com/questions/53976775 | StackExchange | Open Web | CC-By-SA | 2,018 | Stack Exchange | English | Spoken | 227 | 634 | Angular animation with toggle button
I am new to angularjs and am trying to learn how the framework works. Here is my problem.
I wrote a script to have a button showing and hiding the message. At the same time I tried to act animation when the message was being displayed.
Unfortunately, I can either do one of them. As long as I combine the both in the script, I don't know why I have to remove the "hide" button to get the animation work.
Here's my script.
test.html:
<!-- test.html -->
<!DOCTYPE html>
<html ng-app='test'>
<head>
<title>test angular animation</title>
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.4.0/angular.min.js"></script>
<script src="http://ajax.googleapis.com/ajax/libs/angularjs/1.4.0/angular-animate.js"></script>
<script src="test.js"></script>
<style>
div.ng-enter {
transition: 2s linear all;
opacity: 0;
}
div.ng-enter.ng-enter-active {
opacity: 1;
}
</style>
</head>
<body ng-controller="testController as doc">
<!-- TO MAKE THE ANIMATION WORK, THE FOLLOWING HIDE BUTTON HAVE TO BE COMMENTED, PLEASE HELP -->
<button ng-if="doc.div_show" ng-click="doc.div_show=false">hide</button>
<button ng-if="!doc.div_show" ng-click="doc.div_show=true">show</button>
<div ng-if="doc.div_show">Hello World</div>
</body>
</html>
test.js:
/* test.js */
angular.module('test', ['ngAnimate'])
.controller('testController', function() {
var doc = this;
doc.div_show = false;
});
Change your style just as shown in angular docs, like this:
<style>
/* The starting CSS styles for the enter animation */
.fade.ng-enter {
transition:0.5s linear all;
opacity:0;
}
/* The finishing CSS styles for the enter animation */
.fade.ng-enter.ng-enter-active {
opacity:1;
}
</style>
Add a fade class to your div:
<div ng-if="doc.div_show" class="fade">Hello World</div>
| 11,034 |
|
US-201313846704-A_1 | USPTO | Open Government | Public Domain | 2,013 | None | None | English | Spoken | 2,918 | 3,400 | Battery system for vehicle
ABSTRACT
A battery system for a vehicle. The battery system includes: a battery module; a junction box which connects the battery module to other electronic components; and a case which includes the battery module and the junction box. The junction box is integrally mounted on a side surface of the battery module which is fixed to the case, and at least the junction box is non-contact with an inner surface of the case.
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application claims priority from Japanese Patent Application No. 2012-090258 filed on Apr. 11, 2012, the entire contents of which are hereby incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a battery system for a vehicle, and particularly, to a battery system for a hybrid vehicle or an electric vehicle.
2. Description of the Related Art
Some hybrid and electric vehicles released in recent years differ in the configuration in which a battery module to be mounted and a junction box which for connecting the battery module to other electronic components are disposed. For example, Japanese Unexamined Patent Application Publication No. 2007-299593 (hereinafter referred to as JP-A No. 2007-299593) discloses a hybrid vehicle having a configuration in which a center console box between the driver's seat and the assistant driver's seat is provided with a battery pack assembly, and a junction box is disposed on top of the battery pack assembly.
However, when a junction box is disposed on top of the battery module as in the configuration of the technology disclosed in JP-A No. 2007-299593, there is a problem in that the height of the center console box tends to increase, and thus it is difficult to effectively use the space inside the vehicle, for example, by disposing a case, in which the junction box and the battery module are disposed, below the luggage compartment at the rear of the vehicle. Now, an approach may be taken in which the junction box is disposed not on top of the battery module, but at the side of the battery module in the case so as to reduce the height of the case. However, when the junction box and the battery module are fixed to respective surfaces with different heights and vibration is transmitted to the junction box and the battery module, the vibration causes a relative positional difference between the junction box and the battery module, and thus a busbar which connects between the junction box and the battery module may be damaged. When the junction box is directly fixed to the case, operating noise or vibration due to a relay or the like in the junction box is transmitted to the case and further amplified, so that loud noise may be transmitted to the vehicle cabin. In order to prevent such an event, it is necessary to increase the thickness of the plate of the case, and/or provide a reinforcing member. However, this increases the weight of the case and the cost. Replacing the busbar with a more flexible one also increases the cost, and allowing relative motion between the junction box and the battery module in this manner involves a corresponding amount of reserved space in consideration of the relative motion, and thus the space to be reserved may increase.
SUMMARY OF THE INVENTION
The present invention has been made in view of the above-mentioned circumstances, and it is an object of the invention to provide a battery system for a vehicle, which allows the junction box and the battery module to be disposed in a space-saving manner at a low height without increasing the weight, cost, and the overall height of the junction box and the battery module, and in which operating noise or vibration noise due to a relay or the like which occurs in the junction box is not transmitted to the vehicle cabin, and damage of the busbar or the like is prevented.
An aspect of the present invention provides a battery system for a vehicle, the battery system including a battery module; a junction box which connects the battery module to other electronic components; and a case which includes the battery module and the junction box. The junction box is integrally mounted on a side surface of the battery module which is fixed to the case, and at least the junction box is non-contact with an inner surface of the case.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view of a battery pack according to an embodiment of the present invention, the battery pack being disposed below a luggage compartment.
FIG. 2 is an illustrative view from the left side of the battery pack according to the embodiment of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Hereafter, an embodiment of the present invention will be described with reference to the accompanying drawings. In the drawings, numeral 1 indicates a battery pack which serves as a battery system of a hybrid vehicle, and the battery pack 1 is suspended from and supported by the bottom of a luggage compartment between a front cross member 3F and a rear cross member 3R, which are installed in the front-and-rear direction between a rear side frame 2L on the left side of the vehicle, and a rear side frame 2R on the right side of the vehicle.
The battery pack 1 includes a battery module 11, a junction box 12, and a case 13 which houses the battery module 11 and the junction box 12.
The battery module 11 is formed as a battery case 11 a in which e.g., a plurality of battery cells (not illustrated) are stacked, and a slope section 11 b is formed at each of the right and left end portions of the front side of the battery case 11 a in such a manner that the slope section 11 b is downwardly inclined with respect to the upper surface of the battery case 11 a.
The junction box 12 connects the battery module 11 to other electronic components such as a DC-DC converter or an inverter, and includes a relay (not illustrated) which controls a high-voltage circuit of the battery, various sensors (not illustrated) which detect the total voltage and charge/discharge currents of the battery, and a service plug (not illustrated) which blocks the high-voltage circuit with the height dimension of the junction box 12 smaller than the height dimension of the battery module 11. At the right and left end portions of the rear surface of the junction box 12, slope sections 12 a, 12 a are respectively formed in shapes corresponding to the slope sections 11 b, 11 b, at positions corresponding to the slope sections 11 b, 11 b at the front of the battery case 11 a in such a manner that the slope sections 12 a, 12 a are upwardly inclined with respect to the lower surface of the junction box 12.
The lower surfaces of the slope sections 12 a, 12 a of the junction box 12 are then opposed and connected to the upper surfaces of the slope sections 11 b, 11 b of the battery case 11 a, and thus the upper surfaces of the battery module 11 and the junction box 12 are substantially coplanar, and the junction box 12 is integrally mounted on an upper portion of the front side surface of the battery module 11.
Specifically, the integrated battery module 11 and the junction box 12 are housed in the case 13 via a pair of U-shaped right and left fixing frames 14L, 14R, and supported by the front and rear cross members 3F, 3R, the right and left fixing frames 14L, 14R being formed extending in the front-and-rear direction below the undersurface of the battery module 11 and supporting the battery module 11 and the junction box 12 from below.
The left rear end portion of the battery module 11 is fixed to the rear end of the fixing frame 14L by a bolt 21L which penetrates through the upper surface of the battery module 11, and the left front end portion of the battery module 11 along with the junction box 12 is fixed to an approximately center of the fixing frame 14L by a bolt 22L which penetrates through the upper surface of the slope section 12 a at the left rear end of the junction box 12. Similarly, the right rear end portion of the battery module 11 is fixed to the rear end of the fixing frame 14R by a bolt 21R which penetrates through the upper surface of the battery module 11, and the right front end portion of the battery module 11 along with the junction box 12 is fixed to an approximately center of the fixing frame 14R by a bolt 22R which penetrates through the upper surface of the slope section 12 a at the right rear end of the junction box 12.
The left front end portion of the junction box 12 is fixed to a front end portion of the fixing frame 14L via an interposed elastic members 15 such as rubber by a bolt 23L which penetrates through the upper surface of the junction box 12, and the right front end portion of the junction box 12 is fixed to a front end portion of the fixing frame 14R via an interposed elastic members 15 such as rubber by a bolt 23R which penetrates through the upper surface of the junction box 12.
Numeral 16 in FIG. 2 indicates a busbar which connects the battery module 11 to the junction box 12.
In the battery pack 1 according to the thus-configured embodiment of the invention, when vibration is transferred from the vehicle body, the vibration is transmitted via the fixing frames 14L, 14R to the battery module 11 having the front side surface on which the junction box 12 is integrally mounted, and thus the vibration is not separately transmitted to the battery module 11 and junction box 12. For this reason, no relative motion occurs between the battery module 11 and the junction box 1, and thus no stress is applied to the busbar 16 which connects the battery module 11 and the junction box 12, and therefore, without changing the quality of the material of the busbar 16 and increasing the weight or cost for reinforcement, and even without considering extra space allowing relative motion between the battery module 11 and the junction box 1, the battery module 11 and the junction box 1 can be disposed in a space-saving manner and damage of the busbar 16 can be appropriately prevented. It is to be noted that the front end portion of the junction box 12 is supported by the fixing frames 14L, 14R with the elastic member 15 interposed therebetween, and thus vibration transmitted from the fixing frames 14L, 14R is significantly small. By supporting the junction box 12 via the elastic member 15 as in the present embodiment, even when the junction box 12 is supported with a large overhang from the side surface of the battery module 11, the junction box 12 can be stably and integrally supported with the battery module 11.
The junction box 12 is non-contact with the case 13 and integrally mounted on the side surface of the battery module 11, and thus operating noise or vibration due to a relay or the like in the junction box 12 is not transmitted via the case 13 to the vehicle cabin, but is transmitted to the heavy battery module 11 on which the junction box 12 is integrally mounted, and is subsequently transmitted to the fixing frames 14L, 14R. Thus, the operating noise and vibration are absorbed by the battery module 11, thereby preventing an increase in the operating noise and vibration.
In addition, the junction box 12 is integrally mounted on the side surface of the battery module 11, and thus the overall height of the junction box 12 and the battery module 11 is not increased, and so the space in the cabin of the vehicle can be effectively used, for example, the case 13, in which the battery module and the junction box are disposed, can be easily disposed below the luggage compartment at the rear of the vehicle.
According to the embodiment, attachment of the battery module 11 and the junction box 12 can be made using the bolts 21L, 21R, 22L, 22R, 23L, 23R which penetrate from above, thereby providing improved maintenance performance and assembly performance.
Although the upper surfaces of the battery module 11 and the junction box 12 are substantially coplanar in the embodiment of the present invention, the upper surfaces may be non coplanar. When the junction box 12 has a small overhang from the connection surface with the battery module 11, or has a light weight, only the bolts for connection with the battery module 11 may be used. Furthermore, the shape of the vertically crossing portion of the connection between battery module 11 and the junction box 12 is not limited to the shape of the slope sections 11 b, 11 b, 12 a, 12 a in the embodiment of the present invention, and may be in a step-like crossing shape. In addition, although the battery module 11 and the junction box 12 are housed in the case 13 via the fixing frames 14L, 14R, and supported by the front and rear cross members 3F, 3R in the embodiment of the present invention, the battery module 11 and the junction box 12 may be housed in the case 13 without using the fixing frames 14L, 14R, and are supported by the front and rear cross members 3F, 3R.
What is claimed is:
1. A battery system for a vehicle comprising: a battery module; a junction box connecting the battery module to other electronic components; and a case including the battery module and the junction box, wherein the junction box is integrally mounted on a side surface of the battery module which is fixed to the case, and at least the junction box is non-contact with an inner surface of the case, wherein the integrally mounted battery module and the junction box are fixed to the case via a fixing frame, wherein the junction box is provided with an elastic member at a bottom surface, and is supported by the elastic member from below, and wherein an upper surface of the junction box and an upper surface of the battery module are coplanar.
2. The battery system for a vehicle according to claim 1, wherein a connection between the battery module and the junction box forms a vertically crossing portion, and the junction box is vertically secured to the battery module by inserting a bolt which penetrates through the crossing portion.
3. The battery system for a vehicle according to claim 1, wherein the junction box protrudes in a horizontal direction from the battery module.
4. The battery system for a vehicle according to claim 1, further comprising a bulbar which connects the battery module to the junction box.
5. The battery system for a vehicle according to claim 1, further comprising a busbar connecting the battery module to a portion of the junction box which is in non-contact with the battery module.
6. The battery system for a vehicle according to claim 1, wherein the bottom surface of the junction box and a bottom surface of the battery module are non-coplanar.
7. The battery system for a vehicle according to claim 1, wherein the junction box protrudes from the battery module.
8. A battery system for a vehicle comprising: a battery module; a junction box connecting the battery module to other electronic components; and a case including the battery module and the junction box, wherein the junction box is integrally mounted on a side surface of the battery module which is fixed to the case, and at least the junction box is non-contact with an inner surface of the case, wherein the integrally mounted battery module and the junction box are fixed to the case via a fixing frame, wherein the junction box is provided with an elastic member at a bottom surface, and is supported by the elastic member from below, wherein the battery module comprises a slope section that is downwardly inclined with respect to an upper surface of the battery module, wherein the junction box comprises a slope section that is upwardly inclined with respect to a lower surface of the junction box, and wherein the slope section of the junction box is integrally connected to the slope section of the battery module.
9. The battery system for a vehicle according to claim 8, wherein a portion of the slope section of the junction box is non-contact with the battery module.
10. The battery system for a vehicle according to claim 9, further comprising a busbar which connects the portion of the junction box to the battery module.
11. The battery system for a vehicle according to claim 8, wherein an upper surface of the junction box and an upper surface of the battery module are coplanar.
12. The battery system for a vehicle according to claim 11, wherein the bottom surface of the junction box and a bottom surface of the battery module are non-coplanar.
13. The battery system for a vehicle according to claim 8, wherein a portion of the junction box is non-contact with the battery module..
| 7,071 |
https://github.com/jabranr/postcodes-io/blob/master/src/Exception/MalformedJsonException.php | Github Open Source | Open Source | MIT | 2,018 | postcodes-io | jabranr | PHP | Code | 11 | 51 | <?php
namespace Jabranr\PostcodesIO\Exception;
use Jabranr\PostcodesIO\Exception\PostcodeIOException;
class MalformedJsonException extends PostcodeIOException {
}
| 36,432 |
https://cy.wikipedia.org/wiki/Llwydni%20gwlannog%20bresych | Wikipedia | Open Web | CC-By-SA | 2,023 | Llwydni gwlannog bresych | https://cy.wikipedia.org/w/index.php?title=Llwydni gwlannog bresych&action=history | Welsh | Spoken | 203 | 534 | Math a rhywogaeth o ffwng yn nheulu'r Peronosporaceae yw'r Llwydni gwlannog bresych (Lladin: Hyaloperonospora brassicae; Saesneg: Brassica Downy Mildew). Llwydni Dŵr yw'r enw ar lafar ar y grwp mae'r ffwng yma'n perthyn iddo, ond nid yw'n derm gwyddonol. Mae oomycetes I'w cael ar ffurfiau saproffytig a phathogenig, ac yn cynnwys rhai o'r pathogenau mwyaf niweidiol o blanhigion, gan achosi afiechydon dinistriol fel malltod tatws a marwolaeth sydyn coed derw. Mae'r teulu Peronosporaceae yn gorwedd o fewn urdd y Peronosporales.
Ffyngau
Credir fod rhwng 2.2 a 3.8 miliwn o wahanol rywogaethau o ffwng, a'u bod yn perthyn yn nes at grwp yr anifeiliaid nag at blanhigion. Gelwir yr astudiaeth o ffwng yn "feicoleg", sy'n dod o'r Groeg μύκης (mykes) sef 'madarchen'. Mae tua 120,000 o'r rhain wedi'u disgrifio gan naturiaethwyr megis Carolus Linnaeus, Christiaan Hendrik Persoon ac Elias Magnus Fries. Oherwydd mai prin iawn yw gwybodaeth gwyddonwyr am y pwnc hwn, mae tacson y ffyngau'n newid o ddydd i ddydd. Credir bod oddeutu 20,000 o rywogaethau o ffyngau yng ngwledydd Prydain.
Aelodau eraill o deulu'r Peronosporaceae
Mae gan Llwydni gwlannog bresych ambell aelod arall yn y teulu hwn, gan gynnwys y canlynol:
Gweler hefyd
Rhestr Goch yr IUCN
Llên Natur
Cyfeiriadau
Peronosporales
Llwydni Dŵr | 5,004 |
US-4271905-A_2 | USPTO | Open Government | Public Domain | 2,005 | None | None | English | Spoken | 4,735 | 6,234 | Note that in fabric 300, the stitching MD yarns in each stitching MD yarn pair are pulled toward each other by the forces that cause those yarns to couple with the bottom MD yarns. As a result, the stitching MD yarns tend to align themselves approximately halfway between the bottom MD yarns (except at the locations where they couple with a bottom MD yarn), which provides for improved straight through drainage in the fabric. In contrast, in the fabric 100 of FIGS. 1-3, the stitching MD yarns in each stitching MD yarn pair are pulled away from each other toward the bottom MD yarn which they are adjacent to.
The principles of the present invention can be extended to fabrics woven with different repeat patterns. For instance, a triple layer fabric 400 according to the present invention woven on 20 harnesses is depicted in FIGS. 10-12. FIG. 10 depicts a top view of the top fabric layer 402 of the triple layer fabric 400 (i.e., a view of the papermaking surface) while FIG. 11 depicts a top view of the bottom fabric layer 404 of fabric 400 (i.e., a view of the fabric 400 with the yarns that weave exclusively in the top fabric layer 402 removed). FIGS. 12A-12D depict the weave pattern of top MD yarn 410, bottom MD yarn 450, and stitching MD yarns 420 and 425, respectively. The triple layer fabric of FIGS. 10-12 is woven on twenty harnesses, and hence a single repeat of the fabric encompasses twenty machine direction yarns. While FIGS. 10 and 11 only show a single repeat unit of the fabric, those of skill in the art will appreciate that in commercial applications the depicted portion would be repeated many times, in both the machine and cross machine directions.
As seen in FIG. 10, the repeat unit of the top fabric layer 402 includes a set of top MD yarns 410414 and a set of top CMD yarns 430-439 that are interwoven together. The top fabric layer further includes a set of five stitching MD yarn pairs 420, 425; 421, 426; 422, 427; 423, 428; 424, 429 that also interweave with the top CMD yarns 430-439. As shown in FIG. 10, a stitching MD yarn pair, such as for example, stitching MD yarn pair 420, 425, is provided between each pair of adjacent top MD yarns (e.g., yarns 410-411). Each stitching MD yarn pair (such as pair 420, 425) is woven such that while one of the yarns of the pair (e.g., yarn 420) weaves in the top fabric layer 402 to complete the weave pattern in the top fabric layer 402, the other of the stitching MD yarns (e.g., yarn 425) drops down into the bottom fabric layer 404 to bind the top fabric layer 402 and the bottom fabric layer 404 together. In this manner, the stitching MD yarn pairs 420, 425; 421, 426; 422, 427; 423, 428; 424, 429 both complete the weave of the top layer fabric 402 and also serve to bind the top and bottom fabric layers 402, 404 together. As further shown in FIG. 10, the yarns comprising the set of top CMD yarns 430-439 are interwoven with the set of top layer MD yarns 410-414 and the stitching MD yarn pairs 420, 425; 421, 426; 422, 427;
423, 428; 424, 429 in a plain weave pattern, meaning that each of the top CMD yarns 430-439 alternatively pass below one, and then above the next, of the machine direction yarns that at that point are weaving in the papermaking surface.
Referring now to FIG. 11, a repeat unit of the machine side surface of the bottom fabric layer 404 of the fabric 400 is shown. The repeat unit includes a set of bottom MD yarns 450-454 which are interwoven with a set of bottom CMD yarns 460-464. The repeat unit further includes the stitching MD yarn pairs 420, 425; 421, 426; 422, 427; 423, 428; 424, 429 which are described above.
As shown in FIG. 11, the bottom CMI yarns 460-464 of fabric 400 may be constructed using relatively large diameter yarns that are well suited to sustain the wear caused by papermaking machine during use of the fabric 400. As can also be seen in FIG. 11, the weave pattern of fabric 400 provides relatively long cross machine direction “floats” on the machine side surface.
FIGS. 12A-12D depict the individual machine direction yarn paths of representative machine direction yarns in the fabric 400. FIG. 12A depicts the machine direction yarn paths for top MD yarn 410. Top MD yarns 411-414 are woven in identical weave patterns. As shown in FIG. 12A, each of these top MD yarns 410-414 are woven in over-one/under-one patterns with the top CMD yarns 430-439 (and each top MD yarn 410-414 passes over the exact same top CMD yarns 430, 432, 434, 436, 438) and do not weave with any yarns in the bottom fabric layer 404.
FIG. 12B depicts the machine direction yarn path of bottom MD yarn 450. As shown in FIG. 12B, bottom MD yarn 450 weaves with the bottom CMD yarns 460-464 in an over-two/under-one/over-one/under-one pattern—i.e., it passes over bottom CMD yarns 460-461, passes under bottom CMD yarn 462, passes over bottom CMD yarn 463 and passes under bottom CMD yarn 464 in each repeat of the fabric. The other bottom MD yarns 451-454 follow a similar “over-two/under-one/over-one/under-one pattern” weave pattern, although the starting point for the pattern is offset by one bottom CMD yarns 460-464 for each adjacent bottom MD yarn 450-454.
FIG. 12C depicts the machine direction yarn path of stitching MD yarn 420. As shown in FIG. 12C, stitching MD yarn 420 is woven in an under-one/over-four pattern with respect to the bottom CMD yarns 460-464, and is woven in a under-seven/over-one/under-one/over-one pattern with respect to the top CMD yarns 430-439. Stitching MD yarns 421-424 follow the same patterns with respect to the bottom CMD yarns 460-464 and the top CMD yarns 430-439 as stitching MD yarn 420, except that the starting point for the pattern is offset by one bottom CMD yarns 460-464 (and hence two top CMD yarns 430-439) for each adjacent stitching MD yarn 420-424.
FIG. 12D depicts the machine direction yarn path of stitching MD yarn 425. As shown in FIG. 12D, stitching MD yarn 425 is woven in an over-four/under-one pattern with respect to the bottom CMD yarns 460-464, and is woven in a under-one/over-one/under-five/over-one/under-one/over-one pattern with respect to the top CMD yarns 430-439. Stitching MD yarns 426429 follow the same patterns with respect to the top CMD yarns 430-439 as stitching MD yarn 425, except that the starting point for the pattern is offset by one bottom CMD yarns 460-464 (and hence two top CMD yarns 430-439) for each adjacent stitching MD yarn 425-429.
The present invention is directed to “true” triple layer fabrics—meaning triple layer fabrics that include (1) a set of MD yarns and a set of CMD yarns that each weave exclusively in a top fabric layer and (2) a set of MD yarns and a set of CMD yarns that each weave exclusively in a bottom fabric layer—that are stitched together by machine direction yarns. Such machine direction yarn stitched true triple layer fabrics may typically be manufactured less expensively than most high-performance cross machine direction yarn triple layer fabrics while providing improved fiber support (with the plain weave top surface) compared to conventional double layer fabrics. Pursuant to the teachings of the present invention, it will be appreciated that the machine direction yarn stitched true triple layer fabrics may have improved stacking of the machine direction yarns, increased permeability and higher void volumes as compared to double layer fabrics. Additionally, by using yarn pairs that complete the weave in the papermaking surface as the stitching yarns it is possible to bind the fabric together at numerous locations, thereby providing a very stable fabric that is not particularly susceptible to interlayer wear.
Each of the fabrics 100, 200, 300, 400 depicted in the figures includes MD stitching yarn pairs in which the yarns that comprise the pair interlace with the top fabric layer an unequal number of times in each repeat of the fabric. For example, as shown best in FIGS. 3B and 3C, each stitching MD yarn pair 120, 124; 121, 125; 122, 126; 123, 127 of fabric 100 include a stitching MD yarn (e.g, yarn 120) that interlaces with the top fabric layer 102 five time per repeat and a stitching MD yarn (e.g., yarn 124) that interlaces with the top fabric layer 102 three times per repeat unit of the fabric. This “unequal interlacing” configuration may provide improved fabric uniformity—particularly on the top surface. As will be appreciated by those of skill in the art, when the fabric is woven off two warp beams, the crimp of the warp yarns woven off each beam will be different. Thus, by weaving the top MD yarns off the same warp as the stitching MD yarns that interlace the greater number of times in the top fabric layer, it may be possible to provide for a more uniform papermaking surface.
Those of skill in the art will appreciate that numerous modifications can be made to the above described fabrics. By way of example, the stitching MD yarn pairs can have a wide variety of weave patterns in terms which they complete the weave of the top fabric layer. Thus, the number of top MD yarns that each stitching MD yarn passes over to complete the plain weave pattern on the papermaking surface may vary, as may the frequency with which the yarns pass in and out of the top fabric layer. Additionally, a variety of different weave patterns may be employed in the top fabric layer, specifically including 1×2 twill, 2×2 twill, 1×3 twill and 1×4 twill papermaking surfaces, as well as various derivatives of the above-mentioned weave patterns, specifically including broken twill patterns such as those embodied in 4 or 5 harness satin single layer fabrics, which are known in the art as providing a good papermaking surface. Likewise, the frequency of the stitch points and/or the ratio of top-to-bottom machine direction and/or cross machine direction yarns may be varied. Thus, the scope of the present invention should be construed based on the claims appended hereto, as opposed to the illustrative examples of the claimed fabrics which are provided herein to fully enable those of skill in the art to practice the claimed invention.
Another exemplary modification would be to alternate for each adjacent stitching MD yarn pair the warp beam from which the stitching MD yarns are woven. For example, the fabric of FIGS. 1-3 could be modified so that stitching MD yarns 120, 125, 122, 127 are woven off the same warp beam as top MD yarns 110-113 and stitching MD yarns 124, 121, 126, 123 are woven off the same warp beam as bottom MD yarns 150-153 to effect this modification. This reversal of the stitching yarn positions may reduce any diagonal pattern in the fabric and hence improve fabric performance.
Those of skill in the art will likewise appreciate that the stitching MD yarn pairs need not be included between every adjacent pair of top MD yarns. Instead, a stitching MD yarn pair may be provided after every second, third, fourth or fifth top MD yarn. Those of skill in the art will also appreciate that the frequency of interlacing can be varied from that shown in the fabrics pictured herein. However, the stitching MD yarns should sufficiently bind the upper and lower fabric layers together to prevent excessive movement between the fabric layers, as such excessive movement could result in severe inter-layer wear problems.
Yet another exemplary modification would be to shift the positions of the top fabric layer and the bottom fabric layer of the depicted embodiments (or other embodiments) relative to each other. For example, in the fabric 100 of FIGS. 1-3, the position of the top fabric layer 102 with respect to the bottom fabric layer 104 might be shifted by one top CMD yarn.
Pursuant to another aspect of the present invention, the size and or stiffness of selected of the top CMD yarns may be varied to improve fabric performance. As illustrated best in FIG. 1, the papermaking surface of certain fabrics made according to the present invention include “transition points” where one of the stitching MD yarns in a stitching MD yarn pair completes its run on the papermaking surface and dives down into the center of the fabric while the second yarn of the stitching MD yarn pair emerges from the center of the fabric to start its run on the papermaking surface. An example of such a transition point is the point where stitching MD yarns 120 and 124 pass under top CMD yarn 140 in FIG. 1. At these transition points the yarns of the stitching MD yarn pair enter or exit the fabric at a steeper angle as the yarns dive down to, or emerge from, a portion of their run where they weave with the bottom fabric layer 104. This steeper angle may decrease the crimp on the stitching MD yarns at the position where they pass over the last top CMD yarn adjacent to the transition point—i.e., where stitching MD yarn 120 passes over top CMD yarn 139 and where stitching MD yarn 124 passes over top CMI yarn 141—as the stitching MD yarn exerts sufficient force on the top CMD yarn to pull the top CMD yarn slightly farther into the middle of the fabric at this point. Pursuant to the teachings of the present invention, it will be understood that this reduction in the crimp of the stitching MD yarn knuckles adjacent the transition points can be reduced or eliminated by using slightly larger diameter top CMD yarns for the top CMD yarns that bracket each transition point. In the fabric of FIG. 1, this would mean making top CMD yarns 131, 133, 135, 137, 139, 141, 143, 145 slightly larger than top CMD yarns 130, 132, 134, 136, 138, 140, 142, 144. For example, if top CMD yarns 130, 132, 134, 136, 138, 140, 142, 144 are 0.15 millimeters in diameter, then top CMD yarns 131, 133, 135, 137, 139, 141, 143, 145 may be made 0.17 millimeters in diameter. The use of larger diameter and/or higher modulus top CMD yarns may also improve uniformity of the papermaking surface at the transition points themselves. If such yarns are not used, the papermaking surface knuckle formed by the top CMD yarn directly over the transition point may be lower than the remainder of the knuckles formed by the top CMD yarns because the stitching MD yarns at that location dive down at a steeper angle and hence provide less support to the top CMD yarn. By using larger diameter or higher modulus yarns on the top CMD yarn positions that straddle the transition point it is possible to raise the height of the top CMD yarn that passes over the transition point at the transition point location.
Notably, in the bottom fabric layers 104, 204, 304, 404 of fabrics 100, 200, 300, 400, respectively, the set of bottom MD yarns and the set of bottom CMD yarns form a machine-side surface having only “single float” machine direction knuckles. By a “single float” machine-side machine direction knuckle it is meant that when the bottom fabric layer is viewed from the top, no machine direction yarn passes under more than one consecutive cross machine direction yarn (such that the MD yarn is on the machine-side surface) before passing back to the top surface of the bottom fabric layer. In a preferred embodiment of the triple layer forming fabrics of the present invention, the bottom fabric layer is woven so as to have a machine side surface composed exclusively of machine side “single float” machine direction knuckles.
The fabrics pictured and otherwise described and claimed herein may be employed in a variety of applications, including forming fine paper grades, tissue paper, brown paper and newsprint, but is especially beneficial of fine paper, newsprint and brown paper applications.
The configurations of the individual yarns utilized in the fabrics of the present invention can vary, depending upon the desired properties of the final papermakers' fabric. For example, the yarns may be multifilament yarns, monofilament yarns, twisted multifilament or monofilament yarns, spun yarns, or any combination thereof. Also, the materials comprising yarns employed in the fabric of the present invention may be those commonly used in papermakers' fabric. For example, the yarns may be formed of polypropylene, polyester, nylon, or the like. The skilled artisan should select a yarn material according to the particular application of the final fabric.
Regarding yarn dimensions, the particular size of the yarns is typically governed by the mesh of the papermaking surface. In a typical embodiment of the triple layer fabrics disclosed herein, preferably the diameter of the top CMD yarns, and all of the MD yarns is between about 0.10 and 0.20 mm, and the diameter of the bottom CMD yarns is between about 0.22 and 0.50 mm. Those of skill in the art will appreciate that yarns having diameters outside the above ranges may be used in certain applications. In one embodiment of the present invention, the top CML yarns and all of the MD yarns have diameters between about 0.15 and 0.17 mm, and the diameter of the bottom CMD yarns is between about 0.25 and 0.40 mm to provide fabrics with a target top mesh of 75×75 yarns per inch. Fabrics employing these yarn sizes may be implemented with polyester yarns or a combination of polyester and nylon yarns.
Pursuant to another aspect of the present invention, methods of making paper are provided. Pursuant to these methods, one of the exemplary papermaker's forming fabrics described herein is provided, and paper is then made by applying paper stock to the forming fabric and by then removing moisture from the paper stock. As the details of how the paper stock is applied to the forming fabric and how moisture is removed from the paperstock is well understood by those of skill in the art, additional details regarding this aspect of the present invention will not be provided herein.
The foregoing embodiments are illustrative of the present invention, and are not to be construed as limiting thereof. The invention is defined by the following claims, with equivalents of the claims to be included therein.
1-40. (canceled)
41. A triple layer papermaker's forming fabric comprising: a set of top CMD yarns; a set of top MD yarns interwoven exclusively with the top CMD yarns to form at least part of a top fabric layer having a papermaking surface; a set of bottom CMD yarns; a set of bottom MD yarns interwoven exclusively with the bottom CMD yarns to form at least part of a bottom fabric layer having a machine side surface; and a set of stitching MD yarn pairs, wherein at least one of the stitching MD yarns in each stitching MD yarn pair weaves in both the top fabric layer and the bottom fabric layer and wherein the stitching MD yarns in each stitching MD yarn pair are woven such that at locations where the first of the two stitching MD yarns in each stitching MD yarn pair weaves in the top fabric layer the second of the two stitching MD yarns in the stitching MD yarn pair drops below the top fabric layer so that together the two stitching MD yarns in each stitching MD yarn pair complete the weave in the top fabric layer, and wherein at least some of the stitching MD yarns in the stitching MD yarn pairs bind the top fabric layer and the bottom fabric layer together; and wherein each stitching MD yarn couples with a respective one of the bottom MD yarns at locations where each stitching MD yarn passes below one of the bottom CMD yarns.
42. The papermaker's fabric of claim 41, wherein each stitching MD yarn couples with a non-adjacent bottom MD yarn at locations where each stitching MD yarn passes below one of the bottom CMD yarns.
43. The papermaker's fabric of claim 41, wherein each stitching MD yarn couples with an adjacent bottom MD yarn at locations where each stitching MD yarn passes below one of the bottom CMD yarns.
44. The papermaker's fabric of claim 41, wherein in each repeat of the fabric the first stitching MD yarn in each stitching MD yarn pair passes below the same bottom CMD yarn as does the bottom MD yarn directly adjacent to the second stitching MD yarn in each stitching MD yarn pair and the second stitching MD yarn in each stitching MD yarn pair passes below the same bottom CMD yarn as does the bottom MD yarn directly adjacent to the first stitching MD yarn in each stitching MD yarn pair.
45. The papermaker's forming fabric of claim 41, wherein the first of the two stitching MD yarns in each stitching MD yarn pair couples with a first one of the yarns in the set of bottom MD yarns at locations where the first of the two stitching MD yarns passes below a bottom CMD yarn, and the second of the two stitching MD yarns in each stitching MD yarn pair couples with a second one of the yarns in the set of bottom MD yarns that is different than the first one of the yarns in the set of bottom MD yarns at locations where the second of the two stitching MD yarns passes below a bottom CMD yarn.
46. The papermaker's forming fabric of claim 41, wherein no more than two machine-side machine direction knuckles are formed on any bottom CMD yarn in a single repeat of the fabric.
47. The papermaker's forming fabric of claim 41, wherein a stitching MD yarn pair is provided adjacent each top MD yarn.
48. The papermaker's forming fabric of claim 41, wherein the two stitching MD yarns in each pair of stitching MD yarns interlace with different numbers of top CMD yarns in each repeat of the fabric.
49. The papermaker's forming fabric of claim 41, wherein one of the two stitching MD yarns in each stitching MD yarn pair passes over no more than two top CMD yarns in any repeat of the fabric.
50. The papermaker's forming fabric of claim 41, wherein at least some of the top CMD yarns that the stitching MD yarns of the stitching MD yarn pairs pass over immediately before dropping down into the bottom fabric layer have a different modulus of elasticity and/or diameter than the remainder of the top CMD yarns.
51. The papermaker's fabric of claim 41, wherein the top CMD yarns that the top MD yarns pass over have a smaller diameter than the remainder of the top CMD yarns.
52. A triple layer papermaker's forming fabric comprising: a set of top CMD yarns; a set of top MD yarns interwoven exclusively with the top CMD yarns to form at least part of a top fabric layer having a papermaking surface; a set of bottom CMD yarns; a set of bottom MD yarns interwoven exclusively with the bottom CMD yarns to form at least part of a bottom fabric layer having a machine side surface; and a set of additional MD yarns, wherein the additional MD yarns are woven in pairs such that the first of the MD yarns in each additional MD yarn pair weaves in both the top fabric layer and the bottom fabric layer to bind the top fabric layer and the bottom fabric layer together and the second of the MD yarns in each additional MD yarn pair weaves exclusively in the top fabric layer; wherein the MD yarns in each additional MD yarn pair are woven so that together the two MD yarns in each additional MD yarn pair complete the weave in the top fabric layer.
53. The papermaker's forming fabric of claim 52, wherein the MD yarns in each additional MD yarn pair together weave in the top fabric layer as the equivalent of a single yarn woven in an over-one-under-one pattern with the yarns comprising the set of top CMD yarns.
54. The papermaker's forming fabric of claim 52, wherein the second MD yarn in each additional MD yarn pair passes above a total of six of the top CMD yarns in each repeat of the fabric.
55. The papermaker's forming fabric of claim 54, wherein the first MD yarn in each additional MD yarn pair passes below a total of two of the bottom CMD yarns and above a total of two of the top CMD yarns in each repeat of the fabric.
56. The papermaker's forming fabric of claim 52, wherein each yarn in the set of bottom MD yarns passes below the same number of bottom CMD yarns as does each of the first of the MD yarns in each additional MD yarn pair.
57. The papermaker's forming fabric of claim 56, wherein, in each repeat of the fabric, the first MD yarn in each additional MD yarn pair forms two spaced-apart machine side machine direction knuckles and each bottom MD yarn forms two spaced-apart machine side machine direction knuckles, and wherein the number of bottom CMD yarns between the two spaced-apart machine side machine direction knuckles formed by the first MD yarn in each additional MD yarn pair is equal to the number of bottom CMD yarns between the two spaced-apart machine side machine direction knuckles formed by each bottom MD yarn.
58. The papermaker's fabric of claim 52, wherein an additional MD yarn pair is provided adjacent each top MD yarn.
59. The papermaker's fabric of claim 52, wherein each of the second MD yarns in each additional MD yarn pair weaves in the same pattern with respect to both the set of top CMD yarns and the set of bottom CMD yarns, except that the weave pattern is offset by a total of four top CMD yarns for adjacent of the second MD yarns in each additional MD yarn pair.
60. The papermaker's fabric of claim 52, wherein each additional MD yarn pair is woven in a dropped knuckle pattern.
61. The papermaker's fabric of claim 60, wherein the second of the MD yarns in each additional MD yarn pair drops every fourth machine direction knuckle on the papermaking surface.
62. The papermaker's fabric of claim 52, wherein the machine direction knuckles on the machine side surface form a twill pattern.
63. A triple layer papermaker's forming fabric, a repeat of which comprises: a set of top weft yarns; at least first and second top warp yarns, each of which is interwoven exclusively with at least some of the yarns in the set of top weft yarns to form at least part of a top fabric layer having an upper papermaking surface; a set of bottom weft yarns; at least first and second bottom warp yarns, each of which is interwoven exclusively with the bottom weft yarns to form at least part of a bottom fabric layer having a lower machine side surface; and at least a first pair of additional warp yarns provided between the first and second top warp yarns, the first pair of additional warp yarns including a first stitching warp yarn that interlaces with at least one of the yarns in the set of top weft yarns and at least one of the yarns in the set of bottom weft yarns to bind the top fabric layer and the bottom fabric layer together and a first filler warp yarn that weaves exclusively in the top fabric layer and which weaves under each yarn in the set of top weft yarns that the first stitching warp yarn weaves over, wherein the first stitching warp yarn is directly adjacent to the first filler warp yarn;
64. The papermaker's forming fabric of claim 63, wherein the first pair of additional warp yarns are woven so that together the first stitching warp yarn and the first filler warp yarn complete the weave in the top fabric layer.
65. The papermaker's forming fabric of claim 63, wherein the first pair of additional warp yarns is woven in a dropped knuckle pattern..
| 42,146 |
26736faf2240810fec2a1408e85562c3 | French Open Data | Open Government | Licence ouverte | 2,006 | Code du tourisme., article R163-2 | LEGI | French | Spoken | 52 | 65 | Pour l'application du présent livre : 1° Les mots : " région " ou " département " sont remplacés par les mots : " collectivité départementale " ; 2° Les mots : " préfet de région " ou " préfet de département " sont remplacés par le mot : " préfet ". | 29,299 |
https://github.com/dangfan/virblog/blob/master/app/models/enums/PostTypes.scala | Github Open Source | Open Source | Apache-2.0 | 2,017 | virblog | dangfan | Scala | Code | 62 | 178 | package models.enums
import play.api.libs.json._
object PostTypes extends Enumeration {
type PostType = Value
val Post, Page = Value
implicit def reads: Reads[PostType] = new Reads[PostType] {
def reads(json: JsValue): JsResult[PostType] = json match {
case JsString(v) => JsSuccess(PostTypes.withName(v))
case _ => JsError("String value expected")
}
}
implicit def writes: Writes[PostType] = new Writes[PostType] {
def writes(v: PostType): JsValue = JsString(v.toString)
}
} | 49,241 |
sn92053934_1913-11-17_1_9_1 | US-PD-Newspapers | Open Culture | Public Domain | null | None | None | English | Spoken | 5,715 | 9,497 | 7 VI X 3 -4 .1' i ' YES INDEED! BEN IS NOW ft L6TTEE. FOCJ ( INOO SkJI y i s. ill i r -n . l l( Irgus Branch Offices 4 For the vi-i'minKlXloa of Its patrons In vr.'. u (.art of tne it. Aigua Las es abl.snc-1 a ivMtm of branch-offices, where subscriptions and wnnt ad- vertHinx niay be revelvc-d unci any in f Trir.a t.-n left that may pertain to any j Aepan jier.t of tf.e paper. new or buil- ness. It la also pUnr.td to have at each ot these branch office- every evening t-l piy r of J n ArU 01 irie have f illed under any rircumatances to receive it. paper, wul bo sutphed free Tf "Ar, cha.n of branch offlres lnclu!'S trie follxw lr.z: J. J. Kipp s boUou store, 4S1S Fifth vnu. H. K. Riwi pnarmacy. 4111 Four teenth aven-je. Schneider's drue Ft ore. Twenty-seven ' h jirei. Seeniii nvtfiue. ITllerneytr's dr-ia; store, eleventh ave nne. J'IMeinth stret. I'auiey'a iunch room, ill Knurlh a. r. iie. Mrs. f-ondon'o notion store. Seventh Street. Ko'jrteerith tvmut. Ueiu. beck's piirmscy. 2S ThlfJ ave nue. ilricit Eberts' grocery. 2i Eleventh aven ,,r. Ru'l rt drug store. Thirtieth street and K:nh avi.ue. Coilesje priarmac". Seventh avenue end Tl.irtj -eighth street. Olson griKcrif, Thirteenth avenue and Thirtieth street. titelner drug; store, corner Fifth art cue fend Twenty-third nrt?L IlaKiina- I'rurt grwry, 1 7 2S Twenty-sixth street T. K Keiley tt. tion. Kfooery, 1S23 N nth strtet. Ktfit m; I iiui tLs J'OIC RENT -- M"iiern fo1: ro-in ei-tK'- rtt ll''I .ixfji avti. .c. lii'i'iiie ..Sn 1'weifii, iimi. I OK ItENT- EiKi-t-r.-.m n.'ol. m. l.o ise ' J. lii- at 12J I-u. aV'-Ttti-. iulrc 1JJ1 t':lit: auiu' FOR RENT - - r. ). r xt eetl t j, . . ril -a - !ia j ' lleijchls. f I r ii-pi.-Ii IriMiu. I'F:tn Kim k l.l.i For RENT -Two n--v t. m'l'-rn. ifie ?ur.---r.rTi I.'ii'-. 221S f t. .-oit .- i: w. 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FR HKXT- lll-li.tl I o, lion rem ed f-T ;eri - room in Mo.-,, s'.i.r- tn'-dern fur- K I lo.-a- nii l-e rent- t f.it.1 nttil Nov 2.1. 1 . ... If rken ' . r, w. 'i k ness a v f ii ue, 1; k foil'. 'I I O' will e. Ml .flee. reaol 1 i I ! r e Iioi'itc 112 Fo.rtl Mirnl. mil HF.T Fl. T. IK RENT -1 l it.th - Klve-ro IV ell'le. :n modern Mat. FOR RENT Five-loom modern Tat. tin a no -nth. at 1JI2 Ff t h -and-a-half atrnue. In-i nie wit; In. I For RENT - tv. nio.i.rn. furnished fice-ro on flat, to , .le w ithout ( Ml-i ilren Inquire TJ4"; Twei.tj -f-uri u treef. I I'OII IIEST ll9t KLI.ASEOl S. FOR RENT St. r. room, with li:;e fiat above, i-i good I. -.t:"n; rent reus - n al... . Call St 21" Safety b uld;n. I'!. or..' Rock Island 1 1 S. PKOFKSIOS A I. TTOUSEl'B. SEA RLE A MARSH A LL Attorney-at-law. Oltl. H j2-au3 -a:ct baUding. Uui't ls.and. l('kl HI'KST A STAFFORD At-! torneys-at-lav. . Uitir. iu Luck ia.aiad j National batik building. WALKER, INGRAM A SWEENET At. torneys and counselor at law. Money to loan en real estate. lipoma 2oo 23 People s National bank bunding. WILLIAM M. WALKER Attorney; general 1-. w businesa: corporation, probate and ral estate law. 311 peo ples bank bullulr.g. I'liouii Hock la land 34. McENlKY A McENiRY Attorney s-at-law. Loan money in good security; make collections. References. Mitch ell A Lynde. bankers. OSK-. jlitobcli ak Lynda bi'.ilaiug. ' - - APTRACT OF TITLE. AB.-IRACTS of title prei-ared or con tinued to dat covering any ral es tate i the couaty. P:on:pt nnd ac eurate service at rea'nable ratea Rock Inar.d Title Abstract com tny; J J Ins-ram. fresldent; W. J. tvce. nev. accrrtary; I"v-20$. second flocr. !''?' National bank build ing. Rock Island HOlsES WANTED. WE can get you a tenant for your va rti.l house or rooms if yo'i teleph us or snd us a i-ostal as o-n as vacant. Wo do not charge lor this service.; tf':iatorrlit.Ji. 113-115 East accoud I street, Davenport. I toMiurroH asd dhi derj. John VcHis & C. fXSVRACOHS AND Manurscture, i fash. Door Pl!nd r. J sjtairs. Interior nnlsh of all kinds. HardwKd Veneer Foorln-t and deal ers in Glass, ail and 22 Cisbtew.: .use : furnace. I --n il? ... r.- ..f k l-l hi !. In- ! li- v t ! . r. I I (0,000 OM "1 III I TUa 1 Wfc- W . 1 " a ' v-xtt J ( 1 I'OR hi:t-rooi. Tohkk at 17j4 RENT Modern furnished rooms Fifth avenue. Fop. PENT M'ulrm furnished room'. 1'2! Sixteenth street. FOR RENT Light housekeeping" roooi at 217 Sixteenth street. .(' iM-v-r r... I i,..,;tr siT Mi. ,lL, L Ji'"1"" irnished rooms. street. ; F ,,. R E.N'T Nicely furnished roomt. In.i.ire 2'c, Sixteenth street. K, RENT M'xlern room, upstairs, at "e"1" S,reet- Jn'4U,ra 1124 "' KK RENT Modern furnl.'hed room: 12 a v-k. ui of ph'tie, 117 Fourtn aver. ue. KOR RENT Two modern rooms for iirhl housekeeping at 1207 fourth aven ue. Flt R;:XT Modern furnished room. Snoir-v i'lat. 2'16'5 Third avenue. 11 Tun-. K( ItENT Two furnished rooms for Jifcht housekeeping at J45 Twenty- ixtll street. l''ft ItENT A room In modern home. f-r fc.-nUern.iu, t 27'.'4 Eighth. and-a-l:itU uvi-ntie. i'l'.'t RENT Furnished front room, in- lern. ii"nl if desired, at 1)21 .nth avenue. F R RENT N'. jt'y furnished modern l:K!.r niiutkeepiiig rou-ms at bti . triteeiith Mrcet. ytl RENT Two well furnished rooms on car line, alt modern conveniences; 14Uj hcventh avenue. ! FOR RENT One furnished room, with board. .ir genrlemaii, at teenih-and-u-liuif street. 72a Four- !" 'R RENT M-d-rn furnished room : -r liiriit lnoi ke-ping at 112 Fourteenth-and-a-half street. For RENT Two niod-rn furnished looms f"i- liKlit housekeeping. In i'ii'e lils Seventh avenue. FOll RENT Modern furnished rooms at 24 Forty-third street; rent rca- !" near two car lines. FOR ItENT Op.e modern furnished rniit room, suitable f"r one or two Kintlemni, at 1 2 7 fclxth avenue. FOR KENT Modern furnished rooms lor HKht houMvkeeplng; laundry priv. ie;e!?. Inciulre 271 Fifth avenue V'nU f:l-'V-r 1 in., nurllv mnit. rn room f-T li,tt!t housekeeping, with use of laundry and phone, at 42 Sixteenth street. Foil RENT Room for llht house- I keepinM. by quiet, respectable work ing man. AuJrcti ' D. W'' care of 'i'.ie Aikus. I OK RENT Two modern furnished rooms lor llK'lit housekeeping-. I'hone )(ok isian-1 1432-Y. Inquire 2V7 1 if t h an nue. l-'oll RENT Modern furnished roirm, soil. !!: lor one r two gentlemen or ' ni..n :. I i.!e. Inouire 7.14 Twenty- averitti slr--t. fv"...,S:-!T Two iraill unfurnished .hum k.-;'li.(,' rooms. $7 per month ; I i onv. n em to car lines; private ram-' lly; 1111 Mxtli avenue. For RENT Three ri-e large unfur i.ihcii rooms: near Long View park, two blocks f:oin street car. Inquire 1.11 SeventciiIU .tree. FOR RENT: Newly furnished steam heated front room, electric light and bath, let and cold water, private entrance; 12 Sixth avenue. FOR RENT: Modern furnished room for gentleman. Apply Flat No. 1. For Rent: Modern furnished rooms for light housekeeping; use of phone, at 11th, Fourteenth-and-a-half street. Call mornings or evenings. FOR RENT: One light housekeeping room, with water and sewer; also furnished sleeping room; rent reasonable. 4th, Twenty-first street. FOR RENT: Modern front room, suitable for two, on Elm street car fare. Call after 6 p.m.; 712 Twenty-third street. Phone Rock Island 2311. FOR RENT: Furnished front room; heat, electric lights, bath; $2 to $3 a week; convenient to street cars; suitable for two. Phone Rock Island. FOR RENT: Two or three nicely furnished rooms for light housekeeping; also front sleeping room; modern except heat. Call at 1410 Fourth avenue. For Rent: Two rooms and alcove, nicely furnished for light housekeeping, use of phone, to people of good character only: 141 Third avenue, phone Rock Island 2203. DRESSMAKING AND SCHOOL. TAILORING. LEARN Practical Dressmaking and Ladies Tailoring and be Independent and self-supporting. We teach you to cut, fit, design, and make our own garments from our own materials. Positions furnished in my shop, when competent. If desired. G H. Grabbe. Ladies Tailor and Dressmaker. South Putnam building. Davisonport, Eat. 1182. Rates cut to measure. ISAAC. WE WILL BOND YOU Executor. Mip-strator, aruardians', trustee, or any kind of judicial bonds: lodges and society officers; city, state, or U. & government officials; contractor a position of trust; in fact, any kind of bond you will accept bail bonds. Terms reasonable. Hayes Cleveland, resident manager. Fidelity at SSISCELLASEOCS. IF YOU WANT to buy, sell, trade or rent anything, engage help or secure a situation, the Mall and Journal with terms at rate per word is true to all alike. Every Saturday Mail and Journal, use this. THE ROCK ISLAND REALLY LOOKING FOR IT. WANTED: Good, reliable boy about 16 years old, to drive carpenter-wagon. Irm-tire 1014 Twelfth street. WANTED: Young man to advertise and solicit for Rogers' silverware; pay $2 per month. A. A. Cline Advertising, 128 X. Tenth street, Philadelphia. WANTED: Man at once to learn the barber trade; jobs always willing; better wages than you can earn without trade; tools given; few weeks completes, drop a card for particulars. Barber College, Chicago. WANTED: For U.S. army: able-bodied unmarried men between ages of 18 and 18; citizens of United States, of good character and temperate habits, who can speak, read and write the English language. For Information, apply to recruiting officer, Second and Brady streets, Davenport: 219 South Third street, Cedar Rapids; Sixth and Main streets, Dubuque; State Bank building, Rock Island. WANTED: Female help. WANTED: Cook and general storekeeper, second maid at Second Avenue. WANTED: Good cook; references; inquire at Third Avenue. WANTED: Girl to do second work or to assist in the kitchen. Phone Rock Island 1797. WANTED: Cook and housemaid: apply at J wenty-first street. Phone Rock Island. WANTED: A nice, clean girl; some experience as second girl; U43 Thirty-ninth street. Phone Rock Island 1738. WANTED: Woman wanting good home in country, in family if two; no farm hands. Mrs. Eldon, Cambridge, Hi. WANTED: A young girl to assist with care of child and to assist with housework. Inquire at Dies Fifth avenue. Phone Rock Island 1795. WANTED: Twenty young ladies in sewing department in our mitten factory: steady work: special inducement to beginners. Boss Manufacturing company, corner Sixteenth street and Third avenue. Mollie, Ill. LODGE DIRECTORY: Masonic Temple, Eighteenth 243. G. A. R., meets regularly on the second and fourth Saturday evenings of each month at 7:30 in Memorial hall at the courthouse. W. M. Johnston, commander; F. H. Buck, adjutant. COLLECTIONS MADE Hard accounts and claims collected. William M. Walker, lawyer. 311 Peoples Bank building. LOST AND FOUND. LOST Sunday afternoon, a stickpin set with pearls and a pearl. Return to The Argus. Reward. LOST Chain and lavender set with pearls. Finder return to H. F. Paulsen and receive $5 reward; 12th Twelfth street. FOI'ND About Oct. 31. an ear trumpet. n Fifteenth street, near court house, own.-r can have same by calling at The ArguH office and paying for ad. LOST Fox terrier dog; black wit'a white breast, legs and feet, and white spot on hack: black tall. I'hone or re turn to Dr. Bradford. 602 Eighteenth street, and receive reward. LOST Wednesday evening, probably on Second avenue between Eighteenth I r ana .vmru-. ii n creeis. or on tira . as omaervalor. as iu his power under street, car line, a string of amber j the statute, and for that purpose lie beads. Notify Itock Isla n.1 UJo-X. or,,v,ll apt. ear before the probate court of The Argus office. Reward. 1 R.k k Island county. Illinois, at the : 1 - I probate court room, in the court house, . . . In the city i Roc k Island, at the Jan- irrEItt I.IOII HAIR. I uary term, on the first Monday of Jan- - -I uary, A. I. 1514. at which time all per- Sl'PKRFLTOl'S Lair and mole.t on face sons having claims airalnst said estate and arms permanently removed wirhjare notified and requested to attend, for one to six nedles. Address M'ss A. M. the purpose of having the same ad Kittrcdge. Flat 1. Argyle Flats. Brady justed. All persons Indebted to said es- trl, tuventorL i'hone JJavc npoi t ! 318C. PLORISTS. HENRY GAETHJE. proprietor Cfclp plannock nursery. Cut flowers and dexlgna of all kinds. City store. 1607 Second arvenuc Phone Kwi Iaiand 1110. BICYCLE ASD MOTORCYCLES. tTr EsT al r til k esTTaccsso rles la mps. etc : cut prices: $15 Flying Merkle bicycles at wholesale price. $25 (or ange and biu enameled; 20S-210 East Third street. Davenport, 1-KOFESSTOSAL. CARL Kl'EHh Justlc of the Peace; Itvt Third avesoe. Rock Jsland. liL LEGAL. Eieralsrs S t lee. . . c- .... i, u .. .. ..... ---- v.. Tne undersigned having been. pointed executrix of the last will and I testament of Fredru k Htiber. f. tne i-our.ty of Rock Island, state ..r ll!i. ; r.ois. deceased. nereoy gives notice tliat h w,'1!.r,t,?r ht,'v ,h Benja- mm ue.i. juci oi me probate court off Kock Island county, at the probate! court room, in the city of Rook Island, ' at tr.e January term, on tn- first lion- day in January next, at waled time ail persons having claims against said es- fate are notified and requested to at- tend for the rurpos of having the same a A m t an All r.ranfii lnit.n.,a n ...a I. . - . i j. estate are reo-jested to make Immediate .ta r .ne e t to (V. oeaA...r...a Dated frst day "of November A . D I ill. A.viu.Mti HI HKh. Executrix. J. r. Witter, attorney. ARGUS. MONDAY, NOVEMBER 17, 1913. A BETTER HALF I TUP FftSlFST Tr-Wsiti. tfl I I WoR& To 6ET ftWlFEl- j 3-cst i Msg. co" p fApavfMiPM-J M TtAfi TTH rAV ruKc. ' uvji- - i i . IU -e.Vfc. owe. "VsA &-pjF-e opt: WASTED MISCELI.ASEOV9. WANTED Day work, washing prefer red: lul w i-ouriii avenue. WANTED To buy. display table fcr dry goods store. I'liono KOck Island 2208. WANTED Work by man with a good team. Jncjuire -JH seventeenth street. WANTED Lace curtains to launder at 144 8 Fourteenth atreec Mrs. Luella Tltterlngton. WANTED By younsr couple, four un furnished r-"onis in IMnewooU Park. Fhone l.ivenport Bl'HS.V. WANTED To buy. S. A. H. green trading stump books, full-length c-r partly till el. 11M Eleventh street. WANTED Brick laying of all kinds; chimneys and mantels a specialty. Phone KK-k Island 2:5. WANTED To buy. Fresh milch cow. Phone Rock Island 3:5, or inquire W. H. Hill, enter Station. WANTED To buy Furniture, stoves; will pay best price. Call KnirT, Mo line 71; 1C20 Third avenue. Molina. WANTED Wasning and Ironing, to take home. Kulh Lewis. 2o2J Fourth avenue, in the rear, Phone itoyk Island C43-L. WANTED Everybody to order hard-caned chair cases. Put them in for 75 cents and up. Call Ed Nelson, &32 Twenty-first street. WANTED Watches and clocks to repair; work called for and delivered. J. V. Syrett, phone Rock Island 15U-K. Inquire at 3 Fifteenth street. WANTED Savers of S. & H. stamps net to sell their stamps. Persons offering to buy them do so "usually within the meaning of the law to defraud, to cover 6c Hutchinson company. WANTED You to be a detective: earn $100 to $300 per month: travel over the world; stamp for particulars. National Detective Agency, Dept. C. 4. Chicago, Ill. ANTED Furnace and chimney cleaning; will also rent pair chimneys, at reasonable prices; good work guaranteed, inquire O. W. Rind, 42 Ninth street, or phone Rock Island 1053. WANTED To rent, by family of three adults, three furnished rooms or small house in Rock Island; no heat required; rent must be reasonable. Address "Z. 500," care of The Argus. WASTE 'SITUATIONS. WANTED Position as housekeeper or taking care of invalid; can furnish A 1 rcferc-i.cus. Address "C M. S.," care of The Argus, WANTED Work on farm by the year by experienced man with family: must have no use furnished.- Inquire B. Yansicklc. 516 Sixth street, city. WANTED Clerical position by capable gem ie.iian : have had experience in lumber and coal office and as ship ping clerk. Address "K.," care of The Argus. WAN I El -AGENTS, WANTED Agents with soma experi ence in the portrait line. Apply M. V. infield. New iiarpcr. between 1 Said 8 p. in. WANTED We want to start 10i new agents this m:it'i. and are offering speiial fmluct-nieni fi.T quiik action; pay weekly. Address Ferry Nurser ies. Ito, hestcr. N. Y. 1IIMM1 CHASCES. WANTED Man In every town: employ your spare time; be your own loss; pr.rritable busir.ss with little capital; modest income for lite. Advance Machine comrmy Ravenswood Sta tion Chicago IU. i.ix;ai COuservatur'a Notice. Estate of Marsaret Bollrcan, deceased. The und rslgr.ed. conservator of Mar garet Rollman, late of the county of Ito. k Iriand and slate of Illinois, here by gives notice thai the said Margaret Rolltnaii departed this life oh or about the 2'ith day of O toher, A. D. 1913, and that li n-lil t.n .c.-t-.l lo t lose sal. I ...-... tate are requested to make Immediate Payment to the undersigned Dated at Rock Island. 111.. Oct. 23. 1813. REUBEN BOLLMAN. Conservator. Notice r Flaal ett leneat. Estate of Jacob S lia'jm. deceased. Public notice is herehv given that the undersigned. Jacob W. Sc haunt, admin istrator of ti'.e estate of Jacob S.-haum. d- -cased, has this day tiled tits final re pent and settlement M" such, in the pro bate court ni Rork Island county, and hearing on said report has been set for Iwc. !. 191::. at lo Vcork a. m.. at which lime persons interested may appearand make objections thereto, and if no ot je. ti.-r.s are filed, said report will be approved at that time, and the under signed will ask for an order of distribu tion, and will also ask to be dis charged. F.ock Island. 111.. Nov. 13. ISIS JACOB W. Si'llAI'M. Administrator. Rchriver A Sri. river. altullit. ecu tor's Notler. Estate of Ruth Tounj Farthing, de- (ceased. tind'rslcned havir.ir been ap Uoin.,i ,.,nrni .f ll.e ,st wt I and testament of Ruth Young FariMn. ,at(. f ,,ie countv of Rock Island, state ininoj- deceased, hereby gives no. tice that she trill af.pear before the Hon. penlamtn Bell, judge of the pro- hate court of Rock island county, at the probate court room, in the city of Rock Island at the January term, on i nr.i vt.-n.tav in January r.txt. at which time all Wsons having claims ! agaTr.t said esta'te "re notified and re-I to att.nd fo7 ?he parpos of havinr the same adjusted. All wrwpi ..t..a . .....1 . , . - . i,..l ...... ...... . ... . . . .. : naeuieei i f ran csia.t miv to make Immediate paymer.t to the iu - dersigrecl. I IX'cd :ith dav of October A. 1112. chri MART E. T"I NC. Executrix. Iver Si Ecfcriver. attornei. i brchjosOt f stcv euDH &oj SXS coo-C Cf-W-tW CA. TrtE. I . -i FOR S ALE CITV PROPERTY. FOR SALE Modern six-room house: location. 922 Fourteenth-and-a-half street. Inquire lSuO Second avenue. FOR SALE At sacrifice price, my modern nine-room home at 74½ Twenty-third street; very desirable location. George F. Roth, 74½ Twenty-third street. FOR SALE Cheap for cash, modern seven-room house, one block from Long View Park; excellent lot and location. Address "F. M." care of The Argus. FOR SALE In southern Michigan, seven-room house, two lots, large woodshed and well house; corner location. Address Oscar Bryer, Moore Park, Mich., St. Joe county. FOR SALE: The two-story steam-heated pressed brick building at 318-31½-320 Eighteenth street, at a low figure. Inquire of owner. George F. Roth, 748 Twentieth street. FOR SALE Lots in J. G. Schuermann's Sixth addition, from Fifth to Seventh street and Fourteenth avenue, to Eighteenth avenue; payments down. 35 per month. Inquire 1700 Sixth street. Phone Reck Island. FOR SALE The recently remodeled building at 749-751 Twenty-third street; fine location; property never vacant; will net over 5 percent on the investment. Inquire of owner. George F. Roth, 748 Twenty-third street. FOR SALE Lots in South Heights, south of Aiken street, between Twelfth and Seventeenth streets; on easy terms; $25 down, balance in five years. E. W. Robinson, 1464 Richmond street. Phone Rock Island. FOR SALE Modern Property, in good location; terms right; a bargain if taken at once; will trade for good building lots or good automobile; a first-class proposition. Phone Rock Island 265ti. Office hours. 2 to 4 p.m., Wednesday and Saturday evenings. Sater At Viner. 211 People's National Bank building. FOR SALE LANDS. FOR SALE Well Improved 120-acre farm; six miles west of Anacostia. For particulars, see F. J. Schave, the owner, on the place. FOR SALE OR rent, farm, 40 acres or more, suitable for dairy, stock, grain; plenty of pasture. J. R. Farnsworth, Muscatine, Iowa: Lock Box 4-Jt. FOR SALE 69-acre farm, well improved; new eight-room house, good well, all buildings in good condition; located three miles southwest of Milano on Ridgewood road. J. M. Barr, route z, auan. LEGAL Notice. State of Illinois, Rock Island County - Public notice is hereby given that at a special meeting of the stockholders of the Rock Island Exposition company, a corporation organized and existing under and by virtue of the laws of the state of Illinois, and held at the assembly room of the Rock Island club, No. 22 Nine-teenth street, in the city of Rock Island, county of Rock Island, and state of Illinois, on the second day of June, A. D. 1913, at the hour of 7:30 o'clock in the evening of said day, at which meeting stockholders representing at least two-thirds of the whole capital stock of said corporation were present, the following resolution was unanimously adopted by said stockholders, all the votes represented being at least two-thirds of the whole stock of said corporation being cast in favor of said resolution: Whereas, The stockholders of the Rock Island exposition company, an Illinois corporation, desire to abandon the corporate enterprise, surrender the charter, franchises and corporate name, and dissolve the said corporation; and Whereas, The said Rock Island Exposition company has ceased to do business, and all corporate debts have been fully paid and corporate liability discharged, and the corporate assets and property distributed among all persons entitled thereto. Now, therefore, be it resolved, That the corporate enterprise, charter, franchises and corporate name of the company be surrendered and that said corporation be dissolved; and, Be it further resolved, That the secretary be, and he is hereby authorized and directed to attest, as secretary, the record of the proceedings of this meeting and affix the seal of the corporation thereto. Be it further resolved, That the president and secretary be, and he is hereby authorized to cause a complete record of all proceedings in this respect to be verified by his sworn affidavit and attested by the seal of said corporation under his signature, and the corporate seal to be affixed, to be filed for record in the office of the recorder of deeds of Rock Island county, in the state of Illinois, it being the county wherein the principal office of said corporation is located. Be it further resolved, That the president cause a notice of said dissolution to be published for three successive weeks in The Rock Island Argus, a newspaper published in the city of Rock Island, in said county and state aforesaid, and within three months from this date thereon the certificate of recording is executed by the recorder of deeds of said Rock Island county, to be filed in the office of the secretary of state. That the record of said proceedings, signed by the president of the corporation, verified. By his affidavit and attested by the secretary of said corporation, under his corporate seal, has been duly recorded required by law. Dated this 27th day of October, A.D. 1913. Rock Island corporation co. Seal) By William M. Reck, Pres. By R. S. Pert, Secretary. Administrator Nolle. Estate of Oliver Edgar Welsh, deceased. The undersigned having been appointed administrator of the estate of Oliver Edgar Welsh, deceased, hereby gives notice, that she will appear before the court, Benjaej. Beil, judge of the probate court of Rock Island county, at the probate court room, in the city of Rock Island, on January 1st, next, at which time all persons having claims against said estate are notified and requested to appear in person or by attorney. EDNA FOOTWELL. Administratrix. All persons having claims against the estate of Oliver Edgar Welsh, deceased, are hereby notified and requested to appear in person or by attorney. Bows all the time The Argus. Drawn for this oak dining room table, pedestal style, nearly new; 1716 Twenty-sixth street. FOR SALE Two pianos, $150 and $100; terms. People's Loan company, 40 Lane building, Davenport, Iowa. FOR SALE Three-piece mahogany parlor set, almost new. 1122 Twentieth street. Phone Rock Island 1814. FOR SALE Drop head sewing machine, good as new, $8; also other furniture; selling out. Inquire 1530 Sixth avenue. FOR SALE! Good delivery horse, eight years old; two-horse manure wagon; at 771 Hennepin avenue, South Rock Island. FOR SALE Single top buggy; also double seated buggy. Inquire Levi Sandusky, South Heights, Seventeenth street and Twentieth avenue. FOR SALE Several slightly used drop head sewing machines; one latest improved White rotary, used three years, at your own price. Inquire at 4121 Seventh avenue. FOR SALE Coon hounds and varmint dogs; thoroughly trained; free trial; 100-page catalogue and treatise on night hunting. Illustrated, cloth bound. 20 cents. Southern Farm Coonhound Kennels, Selmer, Tenn. FOR SALE Sewing machines, all kinds and all makes, warranted good as new; and up. by pay three times as much as all makes, remember Richards Sewing Machine. He rebuilds old ones; 626 Sixteenth street. FOR SALE Two used automobiles, in line condition, at a A bargain price; cost nothing to look them over; they may be just what you want; these oars are worth the money. Harth, 113 Nineteenth street, one-half block north of Harper house. FOR SALE Fine shotgun, made to my order in Europe, is guaranteed. Piston grip, single trigger, shell ejeator, and finely engraved; or will trade for good gentleman single driver or about 1,100 weight. Call on C. F. Gaetjer, Aiken street, South Rock Island. LEGAL. Publication Notice. State of Illinois, Rock Island County of Probate Court of Rock Island County. To the December Term, A.D. 1913. Cornelius Donovan, executor of the last will and testament of John Holdorff, deceased, vs. William Holdorff, Julia Jacobson, Margaret Theus, Bertha Theus, Christy Holdorff, Hannah Jones, Harry Holdorff, Margaret Holdorff, Bernice Holdorff, Mary Reggle, Minnie Holdorff, and Sarah Holdorff. Petition to sell real estate to pay debts. Affidavit of the non-residence of Christy Holdorff, one of the defendants above named, having been filed in the office of the clerk of the probate court of Rock Island county, notice is hereby given to the said Christy Holdorff, that the said petitioner, executor of the last will and testament of John Holdorff. deceased, has filed his petition in the said probate court of Rock Island county for an order to sell the premises belonging to the estate of said deceased, or an amount of money to be needed to pay the debts of said deceased, and described as follows, to-wit: All the following described lot, piece or parcel of land, situated in South Rock Island, in the county of Rock Island, and state of Illinois, to-wit: That part of the southwest quarter of the southeast quarter of section number three, in township number seventeen north of range number two east of the fourth principal meridian, and described as follows, to-wit: Commencing at the one-eighth section line eight chains south of the northeast corner of the southwest quarter of said section; thence running west four chains and seventy-nine links; thence south eight chains and thirty-six links; thence east four chains and seventy-nine links to said eighth section line; thence north eight chains and thirty-six links to the place of beginning, containing four acres, more or less, and known as lot number ten (10) of said section; and that a summons has been issued out of said court against you, returnable at the December, A.D. 1813. At the courthouse in Rock Island, in Rock Island county, Illinois. Now, unless you, the said Christy Holden, shall personally be and appear before the said probate court of Rock Island county, on the first day of December, 1913, and plead, answer, or demur to the said complainant's petition filed therein, the same and the matters and things therein charged and set will be taken as confessed, and a decree entered against you according to the prayer of said bill. Pork, 1st day of December, 1913. JON F. FLEMING, Clerk. Seal of the County Court of Rock Island County, Illinois. Arbitration Notice. State of Wisconsin, County of Rock Island, ss. The undersigned, having been appointed administrator of the estate of Wilhelmina H. Haskins, deceased, hereby give notice that on the first Monday in January next, at which time, all persons interested in the estate of Wilhelmina Haskins, deceased, are required to appear before the probate court of Rock Island county, at the probate court room, in the city of Rock Island, at the January term, on the first Monday in January next, at which time. Person having claims against the estate are notified and requested to attend for the purpose of having the same adjusted. All persons in interest are requested to make immediate payment to the undersigned. Dated this day of November, A.D. 1913. G. G. STAVE HAZEL. Administrator, Carl Ed MASSAGE. SWEDISH MOVEMENT Miss A. Elnarson, graduated Swedish masseuse, gives treatment in private homes and at office by appointment, Phone Rock Island 2158. Office, 616 Seventeenth street. MADAME MAZCHLA tells past, present and future; 17 Harrison street, Davenport, I.FGAL. Sheriff's Sale. By virtue of an execution and fee bill. Issued out of the clerk's office of the county court of Rock Island county, and state of Illinois, and to me directed, whereby I am commanded to make the amount of a certain judgment recently obtained against Charles L. Bailey, Jr., in favor of Rock Island County Abstract company, out of the lands, tenements, goods and chattels of the said Charles H. Bailey, Jr., I have levied on the following described property, to-wit: The west thirty-five feet of lot six 6, in William McEniry's addition to the town of Millie, Ill.; also in the west of lot four 4, in block seventeen 17, in that part of the city of Kirk Island known as and called Spencer & Caso's addition to said city, all situated in the county of Rock Island and state of Illinois. Therefore, according to said command, I shall expose for sale at public auction, all the right, title and interest of the above named Charles L. Bailey, Jr., in and to the above described property, at 10 o'clock a.m. on Wednesday, the 26th day of November, 1913, at the east door of the courthouse in Rock Island, Dated at Rock Island, Ill., this third day of November, 1913. O. L. BRIENER, Sheriff Rock Island County. Per William H. Brough, deputy. Croup is most prevalent during the dry cold weather of the early winter months. Parents of young children should be prepared for it. All that is needed is a bottle of Chamberlain's Cough Remedy. Many mothers are never without it in their homes and it has never disappointed them. Sold by all druggists. (Adv.) Education is all planned, it does not alter the nature of the wood that it underlies. It only improves its appearance a little. Stanhope. WEEKS TO CHRISTMAS The Stores Are Not Crowded Now as They Will Be Later. Eyes Examined Without Drugging An OPTOMETRIST is one who prescribes and fits glasses without the use of drugs or surgery. Optometry is NOT found on medical science, but on OPTICAL science. A Jens treats LIGHT, not disease. Only optically incompetent practitioners, drug Wealthy eyes. This method is not only dangerous, but painful, and it is only by a miracle if the glasses thus prescribed prove correct. We have brought relief and happiness to thousands of people by employing our scientific knowledge for the correction of defective vision. We use no drugs or "drops" of any kind in our examinations. J. RAM'S SONS OPTOMETRIST. Opposite Harper House. | 38,129 |
https://github.com/Packet-Clearing-House/tableManager/blob/master/examples/sample.sql | Github Open Source | Open Source | MIT | 2,019 | tableManager | Packet-Clearing-House | SQL | Code | 286 | 1,107 |
CREATE DATABASE IF NOT EXISTS tableManagerSample;
CREATE TABLE IF NOT EXISTS tableManagerSample.people
(
id INT PRIMARY KEY NOT NULL AUTO_INCREMENT,
first VARCHAR(255) NOT NULL,
last VARCHAR(255) NOT NULL,
age INT(3) NOT NULL,
sex ENUM('Agender', 'Androgyne', 'Androgynous', 'Bigender', 'Cis', 'Cisgender', 'Cis Female', 'Cis Male', 'Cis Man', 'Cis Woman', 'Cisgender Female', 'Cisgender Male', 'Cisgender Man', 'Cisgender Woman', 'Female to Male', 'FTM', 'Gender Fluid', 'Gender Nonconforming', 'Gender Questioning', 'Gender Variant', 'Genderqueer', 'Intersex', 'Male to Female', 'MTF', 'Neither', 'Neutrois', 'Non-binary', 'Other', 'Pangender', 'Trans', 'Trans*', 'Trans Female', 'Trans* Female', 'Trans Male', 'Trans* Male', 'Trans Man', 'Trans* Man', 'Trans Person', 'Trans* Person', 'Trans Woman', 'Trans* Woman', 'Transfeminine', 'Transgender', 'Transgender Female', 'Transgender Male', 'Transgender Man', 'Transgender Person', 'Transgender Woman', 'Transmasculine', 'Transsexual', 'Transsexual Female', 'Transsexual Male', 'Transsexual Man', 'Transsexual Person', 'Transsexual Woman', 'Two-Spirit') NOT NULL,
comment TEXT
);
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INSERT INTO `people` VALUES (1,'','Doe',56,'Cis','Is john doe.'),(2,'Jane','Doe',2,'Bigender','Jane rocks!'),(3,'Zhang','Wei',82,'Cis',''),(4,'Zhang','Xiu Ying',82,'Gender Fluid',''),(5,'Mohamed','EL-HASHEM',34,'Trans* Female',''),(6,'Meyer','NEJEM',18,'Trans* Man',''),(7,'Abir','Chatterjee',48,'Gender Questioning','');
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-- Dump completed on 2017-03-16 12:07:25
| 18,765 |
US-1610198-A_2 | USPTO | Open Government | Public Domain | 1,998 | None | None | English | Spoken | 1,671 | 2,684 | acid, sodium salt 112 2 29 monohydrate Control 0 0 63 Standard 1X 112 0 29 Standard 2X 224 0 21 17 anthraquinone-2,6-disulfonic acid, disodium 112 50 53 salt 17 anthraquinone-2,6-disulfonic acid, disodium 112 20 50 salt 17 anthraquinone-2,6-disulfonic acid, disodium 112 2 32 salt The preceding description of specific embodiments of the present invention is not intended to be a complete list of every possible embodiment of the invention. What is claimed is:
1. A process for treating a plant with glyphosate comprising the steps of: (a) applying to foliage of the plant an anthraquinone compound; and (b) applying a biologically effective amount of said glyphosate to the same foliage; wherein: said anthraquinone compound is applied in a substantially non-phytotoxic amount of at least about 0.25 g/ha but not sufficient to antagonize effectiveness of said glyphosate; said glyphosate is N-phosphonomethylglycine, a salt of N-phosphonomethylglycine, an ester of N-phosphonomethylglycine, a compound which is converted to N-phosphonomethylglycine in plant tissues, or a compound which otherwise provides N-phosphonomethylglycine in ionic form; and the biological effect on a plant treated with said anthraquinone compound and said glyphosate is greater than the biological effect on a plant treated with said glyphosate but without said anthraquinone compound.
2. The process of claim 1 wherein step (b) occurs within 24 hours before or after step (a).
3. The process of claim 2 wherein step (b) occurs within 24 hours after step (a).
4. The process of claim 1 wherein steps (a) and (b) occur simultaneously and said anthraquinone compound and said glyphosate are applied by spraying a single spray composition containing said anthraquinone compound and said glyphosate.
5. The process of claim 4 which further comprises, prior to steps (a) and (b), a step of mixing said anthraquinone compound and said glyphosate with suitable formulation ingredients to form a concentrate composition, and a step of diluting, dissolving or dispersing said concentrate composition in water to form the spray composition.
6. The process of claim 4 wherein the spray composition further comprises a surfactant.
7. The process of claim 4 wherein said glyphosate is a water-soluble salt of N-phosphonomethylglycine.
8. The process of claim 7 wherein the salt is an alkali metal, ammonium, alkylamine, alkanolamine or alkylsulfonium salt.
9. The process of claim 1 wherein said glyphosate is an alkali metal N-phosphonomethylglycine salt, an ammonium N-phosphonomethylglycine salt, an alkylamine N-phosphonomethylglycine salt, an alkanolamine N-phosphonomethylglycine salt, or an alkylsulfonium N-phosphonomethylglycine salt.
10. The process of claim 1 wherein said anthraquinone compound has the formula:
where R₁ through R₄ and R₅ through R₈ are independently hydrogen, alkyl groups having from 1 to 30 carbon atoms, alkenyl groups having from 2 to 30 carbon atoms, alkoxy groups having from 1 to 30 carbon atoms, halogen, amino groups, alkylamino groups having from 1 to 30 carbon atoms, hydroxy groups, hydroxyalkyl groups having from 1 to 30 carbon atoms, cyano groups, nitro groups, haloalkyl groups having from 1 to 30 carbon atoms, carboxy groups, and aryl groups having 1 to 30 carbon atoms.
11. The process of claim 10 wherein R₁ is hydrogen, —NH₂, or —NHCH₃; R₂ is hydrogen, hydroxymethyl, methyl, or —NH₂; R₅ and R₆ are independently hydrogen or —NH₂; and R₃, R₄, R₇, and R₈ are hydrogen.
12. The process of claim 10 wherein one or two of R₁, R₂, R₃, R₄, R₅, R₆, R₇, and R₈ are independently methyl, ethyl, hydroxymethyl, amino, or methylamino and all other R substituents are hydrogen.
13. The process of claim 10 wherein the anthraquinone compound is applied at a rate of from about 0.25 to about 250 g/ha.
14. The process of claim 10 wherein the anthraquinone compound is applied at a rate of from about 1 to about 25 g/ha.
15. The process of claim 1 wherein said glyphosate is water-soluble.
16. The process of claim 15 wherein the exogenous chemical composition is a salt comprising a biologically active ion and a counterion which has less or no biological activity.
17. A herbicidal process comprising the steps of: (a) mixing together (i) an anthraquinone compound in an amount sufficient to provide a rate of from about 1 to about 25 g/ha, (ii) a herbicidally effective amount of a glyphosate selected from the group consisting of an alkali metal N-phosphonomethylglycine salt, an ammonium N-phosphonomethylglycine salt, an alkylamine N-phosphonomethylglycine salt, an alkanolamine N-phosphonomethylglycine salt, and an alkylsulfonium N-phosphonomethlglycine salt, (iii) one or more surfactants in a total surfactant amount sufficient to emulsify the anthraquinone compound and to enhance the herbicidal effectiveness of the N-phosphonomethylglycine, and (iv) water to form a concentrate; (b) diluting the concentrate in water to form a spray composition; and (c) spraying the spray composition on foliage of plants in a field; wherein the herbicidal effect on foliage treated with said anthraquinone compound and said glyphosate is greater than the herbicidal effect on foliage treated with said glyphosate but without said anthraquinone compound.
18. A plant treatment composition comprising glyphosate and an anthraquinone compound; wherein: when the composition is applied to foliage of a plant with or without prior dilution, dispersion or dissolution in an application medium, the exogenous chemical substance is in a biologically effective amount and said anthraquinone compound is in a substantially non-phytotoxic amount of at least about 0.25 g/ha but not sufficient to antagonize effectiveness of said glyphosate; and said glyphosate is N-phosphonomethylglycine, a salt of N-phosphonomethylglycine, an ester of N-phosphonomethylglycine, a compound which is converted to N-phosphonomethylglycine in plant tissues, or a compound which otherwise provides N-phosphonomethlglycine in ionic form.
19. The composition of claim 18 wherein said anthraquinone compound has the formula:
where R₁ through R₄ and R₅ through R₈ are independently hydrogen, alkyl groups having from 1 to 30 carbon atoms, alkenyl groups having from 2 to 30 carbon atoms, alkoxy groups having from 1 to 30 carbon atoms, halogen, amino groups, alkylamino groups having from 1 to 30 carbon atoms, hydroxy groups, hydroxyalkyl groups having from 1 to 30 carbon atoms, cyano groups, nitro groups, haloalkyl groups having from 1 to 30 carbon atoms, carboxy groups, and aryl groups having 1 to 30 carbon atoms.
20. The composition of claim 19 wherein R₁ is hydrogen, —NH₂, or —NHCH₃; R₂ is hydrogen, hydroxymethyl, methyl, or —NH₂; R₅ and R₆ are independently hydrogen or —NH₂; and R₃, R₄, R₇, and R₈ are hydrogen.
21. The composition of claim 19 wherein one or two of R₁, R₂, R₃, R₄, R₅, R₆, R₇, and R₈ are independently methyl, ethyl, hydroxymethyl, amino, or methylamino and all other R substituents are hydrogen.
22. The composition of claim 18 wherein said glyphosate is water-soluble.
23. The composition of claim 22 wherein said glyphosate is a salt comprising a biologically active ion and a counterion which has less or no biological activity.
24. The composition of claim 18 wherein said glyphosate is an alkali metal N-phosphonomethylglycine salt, an ammonium N-phosphonomethylglycine salt, an alkylamine N-phosphonomethylglycine salt, an alkanolamine N-phosphonomethylglycine salt, or an alkylsulfonium N-phosphonomethylglycine salt.
25. The composition of claim 18 which is an aqueous solution or emulsion concentrate formulation wherein the N-phosphonomethylglycine is present in a concentration of from about 50 to about 500 g a.e./l.
26. The composition of claim 25 wherein the N-phosphonomethylglycine is present in a concentration of from about 350 to about 500 g a.e./l.
27. The composition of claim 25 wherein the N-phosphonomethylglycine is present in a concentration of from about 450 to about 500 g a.e./l.
28. The composition of claim 25 which is an emulsion having an aqueous phase and an oil phase, wherein the N-phosphonomethylglycine is present primarily in the aqueous phase and the anthraquinone compound is present primarily in the oil phase.
29. The composition of claim 18 which is a water-soluble or water-dispersible dry formulation wherein the N-phosphonomethylglycine is present in a concentration of from about 5% to about 80% a.e. by weight.
30. The composition of claim 29 wherein the N-phosphonomethylglycine is present in a concentration of from about 50% to about 80% a.e. by weight.
31. The composition of claim 18 which further comprises one or more surfactants.
32. The composition of claim 31 wherein at least one of the surfactants is nonionic, cationic or amphoteric.
33. The composition of claim 32 wherein at least one of the surfactants is a nonionic surfactant selected from the group consisting of polyoxyalkylene alkyl and alkylaryl ethers, polyoxyalkylene alkyl esters, sorbitan alkyl esters, glyceryl alkyl esters, sucrose esters and alkyl polyglycosides.
34. The composition of claim 32 wherein at least one of the surfactants is a cationic surfactant selected from the group consisting of polyoxyalkylene tertiary alkylamines, quaternary ammonium surfactants and polyoxyalkylene alkyletheramines.
35. The composition of claim 32 wherein at least one of the surfactants is an amphoteric surfactant selected from the group consisting of polyoxyalkylene alkylamine oxides, alkylbetaines and alkyl-substituted amino acids.
36. The composition of claim 18 wherein the anthraquinone compound is present in an amount such that when the composition is applied by spraying, the anthraquinone compound is applied at a rate of from about 0.25 to about 250 g/ha.
37. The composition of claim 18 wherein the anthraquinone compound is present in an amount such that when the composition is applied by spraying, the anthraquinone compound is applied at a rate of from about 1 to about 25 g/ha.
38. A concentrate herbicidal composition comprising (i) from about 1 to about 5 g/l of an anthraquinone compound, (ii) from about 350 to about 500 g a.e./l of an N-phosphonomethylglycine salt selected from the group consisting of an alkali metal N-phosnhonomethlglycine salt, an ammonium N-phosphonomethylglcine salt, an alkylamine N-phosphonomethlglycine salt, an alkanolamine N-phosphonomethlglycine salt and an alkylsulfonium N-phosphonomethylglycine salt, (iii) one or more surfactants in a total surfactant amount sufficient to emulsify the anthraquinone compound, and (iv) water.
39. The composition of claim 38 comprising from about 450 to about 500 g a.e./l of the N-phosphonomethylglycine salt.
40. The composition of claim 38 wherein at least one of the surfactants is a cationic surfactant selected from the group consisting of polyoxyalkylene tertiary alkylamines, quaternary ammonium surfactants and polyoxyalkylene alkyletheramines..
| 3,909 |
https://pl.wikipedia.org/wiki/Martin%20Havik | Wikipedia | Open Web | CC-By-SA | 2,023 | Martin Havik | https://pl.wikipedia.org/w/index.php?title=Martin Havik&action=history | Polish | Spoken | 140 | 313 | Martin Havik (ur. 15 grudnia 1955 w De Koog) – holenderski kolarz torowy i szosowy, dwukrotny medalista torowych mistrzostw świata.
Kariera
Największe sukcesy w karierze Martin Havik osiągnął w 1983 roku, kiedy zdobył dwa brązowe medale podczas mistrzostw świata w Zurychu. Pierwsze zajął trzecie miejsce w wyścigu ze startu zatrzymanego zawodowców, w którym wyprzedzili go tylko Włoch Bruno Vicino oraz rodak Havika - René Kos. Trzeci był również w derny, gdzie uległ jedynie Gertowi Frankowi z Danii i ponownie René Kosowi. Havik startował także w wyścigach szosowych, wygrywając między innymi: Omloop van de Braakman w 1977 roku, Profronde van Pijnacker w 1978 roku oraz wyścig Nijlen-Kessel w 1979 roku. W 1981 roku zajął trzecie miejsce w klasyfikacji generalnej Vuelta a Andalucía. Nigdy nie wystartował na igrzyskach olimpijskich.
Bibliografia
Profil na cyclingarchives.com
Holenderscy kolarze szosowi
Holenderscy kolarze torowi
Urodzeni w 1955 | 32,968 |
https://github.com/JonSaffron/PowerPointFacade/blob/master/Columns.vb | Github Open Source | Open Source | MIT | null | PowerPointFacade | JonSaffron | Visual Basic | Code | 251 | 646 | ' Columns is a 1 based collection of object Column
Public Class Columns
Implements IEnumerable(Of Column)
Implements IEnumerator(Of Column)
Implements IDisposable
Private ReadOnly _columns As Object
Friend Sub New(ByVal columns As Object)
Me._columns = columns
Call Me.Reset()
End Sub
Public ReadOnly Property Count As Integer
Get
Return Me._columns.Count
End Get
End Property
Public Function Add() As Column
Return Me.Add(-1)
End Function
Public Function Add(ByVal beforeColumn As Integer) As Column
Return New Column(Me._columns.Add(beforeColumn))
End Function
Default Public ReadOnly Property Item(ByVal index As Integer) As Column
Get
Return New Column(Me._columns.Item(index))
End Get
End Property
#Region " IEnumerable implementation"
Public Function GetEnumeratorOfColumn() As IEnumerator(Of Column) Implements IEnumerable(Of Column).GetEnumerator
Return Me
End Function
Public Function GetEnumerator() As IEnumerator Implements IEnumerable.GetEnumerator
Return Me
End Function
#End Region
#Region " IEnumerator implementation"
Private _enumeratorPosition As Integer
Public ReadOnly Property CurrentOfColumn As Column Implements IEnumerator(Of Column).Current
Get
Return Me.Item(Me._enumeratorPosition)
End Get
End Property
Public ReadOnly Property Current As Object Implements IEnumerator.Current
Get
Return Me.Item(Me._enumeratorPosition)
End Get
End Property
Public Function MoveNext() As Boolean Implements IEnumerator.MoveNext
Me._enumeratorPosition += 1
Return (Me._enumeratorPosition <= Me.Count)
End Function
Public Sub Reset() Implements IEnumerator.Reset
Me._enumeratorPosition = 0
End Sub
#End Region
#Region " IDisposable Support "
Private _isDisposed As Boolean = False
Protected Overridable Sub Dispose(ByVal isSafeToDisposeManagedResources As Boolean)
If Not Me._isDisposed Then
If isSafeToDisposeManagedResources Then
' no managed resources to free
End If
' no shared unmanaged resources to free
End If
Me._isDisposed = True
End Sub
Public Sub Dispose() Implements IDisposable.Dispose
Call Me.Dispose(True)
Call GC.SuppressFinalize(Me)
End Sub
#End Region
End Class
| 39,707 |
principlesbacte06abbogoog_11 | US-PD-Books | Open Culture | Public Domain | null | None | None | English | Spoken | 7,653 | 10,163 | of its virulence, and that absence of or diminution in virulence can hardly serve to distinguish as separate species these varieties that are otherwise alike ; more- over, the histological conditions found at the site of inoculation in animals that have not succumbed, but in which only the local reaction has appeared, are in most cases characterized by the same changes that are seen at autopsy in animals in which the inoculation has proven fatal. In the course of their observations upon a large number of cases, Roux and Yersin found that it was not difficult to detect in the diphtheritic deposits of one and the same individual bacilli of identical cultural and morphological peculiarities, but of very different degrees of virulence, and that with the progress of the disease toward recovery the less virulent varieties often became quite frequent.* There is, moreover, a mild form of diphtheria affecting only the mucous membrane of the nares, known as membranous rhinitis, from which it is very common to obtain cultures in all respects identical with those from typical diphtheria, save for their power to kill suscepti- ble animals. On inoculation these cultures produce only local reactions, but these are characterized histo- logically by the same tissue changes that follow inocu- lation with the fully virulent organism. Clinically, membranous rhinitis is never such an alarming disease as is laryngeal or pharyngeal diph- theria, and, as stated, the organisms causing it are oft;en of a low degree of virulence, though they are, never- theless, genuine diphtheria bacilli. 1 It must not be assumed from this that the bacilli lose their yirulence entirely, or that they all become attenuated with the establishment of con- valescence. INOCULATIONS WITH B. DIPHTHERIA, 293 For those organisms that are in all respects identical with the virulent bacillus diphtherice, save for their in- ability to kill guinea-pigs, the designation "pseudo- diphtheritic bacillus'' is usually employed, but from such observations as those just cited we are inclined to the opinion that jpseitcto-diphtheritic, as applied to an organism in all respects identical with the genuine bacillus, except that it is not fated to susceptible ani- mals, is a misnomer, and that it would be more nearly correct to designate this organism as the attenuated or non-virulent diphtheritic bacillus, reserving the term "pseudo-diphtheritic'' for that organism or group of organisms (for there are probably several) that is enough like the diphtheria bacillus to attract attention, but is distinguishable from it by certain morphological and cultural peculiarities aside from the question of viru- lence. It is a well-known fact that many pathogenic organ- isms— conspicuous among these being the micrococcus lanceolatus, the staphylococcus pyogenes aureus, and the group of so-called hemorrhagic septicaemia organ- isms— undergo marked variations in the degree of their pathogenic properties ; and yet these organisms, when found either devoid of this peculiarity, or possessing it to a diminished degree, are not designated as "pseudo" forms of these organisms, but simply as the organisms themselves, the virulence of which, from various causes, has been modified. Note. — Prepare cover-slip preparations from the mouth -cavity of healthy individuals and from those having decayed teeth. Do they correspond in any way with those made from diphtheria? Do the same with 294 BACTERIOLOGY, different forms of sore-throat. Do the peculiarities of any of the organisms suggest those of the bacillus of diphtheria? Wherein is the difference? In cultures and cover-slips made from both diphtheria and from innocent sore-throats are there any organisms which are almost constantly present? Which are they, and what are their characteristics ? Which are the predominating organisms in the an- ginas of scarlet fever? Do these organisms simulate, in their cultural and morphological peculiarities, any of the different species with which you have been working? CHAPTER XXI. Typhoid fever— Study of the organism concerned in its production— The bacterium coli commune— Ita resemblance to the bacillus of typhoid fever- Its morphological, cultural, and pathogenic properties— Its differentiation from the baciUus typhi abdominalia. The organism, discovered by Eberth and by Gaff ky, generally recognized as the etiological factor in the production of typhoid fever, may be described as follows : It is a bacillus about three times as long as it is broad, with rounded ends. It may appear at one time as very short ovals, at another time as long threads, and both forms may occur together. Its breadth remains toler- ably constant. Its morphology presents little that will Fig. 56. Fig. 57. BdcUlus typhi abdominalis from BaciUus typhi abdaminalis show- culture twenty-four hours old, on ing flagella stained by LOffler's agar-agar. method. aid in its identification (see Fig. 56). It stains a trifle less readily with the aniline dyes than do most of the other organisms. It is very actively motile, and when 296 BACTERIOLOGY. stained by the special method of LoflBer (see this method in chapter on Stainings) is seen to possess very delicate locomotive organs in the form of fine, hair-like flagella, which are given off in large numbers from all parts of its surface (see Fig. 57). These flagella are not seen in unstained preparations, nor are they ren- dered visible by the ordinary methods of staining. In patients suffering from this disease it has been found during life in the blood, urine, and feces, and at autopsies in the tissues of the spleen, liver, kidneys, intestinal lymphatic glands, and intestines. Gei^atin Plates. — Its growth, when seen in the depths of the medium, presents nothing characteristic, ap- pearing simply as round or oval, finally granular points. On the surface it develops as very superficial, blue-white colonies, with irregular borders. They are a little denser at the centre than at the periphery. When magnified, Colony of baeiUus typhi dbdominalis on gelatin. the colonies present wrinkles or folds, which give to them, in miniature, the appearance seen in the relief maps made to represent mountainous districts. These colonies have sometimes the appearance of flattened pellicles of glass-wool, and usually present more or less of a pearl-like lustre. On Agar-agar the colonies present nothing typical. TYPHOID BACILLI IN MILK. 297 • Stab Cultures. — In stab cultures the growth is mostly on the surface, there being only a very limited development down the track made by the needle. The surface growth has the same appearance in general as that given for the colonies. Potato. — The growth on potato is usually described as luxuriant but invisible, making its presence evident only by the production of a slight increase of moisture at the inoculated point, and by a limited resistance offered to the needle when scraped across the track of growth. While this is true in most cases, yet it cannot be considered as constant, for at times this organism is seen to develop more or less visibly on potato. Potato Gelatin. — The growth is similar to that upon ordinary nutrient gelatin. Milk. — It does not cause coagulation when grown in sterilized milk. It does not liquefy gelatin. It grows both with and without oxygen. It does not produce indol. In bouillon it causes a uniform clouding of the medium and brings about a slightly acid reaction. It does not grow rapidly. It does not produce fermentation, and on lactose- litmus-agar grows as pale-blue colonies, causing no reddening of the surrounding medium. In the fermen- tation tube, in glucose or lactose bouillon, no evolution of gas as a result of fermentation occurs. It does not form spores. The irregularities of stain- ing so commonly seen in this organism have in some instances led to the belief that the pale, unstained por- tions of the bacilli indicate the presence of spores. 298 BACTERIOLOGY, More reliable tests, however, have demonstrated the error of this opinion. It grows at any temperature between 20° C. and 38° C, though more favorably at the latter point. It is very sensitive to high temperatures, being killed by an exposure of ten minutes to 60° C, and in a much shorter time to slightly higher temperatures. Owing to a tendency toward retraction of its proto- plasm from the cell envelope and the consequent pro- duction of vacuoles in the bacilli, the staining of this organism is usually more or less irregular. AX some points in a single cell marked differences in the intensity of the staining will be seen, and here and there areas quite free from color can commonly be detected. These colorless portions are often so cleanly cut in outline as to look as if they had been punched out with a sharp instrument. (Diagrammatically represented in Fig. 59.) Fig. 59. / § V? Diagrammatic representatioD of retraction of protoplasm, with production of pale points, in the baciUus typhi oMominalis. Presence in Tissues. — It is not easy to demonstrate this organism in tissues unless it is present in large numbers. The manipulations to which the sections are subjected in being mounted often rob the bacilli of their staining, and render them invisible, or nearly so. If, however, sections be stained in the carbolic-fuchsin solu- tion, either at the ordinary temperature of the room or at a higher temperature (40° to 45° C), then washed TYPHOID INOCULATION IN ANIMALS, 299 out in absolute alcohol, and cleared up in xylol and mounted in balsam, the bacilli (particularly if the tissue is the liver or spleen) can readily be detected massed together in their characteristic clumps. If used in the same way, the alkaline methylene-blue solution gives also very satisfactory results. In searching for the typhoid bacilli in tissues, their mode of growth under these circumstances must always be borne in mind, otherwise much labor will be ex- pended in vain. In tissues the typhoid bacilli do not lie scattered about in the same way as do the organisms in tissues from cases of septicaemia ; they are not regularly distributed along the course of the capillaries, but are localized in small clumps through the tissues, and it is for tliese clumps, which are easily detected under the low-power objective, that one should search. When the section is prepared for examination, if it be gone over with the low-power objective, one will notice at irregular intervals little masses that look in every respect like particles of staining-matter which have been precipitated upon the section at that point. When these little masses are examined with a higher power objective they will be found to consist of small ovals or short rods so closely packed together that the individuals composing the clump can often be seen only at the very periphery of the mass. This is the characteristic ap- pearance of the typhoid organism in tissues. The little masses are usually in the neighborhood of a capillary. Result of Inoculation into Lower Animals. — A great many experiments have been inade with the view of reproducing the pathological conditions of this disease, as seen in man, in the tissues of lower animals, but with limited success. Fatal results without the 300 BACTERIOLOGY. appearance of the typical pathological changes have fre- quently followed these attempts, but in most cases they could easily be traced to the toxic/ rather than to the truly infective^ action of the materials introduced into the animals. The most successful efforts for the production of the typical typhoid lesions in lower animals are those reported by Cygnseus. By the introduction of the typhoid bacilli into the tissues of dogs, rabbits, and mice he was able to produce in the small intestines conditions that were histologically and to the naked eye analogous to those found in the human subject. Of a number of experiments made by the writer with the same object in view, only one positive result followed the introduction of typhoid bacilli into the circulation of rabbits. In this case the ulcer in the ileum was macroscopically and microscopically identical with those found at autopsy in the small intestine of the human subject dead of this disease. The typhoid bacilli were not only obtained from the spleen of the animal by culture methods, but were also demonstrated microscopically in their characteristic clumps in sections of the organ. In connection with the inoculation of animals with the bacillus typhi abdominalis, observations of a most important nature have recently been made upon the artificial induction of susceptibility to its pathogenic action by Sanarelli.' He found that rabbits, guinea- pigs, and mice could be rendered susceptible to in- 1 Toxic— Poisonous results not necessarily accompanied by the growth of organisms throughout the tissues. 2 Infective or septic— Poisoning of the tissues as a result of the growth of bacteria in them. 8 Sanarelli : Annales de I'Institut Pasteur, 1892, tome yi. TYPHOID INOCULATION IN ANIMALS, 301 fection by this organism by injecting into them the ^products of growth of certain saprophytes — -proteus vulgaris, bacUlvs prodigiosus, and bdderium coli com- mune— and that by whatever means the animal was sub- sequently inoculated with fresh cultures of the typhoid bacillus, either into the circulation or into the perito- neal cavity, death resulted in from twelve to forty- eight hours, with the most conspicuous pathological alterations in the digestive tract, and particularly in the small intestines. In these cases the infection is general and the organisms may be recovered from the blood and internal organs. It is the opinion of Sanarelli that the toxic conditions produced by the preliminary injections of the products of growth of the saprophytic organisms may be considered as analogous to a sim- ilar condition that may occur in man from the ab- sorption of abnormal products of fermentation from the intestinal canal — an auto-intoxication that so re- duces the resistance of the individual as to render him susceptible to infection by the bacillus of typhoid fever, should it gain access to his alimentary tract. More recently it was found by Alessi ^ that rats, guinea-pigs, and rabbits, when permitted to breathe the gaseous products of decomposition from the contents of a cesspool, or from other decomposing matters, grad- ually became susceptible to infection by the typhoid bacillus. After an exposure of from five to seventy- two days in the case of rats, seven to fifty-eight days in the case of guinea-pigs, and three to eighteen days in the case of rabbits, the resistance of the animals was so diminished that inoculation with relatively small 1 Alessi: Centralblatt fUr Bakteriologie u. Parasitenkuude, 1894, Bd. xv., No. 7, p. 228. 14 302 BACTERIOLOGY. amounts of cultures of the typhoid bacillus proved fatal in from twelve to thirty-six hours. Autopsies upon these animals revealed the presence of hemorrhagic enteritis, hypertrophy of Peyer's patches, and enlarge- ment of the spleen. The bacilli were found in the blood, liver, and spleen. The importance of these observations in their bearing upon the etiology of typhoid fever, if they are demon- strated by subsequent experiment to be trustworthy, is too obvious to necessitate emphasis, and it is greatly to be desired that they may not be permitted to pass unnoticed, but that others interested may find occasion to institute experiments in the same direction with the hope that some light may be shed upon the mooted question concerning the influence of gaseous products of decomposition upon the health of individuals, and particularly upon the part played by them in dimin- ishing natural resistance to infection. Because of the variations in the morphology and cul- tural peculiarities of this organism, and because of the difficulty experienced in efforts to reproduce in lower animals the conditions found in the human subject, typhoid fever is bacteriologically one of the most un- satisfactory of the infectious diseases. There are a number of other organisms which botani- cally appear to be so closely related to the typhoid bacil- lus, and which, with our present methods for studying them, so closely simulate it that the difficulty of identify- ing this organism sometimes is very great. In addition to this, the variability constantly seen in pure cultures of the typhoid bacillus itself in no way renders the task more simple. For example, the morphology of the typhoid bacillus TYPHOID INOCULATION IN ANIMALS, 303 is conspicuously inconstant; its growth on potato, which is usually given as characteristic, may, with the same culture, at one time appear as the typical invisible development, at another time it may grow in a way easily to be seen with the naked eye ; and the change of reaction which it is said to produce in bouillon is some- times much more intense than at others. The only properties possessed by it that may be said to be constant are its motility, its inability to cause fermentation of glucose, lactose, and saccharose, its incapacity for coagulating milk, the absence of indol- production, and its growth on gelatin plates ; but there are other organisms which approach these same charac- teristics to a degree that renders their differentiation from the typhoid organism often a matter that requires the careful application of all these differential tests. These points should be borne in mind in the exami- nation of drinking-water supposed to be contaminated by typhoid dejections, for the organisms which most nearly approach the typhoid bacillus in growth and morphology are just those organisms which would appear in water contaminated from cesspools, i. e., the organisms constantly found in the normal intestinal tract. Even in the stools of typhoid-fever patients the presence of these normal inhabitants of the intes- tinal tract renders the isolation of the typhoid organisms somewhat troublesome. The spleen of a patient dead of typhoid fever is the safest place from which to obtain cultures of this organ- ism for study. But it must always be remembered that the same channels through which the typhoid bacillus gains access to this viscus are likewise open to other organisms present in the intestines, and for this reason 304 BACTERIOLOGY, the bacterium coli commune, a normal inhabitant of the colon, may also be found in this locality. Note. — Obtain a pure culture of typhoid bacilli, and from this make inoculations upon a series of potatoes of different age and from different sources. Do they all grow alike ? Before sterilizing, render another lot of potatoes slightly acid with a few drops of very dilute acetic acid ; render others very slightly alkaline with dilute caustic soda. Do any differences in the growth result ? Make a series of twelve tubes of peptone solution to which rosolic acid has been added. Inoculate them all with as near the same amount of material as possible (one loopful from a bouillon culture into each tube) ; place them all in the incubator. Is the color-change, as compared with the control tube, the same in all cases ? Compare the morphology of cultures of the same age on gelatin, agar-agar, and potato. Select a culture in which the vacuolations are quite marked. Examine this culture unstained. Do the or- ganisms look as if they contained spores ? How would you demonstrate that the vacuolations are not spores ? Obtain from the normal feces a pure culture of the commonest organism present. Write a full description of it. Now make parallel cultures of this organism and of the typhoid organism on all the different media. How do they differ? In what respects are they similar ? Bacterium Coli Commune (colon bacillus ; bacillus Neapolitanus of Emmerich). — This organism was found by Escherich, in 1885, in the intestinal discharges of milk-fed infants. It has since been demonstrated to BACTERIUM COLI COMMUNE. 305 be a normal inhabitant of the intestines of man and of certain domestic animals (cattle, hogs, dogs). For a time after its discovery it was considered of but little importance and attracted attention only because of its resemblance, in certain respects, to the bacillus of typhoid fever, with which it was occasionally confounded. In this particular it is still a subject for study, and some have even gone so far as to regard them as modifications of the same species, though in the present state of our knowledge this is certainly overstepping the mark. That they possess in common certain general points of resemblance and often approach one another in some of their biological peculiarities is true; but, as we shall learn, they each possess peculiarities which, when taken together, render their differentiation from one another a matter of but little difficulty. With the wider application of bacteriological methods to the study of pathological processes it was occasion- ally observed that, under favorable circumstances, this organism was disseminated from it« normal habitat and appeared in remote organs, often associated with diseased conditions. This was also, at first, considered of but trifling moment, and its presence in these localities was usually explained as accidental. Its repeated appearance, however, in different parts of the body outside of the intestines and the frequency of its association with pathological conditions ultimately attracted attention to it, and in consequence during the past two or three years a great deal has been written concerning the possible pathogenic nature of this organism. The fact that it is always with us in most intimate association with certain of our life processes, together with the fact that it is known to appear in organs other 306 BACTERIOLOGY. than that in which it is normally located, and that its occurrence in diseased conditions is not rare, justifies the opinion that it is one of the most important of the micro-organisms with which we have to deal. While not generally considered to be a pathogenic organism, there is, nevertheless, sufficient evidence to warrant the statement that, under favorable conditions, with which we are not entirely familiar, this organism may assume pathogenic properties and that its presence in diseased conditions is not always to be considered as accidental, though this is frequently the case. The morphological and cultural peculiarities of the bacterium coli commune are as follows : Morphology. In shape it is a rod with rounded ends, sometimes so short as to appear almost spherical, while again it is seen as very much longer threads. Often both forms will be associated in the same culture. It may occur as single cells or as pairs, joined end-to- end. There is nothing to be said of its morphology that can aid in its identification, for in this respect it simulates many other organisms. It is usually said to be motile, and undoubtedly is motile in the majority of cases, but its movements are so sluggish that a positive opinion is oft;en difficult. By Loffler's method of staining, flagella can be demonstrated, though not in such numbers as are seen to occur on the typhoid fever bacillus. It does not form spores. It grows both with and without oxygen. On gdcUin. When on the surface its colonies appear as small, dry, irregular, flat, blue-white points that are commonly somewhat dentated at the margin. They are a trifle denser at the centre than at the periphery, BACTERIUM COLI COMMUNE, 307 and are often marked at or near the middle by an oval or round nucleus-like mass — the original colony from which the layer on the surface developed. When located in the depths of the gelatin, and examined with a low- power lens, they are at first seen to be finely granular and of a very pale greenish-yellow color ; later they become denser, darker, and much more markedly granular. In shape they are round, oval, and lozenge- like. When the surface colonies are viewed under a low power of the microscope they present essentially the same appearance as that given for the bacillus of typhoid fever, viz.: they resemble flattened pellicles of glass-wall, or patches of finely ground colorless glass. Colonies of this organism on gelatin are frequently encountered that cannot be distinguished from those resulting from the growth of the bacillus of typhoid fever. In stab and smear cultures on gelatin the surface growth is flat, dry, and blue-white or pearl color. Limited growth occurs along the track of the needle in the depths of the gelatin. As the culture becomes older the gelatin round about the surface growth may gradually lose its transparency and become cloudy, often quite opaque. In still older cultures small roots, or branch-like projections from the surface growth into the gelatin are sometimes seen to occur. It does not cause liquefaction of gelatin. Its growth on nutrient agar-agar and on blood- serum is luxuriant but not characteristic. In bouillon it causes difiiise clouding with sedi- mentation. In some bouillon cultures an attempt at pellicle formation on the surface may be seen, but this is not always the case. In old bouillon cultures the 308 BACTERIOLOGY, reaction is seen to have become alkaline, and a decided ecalf odor may be detected. It produces indol in bouillon and in peptone solution. Its growth on potato is rapid and voluminous, appear- ing after twenty-four to thirty-six hours in the incubator as a more or less lobulated layer of a drab, dark-cream, or brownish-yellow color. In neutral milk containing a little litmus tincture the blue color is changed to red afi«r from eighteen to twenty-four hours in the incubator, and in addition the majority of cultures cause a firm coagulation of the casein in about thirty-six hours, though frequently this takes longer. Very rarely, the litmus may indicate the production of acid and no coagulation occur. In media containing glucose it grows rapidly and causes active fermentation with liberation of carbonic acid and hydrogen. If cultivated in solid media to which glucose (2 per cent.) has been added, the gas- formation is recognized by the appearance of numerous bubbles along and about the track of the growth. If cultivated in fluid media, also containing glucose, in the fermentation tube, evidence of fermentation is given by the collection of gas in the closed arm of the tube. On lactose-litmus-agar its colonies are pink and the color of the surrounding medium is changed from blue to red. In Dunham's peptone solution it produces indol in from forty-eight to seventy-two hours. It stains with the ordinary aniline dyes. It is de- colorized when treated with iodine after having been stained by the method of Gram. By comparing what has been said of the badlhis typhi abdomincUis and of the bacterium coli commune it will ANIMAL INOCULATIONS. 309 be seen that while they simulate each other in certain respects they still possess individual characteristics by which they may readily be differentiated. The most important of the differential points are : 1. Motility of the baciUv^ typhi abdcymincdia i& much more conspicuous, as a rule, than is that of the bacterium coll commune. 2. On gelatin the colonies of the typhoid bacillus develop more slowly than do those of the colon bacillus. 3. On potato the growth of the typhoid bacillus is usually invisible (though not always), while that of the colon bacillus is rapid, luxuriant and always visible. 4. The typhoid bacillus does not cause coagulation of milk with acid reaction. The colon bacillus does this in from thirty-six to forty-eight hours in the incubator. 5. The typhoid bacillus never causes fermentation, with liberation of gas, in media containing glucose, lactose, or saccharose. The colon bacillus is conspicuous for its power of causing fermentation in such solu- tions. 6. In nutrient agar-agar or gelatin containing lactose and litmus tincture, and of a slightly alkaline reaction, the color of the colonies of typhoid bacillus is blue, and there is no reddening of the surrounding medium, M'hile the colonies of the colon bacillus are pink and the medium round about them becomes red. 7. The typhoid bacillus does not possess the property of producing indol in solutions of peptone; the growth of the colon bacillus in these solutions is accompanied by the production of indol in from forty- eight to seventy-two hours at 37° to 38° C. Animal inoculationa. As with the bacillus of typhoid 14* 310 BACTERIOLOGY. fever, the results of inoculation of animals with cultures of this organism cannot be safely predicted. According to the observations of Escherich, Emmerich, Weisser, and others, the results that do appear are in most instances to be attributed to the toxic rather than to the infective properties of the culture used. When introduced into the subcutaneous tissues of mice it has no effect, while similar inoculations of guinea-pigs are sometimes (not always) followed by abscess formation at the point of injury, or by altera- tions very similar to those produced by intra-vascular inoculation, viz.: death in less than twenty-four hours, accompanied by redness of the peritoneum and marked hypersemia and ecchymoses of the small intestine; together with swelling of Peyer's patches. The caecum and colon may remain unchanged or present enlarged follicles. There may or may not be an accumulation of fluid in the abdominal cavity, but peritonitis is rarely present. The small intestines may contain bloody mucus. Intra-venous inoculation of rabbits may be followed by similar changes with often the occurrence of diar- rhoea before death, which may, in the acute cases, result in from three to forty hours. In another group of cases acute fatal intoxication does not result, and the animal lives for weeks or months, dying ultimately of what appears to be the effects of a slow or chronic form of infection. For a few hours after inoculation these animals present no marked symptoms ; exceptionally somnolence and diarrhoea have been observed at this period, indicating acute intoxication from which the animal has recovered. The affection is unattended by fever. The most marked symptom is loss of weight. ANIMAL INOCULATIONS, 31 1 This is usually progressive from the first or second day after inoculation, with slight fluctuations until death. At autopsy the animal is found to be emaciated. The subcutaneous tissues and the muscles appear pale and dry. The serous cavities, particularly the peri- cardial, may contain some excess of serum. The viscera are anaemic. The spleen is small, thin, and pale. Exceptionally ulcers and ecchymoses are observed in the caecum, but generally there are no lesions of the intestinal tract. The most striking and constant lesions, those most characteristic of the affection, are in the bile and in the liver ; the quantity of bile may not exceed the normal, but in other cases the gall-bladder may be abnormally distended with bile. The bile is nearly colorless or has a pale yellowish or brownish tint, with little or none of a greenish color. Its consistence is much less viscid than normal, being often thin and watery. It usually contains small, opaque, yellowish particles or clumps which can be seen floating in it, even through the walls of the gall-bladder. These clumps consist microscopi- cally of bile-stained, apparently necrotic, epithelial cells ; leucocytes in small numbers ; amorphous masses of bile pigment, and bacteria often in zoogloea-like clumps. Similar material is found in the larger bile- ducts. The liver frequently contains opaque, whitish or yellowish- white spots and streaks of irregular size and shape, which give a peculiar mottling to the organ when present in large numbers. These areas may be numer- ous^ or only one or two may be found. In size they range from minute points to areas of from 2 to 3 cm. in extent. 312 BACTERIOLOGY, By microscopic examination they are found to repre- sent places where the liver cells have undergone necrosis accompanied with emigration of leucocytes, and the cells about them are in a condition of fatty degeneration. In sections of the liver, masses of the bacilli may be discovered in and about the necrotic foci just described. At these autopsies the colon bacillus is not found generally distributed through the body, but is only to be detected in the bile, liver, and occasionally in the spleen.^ 1 Consult paper by Blachstein on this subject. Johns Hopkins Hospital Bulletin, July, 1891. CHAPTER XXII. The spirillum (comma bacillus) of Asiatic cholera— Its morphological and cultural peculiarities— Pathogenic properties— The bacteriological diagnosis of Asiatic cholera. At the conference held in Berlin in 1884 for the purpose of discussing the cholera question, it was announced by Koch* that he had discovered in the intestinal evacuations of individuals suffering from Asiatic cholera a micro-organism that he believed to be the cause of the malady. The importance of this statement necessarily attracted widespread attention to the subject, and as one of the results there existed, for a short time following, some skepticism as to the accuracy of Koch's claim. These doubts arose as a result of a series of contributions from other observers who endeavored to prove that the organism found by Koch in cholera evacuations was one that is common to other localities, and not a specific accompaniment of this disease. It was not very long, however, before it was evident that the objections raised by the opponents of Koch were based upon untrustworthy observations, and that by reliable methods of investi- gation the organism to which he had called attention could be easily differentiated from either and all of those with which it was claimed to be identical. This organism, known as the spirillum of Asiatic cholera and as Koch's " comma bacillus,'' because of its morphology, is identified by the following peculiarities : » Verhandlungen der Conferenz zur Erorterung der Cholerafiage, 1884, BerUn. 314 BACTERIOLOGY, THE MORPHOLOGICAL AND BIOLOGICAL PECULIARITIES OF THE SPIRILLUM OF ASIATIC CHOLERA. Morphology, It is a slightly curved rod of about from 0.8 to 2 0 i" in length and from one-sixth to one- third in thickness ; that is to say, it is from about one- half to two-thirds the length of the tubercle bacillus, but is thicker and plumper. Its curve is usually not more marked than that of a comma, and, indeed, it is often almost straight; at times, though, the curve is much more pronounced, and may even describe a semicircle. Occasionally the curve may be double, one comma joining another, with their convexities pointing in opposite directions, so that a figure similar to the letter S is produced. In cultures, long spiral or undulating threads may often be seen. From these appearances this organism cannot be considered a bacillus, but rather an intermediate type between the bacilli and the spirilla. Koch thinks it not improbable that the short comma forms represent segments of a true spirillum, the normal form of the organism. (Fig. 60.) Fig. 60. ffm Spirillum of Asiatic cholera. Impression cover-slip from a colouy thirty-four hours old. It does not form spores, and we have no reliable evidence that it possesses the property of entering at CHOLERA SPIRILLUM: MORPHOLOGY, 315 any time a stage when its powers of resistance to detri- mental agencies are increased. It is a flagellated organism, but has only a single flagellum attached to one of its ends. It is actively motile, especially in the comma stage, though the long spiral forms also possess this property. Grouping. As found in the slimy flakes in the intes- tinal discharges frOm cholera patients, Koch likens its mode of grouping to that seen in a school of small fish when swimming up stream, i. e., they all point in nearly the same direction and lie in irregularly parallel, linear groups that are formed by one comma being located ^behind the other without being attached to it. Fig .61. 8 . * , ^"'"'"^ 'V ( ^i c„/ ■.-^...-■ ^, > „ ^. ]^^ ( \* -rj — f ^ '/ f . 4 ' / i «L. i ' >■ - / f ^t^\ e . ■■ * i ^ ^*^ Involution forms of the spirillum of Asiatic cholera, as seen in old cultures. On cover-slip preparations made from cultures in the ordinary way there is nothing characteristic about the grouping, but in impression cover-slips made from young cultures the short commas will nearly always be seen in small groups of three or four, lying together in such a way as to have their long axes nearly parallel to one another. (See Fig. 60.) In old cultures in which development has ceased, it undergoes degenerative changes, and the characteristic 816 BACTERIOLOGY. comma and spiral shapes may entirely disappear^ their place being taken by irregular involution forms that present every variety of outline. (See Fig. 61.) In this stage they take on the staining very feebly, and often not at all. OuUural peculiarities. On plates of nutrient gelatin that have been prepared from a pure culture of this organism and kept at a temperature'of from 20® to 22° C, development can often be observed after as short a period as twelve hours, but frequently not before sixteen to eighteen hours. This is especially true of the first or " original ^' plate, containing the largest number of colonies. At this time the plate will present to the^ naked eye an appearance that has been likened to a ground-glass surface, or to a surface that has been stippled with a very finely pointed needle, or one upon which very fine dust has been sprinkled. This appearance is due to the presence of minute colonies closely packed together upon the surface of the gelatin. In the depth of the gelatin can also be seen, closely packed, small points, likewise representing growing colonies. As growth progresses liquefaction occurs around the superficial colonies, and in consequence this plate is usually entirely liquid after from twenty-four to thirty hours; the developmental phases through which the colonies pass cannot, therefore, be studied upon it. On plates 2 and 3, w^here the colonies are more widely separated, they can be seen after twenty-four to thirty hours as small, round, or oval, white or cream- white points, and when located superficially there can be detected around them a narrow transparent zone of liquefaction. As growth continues, this liquefaction CULTURE OF THE CHOLERA SPIRILLUM, 317 extends downward rather than laterally, and the colony ultimately assumes the appearance of a dense, white mass lying at the bottom of a sharply-cut pit or funnel containing transparent fluid. This liquefaction is never very widespread nor rapid, and rarely extends for more than one millimetre beyond the colony proper. On plates containing few colonies there is but little or no tendency for them to become confluent, and, as a rule, they do not exceed 2 to 3 mm. as an average diameter. Fig. 62. ® @ Developmental stages of colonies of the spirillum of Asiatic cholera at 20° to 22° C. on gelatin. X about 75 diameters, o. After sixteen to eighteen hours. 6. After twenty-four to twenty-six hours, c. After thirty-eight to forty hours, d. After forty-eight to fifty hours, e. After sixty-four to seventy hours. When examined under a low magnifying lens the very young colonies (sixteen to eighteen hours) appear as pale, translucent, granular globules of a very delicate greenish or yellowish-green color, sharply outlined and not perfectly round. (See a. Fig. 62.) As growth progresses, this homogeneous granular appearance is replaced by an irregular lobulation, and ultimately the sharply-cut margin of the colony becomes dentated or 818 BACTERIOLOGY, 8calloj)ed. (See b and c, Fig. 62.) After forty-eight hours (and frequently sooner), liquefaction of the gelatin has taken place to such an extent that the appearance of the colony is entirely altered. Under the magnify- ing glass the colony proper is now seen to be torn and ragged about its edges, while here and there shreds of the colony can be detected scattered through the liquid into which it is sinking. These shreds evidently repre- sent portions of the colony that have become detached from its margin as it gradually sank into the liquefied area. At dy in Fig. 62, will be seen a representation of the several appearances afforded by the colonies at this stage. At the end of the second, or during the early part of the third day the sinking of the colonies into the liquefied pits, resulting from their growth, is about complete, and under a low lens they now appear as dense, granular masses, surrounded by an area of lique- faction through which can be seen granular prolonga- tions of the colony, usually extending irregularly between the periphery and the central mass. (See e. Fig. 62.) If the periphery be examined, it will be seen to be fringed with delicate, cilia-like lines that radiate from it in much the same way that cilia radiate from the ends of certain columnar epithelial cells. These are the more marked phases through which he colonies of this organism pass in their development on gelatin plates. With some cultures the various ap- pearances here given appear more quickly, while in cultures from other sources they may be somewhat retarded. On plates of nutrient agar-agar the appearance of the colonies is not characteristic. They appear as round or CULTURE OF THE CHOLERA SPIRILLUM, 31 9 oval patches of growth that are moist and tolerably transparent. The colonies on this medium at 37° C. naturally grow to a larger size than do those upon gelatin at 22° C. In stab cultures in gelatin there appears at the top of the needle track after thirty-six to forty-eight hours Fig. 63. stab cultures of the spirillum of Asiatic cholera in gelatin, at 18° to 20° C. o. After twenty-four hours, b. After forty-eight hours, e. After seventy- two hours, d. After ninety-six hours. at 22° C. a small, funnel-shaped depression. As the growth progresses, liquefaction will be seen to occur about this point. In the centre of the depression can be distinguished a small, dense, whitish clump, the 820 BACTERIOLOGY, colony itself. As growth continues the depression increases in extent and ultimately assumes an appear- ance that consists in the apparent sinking of the liquefied portion in such a way as to leave a perceptible air-space between the top of the liquid and the surface of the solid gelatin. The growth now appears to be capped by a small air-bubble. The impression given by it at this stage is not only that there has been a liquefaction, but also a coincident evaporation of the fluid from the liquefied area and a constriction of the superficial open- ing of the funnel. (See a, 6, c, and d, Fig. 63.) Lique- faction is not especially active^ along the deeper portions of the track made by the needle, though in stab cultures in gelatin the liquefaction is much more extensive than that usually seen around colonies on plates. It spreads laterally at the upper portion, and after about a week a large part of the gelatin in the tube may have become fluid, and the growth loses its characteristic appearance. Stab- and smear-cultures on agar-agar present noth- ing characteristic. They are usually only an exaggera- tion of the appearance afforded by the single colonies on this medium. Its growth in bouillon is luxuriant, causing a diffiise clouding and the ultimate production of a delicate film upon the surface. In sterilized milk of a neutral or amphoteric reac- tion at a temperature of 36°-38°C. it develops actively, and gradually produces an acid reaction with coagula- tion of the casein. It retains its vitality under these conditions for about three weeks or more. The blue color of milk to which neutral litmus tincture has been added is changed to pink after thirty-six or forty-eight hours at body temperature. CULTURE OF THE CHOLERA SPIRILLUM. 321 Its growth in peptone solution, either that of Dun- ham (see Special Media) or the one preferred by Koch, viz., 2 parts Witte's peptone, 1 part sodium chloride, and 100 parts distilled water, is accompanied by the production of both indol and nitrites, so that after eight to twelve hours in the incubator at 37° C. the rose color characteristic of indol appears upon the addition of sulphuric acid alone. (See Indol Reac- tion.) In peptone solution to which rosolic acid has been added the red color is very much intensified after four or five days at 37° C. Its growth on potato of a slightly acid reaction is seen aft;er three or four days at 37° C. as a dull, whit- ish, non-glistening patch at and about the site of inoc- ulation. It is not elevated above the surface of the potato, and can only be distinctly seen when held to the light in a particular position. Growth on acid potato occurs, however, only at or near the body tem- perature, owing probably to the acid reaction, which is sufficient to prevent development at a lower tempera-. ture, but does not have this effect when the temperature is more favorable. On solidified blood-serum the growth is usually said to be accompanied by slow liquefaction. I have not succeeded in obtaining this result on Loffler's serum, nor have I detected anything characteristic about its growth on this medium. The temperature most favorable for its growth is between 35° and 38° C. It grows, but more slowly, at 17° C. Under 16° C. no growth is visible. It is not destroyed by freezing. When exposed to 65° C. its vitality is destroyed in five minutes. 322 BACTERIOLOGY. It is strictly aerobic, its development ceasing if the supply of oxygen is cut off. It does not grow in an atmosphere of carbonic acid, but is not killed by a temporary exposure to this gas. It does not grow in acid media, but flourishes best in media of neutral or slightly alkaline reaction. It is so sensitive to the action of acids that, at 22° C, its devel- opment is arrested when an acid reaction equivalent to 0.066 to 0.08 per cent, hydrochloric or nitric acid is present (Kitasato). In cultures, the development of this organism reaches its maximum relatively quickly, then remains stationary for a short period, after which degeneration begins. The dying comma bacilli become altered in appearance and assume the condition known as " involu- tion forms." (See Fig. 61.) When in this state they take up coloring reagents very faintly or not at all, and may lose entirely their characteristic shape. | 32,018 |
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export * from "./pattern";
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https://persist.lu/ark:70795/bx6x0p/articles/DTL39_1 | BNL Newspapers (1841-1879) | Open Culture | Public Domain | 1,854 | Inland. | None | German | Spoken | 340 | 612 | Inland. Lurernburg, IN. März. (Eingesandt.) Hin und wieder begegnet man einem neugeprägten Lnremburger Zwci-Sousstücke. DaS ist also die erste eigne Geldmünze des Landes! Wahrlich der Ausfall des ersten Versuches ist wenig geeignet, unserer Eitelkeit zu schmeicheln. Denn 1. wenn man das Gewicht der Münze untersucht, so muß man gestehen, daß zwischen dem innern und dem nominellen Werlhc doch ein gar zu großer Unterschied ist. Unsere Zwci-Souöstückc wiege» kaum mehr, als die früheren einfachen. 2. Dazu kommt, daß die einzelnen Stücke bei gleichem nominellen Werthc sehr ungleiche Größe und Schwere haben. 3. Die Zeichnung ist nichts weniger als gut; die Präge ab« ganz gewöhnlich und roh. 4. Endlich begreift man nicht, mit welchem Rechte man auf den Münzen eines deutschen Bundeslandes eine französische Inschrift habe setzen dürfen. Welches Gesetz erklärt denn allein die französische Sprache für die rechtmäßige in einem Lande, daS ganz deutsch ist! Die Münzen gereichen weder dem Lande, noch denen, welche sie haben schlagen lassen, zur Ehre. Luremburg, 11. März. Während der Krieg vor der Thüre steht, und eine politische Erschütterung alle Länder bedroht, sind noch mehre deutsche Bundesländer durch die Wühlereien der Bürcaukraten gegen die katholische Religion in ihrem Innern erschüttert und beunruhigt. In Luremburg lagert die im Jahre 1848 verübte That noch immer wie ein böses Ge« wissen auf allen Verhältnissen des Landes; in Bade», Nassau, dm beiden Hessen und Wurtemberg spinnt die Büreaukratic die Verhältnisse immer unentwirrbarer in einander. In Mecklenburg endlich erliegen die Katholiken unter dem Drucke der empörendsten Mißhandlung. Bei so bewandten Umständen scheint uns der von achtbarer Seite gemachte Vorschlag (siehe „Mainzer Journal" vom 10. März,) sehr bcherzigenSwerth z„ sein, daß in Anbetracht der drohenden Zeitverhältnisse der Bund gebietend sich in's Mittel lege, und dm kleinen Regierungen befehle, in bestimmter leitfrist ein Abfinden mit der katholischen Kirche zu schließen, wodurch diese vor ferucrcr Beeinträchtigung sicher gestellt werde. Ocsterrcich und Frankreich ist daran gelegen, daß die Kirche nicht schutzlos sei. Echter» ach, 8, März. Seit Menschengedenken ist die Fastnachtszeit nicht so ruhig vorübergegangen, alö eS in diesem Jahre bei uns der Fall war. | 22,240 |
bpt6k1652465b_1 | French-PD-Newspapers | Open Culture | Public Domain | null | None | None | French | Spoken | 11,522 | 19,022 | fQUATRIEME ANNEE. — N1.078PRIX : 25 CENTIMESMARDI 17 DECEMBRE 1935quotidien du m a t iTotal général au huitième jour 169.040 francs soit pour la semaine mutualiste près de 50.000 francs Il nous reste à trouver avant le 31 décembre 30.960 francsLa voie droiteParmi tant d’aspects nouveaux d'une situation politique toujours changeante, un des plus étranges est sans doute l’évolution du parti communiste. Nous le connais sions, il y a deux ans encore, comme un petit troupeau sectaire et fermé, répétant avec dévotion la leçon de Moscou, hors de la quelle il n’y avait qu’anathème; Je voici transformé, en quelques mois, en lin parti beaucoup plus ouvert, attentif (mcine si l’adresse lui manque encore) à comprendre ! les sentiments d’autrui, à éviter j les blessures inutiles, à cultiver j au loin les sympathies, bref, à at-j tirer à lui les recrues d’origine j les plus diverses et à dissiper par la modération de ses mots d’ordre i immédiats les craintes qu’il a si1 longtemps excitées. Chose plus déconcertante, peutclre, aucun, changement de per sonnes n’a accompagné ce brus que renversement de méthodes. Chacun sait que ce n’est pas lui qui a causé le départ de M. Doriol et, depuis lors, point de ces exclusions dont le parti fut autre fois si prodigue. Il a gardé à sa lé le les mêmes chefs, dociles aux mois d’ordre du jour comme ils le furent à ceux d’hier, sans pou voir cire nullement tenus pour les j inventeurs des uns ni des autres.! Ne voir là que feinte et manœu vre ? L’explication serait trop, simple et le mensonge, fort heu! reusement, ne joue pas dans les affaires humaines un tel rôle. Que la doctrine et le but suprême du. parti communiste n’aient point : changé, lui-même le répète cha que jour et nous n’avons pas le droit de douter de ses intentions, i Mais si les mêmes phrases sont encore prononcées, l’esprit qui les anime n’est peut-être plus tout à fait le même. L’on n’est plus maître des ac tes qu’on a posés. Il est des éten dards qu’on ne déploie pas impu nément. Ce n’est pas impunément qu’on bal le rappel pour la dé fense des libertés démocratiques et de la dignité humaine, ou qu’on se porte avec M. Vaillant-Couturier « au secours de la famille ». Il est impossible que ces attitudes, même prises par ordre, ne réagis sent pas, à la longue, plus ou moins profondément dans l’esprit el le cœur de ceux qui les adop tent. D’aucuns ont parle à ce propos de la « modération » communiste. ! Nous ne saurions partager leur avis. Cet esprit nouveau qui ani-! me le parti ne le rend en rien1; moins redoutable. Il est telle in; transigeance doctrinale hautaine, j toujours à la recherche d’une I inaccessible pureté, toujours prête à décourager les concours possi-j blés par des discussions de déJ tail et des querelles de textes, qui empêche radicalement toute ac tion pratique. En se délivrant do celle tare, en comprenant que l’es-1 seul ici n’est pas d’affirmer à cha que instant toute la doctrine, mais j bien de s’en être nourri et de: progresser toujours vers le but sans jamais le perdre des yeux, les! communistes ont fait preuve d’un esprit politique qui les rend plus dangereux. Les faits ne nous mon trent-ils pas que, dans la rue ou dans les scrutins, le poids et l’élan du parti ne sont nullement dimi nués, mais accrus ? Qu’adviendra-t-il de ce souffle nouveau el pourra-t-il un jour fai re circuler un air plus frais dans les étroits cadres marxistes ? Nous l’ignorons et le rechercher n’est point ici notre propos. Ce qui s’impose aujourd’hui est de déga ger pour nous-mêmes les suites possibles de ces faits. Dans leur désir de grouper au-1 tour d’eux les masses, les commu nistes sont loin de négliger les J foules catholiques. Sur divers | points, au contraire, ils multi plient les tentatives de ce côté. Il convient de ne pas être surpris par les faits et d’envisager l’évenlualilc où sur certaines positions que nous savons être les nôtres, ils viendraient se placer plus ou moins bruyamment. Voisinage fâcheux, penseront certains, et qui pourrait provo quer bien des sourires, voire des attaques plus ou moins lovalcs. Tout cela est vrai, sans doute, mais il serait, croyons-nous, bien peu sage de se laisser fasciner jiar ces dangers très réels, au point de suivre désormais les inspira tions de la peur. Joseph Hours. (Voir la suite en 3,; page, e* colonne)L’allocntion consistorialeLe Pape appelle de ses vœux les pies ardents « sur tous les hommes de bonne volonté une paix inséparable de la justice de la vérité et de la charité»Voici le le.xle de l’allocution prononcée par Je Souverain Pontife au cours du Consistoire secret qui s'est tenu hier ma lin au Vatican : Vénérables Frères, Voire vénérable Collé ne a ih1. en ees derniers temps, déplorer des deuils graves et douloureux. Nous coulons parler do ces hommes illustres que Nous vou lons ici. si brièvement que ce soit, com mémorer devant, vousLES PROPOSITIONS FRANCO-BRITANNIQUES POUR LA PAIX EN AFRIQUEM. Pierre Laval fera une déclaration ce matin à la Chambre Le président du Conseil partira ce soir pour Genève où le Conseil de la S.D.N. doit se réunir demainM. Baldwin multiplie h Londres les échangesde vues ministériels L’Ethiopie ne veut pas d’une zone de colonisation'Après avoir adoplé les derniers cha pitres réservés de la loi de finances, la Chambre a volé d’une traite une demi-douzaine de budgets de dépen ses. Quand le budget des Affaires étran gères a élé appelé, M. Bouisson, qui venait de s’enIretenir avec Je prési dent. du Conseil, a déclaré qu’il ien-Pu/iiti vus collègues défunts, qui. sqiiI j droit en discussion ce matin. l'objet de si vifs regrets, Nous tenons, j On apprenait, aussi lût après, dansmm-1 Iloare du 10 décembre prescrivant ,1 sir Sydney Barton d'user de toute son influence auprès de l'empereur d’Ethiopie pour qu’il prit en considération les pro positions qui Jui étaient faites semble diflicilemenl conciliable — du point de mio ile Umtilô de 1ie gouvernementale — avec le détachement marqué à Genève à l'égard de ce document, par les déclara lions de M. F.dcn. Cet aspect particulier d'une si tua lion générale assez délicate ne saurait, dit-on, manquer d’être examiné en com mun par les'ministres. Vu Conseil de cabinet se réunira, d’ail leurs. Ires probablement demain, afin d’arrêter les instructions que M. F.dcn emportera à Genève où il se rendra pour représenter l’Angleterre à la réunion du Conseil du la Société des Nations. Les échanges de vues entre M. Baldwin e1 ses collègues, ce matin, ont duré en viron deux heures.u bon terme la composition du Code ca-. co-brilanniquo. no niqua pour l’Eglise latine, en tarifant président du Conseil a confirmé aussi à pied d œuvre wte œuvre pareille ^ fjn (|e journée, aux membres de pour l balise orientale, quü a assuvié de , Json jntG,ition de faire ce si nombreux cl si ‘importants travaux. ■ j. ,s ; s/ü. mi union u. mu e ce C'est durant toute une suite ü'années matin a la. Chambre une déclaration qu'il Xous u donna, spr.cialçincnt en qun-1 il écrite et dont on peut ulfirmor, lilé de secrétaire délitai, le concours préétant donné les habitudes de l'orateur, ! deux de son activité. Il l’a fait avec latil j qu’elle sera brève et prudente. j Londres, IG décembre.— L’avion suisse de compétence et de dévouement, qu’il i , ,,. ... , _ ! à bord duquel a voyagé sir Samuel Iloare s’est gagné! de Notre part une profonde ! Ajoutons que 1 atmosphère dis eou< ,|G /unVh à Londres, retardé par un fort gratitude cl qu'il a mérité l'admiration I loirs était assez détendue depuis x enj vent contraire, n'est arrivé ù l’aérodromeSir Samuel Hoare est de retour à Londresuniversel!. Quant a l'autre, si versé1 dans les scien ces dicincs et profane# Nous lui. étions denom eau évoqué au jourd'hui putdredi. On s'attendait, cependant que le conflit Halo-éthiopien iïii ce de Croûton qu’à 17 h. o. , depuis longtemps si. uni dans une intime communion d’études et de travaux, qu'il Nous en était devenu plus cher encore. A leurs noms Nous voulons joindre maintenant, celui de Votre frère biçn-aim.è le cardinal Michel f.cgii, qui, ce matin même, est moulé, vers les joies célestes. Evénements heureux et tristesses Mais après avoir, d'un cœur ému, scrGeorge Cierk, ambassadeur lisfail ù ce devoir de charité, Nous ne ! Bretagne à Paris. voulons pas aujourd'hui Nous attarder ù | 3 -ç an long discours, encore que ne Nous en fassent’ point défaut les sujets, événe ments heureux ou aItrista.nl[s. Evénements heureux, disons-Nous, com me le furent, ees imposantes el si pieuses solennités gui. se sont deroulcçs ù Lour des et à, Buenos-Ayres surtout — et purslesgroupes de gauche. Le président du Conseil reçoit sir George Cierk et Vambassadeur d'Italie M. Pierre Laval, président du Conseil, ministre des Affaires étrangères, a reçu successivement, à la fin de l’après-midi, M. Oiriiti, ambassadeur d’Italie, et sir de Grande-25 parts Anonyme, Seine 5U01 Puget, curé de F orgues, par Itieumes, 2u ; lu paris M. Briquet. Strasbourg 2U0 I t.A. Cruchon, Saint-LUenne, 20; M. 11. U parts Ln groupe de Jeunes Amie* j Bertrand, Meulan, 20 ; a nom me louloutle l’aube, Paris 120 I sain, 20; un abonné de s.-cl-O., 20 ; M. G parts M. T. T., Le Puy 120 j l’abbé (hall, curé-doyen de Fouesnan, 30 ; 0 parts M. P. Scelles, Saint-Mandé 125 I 3 Cosnois, amis de l'aube (Nièvre), 2u ; M. 5 parts M. L. Azéma, Montpellier. 100 i Paul Fromond, Cbampagnule, 20 ; M. 5 parts M. E. Masson, Sl-Soulve. 1UU j l’abbé L. Buatoïs, institution Notre-Dame, 5 parts « U11 prêtre très souffrant Valenciennes, 20 ; M. 11. licné, Nancy, qui offre à Dieu son mal pour 20; M. Yiltet, Villeurbanne, 20; M. lal«que notre chère aube vive et se bé Beun, Ilomlsehoote, 20 ; M. l’abbé Starépande toujours davantage ».. 100 ; vaux. Sens, 20 ; M. Cornilleau, Blois, 20 ; 5 parts I n ami de Tunisie 100 j M. P. Lefebvre, Marcq-en-Baroeul, 2o ;100100 100 lue 100 50 ou GU GO5 parts M. L. Dumoulin, Roubaix 5 parts En souvenir de 5 prêtres dans l’au-delà 5 parts Le docteur Leclère, Reims.. 5 parts M. et Mme. Loeffler, Cre.sl.. 5 parts M. Lucien Buis J. IL, Issyles-Moulineaux Madeleine Beis, Issy-les-Moulineaux 3 parts M. Floch, Paris 3 parts Abbé Février, Saint-Lze.... 3 ]»arts 1t. P. E. IL, Lagny « Pour que l'aube i e », Bocquet, 50 ; M. P. Orieux, Nantes, 50 ; « un profes seur de renseignement libre », Paris, 50 ; M. Barbollc, Orléans, 50 ; Amis de L'aube de Sainl-Pierre-Eglise, 50 : M. B. Jacquet, sèvres, O); M. Gaston Dugué, Orléans, lo : M. Boulleaux, Les Sablcs-d'Olonne, ■10 ; Mlle 11. Perrin, Saint-Denis-de-Cabanne, 10 : M. J. Bruchcl, Thunes, -lu; une amie de Caen, 50 ; M. P. Blanc, Mar seille. 25 : M. G. Larrieu, Saiute-Croixdu-Mont, 25 ; « un ancien de t'Echo de Paris, fervent de l’aube, 25 ; trois amis de l’aube. Mention, 25 ; trois amis de l’aube. Niort. 25 ; Mlle Yiry, Venezelle. 25: Mlle Baldini, Lyon. 25 ; « pour que Vavbe éclaire les catholiques <•garés chez les factieux », 10 ; M. Thibault. Trêves, 2o : Union locale des Syndicats libvs, Denain, 20 : M. Crespin, Bayonne, 20 ; M. Branchu, Le Mans, 20 ; M. Weiler, Grenoble, 20: M. Mongie, Fontaines, 2u ; VI. Miette Abel, Alençon. 20 ; M. Th. Bernard, Nantes, ?o : M. Qumeneur, lie île Balz, 25 ; M. l'abbé; (h Dupuy. SainlF.lit ime, 20; M. Palry, Loubans, 20; M. Roger Arènes. Sou il lac. .20 : M. l'abbé Al lais. curé de Savenny, 20 : M. Aculot, Vezc in, 20; M. Julien Lebas, Lille. 20: M. Devise, Chalençon, 20; M. Bouleslreau, Foi 11enay-a 11 x-Roses. 20 ; deux omis du l'aube, Tourcoing, 20 : M. Bouleslreau, Rouen, 20 : « vive Bidault », Aix-en-Provence, 20; M. l'abbéleux institutrices, Chnmprcciet, 20 ; M. Pinon (2J versem.), «Vvallun. 20; M. P. Bicterîé, T. y on, 20 ; M. Tabone, Alger, 20 : M. Bnrbatacei, Ajaccio. 20 ; n° 17.106, Metz, 20 : une part d'un abonné du Nord, 2(i ; M. Vannier (2 versm.), Bouviers, 2u ; M. Jean Maisonncuse, Clichy, 20 ; M. Sentunac, 20 ; Mlle Scnlenac, 10 ; Un syndif|ué chrétien, cheminot catho lique, 20 ; Mlle l’ragano La parte. Juvisy ; 20 ; M. Robin, Yguerande, 20 ; M. T .«'On Dci-lcrcq, C.roix. 20; M. Oiabanne, Saint-Etienne, 20 ; Mlle Vautrin, Chau mont, 35 ; M. L. Goblet, Eaiibonne, 5 ; une abonnée de Puteaux, 15 ; Vf. Isepponi, Nice, 15 ; M. l’abbé Oeslevlc, Obcrnai, lu ; M. Et. Ilutinef, Truyes, 10; un Sommvv igérien, lu : deux ouvriers syndiaués libres, Monlhevme. 10 : M. l'abbé si au ter, curé à Lnikirehen. lo ; A. B., Anuezin-les-Béthime, lu ; M. Cliartivr, ^aint-Vicfor-sur-Bliins, lu ; M. Ctxpiorelle. Saint-C prieti-Atîaf, .10; une insti tutrice publique, Lot-et-Garonne, 10; M. Paul Gômez, Fourmies, jn ; m. v". Mi el ion, Epernay, 10; M. l'abbé Mazard, Naillat. 10; G. et II. .Taillet, ln ; Mlle Clerc. Le Havre, ln ; M. Bielder (2* vers.), Saiiiie-Marie-aux-Mim•<, lu ; M. Hochedé, Toulon. 10 : futurs instituteurs du la Mo selle, 10; MM. Bonin, et Garreau, Villeneuve et Montgeron, lu : quatre chemi nots de l’Etat. 25 : un jeune sympathi sant. 5; anonyme, Mamers, 5 ; M. KoeBch, Suresnes lu: Mlle agnot, Gre noble, 5; M. l’aralief. Saint-?'enis-de-Ca-•anno. 5 : M. l'abbé zcina, Mb siizier, Saint-Barlliétemy, lu. Total de la. 33® liste...Total dt11 sle:T.s précédentes.lu ; M. 4.22(1 IG 1.8211 1GO.u10général.... —0— C/CHEQÜES POSTAUX : PARIS 1656-38fVOJR LA SUITE EN DERNIERE IïEüREJ Témoignage libérateur jLa successm deM.MasarykJacques Maritain vient de publier une Lettre sur 1 indépendance que je souhaiterais voir entre les mains ^ ^ ! de tous nos amis. C’est un petit opusUn conseil fle cabinet restreint ; ulc*,k soixam* ***?-mai^ i* p«,. *ce dépassé singulièrement 1 etendue. S CSl tenu B Londres i Les chefs de parti et les princes du peu—»•»« ! pie le liraient avec profit, s’ils n’avaient Londres. IG décembre. — Les minisires i si peu coutume de faire oraison. A défautAllemagne. Mais Nous ne voulons pas Nous attar der davantage à ce genre de tristesses et Nous arrêter ici aux conflits qui plongent dans l'anxiété non seulement L’Europe et VAfrique, mais l'uniiçrs tout entier. Nous tenons d'autant plus à garder celte réser ve que, parmi tant d:Incertitude des hom mes cl des événements, il est à. craindre que Nos paroles, (/uellcs qu’elles soient, ou ne soient pas bien comprises, ou qu'el les soient meme complètement détournées de leur sens. fVOLR LA SUITE EN TROISIEME PAGE! ■iiianiEieieiemieiiieietaiaieiiDuff Cooper, secrétaire d’Etat à la Guerre, communs désastreux. Nous vivonset celle de M. Walter Bunciman, prési dent du Board of brade. Celle réunion, qui faisait suite aux con versations que le premier minisire avait eues hier avec certains de ses collabora teurs, a eu également pour objet d’exa miner la situation créée, tant à Genève et dans les capitales intéressées que danscore dans le convenu, dans 1 insmeère, dans l’inexact. Sans vaine brutalité, comme sans vaine concession, avec une fermeté qui ne blesse ni n’abdique, M. Jacques Mari tain rappelle à ceux qui vi vent dans la foi le sens oublié de leur ,. .. ■. ... mission et ce qu’exigent d’eux les con ta politique intérieure britannique, pat ln. , i ' n ° -, , .. publication du projet franco-anglais dC j d bons dans lesquelles ils ont a I accompoix, et par le Livre blanc britannique, i pur. Dans les milieux politiques on souligneen-ce matin que le télégramme de sir SaLE BUREAU DE LA C.F.T.C. a mis définitivement au point le plan des syndicats chrétiens Dimanche malin, nu siège des Syndi-, ta un projet de règlement intérieur de icats^ chrétiens, le Bureau confédéral de i la G .F, T. C. la C. F. T. C. tenait sa réunion men! r « ,, réunion men-1 Le « plan » confédéral fut ensuite aborvïr.nài f0113 bceâidence de M. Jules | dé. Soumis au Conseil théologique que zunmeiu. préside Mgr Crépin, il va être mainteCe fut d’abord M. Gaston Tessier, sej riant publié dans une brochure qui coin crctaire général de la C. F'. T. C,’ quiqui présenta son rapport sur la situation gé nérale. Trois faits méritent actuellement une attention particulière : c’est l'accrois sement sensible et malheureusement constant du chômage ; c’est, d’autre part les difficultés que rencontre, en dépit de quelques succès récents, notamment (liez les cheminots et les postiers, la réa lisation (le Limité entre la C. G. T. et la C. G. T U. Enfin. M. Gaston Tessier rap pela lo rôle primordial que joua, au cours de la grève de Saint-Chamond, le syndicalisme chrétien. Pour la première fois, depuis l’obsé dante onse, une grève importante se ter mine véritablement au bénéfice des ou vriers. Pareil succès ajouté à la dignité dont firent continuellement preuve les grévistes, au cours du conflit, est le ré sultat de U intervention des militants chrétiens et notamment de MM. Jean Pé rès et Chacornac. Après M. Gaston Tessier, M. Verdun, président de la Commission des élections professionnelles, présenta un rapport sur les résultats des récentes élections pru d'homales. résultats que notre collabora teur Maurice Bouladoux commente dans sa chronique syndicale. Apres un échange de vues qui .montra le rôle capital de la presse syndicale dans les élections professionnelles, la discussion vint sur les décrets-lois. M. Gaston Tessier fit part des démar ches entreprises auprès des membres de la commission des Finances, et des mo destes résultats qui en résultèrent. Mlle Berd in. MM. Garnier et Broutin intervin rent dans le débat, puis le Bureau adop-prendra, en outre, un certain nombre de documents annexés. Une vaste campagne sera entreprise ensuite pour le faire con naître et Jui gagner les sympathies ac tives de l’opinion, en particulier de l’o pinion ouvrière. Enfin, le bureau confédéral fixa l’ordre du jour du Comité national de janvier et échangea des vues sur l’ordre du jour clu Congrès confédéral. ♦•K Le décret mettant les Cortès en vacances est approuvé par le Conseil des ministres .. «♦»-■ De nouvelles élections auront lieu au début d’avril Madrid, IG décembre. — Au cours du Conseil des ministres qui s’est tenu ce matin, le texte du décret mettant les Coriès en vacances jusqu’au 31 décembre a été approuvé. Elles seront alors dissoutes au mois de janvier, puis, conformément aux prescriptions constitutionnelles, de nou velles élections auront, lieu doux mois après, c’est-à-dire, au début d'avril. Pendant ce court délai qui lui est ré servé le gouvernement se propose de consacrer ses efforts à pacifier les es prits. Disposé à respecter toutes les opi nions, il exigera que tous respectent les lois de la République.Pour les catholiques de notre pays, une longue tradition a muni la croyance religieuse d’un prolongement politique dans lequel, malgré quelques contesta tions, le grand nombre des fidèles voit à la fois une déduction de la logique et une leçon de l’histoire. Ce n’est pas du pomt de vue politique, c’est du point de vue catholique que M. Jacques Maritain examine et rejette cette association. On arriverait .croyons-nous, à la même con clusion si on refaisait le même travail eic partant de l’autre terme. Cette Lettre sur l’indépendance n’u surpe pas son titre, car c’est une admira ble tâche de libération qu’elle accom plit. Libérer le chrétien des liens illégi times et des solidarités serviles qui le compromettent, parfois jusqu’au renie ment implicite, c’est une tâche néces saire et difficile. Celui qui l’entreprend doit s’attendre à la contre-attaque des intérêts lésés, à la révolte des préjugés bousculés. Quel gêneur que celui dont les scrupules viennent déranger la petite vie et les petites idées du bien-pensant ! Quel sacrilège que celui qui refuse de confondre le coffre-fort avec l’arched alliance et le « bon parti bonne cause !» avec laLes catholiques tchèques sont favorables à la candidature de M. BenèsPrague. 10 décembre. — Oiintrc parié; de la. coalition gouvernementale, sur svp!. .'0 son! prononcés ju<qu"ic.i en faveur «!• * la candidature de M. lieues, ministre îles Affaires étrangères, recommandée par M. Masaryk pour la présidence de la Répu j blique. i Los délibérai; •IIS «Ifautre-de T élection.partis, don■ur déeisinu • uilimieiriiiianI*I*X4I*XvIvIvKv.| Ce soir, mardi § & à 20 heures 45 ÿ ♦ »:« 3, rue Garancicre ;♦) | RÉUNION | ►*« £ des dames-vendeuses ^ §de la Vente-Kermesse $ S de « l’aube » £Nous prions toutes nos amies de ►*< venir à cette importante réunion au K ►*< cours de laquelle nous organiserons X X tous les comptoirs. *1* * XCependant, la vérité rayonne d’un éclat avivé par la rafale. M. Jacques Maritain. choisi pour cible par les bé néficiaires des vieux contre-sens, leur répond avec un calme et une intrépidité qui seront un réconfort pour tous ceux qui se sentent, même de loin et d’en bas, ses compagnons. II leur répond sur tout avec une force démonstrative, avec j im’nii moment un éclat de clarté qui ont de quoi foui demain. droyer sur le chemin de Damas l’incrér Ajoutons qu'une grande partie de *i;l du le de bonne foi. ■ pre-ssn, ainsi que fie nombreux groupe| méats sont prêts à a conter leurs sympaNe comptons pas sur ces miracles, j t Lies à M. Benès. Contre l’illumination des esprits par la i u'esl, ain-i que M. Rùckl, président «ht vérité, le régime actuel de la presse dis' ' '* •-rgn nisdi. a i du congres caUm v ■ r ■ que et membre miment « u parti poiuipose ci une puissance presque intime 1 d’étouffement. Mais nous qui ne som mes pas complices, nous tâcherons de refléter la lumière dont nous avons été frappés. Dans les jours qui vont venir, dès que nous le permettra une exigeante actualité, nous essaierons de reprendre |( |mi.M ici quelques-uns des principaux thèmes | m. Benès se posé comme colle d'une pet de la Lettre sur l’indépendance. Car le • somialité d'un renom international ex boisseau s’apprête... I eeptionnel et que la recommandali,m ,1e. M. Mararyk est, pour les catholiques, Georges Bidault. I décisive. UN DISCOURS D’ERNEST PEZET «La morale naturelle et le droit international autorisent-ils de grandes puissances à disposer de territoires appartenant à une puissance faible, au profit d’une quatrième puissance qui, signataire d’un Pacte commun, l’a violé et a été de ce fait condamnée par l’Assemblée des Nations?...»liste Ciillmlique. tchécoslovaque, a dé< • •«.; qui suit dans une interview : N’iMis autres, catholiques, con-idil-rons I. Rimes comme la personnalité qui a montré la plus grande compréhension h l'égard «lu toutes lus questions intéressant, notre cause. » Bia kl souligne que la candidature «leA 'os lecteurs trouveront ci-dessous les principaux passages du discours de M. Ernest Pczct, à V Institut oc eau ographiquej à la grande séance de l As sociation pour la S.D.X., dont nous rendons compte d’autre part. ...J’appartiens à une école socialetraités conclus, la jalousie provoquée par la prospérité d’autrui et, jusque clans la revendication de son propre dû, la méconnaissance des airs modé rateurs que suggère l’équité ou que réclame la fraternité humaine. L’expansion même légitime d'un peuple ne doit pas être assurée paret à un mouvement politique qui ont j pécrasement d’un autre peuple la préoccupation constante de ionder j Concilier, sans doute, concéder mèl’action sur des principes moraux. C’est mej ajUster délibérément aux réalitéssur un parti pris moral, sur une con ception humaine et spiritualiste des rapports entre les peuples que reposent jros vues internationales. La vie internationale étant ordonnée au bien commun de l’humanité com me à sa fin propre, les lois qui la régissent sont universelles ; elles ne sauraient donc être considérées comme suspendues, du fait que les nationsnouvelles et aux besoins reconnus et admis comme légitimes les imperfec tions ou les erreurs que le bon vouloir des auteurs des traités — ils n'étaient pas des surhommes,ni des génies — n'a pas évitées ; «mi, certes ! Mais dans ia justice et la paix, et non par le rapt et la violence. De quel côté est la justice dans la présente aventure ? Et qui a comproa été l’agresdes nations aont une langue, une culture, une civimis la paix ? Quel lisation, une constitution politique ou une religion différentes... La vie internationale, relevant de P ordre humain, les lois que la régis sent sont morales : elles imposent aux peuples le devoir de se montrer, les uns vis-à-vis des autres, sincères, jus tes et bienveillants. Dès lors sont exclues en droit, dans les relations internationales, l’hypocri sie politique qui contribue si efficace ment à corrompre l’esprit public, la violation du respect dû à la liberté, à la propriété, à l’hpnneur des nations,seur .•'... L’unaitimité répondu î... Etrange renversement des idées et des attitudes politiques ! Qui donc accepte aujourd’hui de gaîté de cœur et par les armes la brutale révision des traités de iqo6 ? Bien plus, qui la réclame au nom de la Paix, qui en fait, ainsi que de l’abandon du Pacte, la condition mê me du maintien — pour combien de temps ? — de la paix ?... Qui donc ?... Mais ceux-là mêmes qui, depuis seize ans, avaient fonde toute leur politi-l'infidélité à la narole donnée et aux que extérieure sur le maintien du statu page Zl'aube17-12-35l]>b fP'IWm■iliim y 5 NN]tml’aube Rédaction Administration 3, rue Carancière PAPI5-6* Tét. : Danton. 3-18 cl A partir de 21 h.: LOUVRE 66-96 Chèques postaux Paris 1656.38 Abonnements ordin js de soutien 3 mois*. -o fr. 3 mois. • 25 fl. 6 mois.. 38 » 6 mois.• 5® * 1 an.... *7t; •» 1 an ... 1 >0 *qun, sur l'intangibilité absolue des trai tés (de tous les traites), sur 1 antiic* vi'ionnisme î Ceux-là mêmes qui dans le révision nisme général -— que <lis-je, même dans le simple et sage réformisme, cas par cas, et par consentement mu tuel, des situations intenables nées des traités — dénonçaient la grande ma chine à déchaîner la guerre !... L-i révision, c'est la guerre .1rs cotés, aujourd’hui fourriers du révision nisme européen, étaient naguère rem plis de ce cri réprobateur qui réson nait comme une fanfare !... Et d ac cabler alors l’Italie de critiques et d’objurgations : car le fascisme était révisionniste, bien plus, il était avec l’Allemagne à la tête des partisans de la révision des traités. T e fascisme est resté dans sa ligne et dans la logique : les défenseurs français du révisionnisme africain du fascisme en sont sortis. Pour nous, nous pensons que M. Pierre Laval avait raison, qui, le 19 janvier 1932, disait à la Chambre, dans sa déclaration ministérielle : « ...La politiaue inscrite dans le Pacte est de puis douze ans celle de la France, comme elle est celle de la S.D.N. Xotre pays n’a jamais cesse d’en me surer l’importance économique, poli tique et humaine... » Aujourd’hui l'heure est venue d’ap pliquer sagement les normes de la saQu’adviendrait-i! si on s’y déro bait ?... Quelques questions montre ront, messieurs, ce qu’il adviendrait des principes qui ont fondé le nouvel ordre de l’Europe et du monde... La morale naturelle et le droit in ternational autorisent-ils de grandes puissances à disposer, à leur gré, de territoires appartenant à une puissance faible, hors de son consentement, au profit d’une quatrième puissance qui, signataire d'un Pacte commun, l’a violé et a été de ce fait condamnée par l’Assemblée des Nations ?... Y auraitil un privilège de droit et de juridic tion au profit des forts et au détriment des faibles ?... Serions-nous revenus à la pratique internationale de l'Ego nominor leo ? Comment les jeunes nations, créées par les traités, issues elles-mêmes des pi incipes du Pacte, ne se sentiraientelles pas menacées ? Pessimisme exagéré ? Craintes sans fondement ?... Voyons — pour ne pren dre qu’un exemple : Demain l’Allemagne s’empare de Mernel et de son hinterland immédiat. La légation de Lithuanie à Paris proteste et déclare (je reprends les termes mêmes de la déclaration éthio pienne d’avant-hier) : « La Lithuanie a été victime d’une agression injustifiée qui a été condam née solennellement par l’unanimité du Conseil et par l’Afscmblée de la So ciété des Nations. n Dans ces conditions, le gouverne ment lithuanien est fermement résolu à écarter toutes propositions qui, sous une forme directe ou indirecte, accor deraient une prime à l’agresseur ita lien. méconnaîtrait les principes fonda mentaux affirmés par le Conseil de la Société des Nations et par ses Comités, ainsi que par l’Assemblée, en particu lier le principe de l’intégrité territo riale et politique de la Lithuanie et tendraient à exercer sur un Etat faible une pression pour l’amener à subir la domination d’un gouvernement puis sant qui n’a cessé d’affirmer que, par la force, il assurerait le triomphe de ses ambitions, avec, sans ou contre la Société des Nations. » Que feront l’Angleterre et la France ? Sous prétexte que l’Allemagne me nace de secouer les colonnes dé l’ordre européen, d’étendre le conflit à l’est et au centre européens, l’Angleterre et la France, pour l’apaiser, oseraientelles lui proposer un partage ou une mise en tutelle de la Lithuanie ?... Et si l’Allemagne revendique l’Estafricain, le Cameroun et le Togo — qui lui appartenaient après tout — en menaçant de troubler l’ordre européen si on les lui refuse carrément, après le précédent italo-éthiopien, la France et l’Angleterre, et la S.D.N. pourrontelles refuser ? Buré a raison : « La France ne saurait, sans danger, se rallier à la thèse du chiffon de papier, et faire l’apologie du nietzschéisme gouverne mental ?... Donner une prime à l’agres seur, dans l’état actuel de l'Europe et du monde, c’est travailler pour la guerre générale. Je ne sors pas de là !... M En ce mois crucial de décembre 1935, où sa croisent les routes, où notre destin s’engagera, bien ou mal, pour longtemps, aucune considération hu maine, d’intérêt personnel ou de parti, ne nous empêchera de dire que c’est précisément en prévision d’événements comme ceux qui, en ce moment, tour niez ent l’Europe, écartèlent les opi nions publiques et engagent l’avenir de la paix européenne : oui, pas de so lutions extérieures à la loi des traités qui fondent une paix durable, dans la justice, l'honneur et la probité in ternationale ; oui, la S.D.N. doit mo difier et perfectionner son statut et renforcer son autorité que l’épreuve révèle trop faible et trop lente à con tenir les expansionnismes guerriers; mais elle doit vivre. Aucune considération humaine ne saurait nous empêcher, messieurs, de rappeler que la France avait toujourlié, jusqu’à ce jour, son honneur et scs intérêts les plus haut-,, au respect des contrats internationaux, et qu’il y aurait, pour notre honneur et nos intérêts, à payer d’un abandon, d’un reniement, le prix d’une amitié si chère au’clle soit à nos cœurs — et celle du peuple italien l’est au premier chef. Le sécurité de la France est fondée à la fois sur ses armées et les fron tières fortifiées, et sur le droit public, sur le respect des engageants pris, sur la religion du serment, comme aussi sur l’amitié « des peuples que rap proche de nous le souci de la justice et l’horreur de la violence ». (i Et puis, enfin, messieurs, ne l’ou blions pas : 1» Souvent la peur d’un mal nous conduit dans un pire. » Cette leçon de bon sens s’applique excellemment à la conjoncture : éternelle est sa va leur. C'est un pur Français, de la vieille France, du cœur du royaume qui nous l’a léguée. C'est l’heure, mes sieurs, de la rappeler aux peuples et aux gouvernements. (1) C. T.. Georges Bidault, dans « l'aube ».DEUX JOURNÉES D’AMITIÉ A LA JEUNE-RÉPUBLIQUELa Maison de la Jeune-Ré publique, si calme d’ordinaire, a revêtu samedi et dimanche derniers, pour la quatrième fois, l’aspect bruyant et inaccoutumé des « journées d’ami lié ». Tout était, transformé. Dans le liai! on jouait la comédie. Et 011 ne ménageait pas les applaudis sements h la dernière pièce, piquante cl spirituelle, de Georges Hoog : Spectres. La salle de? commissions était trans formée en buffet. Au secrétariat général, Mme AneeletHustache, dédicaçait ses livres entre un comptoir d'ouvrages de dames et un étalage de bibelots. Un bureau voisin est devenu le ma gasin d’alimentation où l’on achète, sous l'œil paternel de Gernigon, du riz, du chocolat, du sucre... Au second étage, un guignol est ins tallé dans le bureau des Equipes. Les nombreux camarades,* ligueurs et équipiers, qui sont venus donnent à la maison un caractère d’animation et de fête. Des familles entières se disper saient û tous les comptoirs. Des amis étaient là, nombreux, passaient, ache taient. et bavardaient au gré des ren contres et des sympathies. _ Dans cette foule d’amis, les personna lités connues étaient elles-mêmes trop nombreuses pour être citées ici. Après le congrès de Montrouge, ces deux journées sont venues de nouveau apporter la preuve de la vitalité gran dissante de la Jeune-République.TOUR D’HORIZONREACTIONSLe projet franco-britannique, dis* concert, pour le moins une espèce de dé-cuté à Genève et à Addis-A'beba, sou lève en Italie, en Angleterre et en France un certain nombre de réac tions auxquelles la presse faisait lar gement écho hier matin. En les sui vant aujourd’hui, nous verrons mieux combien sont difficiles à trouver les solutions qui mettront fin au conflit italo-éthiopien. I. — EN ITALIE On avait annoncé que Rome ne ré pondrait que le 1S décembre, or, dès dimanche matin, avec son unanimité habituelle, la presse italienne s'éle vait contre les propositions Laval-Sa muel Hoarc. Il s'agit de « valoriser » l'accepta tion que l’on donnera peut-être ces jours-ci au projet que l'on étudie de puis plus d’une semaine. M. Pierre Forestier, à l'Œuvre, présente ainsi la manœuvre : Le. pucc, jusqu’ici, s’était montré pru dent, réservé, circonspect. Il a compris tout d’un coup. EL hier, à heure fixé, avec, un ensemble foc chaut, toute lu pres se fasciste est partie en guerre. Et vol i ce qu'elle pense des sv>j3es tions /lüneorbritanniques, la presse iomairie : un document insuffisant ; vue procédure qui a déçu l'âme cl le cœur des Italiens ; des pthpositions qui rie cor respondent pas, mémo approximativement, nue misons politiques, économi ques .rnildaires qui font agir l'Italie en Afrique ! pour un peu, on reprocherait à M. lierre Lavai et à pir tiamucî lloare de s'élic, montres ingrats, page inij)ideux, mares ! L Ere Nouvelle relève, point par point, les critiques italiennes ; Les critiques portent sur à peu près tous les point -. Les terrains, dont la ces sion à L’Italie est envisagée dans le Tigré ci dons TOgaden, sont considérés comme, tdofftatll aucun intérêt. L’olfre d'Aduqa cl de Ma ko lié est' insuffisante. Home veut aussi Axouin. La zone d'expansion éco nomique et de peuplement proposée cl qui représente pourtant prés de la mojlià du territoire'éthiopien, est encore, infe rieure aux prétentions de l'Ilalic qui en tend obtenir une liaison tjv rflü riale entre l'Erythrée et lu Forri.alie, le long de la frontière du Soudan anglo-égyptien, sé parant celui-ci de l'Ethiopie et induisant, tn définitive, à presque rien la partie du territoire éthiopien qui diiïïLSurCLait indé pendante. Naturellement, XL Gabriel Péri s'empare de ces critiques, dans l'Humanité, et écrit : Ces informations ne coïncident pas du tout avec celles que faisait fabriquer} ces jours-ci M. Laval pour dé.surianLee T opi nion publique. Le présent offert à Musso lini est jugé insuffisajit. Pans le meil leur cas, le Duce ne câUsidézSMle buHn que comme un point de dépari / M. Théodore Vau cher, au Petit Pa risien, essaie au contraire d’expliquer les réserves italiennes, de montrer comment elles peuvent se justifier. 11 rapporte les objections du Messagero qui tentent à réduire la portée des concessions que le projet fait à l’Italie et il poursuit : On comprend la valeur de ccs objec tions qui ,eoniointûüieni à celles qu'ont soulevées d-aulies organes de la presse italienne, vont sans doute, inspirez les de mandes de. pgjjqisions que M. Mussolini adresserait aux gouvernements français et anglais '. Mais le fait que ces objections soient forpivlies ne veut pas dire, évi demment. que les suggestions franno-dnglaises doivent être repoussées apres examen. On demeure, donc dans l'idée que le chef du gouvernement italien est disposé h négocier sur les bases qnclle$ offrent pour une discussion approfondie.. Il apparaît également que, si la presse fasciste met en avant les arguments que nous vêtions de signaler, en guise de c/ilique des dites propositions, en devançant la réponse, du gouvernement, c'est pour réagir contre la campagne menée dans le camp opposé aux principes mêmes du rè glement de l'affaire donnant satisfacfimi à l'Italie, campagne qui fend naturelle ment à exagérer l'importance des con cessions que le plan La val-II ça rç propose à I llalic.Aux Equipes de ^Jeune-République La section, locale de la Jeune-République des 5® et 1> arrondissements organise ce soir, à 20 h. 45, au « Lion d’Afrique », 11, place d’Italie (salle du jev étage), un grand débat réservé aux jeunes, pau! Mon!s, secrétaire générale dès Equipes, et Joseph Betmale prendront la parole. Leurs exposés seront suivis d'une libre discussion ù laquelle tous les jeunes de l'aube et sympathisants de ces deux arrondissements seront cordialement in vités à prendre part.Le correspondant particulier de l'Excelsior, M. Jean Doicoux, voit lui aussi dans la réaction italienne une réponse aux réactions étrangères : Il n’y nui ait peut-être pas eu de. réac tion de lu presse italjçnnq. contre Je plan Laval-Hoarc avant la réponse, de M. Mus solini si. ce même plan n avait soulevé de réaction à Vétranger. Cela ne veut pas dire, sans doute, que, tel qu'il est} il se rait accepté par le gouvernement italien, tuais celui-ci se L‘Quve en présence de, tout un mQtivémenl qui voit dans les sug gestions présentées ù Home par Içs gouvçrnçniéhis fiançais et anglais, de plein 1falliance et un manque de droiture vis-à iis des devoirs « sociétaires ». Il est donc logique que, pour son compte, il tienne, dés a présent, A indiquer qu’il est, en lotit cas, bien [gin de voir dans le plan LavalHoarc le ‘nec plus ultra » des conces sions auxquelles l’Italie pouvait aspirez en Ethiopie. IL — EN ANGLETERRE En Angleterre, fout l’intérêt se con centre, dans les milieux parlementai res et gouvernementaux, sur la ques tion italo-abyssinc. Les entretiens sc sont poursuivis pendant toute la journée de dimanche en attendant la réunion du cabinet. M. Gérard Boutelleau, dans le Figaro, analyse la si tuation : Les ministres apportent, en ce moment toute leur allenlion au développement de la crise intérieure qu'a provoquée en An gleterre la publication du plan de Paris et du débat qui aura lieu d la. ChaïïLbta des communes jeudi giochain, à la fin duquel le gou.vcrncm.ctH demande 14 un vole de confiance. Ce n’est pas l'Opposition des travaillis tes et des libéraux que M. Baldwin re doute, mais la désapprobairon d'un cer tain nombre de cQ.iisCJ'vateqrs, ses pro pres partisans. Le débat, aura lieu après la réunion, du Conseil de la Ligue, mais Fatlituda que l'Angleterre, adoplçra à Genève, peut dé pendre de l'évolution de V opinion. publi que d’ici là. Le Conseil peut rejeter le, plan de Taris à la sui[ç d’un refus du Xégus ; mais ce qui importe} c'est de sa voir si le gouvernement britannique sera assez fort ' pour défendre le prxnçipQ. qui ne repose pus sur un plan juridique, qui tient compte des traitée de .1910 cl des prQMÇStcs fades à l'Italie, en 1910 ; ou si, au contraire, les ministres anglais seront prisonniers des réactions psychologiques de, l'opinion publique, dç sa mysijquc, ci ne seront pas en état de ilûf&ndrc le plan de Paris et de faire front commun, arec la France et à Genève contre certaines petite? puissance;, mais se ifquvçront lit téralement paralysés et incapables d'agir lorsqu'une occasion té elle sc présentera de négocier. 11 nous semble que M. Baldwin, qui a une vue des choses beaucoup plus réalis te qu'on le pense, et sir Samuel lloare ne craindront pas de défendre aux Commu nes les propositions de Paris. L'enjeu est trop grave pour ceux qui surent le prix de nouvelles sanctions éco nomiques (pù devraient être décidées tôl ou lard si les propositions échouaient to talement et si le gouvernement britanni que se heurtait à Genève à Fho.sWjté. des petites puissances. S'il faut en croire le Jour, la ques tion ne fait pas de doute : lie lavis des initiés, le début pourra être très vif et donner lieu à des échanges d'ecplications fort animes, mais ü ne doit, pas compromettre le fond même de l'af faire qui est le compromis Samuel lloareLaval, car une motion de blâme des tra vaillistes ne ferait que resserrer le parti conservateur autour du gouvernement. Et k correspondant de l’Eçfoo de Paris lait écho A un projet de révision du Covenant dont, il serait question depuis quelque temps et que M. Baldwin annoncerait jeudi prochain : Il est. âonq désormais, certain que, M. Baldwin va annoncer rn détail, à bref de lai. le projet de révision de la société des S a tiens auquel songe le Cabinetî britan nique. On ne peut prétendre que la reforme de ïa Société des Valions se trouve ifnpos£e soudainement ù l'Angleterre par une po litique de désespoir après la décision pro voquée par l’inefficacité des sanctions. Dès avant les élections britanniques, le bruit a voaru à Londres, sous le manteau, et ne fut pas démenti, que le gouverne ment avait l'intention de proposer la mo dification du Covenant, de le séparer du traité de Versailles et de Vamputer no tamment du système des sanctions, la grande affaxrç étant de ramener l’Allema gne à Genève et de conclure ultérieure ment un accord avec elle, la France y étant admise en tiers. Tel fui exactement le déroulement de la pensée britannique, malgré les résistances et Vimpétuqsité sanctio&aULe dç certains mV;i$trç.s, III. — EN FRANCE Les réactions de la presse italienne, dles de l’opinion et du gouvernent que l une des concilions misçs par MutsoUni à son agrément magnanime ost le concours de la France et de l’Angle terre, ou même — ce qui serait vraiment le comble des combles, la garantie de la S.D.N. pour l’emprunt qu cmellrait, aus sitôt après la canclusion de L'açcordi la Compagnie à Charte italien.nçAinsi, non seulement la France, l'An gleterre, la S.D.N. légitimeraient l'agres sion, mais clics en acquitteraieni les frais. L’agresseur, que la copimuiiautô 'inter nationale a dçiigné et condamné, ne se rait pas seulement absous. Il serait rému néré et commandité. La S.D.N. ne sc bornerait pas, 'comme les gouverne mollis anglais et fiançais l y poussent, à s'incliner devant un. fait aocompll. On attendrait d'elle un concourt actif, une complicité positive. Le plus intéressant — le plus pi quant aussi — est la réaction de l’Echo de Paris sous la plume de Pertinax et de M. de Kcrillis. Dimanche matin Périmax, qui n’ignore sans doute pas le projet de révision du Co venant dont parlait tout à l’heure le correspondant particulier de l’Echo de Paris, rapportait les critiques que font, au projet Laval-Samuel Hoarc ceux qui veulent conserver à la Socié té des Nations le bénéfice moral et le renouveau de puissance que lui ont apporté la résistance à l'agresseur et l’application des sanctions : J.'Angleterre a d'an seul coup, compro mis l'influence que. depuis septembre, elle exerçait à la Société des Nations. ■Hors, elle avait pris la direction de la j résistance à Tagpesseui. Elle avait prêté à la Société des Nations le bras séculier dont celle-ci a besoin dans les grandes occasions. De l’accord La val-U oarc du S décembre, la plupart, des délégations oui conclu (pic le gouvernement de Londres renonçait à tenir son rôle, qu’il démissionnait. On ne saurait imaginer la fureur de certains Hollandais cl Scajidimvçs par exemple. M. de Kcrillis, hier matin, en pre mière page, défendait ’h fond les pro positions franco-britanniques qui ne pourraient être discutées, s’il faut Ven croire, que par les porte-parole du communisme, du socialisme et de la franc-maçonnerie. Dans laquelle do ces catégories range-t-il donc son col lègue Pertinax ? Il notait que « le pro jetLaval-IIoarc apporte une espéran ce de règlement et de paix » : On parle d'un débat immédiat sur la politique étrangère. Il est douteux que ce débat soit en lui-ménie dangereux pour le gouvernement. Le plaidoyer de M. Laval est trop facile, sa position pacifique trop forle aux yeux de l’opinion. i>ubUqut, dans son immense majorité complètement étrangerà ce déchainemenl de fanatisme et hostile à celte volonté quqspfoVâ de croisade guerrière ! Qu'il ne faille négliger aucune espé rance de règlement et de paix, c’est bien certain, mais toute espérance sera vaine qui ne pourra pas s'ap puyer sur l’acceptation des deux par ties et sur la S. D. N. et, pour le moment, on sait que F accueil fait par l’Ethiopie et par Genève aux proposi tions franco-britanniques ne permet guère d'espoir. Intérim. Le congrès de la Fédération régionaliste française Samedi et dimanche ont eu lieu, à la mairie du 0e arrondissement, les stances du congrès de la Fédération régionaliste française qui, de plus en plus, sous l'im pulsion de eûn délégué général, M. Char les Brun, prend la place qui lui est due, dans le domaine économique aussi bien qu'intellectuel.celles de ropinion w d, ment anglais provoquent à leur tour des réactions dans la presse fran çaise. A propos de "Italie et des proposi tions Laval-Samuel lloare, M. Léon Blum apporte, dans le Populaire, une information qui serait bien, si elle est confirmée, selon l'expression qu’il emploie : un « comble » : Les capitaux nécessaires pour l'exploi tation de la zone réservée seraient avan cés à l’Italie qui n’est guère rn état, U est. vrai, de les fournir elle-mêmeLa trêve de Noël — Tu arrives à un drôle de moment ; mon mari est d'une de ces humeurs, tnè confia l'amie qui m'ouvrit la porte..., un ours de plus en plus mal léché... Je sais bien qu’il a ses raisons... Enfin..., si tu te sens particulièrement intrépide, tu peux pénétrer, il est libre... Je m'autosuggestionnai rapidement pour vite transformer la bête féroce en l’image d’un beau Teddy de peluche, doux, aima ble, de compagnie charmante, puis je me risquai dans son antre confortable. — Qu’est-ce qui vous prend d’arriver ici à 10 heures, grogna-t-il à ma vue. vous ne travaillez donc pas ce matin ? Vous savez pourtant que ma copie est pressée ? ■— Tenez, la voici, cher monsieur... Puis, j’exposai hardiment ma vie à uns nouvelle attaque : — Je voulais vous demander un ser vice. — C’est pas le moment, ce ne sera ja mais plus le moment, mettez-vous bien ça dans la tète. Je suis un homme fatigué, dégoûté, fini, bon à rien... (il me désifinait à terre un tas de journaux) ; tous es matins je risque la congestion et la jaunisse... Vous en avez de la chance, vous, les femmes, de n'avoir pas à tour ner cette salade... Enfin, qu'est-ce que vous voulez ? — Je voudrais, cher monsieur, que vous m'emmeniez faire un petit tour dans Pa ris, une promenade en auto... Après la petite suffocation de surprise, il eut une réaction agréable... — Après tout, c’est une idée..., pour quoi pas. Dix minutes après nous roulions sous sa conduite, sa femme et moi, sur les quais de la Seine embrumée ; des écharpes bleuâtres, traversées de soleil, s'enrou laient autour des pierres noires des vieux monuments, c’était très beau. — Naturellement, je ne vous demande pas si c'est vers les grands magasins que je vous pilote... — C’est évident, cher monsieur. Il haussa un peu narquoisement les épaules et ce fut, escale par escale, Je Louvre, les Galeries, le printemps, etc. Il descendait pour nous accompagner jus qu’aux vitrines pleines de jouets et de compositions, les unes charmantes, les au tres d’un goût moins sûr... Et ainsi tout le monde est content. — J'aime mieux cela que les manne quins d’exposition, finit par me murmurer notre ours-chauffeur, après avoir exa miné, l’œil rajeuni et le visage détendu, tes ingénieuses inventions des étalages et les nouveautés. La mécanique le passion na, mais il ne méprisa pas les animaux en peluche, les ménages, les bergeries. Peut-être fut-il très difficile envers les so sies de Shirley Temple ? Mais le modèle vivant est d’une imitation quasi impos sible... Il écouta aussi les chansons des pick-up... Notre ours était bien plus enthou siaste que nous à la fin de la tournée ; je n'aurais pas été autrement surprise de le voir exécuter une joyeuse danse sur l’air des « Pompiers » que déjà on fre donne partout. Enfin, les jambes lassées, les yeux un peu fatigués, la tête pleine de couleurs et de sons, et, pourquoi ne pas l’avouer, d'envies à contenter, nous primes la rouis du retour... — Je vous remercie de m'avoir rappelé à cette voie de l’enfance, nous dit-il en ar rivant, elle m’a parlé à la fois du passe et de l'avenir. Rien n'est entièrement mauvais ni perdu tant qu’il reste des hommes (je ne parle pas de l’industrie du jouet), mais des inventeurs, des cher cheurs, des artisans qui pensent aux pe tits. à leurs goûts, à leurs désirs, à leurs plaisirs et qui s’ingénient à se maintenir à leur taille pour essayer de les compren dre. Il y aura toujours trop d’adultes et de vieillards travaillant à compromettre le bonheur de leurs vingt ans... La trêve de Noël, c’est le règne des ou vriers au coeur simple, moins préoccupes de politique et de finance que d’inoénieuses et charmantes découvertes, c'est le règne des imagiers et des bâtisseurs de crèches, c’est le triomphe d’une naissance pauvre dent la toute-puissante divinité plane même au-dessus des réjouissances païennes de fin d'année... Cela vaut bien que pour y penser on oublie un moment les vieilles querelles et les vieux soucis. Marguerite George. Petit Courrier des Lettres,On y discuta notamment la participa-1 0 , , 1 lion régionaliste à l’Exposition do 1937 ; ; uCS OCIEIICCS Cl UêS rTlS on admira la maquette de la « Cité des j »♦« — Provinces » qui doit s’y trouver ; on en-1 x La révolution a changé bien fie? visagea la création éventuelle d’une bichoses on Russie. Elle n'a pas modifie biiûthèque régionaliste qui survivrait à lia dan^*. La noble et charmante traccetto manifestation. A la séance de dimanche après-midi, deux discours furent prononcés : l'un par M. Albéric Calmet, président du congrès, et l’autre par le président de séance. M. Lussan, avocat au Conseil d’Etat et à la Cour de cassation, ancien président de l’Ordre. On écouta en outre un rapport fort nourri de M. Hild, sur la Fédération nationale des Associations d’originaires du Rouergue, lequel fut suivi d'une ex posé de M. Pierre Gaudin. L’orateur insista sur la possibilité d'une entente plus intime entre la Société des Provinces ù Paris, dont il est vice-président, l'Union des présidents d’associations et la I'édé-Je me croîs en mesure çV affirme c en cfration régionaliste française.B* Mmm S mm m m mm mm mm mtm mÊ 2 ^ Imontre 9ue cF. T. C. a groupe, cetUP II ■ D El | n El ES rn El H 1 l* SM E fpk te année, sur le nom de ses candidats, ■■■ W ■■ ■ *1 W W SVIBIIIliClEG 34.295 suffrages tandis que dans les mê^ nifîu rirrnncrrî.^tiAnc Inc? fanania A aLE SYNDICALISME CHRÉTIEN et les élections prud’homales La plupart des résultats des élections prud’homales qui se sont déroulées, de puis le début de novembre, dans la plu part des 222 conseils de Prud’hommes qui existent, à l'heure actuelle, en France sont maintenant connus. On sait qu’il s'agissait de remplacer la moitié sortante des conseillers ouvriers •t employés, pour une nouvelle période de six années. Ces élections professionnelles sont les seules, il faut y insiste/, qui permettent aux travailleurs du commerce et de l'in dustrie, groupés dans des catégories par ticulières, de faire connaître leurs opi nions syndicale» En effet, depuis long temps déjà ces élections, mettent le plus souvent en présence des candidats ap partenant aux grandes confédérations ouvrières : C. G. T., C. G. T. U., et C. F. T. C. A de rares exceptions près, les candidats « indépendants » n’ont plus guère de chances que dans les circons criptions prud'homales sans importance, à moins qu’ils ne soient soutenus, çà et là. par les syndicats existants Les syndicats chrétiens qui, de par leurs principes, sont très attachés à cette juridiction professionnelle reposent sur la collaboration des classes, briguent un nombre sans cesse croissant de mandats et le succès, jusqu’à présent, a toujours répondu à leurs efforts, ainsi que nous l’indiquerons tout à l’heure. Cette année,la lutte paraissait beaucoup plus dilficile pour les candidats de la C. F. T. C. puisqu'ils ne trouvaient plus, en face d’eux, qu’un seul adversaire, celui de l’unité syndicale rouge, au lieu du cégétis'e et de l'unitaire qu’ils avaient cou tume d'affronter et qui, bien souvent, se refusaient à un mutuel désistement. Qui conque ignorait le développement de la C. F. T. C., pouvait donc craindre que celle-ci n’enregistrât pas, en cette tin d'année 1935, les succès qui avaient ré compensé ses candidats lors des précé dents scrutins. La lutte promettait d'être d’autant plus chaude que la C. F. T. C. présentait un nombre de candidats nettement plus éle vé qu’en 1932. Elle le fut, en effet, mais une lois de plus, le syndicalisme chrétien a triomphé, démontrant l’importan ce des progrès qu’il réalise d’année en année. Sa victoire est d’autant plus si gnificative que, répétons-le, la C. G. T. et la C. G. T. U. s’étaient assemblées pour lui faire échec. Mais voyons les chiffres,.. La C. F. T. G. a présenté 223 candidats dans 70 circonscriptions prud’homales sur 220 ; 90 ont été élus et, comme la C. F. T. C. n’avait que 60 sortants, elle a donc gagné très exactement 30 sièges : 24 dans les catégories du commerce et 15 dant. les catégories de l’industrie. En 1932. les syndicats chrétiens n’a vaient eu que 70 élus alors qu’ils avaient 46 sortants ; ils n’avaient donc gagné que 24 sièges et ils ne touchaient que 48 circonscriptions... Une statistique^ rapidement établie,mes circonscriptions, les tenants de « l’unité syndicale » en réunissait 53.476 et les indépendants 2.210. La C. F. T. C. a donc recueilli plus de 38 % des suffra. ges exprimés et près de 65 % du nombre de voix obtenu par le bloc de la C. G. T. et de la C. G. T. U. Pour mesurer la valeur de ces résultats, comparons-les avec ceux de 1929 et de 1932. En 1929, les candidats de la C. F. T. C. totalisaient 16.745 voix, ceux de la C. G. T. 20.480, ceux de la C. G. T. U. 11.880 soit, pour le bloc socialistecommuniste : 32.360 et pour les indépen dants 2.225 ; les candidats de la C. F. T. C. obtenaient donc 32,6 % des suffra ges pour 1er 106 catégories des 40 con seils de prud’hommes où ils se présen taient. En 1932, les progrès étaient nets : 161 candidats syndicalistes chrétiens ob tenaient, dans 48 circonscriptions, 25.755 voix contre 32.827 à la C. G. T., 14.782 à la C. G. T. U. (soit, 47.609 pour les deux C. G. T.) et 3.181 aux indépendants ; la C. F. T. G. réunissait donc 33,6 % des suffrages exprimés. Cette progression : 16.745 voix en 1929, 25.755 en 1032 et 34.205 en 1035, soit respectivement 32,6 %, 33,6 % et 38,1 % des suffrages, est d’autant plus intéressante que le nombre de voix doit normalement augmenter, la proportion, elle, devrait, non moins normalement diminuer au fur et à mesure où la G. F. T. G. s’attaque à de nouveaux Conseils dans lesquels les positions de ses adversaires sont assises de longue date... Mais grâce à ses pro grès numériques, qui vont d’ailleurs de pair avec l’extension de son influence morale, la G. F. T. G. peut démontrer qu’elle représente, à l’heure actuelle, pourle commerce et l’industrie, près de 40 % des travailleurs électeurs prud’homaux ; sans compter ceux d’Alsace et de Lorrai ne, soumis à un régime spécial. Après ces considérations, réjouissan tes pour les amis du syndicalisme chré tien, considérons quelques-uns des résul tats particuliers. Le Nord, pour ne pas changer, a été le grand triomphateur, puisque sur ses 30 sièges gagnés, la C. F. T. C. en trouve 17 dans les cinq dépar tements du Nord, du Pas-de-Calais, des Ardennes, de l’Aisne et de la Somme. Les candidats de l’Union régionale des Syndicats libres du Nord ont obtenu 50 % des voix de l’unité syndicale cégétiste et le nombre des conseillers pru d’hommes, nouveaux élus et anciens, en core en f (Mictions pour trois ans, atteint, pour les mêmes départements, 61 contre 14 en 1926. 24 en 1929, 36 en 1932 et 44 après les élections partielles, en 1934. Une autre succès retentissant a été ce lui des syndicats chrétiens de Châlonssur-Marne qui, n’ayant aucun sortant, ont quatre élus, sur neuf sièges, deux allant à des indépendants soutenus par la C. F. T. C. et trois seulement à la C. G. T.-C. G. T. U. A Laval, les syndicats chrétiens enlè vent trois sièges sur quatre ; à Rouen et Darnétal, ils gagnent trois sièges et font réélire leur seul conseiller sortant ; à Vienne, ils enlèvent de haute lutte le siège du textile à la C. G. T. U. et font élire quatre candidats sur sept sièges ; à Orléans, ils triomphent dans le com merce et obtiennent, dans Vensemble des catégories, 552 voix contre 800 à « l’unité syndicale », soit les 2,5 des suf frages exprimés ; à Troyes et à Bayonne deux succès prennent une signification particulière en raison de la personnalité des adversaires battus : l'adjoint au maire de Troyes et un conseiller municipal de Bayonne, conseillers prud’hommes de* puis fort longtemps ; à Rennes, la C. F. T. C. obtient 454 voix contre 388 seule ment au bloc cégétiste ; à Nantes, les syndicats chrétiens réunissent, au second tour de scrutin 2.283 voix contre 2.880 à leurs adversaires unifiés, gagnant ainsi 350 voix sur 1932 tandis que la G. G. T. et la G. G. T. U. restaient sur leurs posi tions. Enfin, il n'est pas nécessaire que nous revenions sur les beaux résultats obtenus par la C. F. T. C. à Paris, dans la catégorie du commerce où elle a réuni 5.215 voix contre 4.487 à ses adversaires, progressant de 1.432 voix tandis que ceuxci n’accroissaient le chiffre de leurs suf frages que de 517 voix. Si nous avions une conclusion à tirer de cet exposé de chiffres, nous dirions que le gouvernement ferait bien de jeter un coup d’œil sur ces statistiques avant de confier à la seule C. G. T. le soin de représenter les salariés du commerce et de l’industrie aux Conférences Interna tionales du Travail, puisqu’il est avéré que la CL F. T. C. est une force de plus en plus « représentative » des travailleurs de notre pays. Maurice Bouladoux.UNE EXPOSITION DE DENTELLES DE CALAISUnion féminine des Carrières libérales et commerciales. 112, boulevard Malesherbes. — Mardi 17 décembre, de 14 à 19 h., exposition do dentelles de Calais. A 16 h. 30, conférence par Mme .waria Vé rone, sous la présidence de M. Léon Vinccnt, député, ancien maire de .Calais.tion de l'art classique, si vivace au ter: moscovite, où l'ont transplantée des maîtres français, devenue vite si chère au peuple' russe, continue ‘-.* s’épanouir en souriant dans ee paxs t>>! on a inventé le mot de balletomanc. on y danse toujours comme à l’époque des tsars. On danse toujours et fort nier, parait-il. le I.ac. 17-12-3Ôl’aub«DERNIÈRES NOUVELLESLes propositions franco-britanniquesLe session du Conseil de la S. D. N.Genève, IG décembre. — Le conseil de la Société des Nations, qui, on le sait, se réunit mercredi à 11 heures, sous lu présidence de M. Ruiz Guinazu, délégué #ie l’Argentine, consacrera sa première gCance à la décision d’ordre purement pratique qu’il doit prendre afin de hâter rétablissement en Syrie des Assyriens fugitifs de l'Irak. C’est donc mercredi après-midi ou même seulement jeudi que le conseil abordera l’examen des suggestions for mulées par la France et la GrandeBretagne en vue de faciliter un règlement à l’amiable du conflit africain. Cette session, en raison même de son importance, attirera à Genève des per sonnalités de premier plan, lin effet, en df-hors de M. Pierre Laval et de M. Eden, on attend ici l’arrivée du négociateur italien, le baron Aloisi, ainsi que de tous 1rs ministres des Affaires étrangères, mem bres du conseil : MM. Titulesco (Rou manie): Beek (Pologne); Bustu Aras (Tur quie'; Monteiro (Portugal).Seu8, M. Lilvinov ne pourra pas venir et V En ion soviétique sera représentée par M. Potemkine, ambassadeur à Paris. Quant S la convocation de Rassemblée de la Société des Nations, réclamée par le gouvernement d’Addis-Abeba, seul, le conseil pourra en décider. K ce propos il convient de relever que M. Edouard Menés se présente mercredi pour la présidence de la République tché coslovaque. Dans 'le cas uù M. Renés serait élu, on s’attend ici qu'il enverra huas ilôt sa démission de président de l’a semblée des nations. Celle-ci se réu nirait, en tout état de cause, au début de janvier pour se donner un nouveau président et pourprocédy à un examen de la situation quant au conflit africain.Un communiqué officiel du secrétaire du Négus Addis-Abeba. IG décembre. — En com muniqué officiel a été publié ce matin par le secrétaire du Négus à Dessié con cernant les propositions franco-britan niques de paix. Ce communiqué dit no tamment ; Les propositions impliquent l'abandon d une partie intégrante du territoire cUiivpien en faveur d'un Etat (pii a~ été unanimement déclaré agresseur par la S.D.X. et donne à l'Italie un point de dépait pour une troisième tentative (Je conquérir VEthiopie. La zone italienne de colonisation et de développement économique projiosée — (le laquelle les citoyens et sociétés éthio piens seraient exclus — constitue une chose pire qu'un mandai parce qu'un mandat sauvegarderait les intérêts de lu population cl impliquerait le principe d'un traitement égal pour tous les etran gers. Le gouvcrnemnl impérial est convaincu que le conseil de la S.U. V., qui se réu nira le 18 décembre, n'acceptera pas des propositions qui partent atteinte à la souveraineté éthiopienne et démembrent le territoire éthiopien en faveur d'un Elut condamné comme étant un agresseur. ■ ' M. Mussolini aurait adressé un questionnaire à Paris et à Londres Londres, IC» décembre. — Le corres pondant romain du Daily Tsilcgruph apprend que M. Mussolini, par ses ambassadeurs à Paris et à Londres, a envoyé aux gouvernements anglais et français un questionnaire sur lu propo sition Laval-llourc. Les milieux bien informés assurent que M. Mussolini demande dans ce questionnaire des précisions sur les con ditions de la colonisation italienne en Abyssinie.Les opérations militairesDes avions italiens bombardent un camp éthiopien Addis-Abeba, IG décembre. — Quinze a lOii.i italiens de bombardement ont sur volé la région de Neghelli, située appro ximativement à 225 kilomètres au nord •le Dolo, entre les rivières Ganali, Os via et Dût, où d'importantes concentrations de guerriers abyssins avaient été repé rées. Pendant deux heures, les avions ita liens volèrent à faible altitude et bom bardèrent, les tentes des Abyssins. Mais il semble Lien que tous les avions no 'Oient pas rentrés à leur base de J.ug Ferra ndi, car les appareils lurent sou mis a une violente 'fusillade, et le bruit < ou H que trois machines auraient été abattues par Je feu des mitrailleuses éthiopiennes. De violents combats auraient eu lieu dans l’Ogaden Addis-Abeba, IG décembre. — Le mi nistère éthiopien de la Guerre vient d'ê tre informé que de violents combats avaient eu lieu ce malin dans la régionde K m a lé, front de TOgaden. Les trou pe^ italiennes et éthiopiennes auraient respectivement conserve leurs positions, mais du coté abyssin, on prétend qu’une dizaine de tanks italiens seraient tom bés aux mains des guerriers abyssins. Le communiqué italien Rome, IG décembre. — Le maréchal Badoglio télégraphie : « Rien à signaler sur le front d’Ery thrée à l'exception de quelques actions de patrouilles le long du Tacazzé. « L’aviation de Somalie a bombardé d’importantes concentrations de Iroupes abyssines non loin de Neghelli. » Le docteur Hockman a été enterré à Addis-Abeba Addis-Abeba, IG décembre. — Aujour d'hui ont eu lieu îles obsèques du docteur américain Robert Hockman, tué à Dagnbur par une bombe italienne qui, au premier contact avec le sol, n’avait pas explosé. Des membres du gouvernement éthio pien, tous les missionnaires résidant à Addis-Abeba, cl de nombreux étrangers assistaient à lu cérémonie.L’allocution consistoriale[SUIT: DE LA PREMIERE PAGE]Aussi bien, sur ce su [et, avons-Xous delà, plus d'une foi*, touchant la vérité, la justice et la charité, manifesté Xotrc pensée de la façon que l’on pouvait juste ment et norm.alem.ent_ attendre de Xous. ht, Xous le savons, les paroles que Xous avons prononcées, quand l'occasion Xous en a élc donnée, ont reçu, par la presse, ta plus large diffusion. '.Ainsi ont-edes pu parvenir à la connaissance de. tous ceux gui. rte désirent pas seulement la vérité, mais qui, avec une pleine sincérité et. va vrai désir d'èirç. ù'UlIls, viennent Xous la demander. Puissent-ils entendre cet avertissement ceux que l'on voit encore s'étonner, voire se scandaliser, gomma si Xous n'avions pus su.lfisoMlRent rempli les devoirs inhé rents au magistère qui XQ.us g clé divine.* ment confie. La paix inséparable de la justice, de la vérité et de la charité Xous n'avons jamais manqué de le dé clarer au moment où il le fallait, Xous n'y manquerons jamais dans l’avenir, cl Xous tenons à Vaffirmer solennellement de nouveau avant de clore cette allocu tion : c'est la paix inséparable de la jus tice, de la vérité cl de la chaude, que de nos vœuv les plus ardents Xous appelons sur « tous les hQDim.es de bonne volonté », où qu'ils soient. C’est cette paix que, de toutes nos forges, Xous Nous applique rons à leur procurer et que Xotre prière In plus }(LLCÇnt_Q sollicite sans cesse de la toute-puissance et de la misùiieorde de Dieu. ous voici au moment d'agréger à vo tre vénérable Collège vingt nouveaux membres de haut mérite, qui, soit dans l'cxerci.cs du ministère épiscopal, soit dans la diplomatie pontificale, soit dans les charges lés plus Pli porta Rte s de la Curie romaine, soit enfin en de persévé rants labeurs pour la ?jIms grande gloire de Dieu, ont excellemment mérité de la cause de VEglise. LA CEREMONIE DU CONSISTOIRE Hier, dans la salle du Consistoire, la cérémonie du Consistoire s’est déroulée suivant le rite traditionnel. En sortant de ses appartements privés, le Pape, qu’attendaient les membres de son anti chambre ecclésiastique et laïque, s’est arrêté dans une salle où il a revêtu sur sa soutane blanche, l’étole et la « lalda » sorte de manteau ù traîne, qui lui ont été présentées par le cardinal premier diacre Laurenti, qu’assistait Mgr Respighi, maître des cérémonies. Dès que, selon le rite, le Pape fut res té seul avec les cardinaux, il prit la pa role. et. après avoir prononcé son impor tante allocution, il proclama les nou veaux cardinaux. Après l’annonce des nouveaux cardi naux, le Pape a donné la liste des ar chevêques et évêques nommés depuis le dernier Consistoire, parmi lesquels Mgr Joseph Gilmore qui est nommé évêque de Ilelena .(Etats-Unis).,Le cortège, s'est alors reformé dans le même ordre que pour l’arrivée, et le Pa pe a regagné ses appartements. Aussitôt après, Mgr Rossignani, maître de chambre du cardinal Pacelli, secrétai re d’Etat, accompagné d’un fonctionnaire de la Chancellerie apostolique, est allé remettre aux nouveaux cardinaux le « billet » de nomination qu’il a accompa gne d'une courte adresse d’hommage.Comment la barrette sera remise à VElysée au cardinal Maglione La barrette arrivera la veille de la cé rémonie, mercredi, sous la garde de l’ablégat et de deux gardes nobles." Déjà on prépare à l’Elysée la réception de ces hô tes insignes. La scène se déroulera dans le salon des Ambassadeurs aux lambris de style Louis XV et qui fut pièce d’honneur le Mme de Pompadour. Seules seront invi tées les personnalités prévues par le pro tocole. Le chef de l'Etat, en habit portant le grand cordon de la Légion d’honneur et l’Ordre de Sa Sainteté, paraîtra seulement entouré des dignitaires de ses maisons militaire et civile. M. Pierre de Conquières, chef du pro tocole j M.Léger, secrétaire général des Affaires étrangères ; M. Eargeton, direc teur des affaires politiques au Quai d’Or say ; M. Canet, conseiller des questions religieuses, prendront part à la cérémo nie. L'ablégat se présentera au chef de l’E tat en lui tendant le parchemin papal. Les gardes nobles, en tunique rouge, cas que scintillant, entoureront le récipien daire, tout de violet vêtu, qui s’agenouil lera sur un coussin précieux. | 29,158 |
CHP/1893/CHP_18930118/MM_01/0007.xml_1 | NewZealand-PD-Newspapers | Open Culture | Public Domain | 1,893 | None | None | English | Spoken | 2,432 | 4,309 | THE PRESS, WEDNESDAY JANUARY 18, 1893. Hotels. (jachiel street, Christchurch. wishes to remind Victors of the COMFORTS at the Hotel brought fresh from 12 to 5 p.m. Sunday 1 P.M. for light Porter. HOTEL. B W'BJ_BR- S* I *SIRN KAILWA"-. is a convenience for those who wish to visit the Hot Springs. Find every comfort and attention at the 9 w *'* Charges strictly moderate. JOHN MCFARLANE. Proprietor. KELLER'S HOTEL, GUTHRIE STREET. HOTEL - by his EXCELLENCY THE Earl of Onslow. of the above Hotel wishes to inform the public that they will have a FIRST CLASS HOTEL. First-class every Modern Convenience, TERMS MODERATE. W. KELLER, Proprietor. Business Notices. YEOVIL IVB RY AND BAIT STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. WAWN LIVERY AND BATH STABLES, Corner of High and Lower High streets, Y. Christchurch. JOHN DALWOOD & SONS. and reliable. A-wi-Un.- or Picnic Parties Supplied. Landaus _f«aHan»om Cabs of the best description on :.^^__________ «BW ZEALAND BOARD OF DIRECTORS: ■!'£&*sSi?} Wellington.: Hon. T. W. Hislop J Assurance in force, over £167,000,000 <31aims paid, over _J3i,00,000 Thos. wishing to Insure should take our advice with this Society under continuous system. particulars obtainable from J. I_ SCARVELL. Chief Agent for Canterbury, it 3 Hereford street. _ S. B. SEYMOUR, j SURGEON DENTIST, a Colombo street, Christchurch. NITROUS OXIDING" GAS USED FOR PAIN _J_3_ EXTRACTION OF TEETH.! Artificial Teeth at Lowest Charges. Telephone, 189. AN ENTHUSIASTIC RECEPTION. THE tremendous reception accorded by the public to the issue of large Opals -with every dozen Cabinets by the Eden George Company, Limited, has caused many imitators to step in the Opal King, j Some of these imitators, who have been selling deposit tickets through canvassers for opals and cabinets, find themselves unable to give an opal enlafgement for the money, and make a paper enlargement and stick it on white glass. So neatly is this done that it takes an experienced eye to detect it; but as it is, it is not too much to expect that it will reveal the fact. Of course, it is obvious that "These paper and so-called miscellaneous enlargements on paper, will soon corrode, while those done by the Eden George Company, Limited, direct on the opal will last a lifetime. So great is the business done by the Eden George Company, Limited, that, necessarily a large number of rumors are seen afloat by opposition photographers, and with these we propose to deal. The firm fully dealt with the rumor that they were not using opal by the advertising of a certificate by Messrs Heywood and Co., some short time back, to the effect that they had cleared and paid Customs duty upon 6000 pieces of real opal for the Eden George Company, Limited, within three months. Hardly was this rumor set at rest than another and still more damaging one was spread, to the effect that the firm were using cheap and impure Chemicals. Immediately Professor Bickerlon was called in and asked to examine and report upon the purity of the chemicals, and we cannot do more than "publish his report":—'"Canterbury College, "Laboratory Department, "Christchurch. September 11th, 1892. * "I hereby certify that I have gone through Mr Eden George's order book, &d have inspected his stock of chemicals, and that 12nd all chemicals and materials - so be of the best brands obtainable in the market, being the specialities of the Srai of Burgoyne. Burbridges and Co., Schering, and Johnson and Son's, firms that take a very high place for the purity of their chemicals." A. W. BICKERTON, Professor of Chemistry and Physics, Canterbury College." extortionate charges is that work cannot be finished well at such low prices, that this rumour is entirely scouted by the fact that Messrs Johnston and O'Shanassy, of Melbourne, who are undoubtedly the leading firm of that city, and whose expenses are abnormally high, "their grant alone being about £1 per week," are now forging their best cabinets at £1 per dozen, while Messrs Wrigglesworth and Binns, the celebrated photographer, of Wellington, whose work cannot be surpassed, have for some period been advertising one established cabinet for £3, or one dozen for £12 8d; and it may be here noted that this in a paid the highest operator's salary in S. Z., viz., £6 per week. Persons after this should have no fear; in patronizing the Eden George Company, Limited, that the low prices mean chemicals, inferior work, and underpaid hands. As a matter of fact, photographers who make extortionate charges are constantly advertising for youths to come to the business, which youths usually come most of the finishing, and as a consequence, in a few years, when the picture would prove a family relic, it is found to be fading, and full of spots. The greatest eulogium of the work of the Eden George Company, Limited, is that of the opposing photographers who show that to advertise the fact that they have either worked themselves or employ someone who has worked for the Eden George Compacts, Limited, is a sufficient guarantee of good work, as the following "articles from advertisements will show." The operating and finishing being under the supervision of W. E. Sorrell (late operator and head Voucher to Eden George)." Mr. C. H. Manning advertised for the wristchurch papers of September 27th, 1832, that he was late operator and finisher. So Messrs. George and Walton. Out concluding advice to people who were present, and by skillfully carrying out all photo contracts entrusted to their care, they were rewarded by having the "best business in" in their hands. New Zealand, Business Notices. OATES' ZEAI.ANDIA BICYCLES (REGISTER!) Holds the Five-mile Horse the Time New Zealand Official Records of the New Zealand City, "Chance THE NEW 93 PATTERN ZEALANDIA WITH EVERY IMPROVEMENT OF TO DATE, Advertised to be the BEST. Acknowledged to be the BEST. Proved to be the BEST. Solid Proof of their Superiority is the fact that the MAJORITY OF RACES THIS SEASON HAVE BEEN WONDERFUL AND DIAS, Including FIRST and SECOND in the NEW ZEALAND 50-MILE ROAD RACE. THE BEST FOR ROAD RIDING. THE BEST FOR THE RACING TRACK. Time Payments or Discount; for Cash. Business Notices, - - - tag. - CONTRACTORS TO THE NEW ZEALAND GOVERNMENT. ASHBY, BERGH & CO. (LATE S. NASHELSKO, WHOLESALE AND RETAIL IRONMONGERS HARDWARE MERCHANTS, AND GENERAL IMPORTERS, 117 HIGH STREET AND 129 HEREFORD STREET, CHRISTIAN, INVITE INSPECTION OF THEIR LARGE AND VARIED STOCK OF ENGLISH, AMERICAN, AND CONTINENTAL HARDWARE In all Branches, which they are now offering at LOWEST POSSIBLE PRICES, In order to Make Room for Extensive Shipments shortly to arrive. STATION AND FARM REQUIREMENTS A SPECIALITY. COMPLETE ASSORTMENT OF BLACKSMITHS, WHEELWRIGHTS, COACH-BUILDERS' and PAINTERS' MATERIALS GHEAPER THAN EVER. EXCEPTIONAL BARGAINS In Ranges, Register Grates, Stoves, Marble and Slate Mantelpieces, Tiles for Hearths, Fenders, Fireproof, coal Scuttles, Chandeliers, Lamps, Electroplated Ware, Cutlery and all Furnishing Goods. GUNS, REVOLVERS, AMMUNITION AND ALL SPORTSMEN'S REQUISITES. INDENTS Undertaken on Most Reasonable Terms for all English, American and Continental Goods. THE LAST WEEK OF CLEARING SALE AT FURNITURE WAREHOUSE, COLOMBO STREET, NEW GOODS ARE NOW ARRIVING BY EVERY STEAMER, UNPACKING EXCHANGE. 12 FEET WIDE BRUSSELS AND TAPESTRY CARPETS BEDSTEADS, CHAIRS Pianos, &c. THB JEAND "ZEALANDIA" ON A BOOT IS A GUARANTEE OF EXCELLENCE. FINISHING this, over for a Minute and CONSIDER what IT MEANS. IT MEANS COMFORT, DURABILITY, ECONOMY, HEALTH, GOOD TEMPER. You will secure all these and more by insisting on having NO BOOTS for yourselves and families that ARE NOT BRANDED. The Dependable School Boots and Paragon (Registered) are TOO. for sale HARD WEAR. DEATH TO PARASITES SHEEP make 100 Gallons Dip. Another well-known Powder Dip costs half as PRICE-CASH. PACKAGES. & CO., CHRISTIAN. }___§ I _!/»___»§ WMm «. H_y -* nffff* j§la i %*&_■ §"i «f flip a ftftjrii-i, I IP' 8 * employe*. ; , Business Notices, .». ELECTRICITY ; m NATURE'S OWN REMEDY innHE Latest Achievement In Electrical 1 »oience. HK-.LTH, SXREN.OIH, VIGOUR. &c, permanently restored. Ail aufferere from lost nerve or physical force who have wasted their tliuo and money sanding io post oflice addresses in other colo nies should not despair, but consult personalv or by post ■»«■■*- FREE, W. NOTMANN. M.E., The Kmlnent Eleotrlcal SpaelaUi. frof Kurooe. wno has made all dlsoaaes ot men and, woman a lite-time study, and. to convinc, th* most sceptical. wiU forward eleotrlcal appU ancea and treatment on easy terms OS par ment. _ * Tkstimoniai--" Christchurch, January 1893.-Your efficacious treatment and tne pleasant soothing currents I always feel from your electric appliances, has thoroughly ro stored mc, and 1 wish I had consulted you years ago, laatead ol sanding- money away as themost; who suffer as I did so foolishly do r but I will write you again, and tell you bow was swindled, and any one wishing to writ* mo you can give tnem my address. — J Clarke." Free trials dally from" 10 a.m. UU 9 P*m. of tho latest and only Reliable and Permanent Cure for rheumatism, lumbago. BOiatfaM. neu ralgia, liver derangement. indigesJon, blaaae* and kidney troubles, bussing In head and ear* dizziness, weak back, tired feeling, spools' be N°nmeX y gme C fui letter, from both sex* can be inspected. -..-.t - r -r\ W. NQTMANN, M.E O 110 Montreal atroor. Christchuroh. __ J WILLIAM STOCKS, MONUMENTAL MASON, MADRAS STREET SOUTH. CHRISTCHURCH WISHES to inform persons in want. of Monumental Work that be intends lo SELL HIS PRESENT LARGE STOCK, consisting of Granite, Marble and other Stone Monumenta. at coa- Ssiderably RiCDUCKD PKIOEB. Iron Fences, Concrete and Stone Kerhinga. reauced in price. Inscriptions and all work in connection with the trade done in nrst-claßß style. Karly inspection invited. Several new lines lately arrived. Auy reasonable offer for tbe present stock will result in a sale. Want to "WILLIAM STOCKS. I PHOTOS by a BEAUTIFUL MATT See Specimens, y , .. STUDIO. 218 High street. Chtiatohurph, _ GLEGG'S CHRISTCHURCH PERAMBULATOR WORMS. Armagh street (One minute's walk from Colombo street*' 7 W holeaale and RetaiL All shapes, styles and" Quakes *o Sfc«el. All BQtl *^ o _* wicker, Wire, &c. Children's Cars in great variety of Wood or Wicker, Sound, well-seasoned Materials and Good Workmanship. Rubber-tyre wheel Perambulators. From £2 10s. Fully Illustrated Descriptive Catalogue Issued. JAMES CLEAGUE, Works and Showroom, 180 and 182 Armagh street, Christiana. Conveyances, HOT SPRINGS, HAN PLAINS. DERBETS, EGYPT MAIL COACHES, THE only Coaches carrying Mule North of Culverden, leave Culverden, daily at the Hotel, via Lahmert's, Jack's Pass Daily from November 1st to April, returning from Hanmer, Plais Dally during the summer months, and every Tuesday and Saturday, returning Mondays and Thursdays from May 1st to October, during winter months. Through tickets are issued at Christchurch Hallway Station daily. Tickets available for two calendar months from date of issue. First class, $5.00 for a round trip. TO ROTHERHAM. Coach leaves Culverden for Culverden, and Waiau Daily, returning from Waiau Daily; Monday's coach to Waiau connects with coach for KtUkoura, leaving Monday's coach leaves Kaikoura Thursday. -Fait ES: Culverden to Blenheim, Single, £3; return, 14s. Culverden to Waiau— Single, £3; return, 14s. Culverden to Waiau— Single, £8; return, 14s. Culverden to Waiau— Single, £8; return, 14s. Urgent telegrams and letters promptly delivered. Parcels iU.*t. «"%_"»*•** Faiclte and Or.eMiett at jjo_M.fc«6tttaole-, Aahbutton. and aleLhvon iivery diuoitß. AanDurum, «»«» NMl| uOet, proprietor. Business Notices. TOSAB FIVE - PALL A DIN Q OLIVE, *To be had of all leading Drapers, S3 J. HABBIS, LAND A GENT, MARTON, RANGITUKEI, N.Z. *OR SAMPLE PROPERTIES and further information SEE FIRST PAGE *WEEKLY PRESS.* * 744 SALE. TO MAKE ROOM FOR NEW GOODS JUST TO HAND AND TO ARRIVE. MRS. POPE HOLD A CLEARING SALE IN A FEW DAYS. Due Notice of which will be given in future. Advertisement. THE ORIGINAL ART NEEDLEWORK AND FANCY REPOSITORY, MORTEN'S BUILDINGS, Christchurch. IMPORTANT NOTICE. MR. ROBERTS, SURGEON DENTIST (English Training). COMPLETE STYLES $7 10s, very best work GUARANTEED. Dining Sets Ue-modelled. Fillings. Gas, Sec. Extractions Is. ODPosits Ballantyne a, FENDALTON BREWERY, -| MCNAMARA AND CO. Proprietors. ALES, XXXX. PALE BITTER. ALE. XXX. DOUBLE BROWN STOUT. Our Ales and Stout are made from the best Malt and Hops only, and are warranted to keep. Bottled Ale and Stout a Specialty. Families Wasted on Daily. 2061 Telephone No. 355. S. SMABT AND SON, ASPHALTERS. SYDENHAM. OftA—Meosrs Scott Bros., Manchester street. TENNIS.COURTS and GARDEN PATHS LAID WITH MIXED ASPHALT Corre Of Measurement Guaranteed. Telephone No. 609. AUSTRALIAN MOTUAL PROVIDENT SOCIETY. NEW ZEALAND BRANCH: Head Office, Custom-house Square, Wellington. Local Board of Directors: The Hon. Morgan S. Grace, M.D., C.M.G., M.L.C. (Chairman) The Hon. Charles J. Johnson, M.L.C. (Chairman) Alfred de Bathe Brandon, Esq. The Hon. Edward Richardson, C.M.G. John Duncan, Esq. Medical Officer: Dr. W.G. Kemp. M.R.C.S. (England). THE OLDEST WEALTHIEST AND MOST PROSPEROUS AUSTRALIAN LIFE OFFICE, AND THE LARGEST IN THE BRITISH EMPIRE. THE ONLY COLONIAL LIFE OFFICE WHICH DECLARES A BONUS EVERY YEAR The Method of Vaccination adopted by this Society is of the Most Stringent Character, and ensures a Considerably Larger Reserve to Meet Liabilities than that held by any other office in the Australian Colonies. ACCUMULATED FUNDS, £10,500,000 (TEN AND A HALF MILLIONS) STERLING All invested to yield nearly 6 percent. POLICIES IN FORCE... 109,333 Sum Assured... £37,066,211 Accumulated Funds... £10,532,036 Annual Income... £1,860,347; Cash Bonuses Divided... £4,930,361 BONUSES. CASH BONUS for ONE Year 1891, £489,828, yielding Reversionary Bonuses amounting to £1,009,000. The Cash Bonus was equal to 42.4 percent, on the premiums received during the year. | 45,588 |
https://github.com/koumingyang/SimpleFileSystem/blob/master/src/vfs.rs | Github Open Source | Open Source | MIT | null | SimpleFileSystem | koumingyang | Rust | Code | 527 | 1,391 | use alloc::{vec::Vec, string::String, rc::{Rc, Weak}};
use core::cell::RefCell;
use core::mem::size_of;
use core;
use core::fmt::Debug;
use core::any::Any;
/// Interface for FS to read & write
/// TODO: use std::io::{Read, Write}
pub trait Device {
fn read_at(&mut self, offset: usize, buf: &mut [u8]) -> Option<usize>;
fn write_at(&mut self, offset: usize, buf: &[u8]) -> Option<usize>;
}
/// Abstract operations on a inode.
pub trait INode: Debug + Any {
fn open(&mut self, flags: u32) -> Result<()>;
fn close(&mut self) -> Result<()>;
fn read_at(&self, offset: usize, buf: &mut [u8]) -> Result<usize>;
fn write_at(&self, offset: usize, buf: &[u8]) -> Result<usize>;
fn info(&self) -> Result<FileInfo>;
fn sync(&mut self) -> Result<()>;
fn resize(&mut self, len: usize) -> Result<()>;
fn create(&mut self, name: &str, type_: FileType) -> Result<INodePtr>;
fn unlink(&mut self, name: &str) -> Result<()>;
/// user of the vfs api should call borrow_mut by itself
fn link(&mut self, name: &str, other: &mut INode) -> Result<()>;
fn rename(&mut self, old_name: &str, new_name: &str) -> Result<()>;
// when self==target use rename instead since it's not possible to have two mut_ref at the same time.
fn move_(&mut self, old_name: &str, target: &mut INode, new_name: &str) -> Result<()>;
/// lookup with only one layer
fn find(&self, name: &str) -> Result<INodePtr>;
/// like list()[id]
/// only get one item in list, often faster than list
fn get_entry(&self, id: usize) -> Result<String>;
// fn io_ctrl(&mut self, op: u32, data: &[u8]) -> Result<()>;
fn fs(&self) -> Weak<FileSystem>;
/// this is used to implement dynamics cast
/// simply return self in the implement of the function
fn as_any_ref(&self) -> &Any;
/// this is used to implement dynamics cast
/// simply return self in the implement of the function
fn as_any_mut(&mut self) -> &mut Any;
}
impl INode {
pub fn downcast_ref<T: INode>(&self) -> Option<&T> {
self.as_any_ref().downcast_ref::<T>()
}
pub fn downcast_mut<T: INode>(&mut self) -> Option<&mut T> {
self.as_any_mut().downcast_mut::<T>()
}
pub fn list(&self) -> Result<Vec<String>> {
let info = self.info().unwrap();
assert_eq!(info.type_, FileType::Dir);
Ok((0..info.size).map(|i| {
self.get_entry(i).unwrap()
}).collect())
}
pub fn lookup(&self, path: &str) -> Result<INodePtr> {
if self.info().unwrap().type_ != FileType::Dir {
return Err(());
}
let mut result = self.find(".").unwrap();
let mut rest_path = path;
while rest_path != "" {
if result.borrow().info().unwrap().type_ != FileType::Dir {
return Err(());
}
let mut name;
match rest_path.find('/') {
None => {
name = rest_path;
rest_path = ""
}
Some(pos) => {
name = &rest_path[0..pos];
rest_path = &rest_path[pos + 1..]
}
};
let found = result.borrow().find(name);
match found {
Err(_) => return Err(()),
Ok(inode) => result = inode,
};
}
Ok(result)
}
}
#[derive(Debug, Eq, PartialEq)]
pub struct FileInfo {
// Note: for normal file size is the actuate file size
// for directory this is count of dirent.
pub size: usize,
pub mode: u32,
pub type_: FileType,
pub blocks: usize,
// Note: different from linux, "." and ".." count in nlinks
// this is same as original ucore.
pub nlinks: usize,
}
#[derive(Debug, Eq, PartialEq)]
pub enum FileType {
File,
Dir,
}
#[derive(Debug)]
pub struct FsInfo {
pub max_file_size: usize,
}
pub type Result<T> = core::result::Result<T, ()>;
/// Abstract filesystem
pub trait FileSystem {
fn sync(&self) -> Result<()>;
fn root_inode(&self) -> INodePtr;
fn info(&self) -> &'static FsInfo;
// fn unmount(&self) -> Result<()>;
// fn cleanup(&self);
}
pub type INodePtr = Rc<RefCell<INode>>; | 48,149 |
compilationoflaw00ohio_16 | US-PD-Books | Open Culture | Public Domain | 1,825 | A compilation of laws, treaties, resolutions, and ordinances, of the general and state governments, which relate to lands in the state of Ohio; including the laws adopted by the governor and judges; the laws of the territorial legislature; and the laws of this state, to the years 1815-16. Published in pursuance of resolutions of the General assembly, passed January 22, 1825 | None | English | Spoken | 7,898 | 10,698 | Sec. 15. That it sliall be lawful for the aforesaid corpo- Trustees mjiy ration, or for the trustees acting under this act as herein after ^*^'^^^ ^J® mentioned, to lease for a small annual rent, on condition of a^^^^^' ** capital sum being paid in hand or secured to be paid, the whole or any part of the house, lots, and out lots of live acres in the town of Athens, laid out agreeably to a resolution of the General Assemby of the Territory, made and approved December the eighteenth, one thousand seven hundred and ninety-nine, by Rufus Putnam, Benjamin Ives Gil man and Jonathan Stone, Esquires, a committee in the said resolution, named and appointed for that purpose ; and the capital sum or sums of money, which shall be so received, or so much j^gj^lgj^ thereof as the corporation shall judge expedient, shall be ap- plied. "^ plied by the trustees to the purpose of erecting buildings for the accommodation of the president, officers and students of the University. Sec. 16. That the before named trustees and their sue- Trustees may cessors, and such others as shall be duly elected members of elect a presi- the said corporation, be, and they are hereby empowered ^^^' to elect a president of the said University, whenever they shall judge it expedient. Sec. 17. That until a president of the said University Who shall shall be elected, and shall have entered upon the duties of supply vacan* his office, and also in all cases of a vacancy or the absence of ^^* the president, the said trustees shall appoint one of their members to preside in their meetings, and all the doings and acts of the trustees, while acting under such circumstances, shall be considered in law as the doings and acts of the cor- poration, as fully and completely as when the president of the University shall be in office and preside. Sec. 1 8. That the legislature of the territory or the legis- Powers r^ lature of the state within which the said University is or served. may be founded, may grant any further and greater powers to, or alter, limit or restrain any of the powers by this act vested in the said corporation,* as shall be judged necessary to promote the best interest and prosperity of the said Uni- *By the act of Feb. 18, 1804, this corporation is dissolved, so far as the creation of another, with different privileges and powers, can work a dis- solution. It is, however, presumed, that it must still operate upon con- tacts made in con/ormitj with its provisions. Hence it is here inserted. 226 LANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS. Hon R Put- "^^^^"^^^7? ^'^^^ ^^^^ necessary powers and authority for the bet- nam may call ter aid, preserTation and government thereof. first meeting. Sec. 19. That the Hon. Rufus Putnam, Esquire, shall be , and he is hereby authorized and empowered, to fix the time and place for holding the first meeting of the said corporation, of which he shall give notice in writing to each member, at least fourteen days previous to such meeting. [ResolutLonp/ April 16, 1803, 1. -v. L. O. p. 148] Resolved^ That Samuel Carpenter, James Wells and Henry poiuteYto^^" Abrams, be appointed commissioners to appraise the land value lands in mcluded within the two college townships in the county of Athenso Washington, at its real value in its original and unimproved state ; to divide and value said land into four different quali- ties or rates, and make return of the quantity conta.ined in each division as near as may be, and the value thereof, to the next General Assembly, on oath. And that the said commissioners also value the land in its .present situation, mentioning the number of houses and quantity of cleared land contained within the two townships. Resolved^ That the trustees appointed by the act, entitled. "An act establishing an University in the town of Athens," be and they are hereby required, to report to the next Gene- ral Assembly of this state, what measures they have taken to carry the said act into operation. [Act of February, 1 8, 1 804, 2 v. L. O. p. 1 93.] An act establishing an University in the town of Athens. ?reamble. Whereas institutions for the liberal education of youth, are essential to the progress of arts and sciences, important to morality, virtue and religion, friendly to the peace, order and prosperity of society, and honorable to the government that encourages and patronizes them: Therefore, Universify Sec. 1. That there shall be an University instituted and established, established in the town of Athens, in the ninth township of the fourteenth range of townships, within the limits of the tract of land purchased by the Ohio Company of Associates, by the name and style of \hc "Ohio University," for the in- struction of youth in all the various branches of liberal arts and scierices, for the promotion of good education, virtue, religion and morality, and for conferring all the degrees ajjd literary honors granted in similar institutions. LANDS rOR THE SUPPORT OT THE GOSPEL AND SCHOOtS* 2^7 Sec. 2. That there shall be and for<*ver remain in the said Corporate University, a body politic and corporate, by the name and ° ^ * style of "The President and Trustees of the Ohio Univer- sity;" which body politic and corporate shall consist of the governor of the slate, (for the time being) the president, and not more than fifteen nor less than ten tiiistees, to be appoint- ed as herein after is provided. Sec 3. That Elijah Backus, Rufus Putnam, Dudley Wood- Persons ap^ bridge, Benjamin Tappan, Bazaleel Wells, Nathaniel Massie, P;;^^^*'^^ ^^■"'■• Daniel Symmes, Daniel Story, Samuel Carpenter, the Rev. James Kilbourn, Griffin Greene, senior, and Joseph Darlin- ton. Esquire?, together with the governor as aforesaid, and the president of the said University (for the time being) to be chosen as herein after directed, be, and the same are hereby created, a body politic and corporate, by the name of "The President and Trustees of the Ohio University ;" and that they, and their successors, and such others as shall be duly elected members of the said corporation, shall be and remain a body politic and corporate in law, by tliat name forever. Sec. 4. That the said trustees shall have power and au- Powers of tie thority to elect a president, who shall preside in the Univer- ^^^^^*^^^* sity, and also to appoint a secretary, treasurer, professors,, tutors, instructors, and all such officers and servants in the University as they shall deem necessary for the carrying mto effect the designs of the institution, and shall have authority, from time to time, to determine and establish the name, num- bers and duties of all the officers and servants to be employ- ed in the University, except wherein provision is otherwise made by this act, and may empower the president or some other member of the corporation, to administer such oaths as they shall appoint and determine, for the well ordering and good government of the University: Provided nevertheless^ Proviso, That no corporation business shall be transacted at any meeting, unless seven of the trustees, at least, shall be pre- sent. Sec. 5. That the said corporation shall have power and Rules, by- authority, from time to time, to make and ordain reasonable ^aws,&c.maj rules, orders and by-laws for the government of the corpora- ^^ "^^^^■ lion, not incompatible with the constitution, laws and ordi- nances of the United States or this state, and the same to repeal as occasion may require, and also to determine the salaries, emoluments and tenures of their several officers. Sec 6. That the said corporation shall have power and Officers may authority to suspend or remove the president or any member ^® ren^ow -of the said corporation, who shall, by his misconduct, render himself unworthy of the office, station or place he sustains, or who, from age or other infirmity, is rendered incapable to perform the duties of his office ; and the said corporation fhall have power and authority to suspend or renaove frojofi 228 tANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS* Corporation may fill va- caocies. the University, any professor, instructor or resident student>, or servant, whenever the corporation shall deem it expedient for the interest and honor of the University. Sec. 7. That whenever the president or any member of the corporation sliall be removed, by death, resignation or otherwise, during the recess of the legislature,* the corpora- tion shall hold a meeting (due notice of the design of which meeting shall be given to the several members) for the sup- plying such vacancy ; and the person elected shall continue in office until the end of the next session of the legislature, and no longer, by virtue of such appointment; and in order to choose a president or member of the corporation, there shall be, at least, two-thirds of the whole number of said trustees present, and the said election shall be by ballot. Sec. 8. That when any member of the corporation shall be removed by death, resignation or otherwise such vacancy shall be supplied at the next meeting of the legislature of the state. Power of the ^^^* ^' That the president and such professors, tutors and Faculty of the ii^structors, as the corporation shall appoint for t!iat purpose. University, shall be styled, "The Faculty of the University," and shall have power and authority, from time to time, to ordain, regu- late and establish, the mode and course of education and instruction to be pursued in the University, and also to make, publish and execute, such code of rules, regulations and by- laws, as they shall deem necessary for the well ordering and good government of the University, and to repeal or amend any part thereof; which rules, regulations and by-laws shall continue in force until altered or disapproved of by the cor- poration; and it shall be the duty of the faculty, to lay be- fore the corporation, from time to time, accurate statements, of all their proceedings; and the faculty shall direct and cause to be holdenin the said University, quarterly, in every year, a public examination, at which time the faculty shall attend, when each class of the students shall be examined relative to the proficiency they shall have made in the parti- cular arts and sciences, or branches of education in which they shall have been instructed. Seal of the ^^^* ^^' That the said corporation may have and keep corporation, one Common seal, which they may change or renew at plea- sure; and that all deeds or instruments of writing, signed and delivered by the treasurer, and sealed with the corpora- tion seal, by order of the president and trustees, shall, when made in their corporate name, be considered in law as the deed and act of the corporation; and the said corporation shall he capable of suing and being sued, pleading and being ri/faysue, &c. impleaded, in any action, real, personal or mixed, and the. same to prosecute and defend to final judgment and execu- tion, by the name of "The President and Trustees of the Oliia Vtovi^Q, University:" Provided, Th^t when any suit shall be commen- LANDS FOR THE SUFPORT OP THE GOSPEL AND SCHOOLS. SStJ' ced against the said corporation, the process shall be by sum- mons, and the service made by the officer leaving an attested copy of such process v/ith the treasurer of the said corpora- lion, at least twenty days before the return day of such pro- cess; and the said corporation shall be capable of having, holding and taking, in fee simpfe, or any less estate, by gift, grant, devise or otiierwise, any lands or other estate, real or pcrsonah Sec. 11. That the two townships numbered eight and Townships nine^ in the fourteenth range of townships, within the grant i^"*^, ^ ^'^^^^^ of land. made. by Congress to the Ohio Company of Associ-J.atio^^.^°^^^ ates, be and they are hereby vested in the corporation, by this act created, in trust, for the sole use, benefit cind support of the said University, forever. Sec. 12. That one or more of the aforesaid trustees (to be Lands to be appointed by the board for this purpose) shall, within si^f jots am/aT>- months from the passage of this act, proceed (by the oath of praised. three disinterested and judicious freeholders) to lay'off the Jands in said township, (those included in the town of Athens excepted) or such part thereof as they may deem expedient, into tracts of not less than eighty nor more than two hundred and forty acres, and to estimate and value the same as in their original and unimproved state (for which service such compensation shall be allowed as the trustees shall think reasonable, to be paid out of the funds of the University) and having thus laid off and estimated said lands, the trus- tees, after giving four weeks notice in the newspaper printed at Marietta, shall proceed to make out leases of the said tracts ^'^^^^^ *^ ^® to such of the present occupante as shall apply for the same, feases made, within three months after such notice given, and to all per- sons that shall apply hereafter, for the term of ninety years, renewable forever, on a yearly rent of six per centum on the amount of the valuation so made by the said freeholders; and the land so leased shall be subject to a revaluation, at the expiration of thirty-five years, and to another revaluation at the expiration of sixty years, from the commencement of the Revaluation term of each lease; which revaluation shall be conducted ^° ^^^^ P^^^^' and made on the principles of the first, and the lessee shall pay a yearly rent of six per centum on the amount of the revaluation so to be made, and forever thereafter on a yearly rent equal to and not exceeding six per centum of the amount of a valuation to be made as aforesaid, at the expiration of the term of ninety years aforesaid (which valuation the trus- tees and their successors are hereby authorized and directed to make:) Provided hoivcvcr^ That such last mentioned rent shall be subject to the following regulations, to wit: At th^ i^Ttrbefp^' expiration of the aforesaid period of ninety years, three re- pointed. ferees shall be appointed, the first by the corporation of the University; the second, by the lessees, under the provisions of this section, of this aet, ^nd ^he third, by the two referees 2S0 LANDS FOR THE SUPPORT OF THE GOS^PEL AND SCHOOLS^ thus chosen, (or in case either or both of the parties shall neglect to choose such referee or referees, or said referees shall neglect to choose an umpire,) the General x4ssembly, at its nest session, shall appoint such number of referees, not exceeding three, as the ca^e may require ; which referees ehall meet within a reasonable time, to be agreed on between them, at the town of Athens, and then and there determine on and declare the medium price per bushel of the article of wheat; which determination shall be grounded on a calcula- tion of the average price of said article at the town of Mari- . etta, for the five preceding j^ears; v/hich declaration shall be made in writing, and entered of record on the books of the corporation ; and at the commencement of each and every succeeding period of tw^enty years thereafter, the amount of rent for such period shall be fixed on and determined by referees, to be chosen upon the principles herein before directed, from a comparison of the aforesaid recorded price of wheat, with its average price at Marietta, for the five years, w'hich shall have been then last past; in which leases shall be reserved a right of distress and of re-entry for non- payment of rent, at any time after it shall have been due two Proviso: cor- months: Provided always^ That the said corporation shall disSain^ '"^^ have power to demand a further yearly rent on the said lands and tenements, not exceeding the amount of the tax imposed on property of like description by the state, which rents shall be paid at such time and place to such person and collected in such manner as the corporation shall direct. ^Trustees to Sec. 13. That the trustees shall lay off the aforesaid town lay out town, of Athens, conformably to a plan made out by Rufus Putnani selflotf^exe- ^"^ others, in pursuance of a resolution of the territoral le- Gute leases, gislature of the eighteenth December, one thousand seven &;c. hundred and ninety-nine, with such variations how^ever, as they may find it expedient to make ; and the same being thus laid off, and a plat of the same with a designation of the uses of the several parts recorded in the office of the recorder of the proper county, and six weeks previous notice given, in at least tw^o of the new^spapers of this state, may proceed to sell, ii'om time to time, at public auction, such of the houses and out-lots as they may think proper, for which lots, on payment bemg made or satifactory security given, according to the conditions of such sale, they shall execute to the purchasers respectively, leases for the term of ninety years, renewable forever on a annual rent, equal to, and not exceeding, six per centum of the amount of the purchase money, which lots^ with the improvements which may be made on the same, shall be subject to such further yearly rent as may be equal to the tax imposed from time to time, on property of like value and description, by the state ; and they arc likewise authorized to deliver a reasonable compensation for the iynprovements LANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS. 231 which have been made on lands within the town of Athens, to be paid out of the funds of the University. Sec. 14. That the clear annual rents, issues and profits, Appmpriatioij. of all the estate, realand personal, of which the said cprpo-*^^'^^^^^'^^' ration shall be seized or possessed, in their corporate capa- city, shall be appropriated to the endowments of the said University, in such manner as shall most effectually pronaote the end of the institution: Provided nevertheless^ That any do- nation which shall hereafter be made and received for parti- Proviso, cular purposes, relative to the design of this institution, shall be applied in conformity to the intention of the donor or donors. Sec. 15. That the treasurer of the said corporation shall, be- Treasurer to fore he enters upon the duties of his office, give bonds to the^ve boad., said corporation, in such sum and with such sureties as they shall approve, conditioned for the faithful discharge of the duties of the said office, and for the rendering a just and true account of his doings therein, when required; and also, for the delivering over to his successor in office, all monies, secu- rities and other property, that shall belong to the president and trustees of the said University, together with all the books and papers in which his proceedings, as treasurer, shall be entered and kept, that shall be in his hands at the expira- tion of his office ; and all money that shall be recovered by virtue of any suit at law upon such bond, shall be paid over to the president and trustees aforesaid, and be subject to the appropriations above directed in this act. Sec 16. That the said corporation shall have full power? Corporatioji from time to time, to contract for, and cause to be erected? °^^J f ^^^^ such building or buildings as they shall deem necessary, for "^ ^^^^' the accommodation of the president, professors, tutors, pupils, and servants, of said University; as also, to procure the ne- cessary books and apparatus, for the use of said University, and shall cause payment therefor to be made out of the funds of the University, and shall reserve such lot or lots in said town of Athens, as they may deem necessary for the purposes aforesaid, and for the erection of buildings for the use of the town and county. Sec 17. That the lands in the two townships, appropri- Lands and ated and vested as aforesaid, with the buildings which are b"i^^ij?gs ex- or may be erected thereon, shall forever be exempted from t^ationr all state taxes. , Sec 18. That until a president of the said University Trustees maj shall be elected, and shall have entered upon the duties of appoint one of bis office, and also, in all cases of a vacancy or the absence t^iei"; n'J"aber of the president, the said trustees shall appoint one of their members to preside in their meetings, and all the doings and acts of tlie trustees, while acting under such circumstances, ^hall bij considered in laAv as the doings and acts gf th^ cof- 232$ LANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS. poration, as fully and completely as when the president of the University shall be in office and preside. Gorernorto Sec. 19. That it shall be the duty of the governor to fix fix time of the time for holding the first meeting of th^ said corporation, first meeting, ^.j^-^j^ ^YislW be in the town of Athens, of which he shall give notice in writing, to each member, at least twenty days pre- vious to such meeting, and all subsequent meetings of the said corporation, shall be in the said town of Athens. velled^^' ^^' ^^^' ^^' '^^^^^ ^^1 ^^^s ^"^^^ parts of acts, containing any thing within the purview of this act, shall be and they arc hereby repealed. [Jld ofFebrimrt/ 21, 1805, 3 v. L. O. p. 79.] An act to amend an act, entitled "An act establishing an University in iht town of Athens." Appraisersap- ^^^* ^* That James Denny, Emanuel Carpenter, jun. Isaac pointed. Dawson, Pelatia White and Ezekiel Deming, residents of this state, are appointed appraisers of the two college town- ships, numbered eight and nine, in the fourteenth range of townships within the grant of land made to the Ohio Com- Their duty. P^-^V ^^ dissociates, and the said appraisers, or any three of ^ them, on oath or affirmation, are hereby required to appraise the townships aforesaid, within nine months^ at the present real value as in its original and uncultivated state, and make report thereof to the board of trustees of the said University ; and the said trustees shall lease the same to any persons who have or may apply, agreeable to law, for the term of ninety- nine years, renewable forever, with a fixed annual rent of Proviso". six per centum on the appraised valuation: Provided^ That no lands shall be leased at a less valuation than at the rate of one dollar and seventy-five cents per aCre. When ap- ^^^* 2» That the commissioners aforesaid shall meet on the praisers shall first day of April next, at the town of Athens, who shall then meet. proceed to discharge the duties imposed on them by this act, and the act to which this act is an amendment, and the same to have performed within the time mentioned in this act. Trustees may ^^^' 3. That the trustees of the corporation of the said remove intru- University lands, are hereby authorized and empowered, to ders. remove, by due course of law, all persons living on said lands, in case such persons refuse or neglect to take leases within six months after the valuation of the lands aforesaid. Secretary of Sec. 4. That the secretary of this state shall cause notice v!^,^^-,^?."^^^^ to be given as soon as convenience will permit, to each of the -/ -?'** *-• commissioners aforesaid, of their oppointment under this act; and the commissioners respectively, on receiving the notice aforesaid, shall within a reasonable time thereafter, forward LANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS. 233 to the governor of this state, their determination to accept or not to accept toe appointment under tiiis act made. Sec. 5. That so much of the aforesaid act, passed the Part of act re* eigliteenth day of February, one thousand eight Imndred and P<^^^^^* four, as is coxitrary to this act, be and the same is hereby repealed. This act shall be in fbrc« from and after the passage Effeei. thereof. [Resolution of February 22, 1803, 3 r. L. O.jo. 459.] A resolution appointing tri>stees to the Ohio Universitj-. Resehed, That William Cveighton, junior, Joseph Buel},, Benjamin Tupper, Jacob Linley and Michael Baldwin, be, and they are hereby appointed trustees of the Ohio Uni- versity. [Act of January 17, .1 806, 4 v. L. O. p, 38.] An act supplementary to the act, entitled "An act to aiiiend an act, entitled "Ah act establishing an University in the town of Athens." Sec. 1. Tiiat Stephen Linley and William Skinner be Trustees ap- iidded to the board of trustees of said University. pointed. Sec. 2. That the trustees of the said University shall each rpu •„ be entitled to receive a sum sumcient to bear their expenses pensation. for all business performed under the autliority of the above recited acts : Providing the same shall not exceed one dollar and fifty cents for each day they shall be necessarily em» ployed, to be paid out of the funds of the said University, [Ad of January 23, 1807, 5 v, L. O, p. 85.], An act to amend the several acts establishing an University in the town of • Atheas. Sec 1. That the trustees of the Ohio University be, and Trustees may they are hereby 'authorized to lease the appraised lots of grant leases, land, lying in the two College townships, numbers eight and iiine^ in the fourteenth range of townships in the Ohio Com- panj-'s Purchase, that have been appraised at a less value than one dollar and seventy-five cents per acre at six per cent, on the appraised value. Sec 1. That the said trustees be, and they are hereby May appoint authorized to appoint appraisei-s, to appraise such parts of^ppraiser?. 2 F 234- LAKDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS. Part of act re^ pealed. Effect, the aforesaid townships, as have not been heretofore ap- praised, whenever they may deem it expedient. Sec. 3. That so much of the act, entitled "An act to amend the act, entitled "An act establishing an University in the town of Athens," passed the twentv-first day of Feb- ruary, one thousand eight hundred and five, as is contrary to the provisions of this act, be, and the same is hereby re- pealed. This act shall take effect, and be in force, from and after the passage thereof. [Ad of February 20, 1808, 6 v. L. O. p 172.] An act altering several acts, establishing an University in the town ct Atlicns. Freeholders. Sec. 1. That all persons residing in either of the two Col- lege townships, numbered eight and nine, in the Ohio Com- pany's Purchase and hold leases of land shall be considered as freeholders. • Part of act repealed. Sec. 2. That the second section of the act, entitled "An act supplementary to the act, entitled "An act to amend an act, entitled "An act establishing an University in the town of Athens," which allows a compensation to the trustees for their services, be, and the same is hereby repealed. Treasurer's & Sec. 3. That it shall be the duty of the treasurer of the collectors' du- corporation of the Ohio University, in all cases where the seerare delin-^^^^ of any person or persons have been due for two months, quent. immediately to transmit a certified copy, under his hand and the seal of said corporation, to the collector of the said cor- poration, an accurate list of all such delinquents, which said list, certified as aforesaid, shall be suftlcieiit power for the collector to distrain on the goods and chattels, of each and ev- ery delinquent, and the same to advertise in three public places in the township in which said goods and chattels are distrain- ed, ten days previous to the sale; and the said collector shall then- proceed to sell the same at public vendue, and the rent and costs forthwith to pay to the treasurer of said Ohio Uni- versity, and the overplus, if any, to refund to the dehnquent: and for want of goods and chattels to re-enter and take pos- session of the premises for the use of the trustees of the said University, as is provided by law: and the said collector shall receive the same compensation for bis services as Proviso. sheriffs do in similar cases: Provided hozocver^ That if any de- linquent or delinquents, shall think himself aggrieved, he shall have his action against the said treasurer or collector, (as the case maybe) or both, and shall recover all damages he may unjustly sustajn. LANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS-. 235 Sec. 4* That Eliphaz Perkins, Silvanus Ames, Jehiel '^"istccs ap- Gregory, Abel Miller, Leonard Jewitt, and Moses Hewitt, be po^^^ed. appointed in addition to the present number of trustees of said Ohio University. Sec. 5. That the said corporation shall have power and Number of authority to adjourn to any period ihcy may think proper; ^^'^^^^^^^* and the number of trustees of said University, shall never exceed nineteen, nor be less than eleven, any five of whom shall be a quorum to transact. any business of, said corpora- tion. Sec. G. That all laws, and parts of laws, that are contra- Laws repeals ry to the provisions of this act, be, and the same are hereby ed. repealed. This act to be in force from and after its passage. Effect. \Act of February 15, 1809,- 7 v. L. O. p. 167.] Ah act amendatory to the several acts appointing trustees to the Ohio Uni* versity, and for other purposes. Sec. 1. That Robert G. Wilson, Jesup N. Couch, John P. Trustees ap- H. Bureau, Elijah Hatch, junr. and Henry Abrams, be, and pointed. they are hereby appointed trustees of the Ohio University. Sec 2. That the trustees shall have power and authority. Trustees may until the year one thousand eight hundred and eleven, to re- ''^'^^^^"^ P'^*^' ceive of any of the lessees in payment of rent, such article or ^^^' articles of produce as may by them be agreed on at any regu- lar meeting of said trustees: Provided, it shall not exceed two- thirds of the annual rents. Sec 3. That nine of the trustees of said University, shall be ]y,jnjbpj. f.^ hereafter necessary to form a quorum to transact the bu si- form a quorum ness of said corporation, any law to the contrary notwith- standing. • Sec. 4. That the trustees shall have authority to resurvey. Lands to be or cause to be resurveyed, any large tract of land (at the re- lesurveyed. quest and expense of the lessee) and the same to lay off in such lots as they shall think will best promote the interest of said institution. Sec 5. That when a tract of land has beeh surveyed and Leases may leased to one or more persons, and by him or them sold to^® sued in one or more persons, he, she, or they, shall be entitled to re- Ji^iJlJeH. ^^ ceive from the treasurer of said institution, separate leases in their own names, by paying a reasonable compensation there- for, to be agreed on by the trustees, at a regular meeting. This act to take effect, and be in force, from and aftar its passage. 236 LANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS? [Ad of January '28, 1811, 9 r. L. 0. p. 57.] An act to incorporate the to-\Tn of Athens, and for other purposes. Sec. 11. That the trustees of the Ohio University are Trustees of O. inay^lease^lots hereby authorized and directed to lease to the commissioners to the county of the county of Athens, for the time beir:g, in-lots number of Athens. thirty-five and thirty-seven, on which the court-house and jail now stand, and also in-lot number eighteen, reserved for the purpose of building a school-house and meeting-house, on a nominal rent for ninety-nine years, renewable forever; also, to lease on the terms aforesaid, the ground reserved for a burying ground. Effect. This act to be in force from and after the passa§:€ thereof. [Act of January 29, 1811, 9 v, L. O, p, 63.] An act to amend the act, entitled "An act amendatoryto the several acts appointing trustees to the Oliio University, and for other purposes," passed February fifteenth, one thousand eight hundred and nine. Part of act ^'^^* !• That the second section of the above recited act revived. be, and the same is hereby revived, and declared to be in force until repealed by a future legislature. p„ . This act to be in force from and after its passage. [Ad of February 15, 1812,.10 v. L. O. p. 96.] An act to amend the act, entitled "An act to incorporate the town of Athens, and for other purposes." Trustees of O. Sec. 1. That the trustees of the Ohio University arc University here^by authorized and directed to lease to the trustees and lease for nomi-^^^^^^ successors in office, of the town of Athens, town lot iial rent. number eighteen, reserved for the purpose of building a meeting-house and school-house thereon, for the use of the town aforesaid, on a nomiudl rent for ninety-nine years, renewable forever. Also, to lease on the terms aforesaid, the lot laid out for a burying ground, for the use of all who may wish to inter their friends therein. Also, to lease to the Methodist society in the town of Athens, on the terms aforesaid, a piece of the public commons which adjoins out- lot number sixty-one, beginning at the southeast corner of said iot; thence cast four chains; thence north eight chains; thence west four chains; thence south to the place of begin- ning; which lot, when laid out, shall be for the use of said LASTDS for THt SUPPORT OF THE GOSPEL AND SCHOOLS. Methodist society for the purpose of ahurying ground, and to build a raeetii^g-house thereon, and such other uses as the said ijociety may think proper, for the purposes of worship, agreeably to their profession and faith. [Jd of February 15, 1812, 10 r. L. O. p. 97.] ' n act to authorize the trustees of the Ohiq Universit}' to issue orders in cer- tain cases, and for other pui-poses. {Preamble,) Sec. 1. That the trustees of said University be, and they Trustees au- hereby are authorized, from time to time, to loan, at the rate j'-o^zed to , . - ^ i. r ^i n -t- J r 1 loan the fund, ot six per centum per annum, any part o! the collected funds of the institution, not by them deemed necessary, immedi- ately to apply to the support and improvement of the semi- nary: Provided, That none be let or loaned for a longer time Proviso, than one year, and to no person whatever, unless good secu- rity be given for the punctual repayment thereof. Sec. 2. That it shall be lawful for the trustees afore- They may ■said, if to them it seem for the benefit of said institution, to'i'^aw order?. anticipate the collection of the rents aforesaid, by issuing orders upon the treasurer in favor of any person or persons, oy way of loan: Provided ahcays, That when such orders are Proviso, given for the purpose of loaning as aforesaid, the person or persons applying therefor, shall give security as aforesaid for the faithful repayment of the amount thereof, with legal interest in one year from the date of such order or orders; and the orders so issued, annually, shall never exceed the whole amount of rents, payable the succeeding year; and such orders shall be negociablc, and shall be received by the collector or treasurer in payment of rents, or any other debts due from individuals to the said institution from the time such orders may he payable, and such orders shall not bear interest. Sec 3. That the trustees aforesaid shall, at their next Conditions of regular session, by an ordinance by them to be passed, estab- "^^^^"S ^o'^^^-" lish the form and conditions of making such loans, and the form and times of making application therefor, and also any proper regulations relative to the repayment of the sums loaned: Provided, airways, That no loan shall be made for a Proviso, smaller sum than fifteen dollars; ard such applicants as may desire small loans, not exceeding forty dollars, shall have the preference: Provided, Unexceptionable security be given as proviso., aforesaid; and for the purpose of enabling such applicants for small sums to obtain such preference, the trustees afore- said shall appoint the month of April, annually, during which >maU loans only shall be made. 23S L.iNDS fOR THE SUPPORT OF THE GOSPEL AND SCHQOLS.. I^^To'riatll ^^^' ^* ^^^^ ^^^^ amount of interest made and collected. appropriacet . ^^ reason of any loan by this act authorized, shall be a fund* subject to pay the reasonable and contingCit expenditures incurred in the transaction of the business of said institu- tion, and subject to the order and appropriation of said trus- tees for such purpose. [Resolution of February 20, 1812, 10 d. L, O. p. 198.] ■ Resolution appointing, trustees of the Ohio University. Resolved^ That Samuel P. Hildreth and Seth Adams, be and they are hereby appointed trustees for the Ohio Uniyer- sity, in place of Jehiei Gregory and John P. R. Bureau* resigned. {Ad of January 12, 1813, 11 z?. L. O. jt?. 27.] An act to enlarge the College green in the. town of Athens. P. & trustees Sec. 1. That the president and trustees of the Ohio Uni- oithe O^ Urn- yersity be, and they are hereby authorized, to vacate in-lots vacate lois*^ numbers fifty-five and fifty-six in the town of Athens, provi- ded, said lots remain unsold ; and the president and trustees aforesaid, are hereby empowered to purchase in-lots num- bers fifty-seven and fifty-eight, for a reasonable value, to be paid the proprietors thereof out of the funds of the Univer- sity, or to exchange therefor such other unsold lot or parcels of land belonging to the College township, as may best pro- mote the interest of the University, and that they be requir- ed to attach the ground vacated and purchased as aforesaid, to the College green in said town. A street may Sec. 2. Tha.t the president and trustees aforesaid, are fee extended, hereby authorized to extend Court-street south to the ex- treme point of in-lot number seventy-seven, in the town aforesaid. [Resolution of February 6, 1813, 11 i). jC. O.;?. 178.] Resolved^ That so much of the resolution, entitled "A re- solution for the election of a senator in Congress, and other officers," as requires that a trustee of the Ohio University, be elected, by ballot, be repealed, and that WiUiam Wilson., esquire, be appointed a trustee in the room of Joseph BuelK esquire, deceased.* *Nd such resolution as the one referred to ca,n be found. LANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS. 23jdf [Resolution of February 16, 1815, 13^. L. O.;?. 332.] Resolved, That John LawreDce Lewis, esquire, and Joseph Wood, esquire, of Washington county; the Reverend James Culbertson, of Muskingum county; and Charles R. Siierman, of Fairfield county, be, and they are hereby appointed trus- tees for' the Ohio University, In place of Benjamin Tupper and Moses Hewett, deceased, and Henry Abrams, resigned," and Leonard Jewett, expelled. MIAMI UNIVERSITY. [Act of April 15, 1803, 1 v. L. O, p, 66.] An act to provide for the locating a College township in the district of Cin- cinnati. Sec. 1. Tlmt one complete township in the district of To^vnship for Cincinnati, or so much of any one complete township within f^"^^'^'^^^''^^, the same as may remain unsold together with as many ad- ^^ ^\^^ district joining sections as shall have been sold in the said township, of Cincinnati, so as to make in the whole thirty-six sections, shall be located and entered in due form with the register of the United States land office at Cincinnati, on or before the first day of October next, for the use and support of an Academy, in lieu of the College township heretofore granted in trust to John C. Symmes, and his associates, by the United States, and in pursuance of and agreeably to an act of Congress, entitled "An act in addition to and in modification of the propositions o.ontained in the act, entitled "An act to enable the people of the eastern division of the territory northwest of the river Ohio, to form a constitution and state government, and for the admission of such state into the union, on an equal footing with the original states and for other purposes." Sec. 2. That Jeremiah Morrow, Jacob White and Wil-^^°^^^j^'^^Pj' liam Ludlow, be constituted and the same are hereby consti- their duty, tuted and appointed commissioners, to do, perform, and trans- act . all and every matter and thing that is necessary to be done in locating and registering the said College township or thirty-six sections of land. And the said cpmmisioners after being duly sworn, faithfully to discharge their trust, in this behalf, shall proceed without loss of time, to explore the vacant or unlocated lands of the United States in the said district of Cincinnati, and after due examination shall select such tract or tracts (as the case may require) as are the most valuable, having due regard to the quality of the land, the situation for health, the goodness of the water, and the ad- vantage 9f inland navigatipp. And after the location shall. •240 LANDS FOR THE SUPPORT OF THE GOSPEL AIsD SCHOOL^, have been so made and registered, • the said commissioners shall procure two fair copies of the same location and entry from the register of the land office, one of which shall be traRsmitted to the secretary of the treasury of the United States and the other shall be deposited with the secretary of the State of Ohio: Promded kozuever^ That if any of the afore- said commissioners should die, remove or refuse to act, then and in that case the two remaining commissioners shall pro- ceed to locate and register the said College lands in the man- ner prescribed by this act. {Act of February/ 9, 1809, 7 v. L, O, p. 184.] An act to establish the Miami University, Universify Sec. 1. That there shall bean University established and estabhshecL instituted, in the manner hereafter directed, within that part of the country known by the name of Joim Cleves Symmes' Purchase, which University shall be designated by the name and style of the Miami University, for the instruction of youth in ail the various braaches of the liberal arts and sciences, for the promotion of good educa.tion, virtue, religion and morali- ty, and for conferring all tiae literary honors granted in similar institutions; and the benefits and advantages of the said Uni- versity shall be open to all the cit'zens w^ithin this state. Body politic. Sec. 2. That the president and trustees of the Miami Uni- versit}^, are hereby created a body politic and corporate by the name of '^The President and Trustees of the Miami Uni- versity," which body politic shall consist of a president and not more than fourteen, nOr less that seven trustees, whose time of service or appointment shall be for three years. Names oi'truE- Sec. 3. That Hiram. Mirach-Curry and William Ward, of tecs.- Champaign county; James Brown and David H. Morris, of Miami county; Yv'^illiam M'Clure and Benjamin Van Gleve, of Montgomery county; Benjamin Whiteman and Andrew Reed, of Greene county; John Bigger and Ichabod B.Halsey, of Warren county; John Reily and Thomas Irwin, of Butler county ; John Riddle and Joseph Vanhorn, of Hamilton coun- ty, together with the president for the time being, be, and they are hereby erected a body politic and corporate, by the name of the President and Trustees of the Miami University; and that they, and their successors and such others as shall be duly elected members of the said corporation, shall be and remain a body politic and corporate in law, by that name. , Sec 4. Tiiat the said trustees shall have power and au- Tresident? thority to elect a president, who shall preside in the said Uni- versity; and also to appoint a secretary, treasurer, collector, professors, tutors.iastructors. and all such officers and seiTants t-ANDS FOR THE SUPPORT OF THE GOSPEL AND SCHOOLS* 241 miho Universit}', as they shall deem necessary for carrying in- to effect the design of the institution, and -^hall have authori- ty, from time to lime, to establish the name and number, and ■prescribe the duties of all the otTicersand servants to be en>- ployed in the University, except herein otherwise provided, ^ and may empower the president or some other member of the corporation, to administer such oaths as they shall authorize, oaths. for tlie good government and- well -ordering of the said Uni- versitv: Provided, That no business of the corporation shall Proviso. be transacted at any meeting, unless seven of the said trus- tees shall be present. Sec. 5. That the said corporation shall have power and Rules, by- authority, from time to time-, to make and ordain rules, ordi-iaws, &c. nanees aijd by-laws, for the government of the corporation, not incompatible with the laws of the United States or this «tate,' and the same to repeal as occasion may require, and also to determine the salaries, emoluments and tenures of their several officers, [offices.] Sec. 6. That the said corporation shall have power and Corporation authority to suspend and dismiss the president, or any mem- "|j^^ ^^"^^^^ her of the said corporation, w^ho shall, by his misconduct^ ren- der himself unworthy of the office, station or place he sustains, or. who from age or other infirmity, is rendered incapable to perform the duties of his office ; and the said corporation shall have power And iauthority to suspend, dismiss and remove from the University, any professor or instructor, whensoever the corporation shall deem it expedient for the interest and honour of the University: Provided^ That two-thirds of the - corporation shall be present, w^hen any such person shall or mn.y be suspended, removed or dismissed. . Sec. 7. That the trustees shall have power to fill all vacan- Vacancies, cies, which may happen in their board* during the recess of^®^^^^^* the legislature, out of the counties where such vacancy shall happen^ who shall continue in office until the end of the next session of the legislature; and the president shall make re- port thereof to the governor, to enable him to lay the same before the next legislature. | 16,760 |
https://github.com/cpplibv/libv/blob/master/test/libv/math/convert_test.cpp | Github Open Source | Open Source | Zlib | 2,019 | libv | cpplibv | C++ | Code | 74 | 297 | // Project: libv.math, File: test/libv/math/convert_test.cpp, Author: Császár Mátyás [Vader]
#include <catch/catch.hpp>
#include <libv/math/fixed_point.hpp>
using namespace libv;
// -------------------------------------------------------------------------------------------------
template <typename T>
T encode_decode(T value) {
return convert_from_s24_8<T>(convert_to_s24_8(value));
}
TEST_CASE("encode decode") {
for (float i = -56048.4f; i < 50400.6f; i += 462.2f) {
CHECK(std::fabs(encode_decode(i) - i) < 0.1f);
}
for (double i = -36408.4; i < 83043.6; i += 743.2) {
CHECK(std::fabs(encode_decode(i) - i) < 0.1);
}
CHECK(std::fabs(encode_decode(0.f)) < 0.1f);
CHECK(std::fabs(encode_decode(-0.f)) < 0.1f);
}
| 31,186 |
https://pt.wikipedia.org/wiki/%C3%8Anio%20de%20Freitas%20e%20Castro | Wikipedia | Open Web | CC-By-SA | 2,023 | Ênio de Freitas e Castro | https://pt.wikipedia.org/w/index.php?title=Ênio de Freitas e Castro&action=history | Portuguese | Spoken | 419 | 770 | Ênio de Freitas e Castro (Montenegro, 27 de junho de 1911 - Porto Alegre (?) 21 de junho de 1975) foi um professor, compositor, pianista, maestro, folclorista e musicólogo brasileiro.
Começou seus estudos em Vacaria. Com apenas 13 anos de idade já era pianista do cinema local. Em 1925 mudou-se para Porto Alegre, ingressando no Conservatório do Instituto de Belas Artes, onde estudou com Antonina Maineri (piano) e Assuero Garritano (teoria musical e harmonia). Deu seu primeiro recital em 1930 e depois se transferiu para o Rio de Janeiro, a fim de se aperfeiçoar no Instituto Nacional de Música.
Ali foi aluno de piano de Guilherme Fontainha, concluindo seu curso em 1932 com Medalha de Ouro, por unanimidade. Em 1937, terminou o curso de composição e regência, sob a orientação de Paulo Silva (contraponto e fuga), Francisco Braga (composição e instrumentação), Francisco Mignone (regência) e Octávio Bevilacqua (história da música). Mas antes de concluir os estudos foi convidado a assumir a cátedra de Harmonia no Instituto de Belas Artes. Além de professor, foi concertista e maestro da Orquestra Filarmônica de Porto Alegre. Entre 1954 e 1955 esteve em Paris para outros estudos avançados. Foi fundador e dirigente da Associação Rio-Grandense de Música e membro fundador da Cadeira n. 29 da Academia Brasileira de Música.
Foi o primeiro Superintendente de Educação Artística e o primeiro Diretor da Divisão de Cultura da Secretaria de Educação do Rio Grande do Sul, sendo o responsável pela criação da Discoteca Pública, da Biblioteca Pública Infantil, do Instituto de Tradições e Folclore e do Serviço de Radiodifusão Educativa. Escreveu artigos para o Diário de Notícias e deixou o livro Princípios de Arquitetura Musical (Porto Alegre, 1940). Outros artigos apareceram nos livros Rio Grande do Sul - Imagem da Terra Gaúcha (Porto Alegre, 1942) e Fundamentos da Cultura Rio-Grandense (Porto Alegre, 1960).
Principais composições
Música orquestral: Sinfonia e Suite, para orquestra de cordas
Música de câmara: Trio, para piano, violino e violoncelo e Quarteto de cordas
Canto e piano: Historietas, Mar, Ouve o canto da noite, Porque, A velha carta e A vida.
Ver também
História da música erudita em Porto Alegre
Folclore do Rio Grande do Sul
Instituto de Artes da UFRGS
História de Porto Alegre
Cultura de Porto Alegre
Referências
Professores da Universidade Federal do Rio Grande do Sul
Compositores do Rio Grande do Sul
Pianistas do Rio Grande do Sul
Folcloristas do Rio Grande do Sul
Naturais de Montenegro (Rio Grande do Sul)
Maestros do Rio Grande do Sul
Música de Porto Alegre | 3,880 |
https://github.com/ani03sha/RedQuarkTutorials/blob/master/LeetCode/Java/src/main/java/org/redquark/tutorials/leetcode/LetterCombinationsOfAPhoneNumber.java | Github Open Source | Open Source | MIT | 2,022 | RedQuarkTutorials | ani03sha | Java | Code | 163 | 497 | package org.redquark.tutorials.leetcode;
import java.util.ArrayList;
import java.util.List;
/**
* @author Anirudh Sharma
*/
public class LetterCombinationsOfAPhoneNumber {
private static List<String> letterCombinations(String digits) {
// Resultant list
List<String> combinations = new ArrayList<>();
// Base condition
if (digits == null || digits.isEmpty()) {
return combinations;
}
// Mappings of letters and numbers
String[] lettersAndNumbersMappings = new String[]{
"Anirudh",
"is awesome",
"abc",
"def",
"ghi",
"jkl",
"mno",
"pqrs",
"tuv",
"wxyz"
};
findCombinations(combinations, digits, new StringBuilder(), 0, lettersAndNumbersMappings);
return combinations;
}
private static void findCombinations(List<String> combinations, String digits, StringBuilder previous, int index, String[] lettersAndNumbersMappings) {
// Base condition for recursion to stop
if (index == digits.length()) {
combinations.add(previous.toString());
return;
}
// Get the letters corresponding to the current index of digits string
String letters = lettersAndNumbersMappings[digits.charAt(index) - '0'];
// Loop through all the characters in the current combination of letters
for (char c : letters.toCharArray()) {
findCombinations(combinations, digits, previous.append(c), index + 1, lettersAndNumbersMappings);
previous.deleteCharAt(previous.length() - 1);
}
}
public static void main(String[] args) {
System.out.println(letterCombinations("23"));
System.out.println(letterCombinations(""));
System.out.println(letterCombinations("2"));
}
}
| 19,896 |
BXycny6jkmE_1 | Youtube-Commons | Open Web | CC-By | null | Live Day Traders Show with Fausto Pugliese | $DTST, $DARE, $JAGX, $CLOV, $BDR | | None | English | Spoken | 1,710 | 1,938 | Beautiful. Got to share another screen. Hold here. Hold on a second. All right. Perfect. All right. Good to see everybody. Welcome back Hope everyone had a Nice little fortage live weekend. I know I'm sorry was gone yesterday, but you know, it's my niece's birthday So we got stuck in out east really nice weather and then we'll so we got what a major storm Coming back, but it was beautiful and this is what you train for you go out there You enjoy life you make your money and that's it Listen the great thing about what we're doing is that we could just show up every day is a brand-new day here at Cybertry University is a day trading means you day trade you make your days paying. That's it a couple of good stocks Obviously made some big moves. I told you that yesterday So there's a couple of not too many too much out there right now And I'm not expecting it probably till like maybe tomorrow. We'll get some good stuff But I think today we'll have some good stuff a lot of the brand name stocks are actually all the high tech stocks Have been done phenomenal The last couple of probably two months, which is kind of awkward and weird that like Facebook Google all of them. I mean look at these stocks since May. I mean 2300 to 2600 Facebook went from in May went from 300 to 350 the big one is obviously is you know Twitter did the same thing Who's the other one? NVIDIA NVIDIA has just been an animal this thing is almost like double and it just won't stop every day It's up like $10 every day now The big thing that I just want you kind of explain that I know that we don't really focus and trade on stocks like this and But the thing is I know a lot of you like to day trade I mean like to me do some options trade you got to know how to day trade first Because I know a lot of you look at you can't afford it But if you know what happens as a day trader you'll know how to trade stocks like this now There are a couple of stocks that are moving this morning that are doing pretty well Like the stock that we found this DTST that did really really well But before we get into that let's talk about what happened as of yesterday because there were a couple of stocks That did make some nice moves and want to touch on touch upon those and then we'll go through the watch list We'll see what's with the big money is following this morning on the on the level 4 and the level 3 This bsqr had a really decent move in the morning. You can see right here I'm just blowing this up so you guys see a little bit better So here you have the stock had a really nice move from $4 went away to 750 Nice little move had it kept breaking higher highs had a couple of shakes You could see right here that were pretty nasty but you know we got this nice little sling shot that happened right here and It really ran away up to about 1230 which you know what pretty much done around that 10 o'clock time frame So that one did pretty well. Yeah, this OS OSAT also that did pretty did nice move looks like got halted here Had a big big pop right here, but nice little cheap little stock Did a little bit shake made a pop did it? Hit it double top pop from that 750 all the way up to about 925 then they got Really hairy when it got around this time frame and then obviously did this But you know what right here is all you really need is this little move right there So that won't look pretty nice for some of you that jumped into that one And then this one going into the afternoon look like it did really well at 2 o'clock This was a really pretty steady mover not expensive. You could have trade several thousand shares of the stock You probably couldn't wait until like 3 o'clock when it made that big move And then obviously you could see it went all the way up to right around 6 o'clock And it all into half the hours he went away to 290 so nice move from 220 up to 290 Even if you got out there at 260 cheap little stock very nice little stock, but anyway, that's the past We're gonna turn the page and let's focus on what's going on today So a couple of stocks that I did find that I thought that were pretty decent. I don't think there's a lot out There's not a lot out there. I mean I only found right now four of them We all know that when the market opens up things start, you know changing for the better But we got a couple of decent moves. We got this stock right here The stock a DT a DT ST has a nice little push made a really nice move at that seven o'clock move right there Went all the way up to right around 1350. I'm looking over here on the level four. I'm not really Super impressed There were a couple iceberg orders that were getting hit Somebody keeps going out there and keeps selling some big block orders So it kind of like gets me a little nervous looking at that There is a big 19,000 share seller here 14, but I'm not really seeing any real Significant buyers out there. This guy got done, which is a pretty good sign for support levels at 1280 So we're gonna keep an eye on that stock that one looks like it's got some good move Just be a nice little pop though right at that 855 it ran from that 1220 all the way up to about 13 bucks Another little cheap little stock that I found this morning that also I called out This one moved really really nice comfortable stock and then she kind of backed off right around 830 She ran to about 260 this morning I mean if you came in and came in when you were supposed to when we started on eight o'clock It didn't go from 213 to that 260. That was a really nice move right there and When I go over here this stock had a nice ladder You could see it how it built the ladder right there, which we all focus on in class We had that ladder build up guy came out there guy came out They kept bidding it up bidding up bidding up and then obviously stop bidding it up anymore And that's when they started coming back down. You got a nice little 275,000 share seller right there right around 270 kind of makes sense why it didn't break that Early in the pre-market, but they we know there is a very big substantial order out there on that one Jag and a little cheap stock. I think the stock could be a sleeper. I'll tell you why this is a long shot for me Remember we trade the stock in January ran from a dollar ran away to four dollars She's got some volume pick it up Brimley and shares I'm just gonna put it as a long shot and just see how it works out But because I didn't find and have a really good list another one I put on as a long shot is the VXRT You remember this back in February this stock ran from seven dollars all the way to twenty five dollars It was not only a good day trade. It was a good short-term swing trade You know, I'm seeing some good volume that came in right around here. She's hovering around the highs You know, I'm looking over here on level four You got a couple of decent iceberg orders hovering right around here around 19,000 and 23,000 right around that eight dollars, but the guy gets done I mean you got another big order here at 840 But I want to see where these guys get done if they're gonna get executed and if they do It's that's a very strong sign for the stock to go up. So those stocks obviously look pretty decent I'm gonna keep an eye on those but but other than that is not that much. I found this morning that I fell in love with Donut, you know, I was a fan of crispy cream. I got a little nervous on it I'm telling you right now if it breaks this where it started where it opened up the stock is You know, that's not a very good sign. So, um, I sold some of I sold my day trading holding my swing trading But I'm not really down that much. I went around 17 40 so I'm kind of like I was doing great when it first came out But but I'm really focusing on that support level. So, you know, right now. I'm pretty much breaking even that's where I'm at So I'm gonna keep a close eye on that stock, but other than that on the swing trades, you know Chewie's doing pretty well a lot of things are doing pretty well. Don't make a nice little comebacks owned everything here pretty cheap So, you know, a lot of them took major major hits there was some great buying opportunities right when when they came around and I guess a lot had to do that was part of when they came out with the You know, they're talking about the infrastructure deal. So we'll keep a little keep a close eye on some of these stocks But there's always new ones that popped up now anything. I'm missing. I did not call out Jeff on YouTube is saying faster. | 35,534 |
https://github.com/n11-TalentHub-Java-Bootcamp/n11-talenthub-bootcamp-graduation-project-tarikcoskun94/blob/master/src/main/java/com/n11/graduationproject/entity/CreditScore.java | Github Open Source | Open Source | MIT | 2,022 | n11-talenthub-bootcamp-graduation-project-tarikcoskun94 | n11-TalentHub-Java-Bootcamp | Java | Code | 56 | 179 | package com.n11.graduationproject.entity;
import lombok.Getter;
import lombok.Setter;
import javax.persistence.Column;
import javax.persistence.Entity;
import javax.persistence.Table;
import java.io.Serializable;
@Getter
@Setter
@Entity
@Table(name = "credit_scores")
public class CreditScore extends BaseEntity implements Serializable {
@Column(name = "score",
nullable = false)
private Long score;
@Column(name = "tc_identification_no",
length = 11,
unique = true,
nullable = false,
updatable = false)
private String TCIdentificationNo;
} | 26,036 |
https://github.com/felixonmars/sakemake/blob/master/examples/mixer/mixer.cpp | Github Open Source | Open Source | MIT | null | sakemake | felixonmars | C++ | Code | 238 | 730 | // Based on https://gist.github.com/armornick/3497064 and
// https://stackoverflow.com/a/1641223/131264
#include <SDL2/SDL.h>
#include <SDL2/SDL_mixer.h>
#include <csignal>
#include <cstdlib>
#include <iostream>
#include <unistd.h>
// RESOURCEDIR is defined by sakemake, so that the path will be correct both at development-time
// and at installation-time
#define WAV_PATH RESOURCEDIR "Roland-GR-1-Trumpet-C5.wav"
#define MUS_PATH RESOURCEDIR "HR2_Friska.ogg"
// Wave file
Mix_Chunk* wave = NULL;
// Music file
Mix_Music* music = NULL;
// Interrupted?
bool interrupted = false;
// Signal handler
void my_handler(int s) { interrupted = true; }
int main(int argc, char* argv[])
{
// Initialize SDL2
if (SDL_Init(SDL_INIT_AUDIO) < 0) {
return -1;
}
// Prepare my_handler as a signal handler
struct sigaction sigIntHandler;
sigIntHandler.sa_handler = my_handler;
sigemptyset(&sigIntHandler.sa_mask);
sigIntHandler.sa_flags = 0;
// Set up a signal handler for ctrl-c
sigaction(SIGINT, &sigIntHandler, NULL);
// Initialize SDL_mixer
if (Mix_OpenAudio(22050, MIX_DEFAULT_FORMAT, 2, 4096) == -1) {
return -1;
}
// Load the sound effect sample
wave = Mix_LoadWAV(WAV_PATH);
if (wave == NULL) {
return -1;
}
// Load the music sample
music = Mix_LoadMUS(MUS_PATH);
if (music == NULL) {
return -1;
}
if (Mix_PlayChannel(-1, wave, 0) == -1) {
return -1;
}
if (Mix_PlayMusic(music, -1) == -1) {
return -1;
}
// Play while not interrupted by ctrl-c
while (Mix_PlayingMusic()) {
if (interrupted) {
std::cout << std::endl;
break;
}
}
// Free the memory
Mix_FreeChunk(wave);
Mix_FreeMusic(music);
// Quit SDL_Mixer
Mix_CloseAudio();
// Friendly message at the end
if (interrupted) {
std::cout << "Bye!" << std::endl;
return 1;
}
return 0;
}
| 29,119 |
https://stackoverflow.com/questions/59721661 | StackExchange | Open Web | CC-By-SA | 2,020 | Stack Exchange | Androidcoder, from56, https://stackoverflow.com/users/1324802, https://stackoverflow.com/users/7690376 | English | Spoken | 221 | 370 | In BillingClient setup .setListener(this) references my calling activity instead of a PurchasesUpdatedListener
The docs show the following for setting up a Billingclient.
private BillingClient billingClient;
...
billingClient = BillingClient.newBuilder(activity).setListener(this).build();
In .setListener(this), the 'this' part is supposed to reference a PurchasesUpdatedListener, even though you don't explicitly create one to put in these parenthesis. Apparently just using 'this' is supposed to be enough. In the docs and all the examples I've seen, a PurchasesUpdatedListener is never created to put here, it just uses 'this', apparently self-referencing the billingclient being created. This hasn't worked for me though, and I keep getting:
Should I use something else for the (activity) part than (getApplicationContext())? I've tried (this) and various other things here as just the word 'activity' isn't recognized.
Instead setListener(this) put setListener(new PurchasesUpdatedListener(){... }) and implement the required methods (usually AndroidStudio does it automatically)
Or
add .. implements PurchasesUpdatedListener at the end of your MainActivity declaration
the same thing as you can do on many listeners, for example the well known OnClickListener
I have attempted this too, despite there being no examples of doing this in the docs, but it introduces method clash errors, an issue I'm also having with billingClient.startConnection(new BillingClientStateListener()...
it seems that more than a problem with the InApp billing library you have a problem in how to use listeners in general
| 14,615 |
https://ru.wikipedia.org/wiki/%D0%9D%D1%8C%D1%8E%D1%82%D0%BE%D0%BD%D0%B8%D0%B9 | Wikipedia | Open Web | CC-By-SA | 2,023 | Ньютоний | https://ru.wikipedia.org/w/index.php?title=Ньютоний&action=history | Russian | Spoken | 696 | 2,047 | Ньютоний ( в честь Исаака Ньютона) — легчайший гипотетический химический элемент, существованием которого Д. И. Менделеев пытался объяснить химическую природу мирового эфира.
История
Концепция мирового эфира получила развитие в середине XIX века в рамках волновой оптики и электромагнитной теории Максвелла. Мировой эфир стал рассматриваться как гипотетическая всепроникающая сущность, заполняющая мировое пространство и передающая свет, тепло и гравитацию.
Очевидно, что открытым оставался вопрос о химической природе эфира: он должен был состоять из легчайших, абсолютно инертных элементов, атомы которых не удерживались бы гравитационными силами. Ни легчайший известный элемент, водород, ни гипотетический короний категорически не годились на эту роль. Таким образом, концепция мирового эфира оказалась тесно связанной с решением проблемы нижней границы периодической системы химических элементов.
Задачу тяготения и задачи всей энергетики нельзя представить реально решёнными без реального понимания эфира, как мировой среды, передающей энергию на расстояния. Реального же понимания эфира нельзя достичь, игнорируя его химизм и не считая его элементарным веществом.
Д. И. Менделеев, открыв Периодический закон, понимал, что явление периодичности не имеет физического обоснования, и не видел прямых путей, ведущих к его отысканию. Ещё в ранних работах по периодичности Менделеев предполагал, что эфир мог быть специфическим состоянием газов при большом разрежении или особым газом с очень малым весом. Открытие в конце XIX века инертных газов актуализировало вопрос о сущности химических элементов. По предложению Уильяма Рамзая Менделеев формирует нулевую группу периодической таблицы, но также оставляет место для более лёгких, чем водород, элементов. По мнению Менделеева, группа инертных газов могла быть дополнена коронием и ещё более лёгким, пока неизвестным элементом. Свои соображения Менделеев высказал в статье «Попытка химического понимания мирового эфира» (1902, опубл. в 1905) и 8-м издании учебника «Основы химии» (1906).
Если же аналоги аргона вовсе не дают соединений, то очевидно, что нельзя включать ни одну из групп ранее известных элементов, и для них должно открыть особую группу нулевую… Это положение аргоновых аналогов в нулевой группе составляет строго логическое следствие понимания периодического закона… Теперь же, когда стало не подлежать ни малейшему сомнению, что перед той I группой, в которой должно помещать водород, существует нулевая группа, представители которой имеют веса атомов меньше, чем у элементов I группы, мне кажется невозможным отрицать существование элементов более лёгких, чем водород.… я прибавляю в последнем видоизменении распределения элементов по группам и рядам не только нулевую группу, но и нулевой ряд, и на место в нулевой группе и в нулевом ряде помещён элемент x (мне бы хотелось предварительно назвать его «ньютонием» — в честь бессмертного Ньютона), который и решаюсь считать, во-первых, наилегчайшим из всех элементов, как по плотности, так и по атомному весу, во-вторых, наибыстрее движущимся газом, в-третьих, наименее способным к образованию с какими-либо другими атомами или частицами определенных сколько-либо прочных соединений, и, в-четвертых, — элементом, всюду распространённым и всё проникающим, как мировой эфир.
Менделеев привёл свои расчёты массы атома ньютония, исходя из «возможности движущимся частицам вырываться из сферы притяжения земли, солнца и звёзд». Она, по расчетам ученого, может колебаться в пределах 9.6·10−7 до 5.3·10−11 от массы атома водорода: «…для понимания множества явлений совершенно достаточно признать пока, что частицы и атомы легчайшего элемента х, могущего свободно двигаться всюду, имеют вес, близкий к одной миллионной доле веса водородного атома, и движутся со средней скоростью, недалекою от 2250 километров в секунду».
Следует отметить, что ни в цитируемой выше статье, ни в 7-м и 8-м издании «Основ химии» Менделеев не включил ньютоний и короний в прилагаемые периодические таблицы, признавая очевидное отсутствие экспериментальных доказательств их реальности. При всей умозрительной направленности исходных предпосылок основным и наиболее важным результатом в области физики, полученным благодаря им Д. И. Менделеевым, явился вывод уравнения идеального газа.
Гипотеза о существовании ньютония потеряла актуальность вместе с представлениями о мировом эфире после появления специальной теории относительности и создания квантово-механической модели атома. К 1930-м годам проблема «эфира» уже не существовала в науке, равно как и вопрос об элементах легче водорода. Неоднократные попытки отдельных учёных возродить концепцию эфира в той или иной форме (например, связать эфир с физическим вакуумом) успеха не имели.
См. также
Эфир (физика)
Короний
Список несуществующих химических элементов
Предсказанные Менделеевым элементы
Список объектов, названных в честь Исаака Ньютона
Примечания
Литература
Менделеев Д. И. Основы химии, VIII издание. СПб, 1906.
Менделеев Д. И. Попытка химического понимания мирового эфира. СПб., 1905
Несуществующие химические элементы
Гипотетические материи
Элементы, предсказанные Дмитрием Менделеевым
Химические гипотезы
Физические гипотезы
Гипотетические объекты физики | 25,768 |
https://github.com/roadiz/rozier/blob/master/src/Resources/app/RozierMobile.js | Github Open Source | Open Source | MIT | 2,023 | rozier | roadiz | JavaScript | Code | 817 | 3,085 | import $ from 'jquery'
import { TweenLite, Expo } from 'gsap'
import { addClass, removeClass } from './utils/plugins'
/**
* Rozier Mobile
*/
export default class RozierMobile {
constructor() {
// Selectors
this.$menu = $('#menu-mobile')
this.$adminMenu = $('#admin-menu')
this.$adminMenuLink = this.$adminMenu.find('a')
this.$adminMenuNavParent = this.$adminMenu.find('.uk-parent')
this.$searchButton = $('#search-button')
this.$searchPanel = $('#nodes-sources-search')
this.$treeButton = $('#tree-button')
this.$treeWrapper = $('#tree-wrapper')
this.$treeWrapperLink = this.$treeWrapper.find('a')
this.$userPicture = $('#user-picture')
this.$userActions = $('.user-actions')
this.$userActionsLink = this.$userActions.find('a')
this.$mainContentOverlay = $('#main-content-overlay')
this.menuOpen = false
this.searchOpen = false
this.treeOpen = false
this.adminOpen = false
this.menuClick = this.menuClick.bind(this)
this.adminMenuLinkClick = this.adminMenuLinkClick.bind(this)
this.adminMenuNavParentClick = this.adminMenuNavParentClick.bind(this)
this.searchButtonClick = this.searchButtonClick.bind(this)
this.treeButtonClick = this.treeButtonClick.bind(this)
this.treeWrapperLinkClick = this.treeWrapperLinkClick.bind(this)
this.userPictureClick = this.userPictureClick.bind(this)
this.userActionsLinkClick = this.userActionsLinkClick.bind(this)
this.mainContentOverlayClick = this.mainContentOverlayClick.bind(this)
// Methods
this.init()
}
/**
* Init
* @return {[type]} [description]
*/
init() {
if (this.$userPicture.length) {
// Add class on user picture link to unbind default event
addClass(this.$userPicture[0], 'rz-no-ajax-link')
}
// Events
this.$menu.on('click', this.menuClick)
this.$adminMenuLink.on('click', this.adminMenuLinkClick)
this.$adminMenuNavParent.on('click', this.adminMenuNavParentClick)
this.$searchButton.on('click', this.searchButtonClick)
this.$treeButton.on('click', this.treeButtonClick)
this.$treeWrapperLink.on('click', this.treeWrapperLinkClick)
this.$userPicture.on('click', this.userPictureClick)
this.$userActionsLink.on('click', this.userActionsLinkClick)
this.$mainContentOverlay.on('click', this.mainContentOverlayClick)
window.addEventListener('pageload', this.mainContentOverlayClick)
}
/**
* Menu click
* @return {[type]} [description]
*/
menuClick(e) {
if (!this.menuOpen) this.openMenu()
else this.closeMenu()
}
/**
* Admin menu nav parent click
* @return {[type]} [description]
*/
adminMenuNavParentClick(e) {
let $target = $(e.currentTarget)
let $ukNavSub = $(e.currentTarget).find('.uk-nav-sub')
// Open
if (!$target.hasClass('nav-open')) {
let $ukNavSubItem = $ukNavSub.find('.uk-nav-sub-item')
let ukNavSubHeight = $ukNavSubItem.length * 41 - 3
$ukNavSub[0].style.display = 'block'
TweenLite.to($ukNavSub, 0.6, { height: ukNavSubHeight, ease: Expo.easeOut, onComplete: function () {} })
$target.addClass('nav-open')
} else {
// Close
TweenLite.to($ukNavSub, 0.6, {
height: 0,
ease: Expo.easeOut,
onComplete: function () {
$ukNavSub[0].style.display = 'none'
},
})
$target.removeClass('nav-open')
}
}
/**
* Admin menu link click
* @return {[type]} [description]
*/
adminMenuLinkClick(e) {
if (this.menuOpen) this.closeMenu()
}
/**
* Open menu
* @return {[type]} [description]
*/
openMenu() {
// Close panel if open
this.closeSearch()
this.closeTree()
this.closeUser()
// Translate menu panel
TweenLite.to(this.$adminMenu, 0.6, { x: 0, ease: Expo.easeOut })
if (this.$mainContentOverlay.length) {
this.$mainContentOverlay[0].style.display = 'block'
TweenLite.to(this.$mainContentOverlay, 0.6, { opacity: 0.5, ease: Expo.easeOut })
}
this.menuOpen = true
}
/**
* Close menu
* @return {[type]} [description]
*/
closeMenu() {
let adminMenuX = -window.Rozier.windowWidth * 0.8
TweenLite.to(this.$adminMenu, 0.6, { x: adminMenuX, ease: Expo.easeOut })
TweenLite.to(this.$mainContentOverlay, 0.6, {
opacity: 0,
ease: Expo.easeOut,
onComplete: () => {
if (this.$mainContentOverlay.length) {
this.$mainContentOverlay[0].style.display = 'none'
}
},
})
this.menuOpen = false
}
/**
* Search button click
* @return {[type]} [description]
*/
searchButtonClick(e) {
if (!this.searchOpen) this.openSearch()
else this.closeSearch()
}
/**
* Open search
* @return {[type]} [description]
*/
openSearch() {
// Close panel if open
this.closeMenu()
this.closeTree()
this.closeUser()
// Translate search panel
TweenLite.to(this.$searchPanel, 0.6, { x: 0, ease: Expo.easeOut })
if (this.$mainContentOverlay.length) {
this.$mainContentOverlay[0].style.display = 'block'
TweenLite.to(this.$mainContentOverlay, 0.6, { opacity: 0.5, ease: Expo.easeOut })
}
// Add active class
this.$searchButton.addClass('active')
this.searchOpen = true
}
/**
* Close search
* @return {[type]} [description]
*/
closeSearch() {
let searchPanelX = -window.Rozier.windowWidth * 0.8
TweenLite.to(this.$searchPanel, 0.6, { x: searchPanelX, ease: Expo.easeOut })
TweenLite.to(this.$mainContentOverlay, 0.6, {
opacity: 0,
ease: Expo.easeOut,
onComplete: () => {
this.$mainContentOverlay[0].style.display = 'none'
},
})
// Remove active class
this.$searchButton.removeClass('active')
this.searchOpen = false
}
/**
* Tree button click
* @return {[type]} [description]
*/
treeButtonClick(e) {
if (!this.treeOpen) this.openTree()
else this.closeTree()
}
/**
* Tree wrapper link click
* @return {[type]} [description]
*/
treeWrapperLinkClick(e) {
if (e.currentTarget.className.indexOf('tab-link') === -1 && this.treeOpen) {
this.closeTree()
}
}
/**
* Open tree
* @return {[type]} [description]
*/
openTree() {
// Close panel if open
this.closeMenu()
this.closeSearch()
this.closeUser()
// Translate tree panel
TweenLite.to(this.$treeWrapper, 0.6, { x: 0, ease: Expo.easeOut })
this.$mainContentOverlay[0].style.display = 'block'
TweenLite.to(this.$mainContentOverlay, 0.6, { opacity: 0.5, ease: Expo.easeOut })
// Add active class
this.$treeButton.addClass('active')
this.treeOpen = true
}
/**
* Close tree
* @return {[type]} [description]
*/
closeTree() {
let treeWrapperX = -window.Rozier.windowWidth * 0.8
TweenLite.to(this.$treeWrapper, 0.6, { x: treeWrapperX, ease: Expo.easeOut })
TweenLite.to(this.$mainContentOverlay, 0.6, {
opacity: 0,
ease: Expo.easeOut,
onComplete: () => {
this.$mainContentOverlay[0].style.display = 'none'
},
})
// Remove active class
removeClass(this.$treeButton[0], 'active')
this.treeOpen = false
}
/**
* User picture click
* @return {[type]} [description]
*/
userPictureClick(e) {
if (!this.userOpen) this.openUser()
else this.closeUser()
return false
}
/**
* User actions link click
* @return {[type]} [description]
*/
userActionsLinkClick(e) {
if (this.userOpen) {
this.closeUser()
}
}
/**
* Open user
* @return {[type]} [description]
*/
openUser() {
// Close panel if open
this.closeMenu()
this.closeSearch()
this.closeTree()
// Translate user panel
TweenLite.to(this.$userActions, 0.6, { x: 0, ease: Expo.easeOut })
if (this.$mainContentOverlay.length) {
this.$mainContentOverlay[0].style.display = 'block'
TweenLite.to(this.$mainContentOverlay, 0.6, { opacity: 0.5, ease: Expo.easeOut })
}
// Add active class
this.$userPicture.addClass('active')
this.userOpen = true
}
/**
* Close user
* @return {[type]} [description]
*/
closeUser() {
let userActionsX = window.Rozier.windowWidth * 0.8
TweenLite.to(this.$userActions, 0.6, { x: userActionsX, ease: Expo.easeOut })
TweenLite.to(this.$mainContentOverlay, 0.6, {
opacity: 0,
ease: Expo.easeOut,
onComplete: () => {
this.$mainContentOverlay[0].style.display = 'none'
},
})
// Remove active class
this.$userPicture.removeClass('active')
this.userOpen = false
}
/**
* Main content overlay click
* @return {[type]} [description]
*/
mainContentOverlayClick(e) {
this.closeMenu()
this.closeTree()
this.closeUser()
this.closeSearch()
}
/**
* Window resize callback
* @return {[type]} [description]
*/
resize() {}
}
| 37,333 |
https://uk.wikipedia.org/wiki/%D0%84%D0%B7%D0%B5%D1%80%D0%BE%20%28%D0%91%D1%80%D0%B5%D0%B7%D0%BE%D0%B2%D0%B8%D1%86%D1%8F%29 | Wikipedia | Open Web | CC-By-SA | 2,023 | Єзеро (Брезовиця) | https://uk.wikipedia.org/w/index.php?title=Єзеро (Брезовиця)&action=history | Ukrainian | Spoken | 26 | 90 | Єзеро () — поселення в общині Брезовиця, Осреднєсловенський регіон, Словенія. Висота над рівнем моря: 301 м.
Посилання
Статистичне бюро Республіки Словенія, населення, 2002
Населені пункти Словенії | 30,665 |
https://github.com/JulNadeauCA/edacious/blob/master/macro/logic_probe.c | Github Open Source | Open Source | BSD-2-Clause | 2,022 | edacious | JulNadeauCA | C | Code | 420 | 1,186 | /*
* Copyright (c) 2006-2009 Julien Nadeau ([email protected])
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
* USE OF THIS SOFTWARE EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Ideal logic probe.
*/
#include <core/core.h>
#include "macro.h"
const ES_Port esLogicProbePorts[] = {
{ 0, "" },
{ 1, "A" },
{ -1 },
};
static void
Draw(void *p, VG *vg)
{
ES_LogicProbe *r = p;
VG_Polygon *vp;
vp = VG_PolygonNew(vg->root);
if (r->state) {
VG_SetColorRGB(vp, 200,0,0);
} else {
VG_SetColorRGB(vp, 0,0,0);
}
VG_PolygonVertex(vp, VG_PointNew(vp, VGVECTOR(0.156, -0.125)));
VG_PolygonVertex(vp, VG_PointNew(vp, VGVECTOR(0.156, 0.125)));
VG_PolygonVertex(vp, VG_PointNew(vp, VGVECTOR(0.500, 0.125)));
VG_PolygonVertex(vp, VG_PointNew(vp, VGVECTOR(0.500, -0.125)));
}
static void
DC_StepEnd(void *obj, ES_SimDC *dc)
{
ES_LogicProbe *lp = obj;
M_Real v1 = ES_NodeVoltage(COMPONENT(lp)->ckt,PNODE(lp,1));
M_Real v2 = ES_NodeVoltage(COMPONENT(lp)->ckt,PNODE(lp,2));
lp->state = ((v1 - v2) >= lp->Vhigh);
}
static void
Init(void *p)
{
ES_LogicProbe *lp = p;
ES_InitPorts(lp, esLogicProbePorts);
lp->Vhigh = 5.0;
lp->state = 0;
COMPONENT(lp)->dcStepEnd = DC_StepEnd;
M_BindReal(lp, "Vhigh", &lp->Vhigh);
AG_BindInt(lp, "state", &lp->state);
}
static void *
Edit(void *p)
{
ES_LogicProbe *r = p;
AG_Box *box = AG_BoxNewVert(NULL, AG_BOX_EXPAND);
M_NumericalNewRealPNZ(box, 0, "V", _("HIGH voltage: "), &r->Vhigh);
return (box);
}
ES_ComponentClass esLogicProbeClass = {
{
"Edacious(Circuit:Component:LogicProbe)"
"@macro",
sizeof(ES_LogicProbe),
{ 0,0 },
Init,
NULL, /* reinit */
NULL, /* destroy */
NULL, /* load */
NULL, /* save */
Edit
},
N_("Logic Probe"),
"LPROBE",
"Generic|Digital|Probes",
&esIconLogicProbe,
Draw,
NULL, /* instance_menu */
NULL, /* class_menu */
NULL, /* export */
NULL /* connect */
};
| 43,697 |
https://github.com/Palash2406/gov/blob/master/app/Menu.php | Github Open Source | Open Source | MIT | null | gov | Palash2406 | PHP | Code | 39 | 153 | <?php
namespace App;
use Illuminate\Database\Eloquent\Model;
use Illuminate\Database\Eloquent\SoftDeletes;
class Menu extends Model
{
//
use SoftDeletes;
public function parent()
{
return $this->belongsTo(Menu::class, 'parent_id');
}
public function children()
{
return $this->hasMany(Menu::class, 'parent_id');
}
public function attachment()
{
return $this->hasMany('App\Attachment');
}
}
| 18,081 |
https://ur.wikipedia.org/wiki/%D8%AF%D8%A7%D8%AA%D9%88%20%D9%85%D9%88%D9%86%D8%AA%D8%A7%D9%88%D8%A7%D9%84%D8%8C%20%D9%85%D8%A7%DA%AF%D9%88%D8%A6%D9%86%D8%AF%D8%A7%D9%86%D8%A7%D8%A4 | Wikipedia | Open Web | CC-By-SA | 2,023 | داتو مونتاوال، ماگوئنداناؤ | https://ur.wikipedia.org/w/index.php?title=داتو مونتاوال، ماگوئنداناؤ&action=history | Urdu | Spoken | 56 | 201 | داتو مونتاوال، ماگوئنداناؤ فلپائن کا ایک فلپائن کی بلدیات جو ماگوئنداناؤ میں واقع ہے۔
تفصیلات
داتو مونتاوال، ماگوئنداناؤ کا رقبہ 461.10 مربع کیلومیٹر ہے اور اس کی مجموعی آبادی 31,265 افراد پر مشتمل ہے۔
مزید دیکھیے
فلپائن
فہرست فلپائن کے شہر
حوالہ جات
بلدیات ماگوئنداناؤ
صفحات مع گراف
فلپائن سانچے
Short description is different from Wikidata | 10,474 |
https://it.wikipedia.org/wiki/Alluwamna | Wikipedia | Open Web | CC-By-SA | 2,023 | Alluwamna | https://it.wikipedia.org/w/index.php?title=Alluwamna&action=history | Italian | Spoken | 119 | 231 |
Biografia e regno
Sposò Harapšili, figlia del re Telipinu e avrebbe dovuto essere il primo nell'ordine di successione sul trono ittita. Ma entrambi, figlia e genero, furono esiliati per aver appoggiato la rivolta di Šanku, un ribelle che aveva rifiutato di pagare il tributo di grano e vino.
Alla morte di Telipinu è probabile il trono sia stato occupato/usurpato dal cugino Tahurwaili per un certo periodo. L'interregno di Tahurwaili è di difficile collocazione, non si può escludere sia asceso al trono in un periodo successivo.
Il figlio di Alluwamna fu Hantili II, come attesta un documento di concessione terriera emanato a suo favore. Quando Hantili divenne successivamente re, fu il primo per successione lineare padre-figlio dopo molte generazioni.
Note | 1,834 |
https://github.com/lneisenman/netutils/blob/master/netutils/spikerecorder.py | Github Open Source | Open Source | BSD-3-Clause | null | netutils | lneisenman | Python | Code | 145 | 422 | # -*- coding: utf-8 -*-
from __future__ import (print_function, absolute_import, unicode_literals,
division)
import csv
from neuron import h
class SpikeRecorder(object):
''' class for saving network firing times
this class creates two hoc vectors (tvec and idvec) which record the
time that each neuron in the network fires.
Pass a list of the cells in the network when creating, e.g.::
recorder = SpikeRecorder(net.cell_list())
Based on Hines JNM 2008
'''
def __init__(self, cell_list):
self.tvec = h.Vector()
self.idvec = h.Vector()
for i, cell in enumerate(cell_list):
nc = cell.connect2target(None)
nc.record(self.tvec, self.idvec, i)
def print_spikes(self):
''' print firing times to the main console '''
print("\ntime\tcell#")
for t, idv in zip(self.tvec, self.idvec):
print('{:.2f}\t{:d}'.format(t, int(idv)))
def save_spikes(self, filename='output.csv'):
''' save firing times to an excel csv file
..parameter: filename - text
'''
with open(filename, 'w') as datafile:
writer = csv.writer(datafile, dialect='excel')
writer.writerow(['time', 'cell id'])
for t, idv in zip(self.tvec, self.idvec):
writer.writerow([t, int(idv)])
| 46,456 |
https://github.com/developers-payu-latam/payu-latam-net-payments-sdk/blob/master/PayuNetSdk/PayU/Model/Subscriptions/Subscription.cs | Github Open Source | Open Source | MIT | 2,019 | payu-latam-net-payments-sdk | developers-payu-latam | C# | Code | 333 | 911 | // <copyright file="Subscription.cs" company="PayU Latam">
// PayU Latam. All rights reserved.
// </copyright>
// <author>Jorge D. Porras</author>
namespace PayuNetSdk.PayU.Model.Subscriptions
{
using System.Xml.Serialization;
using System.Collections.Generic;
using PayuNetSdk.PayU.Util.DataStructures;
using PayuNetSdk.PayU.Model.Customers;
using System;
using PayuNetSdk.PayU.Model.Plans;
using PayuNetSdk.PayU.Validators.Base;
[XmlType("subscription")]
public class Subscription : IValidatable<Subscription>
{
/// <summary>
/// Gets or sets the identifier of the order.
/// </summary>
/// <value>
/// The identifier of the order.
/// </value>
[XmlElement("id")]
public string Id { get; set; }
/// <summary>
/// Gets or sets the subscription plan.
/// </summary>
/// <value>
/// The subscription plan.
/// </value>
[XmlElement("plan")]
public SubscriptionPlan Plan { get; set; }
/// <summary>
/// The customer
/// </summary>
[XmlElement("customer")]
public Customer Customer { get; set; }
/// <summary>
/// Gets or sets the number of trial days
/// </summary>
/// <value>
/// The number of trial days
/// </value>
[XmlElement("trialDays")]
public int? TrialDays { get; set; }
public bool ShouldSerializeTrialDays() { return TrialDays.HasValue; }
/// <summary>
/// Gets or sets the quantity.
/// </summary>
/// <value>
/// The quantity.
/// </value>
[XmlElement("quantity")]
public int? Quantity { get; set; }
public bool ShouldSerializeQuantity() { return Quantity.HasValue; }
/// <summary>
/// Gets or sets the installments.
/// </summary>
/// <value>
/// The installments.
/// </value>
[XmlElement("installments")]
public int? Installments { get; set; }
public bool ShouldSerializeInstallments() { return Installments.HasValue; }
/// <summary>
/// Gets or sets the current period start.
/// </summary>
/// <value>
/// The current period start.
/// </value>
[XmlElement("currentPeriodStart")]
public DateTime? CurrentPeriodStart { get; set; }
public bool ShouldSerializeCurrentPeriodStart() { return CurrentPeriodStart.HasValue; }
/// <summary>
/// Gets or sets the current period end.
/// </summary>
/// <value>
/// The current period end.
/// </value>
[XmlElement("currentPeriodEnd")]
public DateTime? CurrentPeriodEnd { get; set; }
public bool ShouldSerializeCurrentPeriodEnd() { return CurrentPeriodEnd.HasValue; }
/// <summary>
/// Gets or sets the credit card token.
/// </summary>
/// <value>
/// The credit card token.
/// </value>
[XmlElement("creditCardToken")]
public string CreditCardToken { get; set; }
public bool Validate(IValidator<Subscription> validator, out IEnumerable<string> brokenRules)
{
brokenRules = validator.BrokenRules(this);
return validator.IsValid(this);
}
}
}
| 50,974 |
https://github.com/gorco/gf/blob/master/app/public/js/controllers/analysis.js | Github Open Source | Open Source | Apache-2.0 | 2,020 | gf | gorco | JavaScript | Code | 404 | 1,048 | /*
* Copyright 2016 e-UCM (http://www.e-ucm.es/)
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* This project has received funding from the European Union’s Horizon
* 2020 research and innovation programme under grant agreement No 644187.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0 (link is external)
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
angular.module('analysisApp', ['ngStorage', 'services'])
.controller('AnalysisCtrl', ['$scope', '$attrs', '$http', 'Games', 'Versions', 'Analysis', 'Role', 'CONSTANTS',
function ($scope, $attrs, $http, Games, Versions, Analysis, Role, CONSTANTS) {
var gameId, versionId;
var load = function(gameId, versionId) {
var afterLoad = function() {
if ($scope.game && $scope.version) {
updateAnalysis();
}
};
Games.get({gameId: gameId}).$promise.then(function(game) {
$scope.game = game;
afterLoad();
});
Versions.get({gameId: gameId, versionId: versionId}).$promise.then(function(version) {
$scope.version = version;
afterLoad();
});
};
$attrs.$observe('gameid', function() {
gameId = $attrs.gameid;
if (gameId && versionId) {
load(gameId, versionId);
}
});
$attrs.$observe('versionid', function() {
versionId = $attrs.versionid;
if (gameId && versionId) {
load(gameId, versionId);
}
});
$scope.init = function(game, version) {
};
$scope.analysisFile = undefined;
// Analysis file management
$scope.submit = function () {
if ($scope.analysisFile) {
if ($scope.analysis && $scope.version._id === $scope.analysis._id) {
$scope.deleteAnalysis();
} else {
$scope.upload($scope.analysisFile);
}
}
};
$scope.deleteAnalysis = function () {
Analysis.delete({versionId: $scope.version._id}, function () {
$scope.analysis = undefined;
$scope.upload($scope.file);
});
};
// Upload on file select or drop
$scope.upload = function (file) {
var formData = new FormData();
$scope.loadingAnalysis = true;
formData.append('analysis', file);
$http.post(CONSTANTS.PROXY + '/analysis/' + $scope.version._id, formData, {
transformRequest: angular.identity,
headers: {
'Content-Type': undefined,
enctype: 'multipart/form-data'
}
}).then(function successCallback(response) {
// This callback will be called asynchronously
// when the response is available
// Check if the version has an analysis uploaded
updateAnalysis();
$scope.loadingAnalysis = false;
}, function errorCallback(response) {
// Called asynchronously if an error occurs
// or server returns response with an error status.
console.error('Error on post /analysis/' + $scope.version._id + ' ' +
JSON.stringify(response, null, ' '));
// Check if the version has an analysis uploaded
updateAnalysis();
$scope.loadingAnalysis = false;
});
};
var updateAnalysis = function () {
if ($scope.version && Role.isDeveloper()) {
$scope.analysis = Analysis.get({versionId: $scope.version._id});
}
};
}
]);
| 36,567 |
2013/92013E012695/92013E012695_EN.txt_5 | Eurlex | Open Government | CC-By | 2,013 | None | None | English | Spoken | 7,436 | 11,466 | (English version)
Question for written answer E-012506/13
to the Commission
Mara Bizzotto (EFD)
(5 November 2013)
Subject: Allocation of digital terrestrial frequencies in Veneto/north-east Italy and objections by local broadcasting stations
Further to my written question on the ‘allocation of digital terrestrial frequencies in Veneto/north-east Italy and objections by local broadcasting stations’ (P‐5589/2010), can the Commission say:
What view it takes of the decisions made by the Italian authorities when allocating radio frequencies?
Does it think that decisions by those authorities not to allocate frequencies of proven quality and serviceability to local broadcasters are consistent with EC law?
Does it think that the criteria used to allocate the digital frequencies are fully consistent with the requirements laid down in Directives 2002/20/EC, 2002/21/EC and 2002/77/EC?
Answer given by Ms Kroes on behalf of the Commission
(6 January 2014)
Italy, as all EU Member States, is a signatory to the ITU Geneva-06 agreement, a binding inter-governmental treaty which aims at a fair distribution of digital transmitter channels between neighbouring ITU Member States. The Commission understands that Italian transmitters have earlier used TV channels that were allotted by that treaty to neighbouring countries, creating interference with the transmitters operating in those countries.
The Radio Spectrum Policy Group, composed of EU High-Level Member States representatives has as a work strand to provide good offices to resolve situations as described above. The Commission supports these efforts and appreciates the willingness of all involved parties to acheive a fruitful outcome. It would, however, seem inevitable that the total number of transmitting channels available for use in Italy would decrease in comparison with the situation a few years ago as a consequence, or at least have to operate at power levels that do not create cross-border interference. The introduction, by Italy, of Single Frequency Networks should at least partly alleviate this effect.
In this complex and still evolving situation, any alleged infringement regarding the compatibility of the AGCOMDecisions with national law that allocates a predefined share of the available frequencies to local broadcasters would have to be referred to the competent national authorities, including the national courts. The Commission in parallel continues to monitor the compliance of national radio spectrum allocations and assignment with EU rules.
(Versione italiana)
Interrogazione con richiesta di risposta scritta E-012507/13
alla Commissione
Mara Bizzotto (EFD)
(5 novembre 2013)
Oggetto: Aggiornamento sull'utilizzo del Fondo sociale europeo a favore di rom e sinti
Con riferimento alla mia interrogazione E-002940/2010, è la Commissione in grado di fornire dati aggiornati sui progetti — quantità, contenuto e ammontare complessivo — che l'Unione europea ha sostenuto nell'ambito del Fondo sociale europeo (FSE), dal 2010 a oggi, per sovvenzionare l'inclusione sociale delle comunità rom e sinti in Europa?
Risposta di László Andor a nome della Commissione
(7 gennaio 2014)
Nessuna categoria specifica del sostegno del Fondo sociale europeo (FSE) è destinata ai Rom. Per tale motivo gli Stati membri non presentano relazioni sui finanziamenti dell'FSE a favore dei Rom ed alcuni vietano addirittura la registrazione dell'origine etnica delle persone. Una cifra approssimativa potrebbe essere estrapolata dalle relazioni degli Stati membri relative alla più ampia priorità Percorsi d'integrazione e reinserimento nel mondo del lavoro per le persone con difficoltà; lotta alla discriminazione e nell'accesso al mercato del lavoro e nell'avanzamento nello stesso e promozione dell'accettazione della diversità sul posto di lavoro, che comprende la maggior parte dei programmi di inclusione dei Rom, ma non ad esclusione di altri gruppi. A tutto il 2012 erano stati impegnati per tale priorità 7,8 miliardi di euro. Inoltre, il finanziamento di misure destinate alle persone svantaggiate in generale, di cui i Rom fanno parte, andrebbe a sua volta preso in conto anche se i beneficiari comprendono anche i non Rom.
(English version)
Question for written answer E-012507/13
to the Commission
Mara Bizzotto (EFD)
(5 November 2013)
Subject: Update on the use of the European Social Fund for the Roma and Sinti
With reference to my Written Question E-2940/2010, can the Commission provide new updates on the projects (quantity, content and total amount of expenditure) that the European Union has supported under the European Social Fund (ESF) from 2010 to the present day, to subsidise the social inclusion of the Roma and Sinti communities in Europe?
Answer given by Mr Andor on behalf of the Commission
(7 January 2014)
No specific category of European Social Fund (ESF) support is earmarked for Roma people. Therefore Member States do not report on ESF funding for Roma and some Member States even prohibit the registration of people’s ethnic origin. An approximate figure could be deduced from Member State reports on the broader priority ‘Pathways to integration and re-entry into employment for disadvantaged people; combating discrimination in accessing and progressing in the labour market and promoting acceptance of diversity at the workplace’, which includes most Roma inclusion programmes, but not to the exclusion of others. Up to the end of 2012, EUR 7.8 billion was committed to that priority. In addition, the funding of measures benefiting disadvantaged people in general, of whom Roma are one target group, should be taken into account, though the beneficiaries include non-Roma, too.
(Deutsche Fassung)
Anfrage zur schriftlichen Beantwortung E-012509/13
an die Kommission
Martin Häusling (Verts/ALE)
(5. November 2013)
Betrifft: Exportkreditgarantien für in der EU verbotene Tierhaltungssysteme
Die deutsche Bundesregierung (86) (BR)gab an, dass 2009-2012 staatlich gedeckte Exportkreditgarantien in Höhe von 40,86 Mio. EUR für den Anlagenbau zur Käfighaltung von Hühnern (Legehennen und Masthühner) vergeben wurden. Diese Anlagen wurden in der Türkei, der Ukraine, Russland, Kasachstan und Usbekistan errichtet
Zwei dieser Projekte dienten der Kapazitätserweiterung von Avangardco, des nach Eigenangaben größten Eierproduzenten Europas, durch den Bau von zwei Legehennenfabriken für 3 bzw. 5 Mio. Tiere in der Ukraine. Die Frage, ob die Haltungen EU-Recht entsprechen, verneinte die Bundesregierung (87). Avangardco erwartete, ab 2013 Eier und Eiprodukte in die EU zu exportieren.
Die Bundesregierung argumentiert u. a. mit der „Wettbewerbsgleichheit unter den Exporteuren“, da „der Projektdurchführer anderenfalls auf Lieferungen aus einem anderen Land zurückgreifen“ könne.
1.
Können Eier oder Eiprodukte aus Anlagen in der Ukraine, der Türkei oder anderen Drittstaaten auf den EU-Markt gelangen, auch wenn die Haltung der betreffenden Hühner nicht den EU-Normen (88) entspricht?
2.
Wird die Kommission eine gemeinsame Position der Mitgliedstaaten der EU initiieren und vorantreiben mit dem Ziel, dass die Exportkreditagenturen der Mitgliedstaaten die Errichtung von Anlagen zur Tierhaltung nur noch dann mit Exportkreditgarantien unterstützen, wenn die Anlagen mindestens die in der EU geltenden Bestimmungen für die Tierhaltung erfüllen? Wird die Kommission dasselbe Ziel auch innerhalb der einschlägigen OECD-Gremien aktiv verfolgen? Wenn nein, warum nicht?
3.
Die „Gemeinsamen Ansätze“ (Common Approaches) der OECD beziehen sich u. a. auf die EHS-Leitlinien der Weltbankgruppe. Wird sich die Kommission im Zuge der für 2014 vorgesehenen Überarbeitung dieser Leitlinien aktiv für die Aufnahme von verbindlichen Mindeststandards für die landwirtschaftliche Tierhaltung einsetzen, die den EU-Standards gleichwertig sind?
Antwort von Tonio Borg im Namen der Kommission
(7. Januar 2014)
Die Einhaltung der EU-rechtlichen Tierschutzstandards kann von Drittländern nicht direkt verlangt werden. Bisher gibt es nur wenige Ausnahmen, wie die Standards zum Schutz der Tiere bei der Schlachtung, die auf internationalen Leitlinien der Weltorganisation für Tiergesundheit beruhen. Seit Januar dieses Jahres darf nur Fleisch in die EU importiert werden, das von gemäß den Anforderungen der Verordnung (EG) Nr. 1099/2009 (89) geschlachteten Tieren stammt. Wenn die Importbedingungen für ein bestimmtes Erzeugnis tierischen Ursprungs eingehalten werden, darf dieses Erzeugnis in die EU eingeführt werden. Die Kommission setzt sich bei Handelspartnern und multilateralen Organisationen fortlaufend für die Einhaltung von Tierschutzstandards ein.
Für nationale Finanzierungsvorhaben sind allein die Mitgliedstaaten verantwortlich.
Die Weltbankgruppe wird von ihren Mitgliedern geleitet, deren Finanzminister im Gouverneursrat vertreten sind. Die Kommission kann keine verbindlichen Mindestnormen vorschlagen. Die Lage ist ähnlich wie bei der OECD, d. h. die EU hat keine Möglichkeit, diese Organisationen zur Einhaltung von EU-Recht zu zwingen.
Zum Thema Finanzierung von Nutztierhaltungsbetrieben in Drittländern verweist die Kommission den Herrn Abgeordneten ferner auf ihre Antworten auf die schriftlichen Anfragen E-7102/2013, E‐7559/2013 und E‐7200/2013 (90).
(English version)
Question for written answer E-012509/13
to the Commission
Martin Häusling (Verts/ALE)
(5 November 2013)
Subject: Export credit guarantees for animal housing systems prohibited in the EU
The German Government (91) has stated that, between 2009 and 2012, export credit guarantees underwritten by the state amounting to EUR 40.86 million were issued for the construction of cage systems to house chickens (laying hens and broilers). These systems were erected in Turkey, Ukraine, Russia, Kazakhstan and Uzbekistan.
Two of these projects served to expand the capacity of Avangardco, which claims to be the largest egg producer in Europe, through the construction of two egg production factories for three and five million animals, respectively, in Ukraine. In response to the question of whether the housing complied with EC law, the German Government stated that it did not (92). Avangardco expected to export eggs and egg products to the EU from 2013 onwards.
The German Government’s reasoning related, among other things, to fair competition among exporters, as the party implementing the project could otherwise resort to obtaining supplies from another country.
1.
Is it possible for eggs or egg products from systems in Ukraine, Turkey or other third countries to end up on the EU market even if the chickens in question have not been housed in accordance with EU standards (93)?
2.
Will the Commission initiate and promote a common position for the EU Member States, seeking to ensure that the export credit agencies of the Member States only support the construction of animal housing systems with export credit guarantees if the systems, as a minimum, comply with the animal housing provisions in force in the EU? Will it actively pursue this same aim within the relevant OECD bodies, too? If not, why not?
3.
One of the things to which the OECD common approaches relate is the ETS guidelines of the World Bank Group. During the review of these guidelines scheduled for 2014, will the Commission actively support the inclusion of binding minimum standards for farm animal husbandry that are equivalent to EU standards?
Answer given by Mr Borg on behalf of the Commission
(7 January 2014)
The standards for animal welfare provided in the EU legislation cannot be directly demanded of third countries. A few exceptions exist at present such as welfare standards at slaughter that are based on the international guidelines adopted by the World Organisation for Animal Health. Since January this year, the meat imported into the EU must derive from animals killed in accordance with the requirements of Regulation (EC) 1009/2009 (94). As long as the import conditions for a specific product of animal origin are certified, such products may be imported to the EU. The Commission constantly promotes the acceptance of animal welfare standards with its trading partners and in multilateral organisations.
National funding remains the competence of the Member States.
The World Bank Group is governed by its Member Countries and it is their Ministers of Finance who are representatives of the Board of Governors. It is not within the competence of the Commission to propose binding minimum standards. The situation is similar with regard to the OECD, i.e. the EU is not in a position to impose Union law on these organisations.
On other issues related to funding of farm animal holdings in third countries the Commission would refer the Honourable Member to its answers to written questions E-7102/2013, E‐7559/2013 and E‐7200/2013 (95).
(Versione italiana)
Interrogazione con richiesta di risposta scritta E-012514/13
alla Commissione
Mario Borghezio (NI)
(5 novembre 2013)
Oggetto: Raggiri fiscali delle multinazionali USA
Da fonti di stampa, si apprende che dal gennaio 2015 in Irlanda entreranno in vigore norme fiscali restrittive che non eviteranno ad importanti multinazionali americane di non dichiarare alcun paese come domicilio fiscale e far rientrare così l'Irlanda nella lista dei cosiddetti paradisi fiscali.
Sembra inoltre che diverse multinazionali statunitensi con sede in Irlanda, sfruttando una triangolazione con una propria sussidiaria nei Paesi Bassi, versino le tasse in un paradiso fiscale dove l'aliquota per le aziende è pari a zero.
È la Commissione europea a conoscenza di questi raggiri fiscali da parte di multinazionali americane sul territorio europeo e come intende reagire?
È la Commissione europea a conoscenza di altri paesi coinvolti in queste «triangolazioni» per poter evadere il fisco?
Risposta di Algirdas Šemeta a nome della Commissione
(3 gennaio 2014)
La Commissione è a conoscenza del problema dell'elusione fiscale da parte delle multinazionali, che assume una molteplicità di forme. La questione è una priorità dell'UE e negli ultimi dodici mesi la Commissione ha avviato una serie di iniziative per porvi rimedio. Nel dicembre 2012 ha adottato il piano d'azione per rafforzare la lotta alla frode fiscale e all'evasione fiscale e le due raccomandazioni di accompagnamento sulla pianificazione fiscale aggressiva e sui paradisi fiscali (96). Nell'aprile 2013 ha istituito la piattaforma sulla buona governance fiscale (C(2013)2236) per assicurare il seguito attuativo di queste raccomandazioni. Il mese scorso ha istituito il gruppo di esperti sulla tassazione dell'economia digitale (97) che si occuperà, tra l'altro, di questioni specifiche riguardanti la pianificazione fiscale aggressiva nell'economia digitale. Il 25 novembre 2013, infine, la Commissione ha presentato una proposta di rafforzamento della direttiva sulle società madri e figlie per evitare che le sue norme siano aggirate al fine di eludere le imposte sulle società (98). L'elusione fiscale da parte delle società occupa un posto prominente anche nell'agenda politica mondiale, come dimostra il progetto del G20/OCSE sull'erosione della base imponibile e sul trasferimento degli utili varato nel settembre 2013 al Vertice del G20 di San Pietroburgo. L'UE sostiene con forza il progetto e tanto la Commissione quanto gli Stati membri partecipano attivamente al suo sviluppo e alle sue realizzazioni.
La soluzione non può essere puntare il dito verso alcuni paesi e risolvere il problema al loro interno, perché le imprese non incontrerebbero difficoltà a reperire alternative. La sfida si pone a livello sia mondiale sia di UE; per vincerla occorrono norme fiscali internazionali più vincolanti combinate con un approccio coordinato nell'UE che sfoci in una rigorosa normativa europea comune.
(English version)
Question for written answer E-012514/13
to the Commission
Mario Borghezio (NI)
(5 November 2013)
Subject: Tax dodging by US multinationals
According to press reports, in January 2015 the Republic of Ireland will roll out new, more restrictive tax rules preventing large American firms from declaring themselves ‘stateless’ for tax purposes — an arrangement that had led to Ireland being labelled a ‘tax haven’.
What is more, it appears that a number of US multinationals based in the Republic of Ireland with subsidiaries in the Netherlands have been taking advantage of triangulation arrangements to ‘pay taxes’ in tax havens with zero corporate rates.
Is the Commission aware that US multinationals have been engaging in tax dodging in Europe? How does it intend to respond?
Does it know which other countries are involved in triangulation arrangements used to avoid tax?
Answer given by Mr Šemeta on behalf of the Commission
(3 January 2014)
The Commission is aware of the issue of international corporate tax avoidance, which takes a multitude of forms. It is a high priority in the EU and the Commission in the past year has launched a series of initiatives to address it. In December 2012, the Commission agreed an Action Plan to strengthen the fight against tax fraud and tax evasion and two accompanying Recommendations on aggressive tax planning and tax havens (99). In April 2013 the Commission established a Platform for Tax Good Governance, C(2013)2236, to follow-up on the implementation of these recommendations. Last month, the Expert Group on Taxation of the Digital Economy was established (100) which will, amongst other matters, address specific issues relating to aggressive tax planning in the digital economy. On 25 November 2013 the Commission came forward with its proposal to strengthen the Parent-Subsidiary Directive to prevent the directive being misused for corporate tax avoidance (101). Corporate tax avoidance is also high on the political agenda globally as indicated by the G20/OECD project on Base Erosion and Profit Shifting established at the G20 Summit in St-Petersburg in September 2013. The EU strongly supports the project and both the Commission and Member States are actively involved in its development and delivery.
The problem cannot be solved by singling out and addressing individual countries. Businesses will easily find alternatives. It is both a global and an EU challenge, which requires stronger international tax standards combined with a coordinated approach in the EU aimed at strict common domestic rules.
(Versione italiana)
Interrogazione con richiesta di risposta scritta E-012515/13
alla Commissione
Claudio Morganti (EFD)
(5 novembre 2013)
Oggetto: Costi di fabbricazione dell'euro
Negli ultimi giorni, in Italia, diversi organi di stampa hanno riportato notizie circa il costo del conio delle monete.
Dai dati risulterebbe che per la fabbricazione di una moneta da un centesimo se ne spendono oltre quattro, mentre il costo unitario per la moneta di due centesimi ammonterebbe a oltre cinque, ovvero più del doppio rispetto al valore della stessa.
Può la Commissione europea verificare e comunicare il reale costo di fabbricazione delle monete da 1, 2 e 5 centesimi in Italia e negli altri paesi dell'area dell'euro?
Risposta di Olli Rehn a nome della Commissione
(13 dicembre 2013)
Nella comunicazione «Questioni relative al proseguimento dell’emissione delle monete in euro da 1 e 2 cent» (COM(2013) 281final), del 14 maggio 2013, la Commissione ha constatato che i costi di produzione e di emissione di tali monete sono in generale elevati. La maggior parte degli Stati membri sostiene costi di acquisizione superiori fino a quattro volte al valore facciale delle monete stesse. Sulla base delle indicazioni fornite da cinque Stati membri, il prezzo di acquisizione medio non ponderato di queste monete per il rispettivo Tesoro rappresenta circa il 150 % del valore facciale. La Commissione non dispone di indicazioni circa il prezzo di acquisizione delle monete da 5 cent. Sui prezzi di acquisizione in Italia s’invita l’Onorevole deputato a rivolgersi alle autorità italiane.
(English version)
Question for written answer E-012515/13
to the Commission
Claudio Morganti (EFD)
(5 November 2013)
Subject: Euro coin minting costs
Various Italian media outlets have recently carried reports on the cost of minting euro coins.
Those reports indicate that it costs more than four cents to mint a one-cent coin and more than five cents to mint a two-cent coin — i.e. well over twice the coins’ nominal value.
Would the Commission find out how much it costs to mint one-, two‐ and five-cent coins in Italy and the other eurozone Member States, and then pass on that information?
Answer given by Mr Rehn on behalf of the Commission
(13 December 2013)
In its communication of 14 May 2013 (COM(2013) 281 final) on issues related to the continued issuance of the 1 and 2 euro cent coins, the Commission came to the conclusion that the costs of production and issuance of 1 and 2 euro cent coins are generally high. Most Member States are confronted with acquisition costs exceeding up to four times the face value of these denominations. Based on the indications provided by 5 Member States, the non-weighted average acquisition price of these coins for the respective Treasuries represents around 150% of their face value. The Commission has no indications on the acquistion price of 5 euro cent coins. For the acquisition prices in Italy, the Honourable Member may ask the Italian authorities.
(English version)
Question for written answer E-012517/13
to the Commission
Derek Vaughan (S&D)
(5 November 2013)
Subject: UK slate tax exemption
The slate industry in Wales employs 200 people in its four operations, with approximately a further 100 personnel employed in sectors which rely directly on the slate industry.
Starting on 1 April 2002, the UK authorities introduced a levy on aggregates which applied to rock, sand and gravel on its first extraction, when used for the manufacture of products containing a proportion of aggregate. Slate was excluded from this levy.
However, on 1 August 2013 the UK Government received a notification from the Commission stating that it had decided to open a formal investigation in relation to certain exemptions, exclusions and tax reliefs from the aggregates levy.
1.
Could the Commission please give an expected timeline of when the UK slate industry will be informed of a decision regarding its exemption status, and a start date of when this decision will be implemented?
2.
Should the exemption of slate be lifted, could the Commission please clarify whether the levy would be paid retrospectively, with a starting point of tax to be paid from 1 April 2002?
Answer given by Mr Almunia on behalf of the Commission
(10 January 2014)
Further to the judgment of the General Court of 7 March 2012 (T-210/02 RENV), the Commission had to reassess the levy on aggregates and the exemptions. Since the Commission could not exclude that some of the exemptions, including that for slate, constituted aid on the basis of the information available, and as their compatibility with state aid rules had not yet been demonstrated, the Commission had to open a formal investigation procedure to examine them more in detail. This decision was published in OJ C 348/162of 28/11/13 and is also available at:
http://ec.europa.eu/competition/state_aid/cases/249594/249594_1474636_30_2.pdf.
The formal investigation procedure gives the slate industry the possibility to comment on the opening decision and to provide any information it deems liable to demonstrate that the exemption for slate does not constitute aid or is compatible aid. Opening the formal investigation procedure does not prejudge the outcome of the investigation. At the end of the investigation, the Commission can conclude that the exemption does not constitute aid, is compatible aid or is not compatible with state aid rules. A date for the outcome of the formal investigation is not yet known, but in general the Commission strives to conclude formal investigations within 18 months after opening.
If at the end of the investigation the Commission has to conclude that the exemption for slate constitutes aid and is incompatible with the internal market, the aid has to be re-paid as from the date it was granted, provided this recovery is not contrary to a common principle of European law.
(Versão portuguesa)
Pergunta com pedido de resposta escrita P-012519/13
à Comissão
Nuno Teixeira (PPE)
(5 de novembro de 2013)
Assunto: Relatório do Eurostat no âmbito do procedimento por défice excessivo
Considerando que:
—
A edição do dia 4 de novembro do Diário Económico noticia que «o Eurostat quer receber uma lista das sanções potenciais para a Região Autónoma da Madeira, por suspeita de ter escondido dívida de forma deliberada», para além de solicitar ser informado de quaisquer desenvolvimentos no âmbito de uma investigação a cargo do Ministério Público;
—
A citada notícia reproduz alegados trechos do relatório final, datado de 10 de outubro, sobre as reuniões ocorridas em Lisboa em novembro passado, nomeadamente que «o Eurostat espera que o INE o informe sobre os progressos feitos na investigação ao caso, em particular, sobre as descobertas da investigação e as sanções que tenham sido aplicadas, ou que possam estar a ser consideradas»;
—
O relatório menciona ainda que «as autoridades portuguesas vão reenviar uma cópia do documento sobre as sanções possíveis para a Madeira, preparadas pelo Conselho Nacional de Estatística», mas que, contudo, «ainda não foram, até à data, recebidas quaisquer informações», estando assim por cumprir a exigência do envio da lista sobre as potenciais sanções a aplicar à Madeira;
Pergunta-se à Comissão:
Tem conhecimento da existência do citado relatório final, datado de 10 de outubro, a que se reporta a notícia em causa?
Existindo tal relatório, encontra-se o mesmo disponível ao público em geral? Em caso afirmativo, onde, quando e de que forma foi o mesmo divulgado?
Não sendo público o relatório em causa, como se justifica que um órgão de comunicação social tenha tido acesso ao seu conteúdo?
Partindo do pressuposto que o teor do relatório citado pela notícia é correto e fidedigno, como é que ele se coaduna com o princípio da separação de poderes e com a independência do Ministério Público em Portugal, nomeadamente na parte em que o Eurostat solicita informação sobre as sanções que possam estar a ser consideradas no âmbito de um inquérito que se encontra em curso, e como tal, sujeito a segredo de justiça?
A que tipo de sanções se refere o Eurostat? Às sanções que possam eventualmente decorrer do citado inquérito, ou a outras?
Resposta dada por Algirdas Šemeta em nome da Comissão
(2 de dezembro de 2013)
1.
A Comissão tem conhecimento do relatório a que o Senhor Deputado se refere.
2.-3. Esse relatório, com data de 10 de outubro de 2013 e disponível ao público desde 24 de outubro de 2013 (102), apresenta as conclusões finais da visita de diálogo normal no âmbito do procedimento relativo aos défices excessivos (PDE) realizada pelo Eurostat em Portugal, em 22 e 23 de novembro de 2012.
4.
Convém recordar que a existência de indicações sérias da existência de factos suscetíveis de constituir uma comunicação incorreta de dados relativos à dívida e ao défice, quer intencionalmente, quer por negligência grave, pode dar azo ao início de uma investigação pela Comissão, nos termos do Regulamento (UE) n.° 1173/2011 e da Decisão Delegada 2012/678/UE da Comissão. Se for detetada a existência de tais declarações incorretas, a Comissão pode recomendar ao Conselho que imponha uma sanção pecuniária ao Estado‐Membro em causa. Essas sanções, contudo, só podem ser aplicadas às declarações incorretas ocorridas após a entrada em vigor do regulamento, em 13 de dezembro de 2011.
Durante a referida visita, as autoridades estatísticas portuguesas informaram o Eurostat do seguimento dado ao anterior caso de comunicação incorreta de estatísticas da Região Autónoma da Madeira (discutido numa visita do Eurostat a Portugal, em 2011), incluindo a investigação iniciada a nível do Ministério Público, as conversações mantidas no Conselho Estatístico e a legislação nacional no domínio estatístico, em que se preveem sanções.
5.
As sanções referidas no relatório são as previstas pela legislação nacional no domínio estatístico e não pela legislação da União.
(English version)
Question for written answer P-012519/13
to the Commission
Nuno Teixeira (PPE)
(5 November 2013)
Subject: Eurostat report relating to the excessive deficit procedure
On 4 November 2013, the news site Diário Económico reported that ‘Eurostat wants a list of penalties which could be imposed on the Autonomous Region of Madeira, which is suspected of having deliberately hidden its debt’, and has also asked to be kept informed of any developments linked to an investigation being carried out by the Ministry of Justice.
The article reproduces what it claims are parts of the final report, dated 10 October 2013, on the meetings held in Lisbon in November 2012, and reports that ‘Eurostat is awaiting information from the National Statistics Institute (INE) on progress made in investigating the case, particularly the results of the inquiry and penalties which have been applied or may be under consideration’.
The report is also quoted as stating that the Portuguese authorities are to forward to Eurostat a copy of the document detailing possible penalties against Madeira drawn up by the National Statistics Council, but that no such information has as yet been received and that this requirement has therefore not yet been complied with.
1.
Is the Commission aware of the existence of the abovementioned final report, dated 10 October 2013, on which this news item is based?
2.
If such a report exists, is it available to the general public? If so, when and how was it published?
3.
If this report is not publicly available, how is it possible that a media organisation has been able to access it?
4.
Assuming that the content of the report, as quoted by the news site, is correct and reliable, how does this tally with the principle of separation of powers and the independence of the Portuguese Ministry of Justice, particularly with respect to Eurostat’s request for information about penalties under consideration as part of an inquiry which is still underway and therefore sub judice?
5.
What type of penalties is Eurostat referring to? Are these penalties which may arise from the abovementioned investigation, or of some other type?
Answer given by Mr Šemeta on behalf of the Commission
(2 December 2013)
1.
The Commission is aware of the report referred to by the Honourable Member.
2-3. This report, dated 10 October 2013 and available to the general public since 24 October 2013 (103), presents the final findings of the excessive deficit procedure (EDP) standard dialogue visit carried out by Eurostat to Portugal on 22-23 November 2012.
4.
It is worth recalling that serious indications of the existence of facts liable to constitute a misreporting of deficit and debt data, either by intent or by serious negligence, may lead to an investigation launched by the Commission in accordance with Regulation (EU) No 1173/2011 and Commission Delegated Decision 2012/678/EU. If the existence of such misrepresentation is established, the Commission may recommend to the Council imposing a fine upon the Member State concerned. Such sanctions can however only be applied to misrepresentations which have taken place after the entry into force of the regulation on 13 December 2011.
During the abovementioned visit, the Portuguese statistical authorities informed Eurostat on the follow-up of the previous statistical misreporting case in the Autonomous Region of Madeira (discussed in a visit by Eurostat to Portugal in 2011), including the investigation launched at national level by the Public Prosecutor, the discussions held in the Statistical Council and the national statistical law, where sanctions are foreseen.
5.
The sanctions referred to in the report are those foreseen by the national statistical law and not sanctions under Union legislation.
(Versão portuguesa)
Pergunta com pedido de resposta escrita E-012520/13
à Comissão
Nuno Teixeira (PPE)
(5 de novembro de 2013)
Assunto: Relatório do Eurostat no âmbito do procedimento por défice excessivo
Considerando que:
—
A edição do dia 4 de novembro do Diário Económico noticia que «o Eurostat quer receber uma lista das sanções potenciais para a Região Autónoma da Madeira, por suspeita de ter escondido dívida de forma deliberada», para além de solicitar ser informado de quaisquer desenvolvimentos no âmbito de uma investigação a cargo do Ministério Público;
—
A citada notícia reproduz um alegado relatório concluído no verão do ano passado sobre a visita de setembro de 2011, onde, de acordo com o respetivo teor, o Eurostat teria frisado que queria sanções «severas» para a Madeira;
—
A notícia cita um alegado trecho do relatório onde se afirma que «o Eurostat tem em conta que este é um caso de má transmissão deliberada de uma entidade das administrações públicas (portuguesas)» e que, no relatório elaborado pela equipa de peritos que visitou Lisboa, constava que este erro «é sério e deve ser severamente sancionado».
Pergunta-se à Comissão:
Tem conhecimento da existência do citado relatório, concluído no verão do ano passado, a que se reporta a notícia em causa?
Existindo tal relatório, encontra-se o mesmo disponível ao público em geral? Em caso afirmativo, onde, quando e de que forma foi o mesmo divulgado?
Não sendo público o relatório em causa, como se justifica que um órgão de comunicação social tenha tido acesso ao seu conteúdo?
Qual a composição da equipa de peritos que se deslocou a Portugal para o efeito?
Quais são os objetivos que foram fixados às equipas de peritos que se deslocaram a Portugal no âmbito do procedimento de défices excessivos e como se delimitam as respetivas competências?
Quantas visitas de peritos a Portugal já foram efetuadas neste âmbito e quantos relatórios foram produzidos?
Foram tais relatórios notificados às autoridades estatísticas de Portugal? Em caso afirmativo, como e quando?
Não tendo tais relatórios sido publicamente divulgados, estão os mesmos sujeitos a algum tipo de classificação? Pode a Comissão disponibilizar cópias integrais dos mesmos?
Resposta dada por Algirdas Šemeta em nome da Comissão
(16 de dezembro de 2013)
1.-2.-3. O relatório mencionado pelo Senhor Deputado apresenta as conclusões finais da visita de diálogo normal no âmbito do procedimento relativo aos défices excessivos (PDE) a Portugal, realizada em 22-23 de novembro de 2012, publicadas no sítio web do Eurostat em 24 de outubro de 2013 (104).
4.-5. A composição da equipa de peritos consta do relatório publicado. A visita faz parte das visitas regulares do Eurostat aos Estados-Membros, em conformidade com o Regulamento (CE) n.° 479/2009 do Conselho.
6.
No sítio web do Eurostat encontram-se disponíveis todas as datas e os relatórios das visitas a Portugal.
7.-8. Todos os relatórios foram enviados às autoridades estatísticas portuguesas para observações antes da publicação no sítio web do Eurostat.
(English version)
Question for written answer E-012520/13
to the Commission
Nuno Teixeira (PPE)
(5 November 2013)
Subject: Eurostat report as part of the excessive deficit procedure
According to a report in the newspaper Diário Económico on4 November 2013, Eurostat wants to receive a list of potential sanctions for the Autonomous Region of Madeira, which is suspected of deliberately concealing debt, and has asked to be kept abreast of any developments in the investigation by the Public Prosecutor.
The aforementioned news report reproduces a report allegedly drawn up last summer concerning the visit of September 2011, in which Eurostat stressed that it would seek ‘severe’ sanctions for Madeira.
The news report quotes wording allegedly taken from the report, according to which Eurostat felt that this was a case of deliberate misreporting on the part of a (Portuguese) government body and, in the report drawn up by the team of experts that visited Lisbon, it noted that this oversight was serious and warranted severe sanctions.
1.
Does the Commission know whether the abovementioned report, drawn up last summer and quoted in the newspaper report in question, exists?
2.
If this report does exist, is it available to the public? If so, where, when and how was it published?
3.
If the report in question is not publicly available, how can a media outlet justifiably have had access to it?
4.
Who was on the team of experts that travelled to Portugal in that connection?
5.
What objectives were set for the team of experts that travelled to Portugal as part of the excessive deficit procedure and what were the limits of their powers?
6.
How many visits to Portugal by experts have there been in this regard and how many reports have been produced?
7.
Have these reports been notified to the Portuguese statistical authorities? If so, how and when?
8.
If these reports have not been made public, are they classified in any way? Can the Commission provide full copies of the reports?
Answer given by Mr Šemeta on behalf of the Commission
(16 December 2013)
1, 2 and 3. The report mentioned by the Honorable Member represents the final findings of the EDP standard dialogue visit to Portugal on 22-23 November 2012, published on Eurostat’s website on 24 October 2013 (105).
4 and 5. The team of experts are included in the published report. The visit is part of Eurostat’s regular visits to Member States, in accordance with Council Regulation 479/2009.
6.
All the dates and reports from the visits to Portugal are available on Eurostat’s website.
7 and 8. All the reports were sent to the Portuguese statistical authorities for comments before publication on Eurostat’s website.
(Version française)
Question avec demande de réponse écrite E-012522/13
à la Commission
Véronique Mathieu Houillon (PPE) et Kinga Göncz (S&D)
(5 novembre 2013)
Objet: Financement de la formation policière européenne
L'Université de Strasbourg a annoncé, jeudi 17 octobre, le lancement d'un collège européen pour la formation des fonctionnaires de police et de justice de l'Union européenne aux investigations financières afin de lutter contre la criminalité organisée (Ceifac). Doté d'un budget de 940 000 euros sur deux ans, le CEIFAC est financé à 90 % par la Commission européenne.
La Commission peut-elle expliquer pourquoi elle finance une nouvelle structure de formation des policiers européens alors qu'elle propose la fusion du Collège européen de police avec Europol pour des motifs de restrictions budgétaires?
Réponse donnée par Mme Malmström au nom de la Commission
(23 décembre 2013)
La Commission a octroyé une subvention à un projet d'une durée de deux ans sélectionné à la suite de l'appel à propositions ouvert lancé en 2012 dans le cadre du programme «Prévenir et combattre la criminalité». Ce projet a été proposé, en association avec des partenaires, par l'Université de Strasbourg, l'Office anti-fraude de la Catalogne (Espagne) et la Commission d'enquête sur les biens acquis dans le cadre d'activités criminelles (Bulgarie).
Le financement couvre l'élaboration et la mise en œuvre d'un vaste programme de formation doté d'une composante recherche, conforme aux nouvelles normes du Groupe d'action financière (GAFI) et au rapport final du Conseil sur la cinquième série d'évaluations mutuelles relatives à la criminalité financière et aux enquêtes financières (106).
Le financement ne porte pas sur une nouvelle infrastructure de formation, comme on peut le lire dans la question, mais sur une action spécifique, à savoir une formation dotée d'une composante recherche et de durée limitée.
La formation en question concorde avec les objectifs du programme européen de formation des services répressifs proposé par la Commission (107), qui vise à combler les lacunes que présente la formation des services répressifs sur les questions transfrontières par l'apport d'un soutien financier en faveur des formations dispensées par les centres d'excellence européens et nationaux, et par leur coordination.
La proposition de la Commission relative au règlement Europol (108), qui comprend la fusion du Collège européen de police avec Europol, vise à améliorer l'efficacité de la coopération policière et de la formation des agents des services répressifs. Elle vise à réaliser non seulement des économies financières, mais, surtout, des synergies fonctionnelles, conformément à l'approche commune sur les agences décentralisées.
(English version)
Question for written answer E-012522/13
to the Commission
Véronique Mathieu Houillon (PPE) and Kinga Göncz (S&D)
(5 November 2013)
Subject: Funding of European police training
On Thursday 17 October 2013, the University of Strasbourg announced the launch of a European college for training police officers and judicial officials in order to combat organised crime (CEIFAC). With a budget of EUR 940 000 over two years, CEIFAC is 90% funded by the Commission.
Can the Commission explain why it is funding a new training facility for European police officers while it is proposing to merge the European Police College and Europol because of budget cuts?
Answer given by Ms Malmström on behalf of the Commission
(23 December 2013)
The Commission awarded a grant for a two-year project, arising from the 2012 open call for proposals under the Prevention of and Fight Against crime (ISEC) programme, and based on a proposal submitted by the University of Strasbourg with the anti-fraud office of Catalonia (Spain) and the Commission for establishing of property acquired from criminality (Bulgaria) together with associated partners.
The funding provides for the development and delivery of an extensive training programme, including a research component, in line with the new Financial Action Task-Force standards and with the Council's Final report of the Vth round of mutual evaluations on financial crime and financial investigation (109).
The funding is not for a new training facility, as suggested in the question, but for a specific action — a training course with a research component — of limited duration.
The training in question is consistent with the objectives of the European Law Enforcement Training Scheme proposed by the Commission (110), which aims to address gaps in existing law enforcement training on cross-border matters by supporting and coordinating the delivery of training by European and national centres of excellence.
As to the Europol Regulation (111), including the proposed merger of CEPOL and Europol, the Commission's proposal aims at improving the effectiveness of police cooperation and training. It is designed to achieve not only cost savings, but also and more importantly, functional synergies in accordance with the Common Approach on decentralised agencies.
(Version française)
Question avec demande de réponse écrite E-012523/13
à la Commission
Véronique Mathieu Houillon (PPE)
(5 novembre 2013)
Objet: Consultations publiques de la Commission
La Commission peut-elle indiquer dans quelle mesure elle tient compte des résultats des consultations publiques qu'elle lance?
Pourrait-elle indiquer en particulier la prise en compte des résultats de la consultation publique «Une approche commune en vue de réduire les dommages dus à l'usage criminel d'armes à feu dans l'UE», pour laquelle elle a reçu 85 673 réponses?
Dans ce nombre, 80 % des répondants expriment leur opposition à une modification des règles européennes concernant l'utilisation légale des armes à feu. La communication de la Commission du 21 octobre 2013 (COM(2013) 0716) reflète au contraire une volonté de modifier substantiellement les règles existantes.
Réponse donnée par Mme Malmström au nom de la Commission
(6 janvier 2014)
La consultation en ligne réalisée au début de l'année 2013 a permis de recueillir les réponses d'un très grand nombre de citoyens européens. Un pourcentage important des personnes qui ont répondu à cette consultation ont déclaré être affiliées à des associations liées à l'utilisation d'armes à feu. Lors de cette consultation, plus de 73 % des personnes interrogées ont indiqué que la criminalité liée aux armes à feu n'était pas «grave» tandis que 50 % ont déclaré que les États membres ne devraient «jamais» faire état de leurs progrès dans la lutte contre le trafic des armes à feu. 72 % ont estimé que l'UE ne devrait pas prendre de mesures concernant l'utilisation des armes à feu à des fins terroristes, 53 % ont déclaré que l'UE ne devrait pas inclure la lutte contre le trafic d'armes à feu dans ses accords avec des pays voisins et, enfin, 56 % ont indiqué que l'UE ne devrait pas instaurer de mécanisme commun pour la collecte de statistiques sur le trafic des armes à feu.
En revanche, dans l'enquête Eurobaromètre de septembre 2013, 49 % des personnes interrogées ont estimé que la criminalité liée aux armes à feu était élevée et 58 % s'attendaient à ce qu'elle progresse au cours des cinq prochaines années, tandis que 64 % pensaient que la coopération entre l'UE et les autorités nationales était la meilleure façon de traiter le problème. Cette enquête Eurobaromètre a utilisé un échantillon aléatoire de citoyens de l'Union et est, par conséquent, globalement représentative des vues dans l'ensemble de l'UE.
La Commission a tenu compte des résultats de la consultation publique et d'autres informations pertinentes. La diversité des avis mise en évidence par la consultation publique et l'enquête Eurobaromètre, ainsi que l'évolution inquiétante de la criminalité liée aux armes à feu dans l'UE, se reflètent dans la communication (112) de la Commission du 21 octobre 2013.
(English version)
Question for written answer E-012523/13
to the Commission
Véronique Mathieu Houillon (PPE)
(5 November 2013)
Subject: Public consultations by the Commission
Can the Commission say to what extent it takes account of the results of its public consultations?
In particular, could it say how much attention it paid to the results of the public consultation ‘A common approach to reducing the harm caused by criminal use of firearms in the EU’, which received 85 673 responses?
Of that number, 80% of respondents said they were opposed to a change in European rules on the legal use of firearms. The Commission’s Communication of 21 October 2013 (COM(2013)0716), on the other hand, shows that there is a desire to see the existing rules changed substantially.
Answer given by Ms Malmström on behalf of the Commission
(6 January 2014)
The online consultation carried out in early 2013 elicited answers from a very large number of European citizens. A large proportion of respondents to this consultation declared their membership of associations related to firearms use. In this consultation, over 73% of respondents said that firearms crime was ‘not serious’ while 50% said Member States should ‘never’ report their progress in tackling firearms trafficking. 72% said EU should not take action on terrorist use of firearms, 53% said EU, in its agreements with third countries in its neighbourhood, should not include action to tackle trafficking in firearms and, finally, 56% EU should not establish a common mechanism for collecting statistics on firearms trafficking.
However, in the Eurobarometer survey of September 2013, 49% considered firearms-related crime to be high and 58% expected it to increase over the next five years, and where 64% considered that the problem was best tackled by the EU working in cooperation with national authorities. This Eurobarometer survey used a random sample of EU citizens, and is therefore broadly representative of views across the EU.
The Commission took the results of the public consultation into account, along with other relevant information. The diversity of opinion, evidenced by the public consultation and the Eurobarometer survey along with worrying trends on firearms crime across the EU, is reflected in the Commission communication (113) of 21 October 2013.
| 24,827 |
http://data.theeuropeanlibrary.org/BibliographicResource/3000051778816 http://www.theeuropeanlibrary.org/tel4/newspapers/issue/3000051778816 http://anno.onb.ac.at/cgi-content/annoshow?call=apr|18640520|1|10.0|0 http://www.theeuropeanlibrary.org/tel4/newspapers/issue/fullscreen/3000051778816_4 | Europeana | Open Culture | Public Domain | null | Die Presse | None | German | Spoken | 793 | 1,919 | qupA-Vg i , qusSq msq <zzj;Z upup »M, sZi<? P»h» M 'wz^iM. pizvq plhi zp^pz. 'azm 1ÄZja»q ^vcuzk.zihz ui LDciWM, uMWM^nsmWoA -lvg^ söv;uvA asq jnv «pigavqpL uztz>j;jzu;hx> asq uahyjim uq' 'cuviZ «s? um Sjti ?Wtz 'üsLvaiÄli! ÜWM ms W P'q,,'' ^»MWÄF- -Wvch aZL U MAn! .Ullv^Ätla^ FakttM'^ ^ ' lxij uv Kuojizo).lv.>k ,izh)ii.,h?j>ö yzq zjciuiv<x,,q mn ^L.'jjct m,mqiq. m <p^ ^ M « ,«-W. ^ MMMi.ssMz.sM« «tz sWi n^UvMMK WH/ - ; oj «».M ,? ^ ,. mn!6S5',Wvch.u.O»MyU»«' ,A»', «up IMs uMgW uchzq M U-IMZ ^ ^ ^ -uvA saopoT ssq ,M<,zw^ siq vq 'uzuhaauü'izq zjpFZ .oupj ,u ?OK 'Vnvj nvm />,!uv, umu 'zpsqnv^ uvW. -pnan? uzSunlZyu!ZaZA mah; MZZ '(UMZ? öun^vMM ,u»,j UV PUZ gnm uvui) quiNk) II.'1Ä ci>vh> aZ n? 'Mn.ug uzuMWaa z,q WnulD^nW ^ ^ i9 ^ " i'L — 60 — beigetragen, die Stimmung zu beleben, und insbesondere di^. MuutMit-der Täuzninueu zu sttigcrp. ,, 7 / , ^ ,' Uuyr dixse^. he^u«d«r<e Mn.Hicher.vor tmtödt«rs, LeM». Jn dcr That^tvar sie trotz ^ VtthUrMA' MN ^ , Siri iil ihrer Mundhöhle ängerichtxt, .'kme auzichcndc Gädlst, ÄP'IMkev.' Teint, ihre feurigen Augen, voll herausfordernder .Koketterie, verhliideten,. daß. sie an.den Vergnügungen des Abends erhöhten,MHM,.,ES.'ihr. ^. nicht an Huldigungen aller Naceu und Farben. Ein hübscher ?teger ans Congo, ein safrangelber Indier und ein Hochbootsmann der „Gerlrude" schienen ihr darunter die ivillkouimeilsten. Alle Drei, waren sie nicht iin Stande, ihr ihre Verchrung in Worten auszudrücken, was die Verschiedenheit, der Dprachen nicht, zMß« W. aber' die AWensprache sowie' dif Gebärden- spräche nicht verboten waten, N blieben ihr die Hlipfindungen nicht unhe-. lannt, welche sie ihnen einflößte. JnWischen schien der junge HochkoptSmann unter den Dreien sich eines besonderen BorMs zu erfreuen. Auch war die. elegante Büchse der Gadise von dein galanten Seefahrer schon mehr als ein mal gefüllt worden. '. ^^ .. Der ElephMenjMex Wen »bex, iie LokMriM ftiner ToAttt wenig " bekümm^ MMMMWMru dks.HgKaWmp^^ ^ hiyMMt,..-M..er, sich dürch solche Kkeinigkeik» nicht anfechten. Sein Hqhn war verwunde^ und ^ alle Sorgfalt, die Van-Stetten aufgeboten, hatte ihn nicht in Mand sehett können, schon fetzt seinen Heldenlauf wieder aufzunehmen. Aber der Elephan-- teutödter wettete auf die anderen, und. merkte mit hochgesteigertem Interesse auf die verschiedenen Wendnngen ihres KämpferglückeS. Eimnal jedrch, wäh rend eines Stillstandes im Hahnenkampse, der in Folge der Ermüdung und Verwundung, seiner vorzüglichsten Vertreter eingetreten war,, nahm er sich Zeit, einen Blick an den Ort zurückzuwerfen, wo sich LegSre befinden sollte. Er gewahrte ihrer sogleich, und sah, wie sie voll Uebermuth lachte. Die Schärpe, Salindani genannt, deren sie sich zur Bildung reizender Attitüden bediente, noch in der Hand«, stand sie unter ihren Gesährtinuc», den übrigen Gadiseu. Um sie schwärinten ihre drei, Anbeter, von denen sie keinen verzweifeln lassen wollte. Plötzlich furchte der Elephanteutödter die Stirne, drängte sich durch die Menge und sagte seiner Tochter in rauhen, Gebietertone auf Malayisch: ' — Erinnere Dich an Deine Mutter, die Nongine! Bei Nennung dieses Namens mochte sich Legere wie vom Blitze berührt wähnen. Das Lächeln schwang von ihren Lippen; ihr Antlitz, das früher " von Freude gestrahlt, nahm den Ausdruck der Wildheit an. Den drohenden Blick des Vaters aber erwiderte sie mit einem ebenso drohenden, daim schlug sie die Augen zu Boden. Ihre Aicketer ungeduldig auseinandertreibend, warf sie ihre Schärpe über ihre Schultern znrück. verließ .den Tanzplatz, und fetzte sich zwischen zwei bejahrte Frauen, welche sich mit der Rotte der Znschanerin nen bei dein Feste begnügten. Der junge Hochbootsmann säumte nicht, ihr zu folgen. Der Neger aber und^ deß.Hindu, welche die WW-des Baters verstanden hatten, verschivaudm^ und. waAen es während der ganzen übrigen Dauer des Festes nicht mehr, sich der Gadise zu nähern. ' AM der entMeiMetzten Seite .des BMehs, bei. ..den Opiumrauchern, spielte sich eine SkWe eütgtgengeseßtxr NfttUr ab. May wird nichts Mhere» erw Krft n, M daß der Camerad des Elephantentödtexs siH >ort b^anh/ > '— L5 "»» — Ich will -sie i« -zipei W»>-tm gchm^ tÄMnete. der? Doetov. Der Elephantentödter bewohnte vor einigen Jc>M»MchzseiN-.WHunsland^. und hatte -ein Weib, das-ex- licht»t^s«Wj.h«eiUM«ttO MiKnM> Die FraU'tmr schSn^ind^hieß^ygMMiW spräche die „Nongine". Denn daß die Malayen keine Namen haben, .svitderw blos Beinamen, werde»' Si« phnMeS i, schW Msey,. sDi^Li«lgi«^hMe ihren Beinamen nicht umsonst; sie li^te. den .Tanz und. fehlte. bei keinem Feste. Die Folge dapon war, MM sie erschlug. — Das ist eben keine ueus Geschichte, Doowr!. So„ ewG bkM- sich wol auch in civilisirten-Ländern.,. - , ^ — Geduld, Herr Smith! Wenn der Anfang an europäischen schmack crinnevt,- so HM sich, daß Md^ .gänzlich M..MW dsr-.childei,!. , D«r Elephantentödter hatte also.sejn WM-erschAseM W?p bei.Hm daheim? wird nicht die Frau blos, die sich.'vergDgU, bestraft, MrMW-. - Der Elephantentödter führte- hei UchschM Kl«W> .uO de«LiKWer.!tlMe zu der in solchen Fälleu üWchen. Straft peWxtheil^-. ' Und woriW besteht diese.Hblichx StWfe?.. ^ — Auf öffentlichem Platze , lebmdig gIsr es.s en zu werden'! Der^ Gatte^- der Gruder,. | 11,955 |
https://github.com/rollick/onepercentclub-site/blob/master/apps/fund/locale/nl/LC_MESSAGES/django.po | Github Open Source | Open Source | BSD-3-Clause, BSD-2-Clause | 2,013 | onepercentclub-site | rollick | Gettext Catalog | Code | 1,953 | 5,687 | # SOME DESCRIPTIVE TITLE.
# Copyright (C) YEAR THE PACKAGE'S COPYRIGHT HOLDER
# This file is distributed under the same license as the PACKAGE package.
#
# Translators:
# gannetson <[email protected]>, 2013
# nieja <[email protected]>, 2013
# onepercentclub <[email protected]>, 2013
msgid ""
msgstr ""
"Project-Id-Version: Project Bluebottle\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2013-11-07 16:07+0100\n"
"PO-Revision-Date: 2013-11-07 15:07+0000\n"
"Last-Translator: gannetson <[email protected]>\n"
"Language-Team: Dutch (http://www.transifex.com/projects/p/bluebottle/language/nl/)\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"
"Language: nl\n"
"Plural-Forms: nplurals=2; plural=(n != 1);\n"
#: admin.py:14 admin.py:113 models.py:105 models.py:173
msgid "Status"
msgstr "Status"
#: admin.py:20 admin.py:119 admin.py:197
msgid "All"
msgstr "Alles"
#: admin.py:189
msgid "Active"
msgstr "Actief"
#: admin.py:192
msgid "Yes"
msgstr "Ja"
#: admin.py:193
msgid "No"
msgstr "Nee"
#: fields.py:11
msgid "Dutch bank account numbers have 1 - 7, 9 or 10 digits."
msgstr "Nederlandse bankrekening nummers hebben 1-7, 9 of 10 cijfers."
#: fields.py:28
msgid "Invalid Dutch bank account number."
msgstr "Ongeldig Nederlands bankrekening nummer."
#: models.py:29 models.py:107 models.py:177
msgid "Created"
msgstr "Aangemaakt"
#: models.py:30 models.py:108 models.py:178
msgid "Updated"
msgstr "Gewijzigd"
#: models.py:35
msgid "amount"
msgstr "Bedrag"
#: models.py:82
msgid "New"
msgstr "Nieuw"
#: models.py:83
msgid "In progress"
msgstr "In behandeling"
#: models.py:84
msgid "Pending"
msgstr "In behandeling"
#: models.py:85
msgid "Paid"
msgstr "Betaald"
#: models.py:86
msgid "Failed"
msgstr "Mislukt"
#: models.py:94
msgid "One-off"
msgstr "Eenmalig"
#: models.py:95 models.py:164
msgid "Recurring"
msgstr "Periodieke"
#: models.py:96
msgid "Voucher"
msgstr "Bonnen"
#: models.py:98
msgid "amount (in cents)"
msgstr "bedrag (in centen)"
#: models.py:99
msgid "currency"
msgstr "valuta"
#: models.py:102
msgid "User"
msgstr "Gebruiker"
#: models.py:103
msgid "Project"
msgstr "Project"
#: models.py:110
msgid "Ready"
msgstr "Klaar"
#: models.py:112
msgid "Type"
msgstr "Type"
#: models.py:114
msgid "Order"
msgstr "Bestel"
#: models.py:127
msgid "Gift Card"
msgstr "Giftcard"
#: models.py:132
msgid "donation"
msgstr "donatie"
#: models.py:133
msgid "donations"
msgstr "donaties"
#: models.py:163
msgid "Current"
msgstr "Huidig"
#: models.py:165 models.py:180
msgid "Closed"
msgstr "Gesloten"
#: models.py:172
msgid "user"
msgstr "gebruiker"
#: models.py:175
msgid "Order Number"
msgstr "Aantal"
#: models.py:212
msgid "GIFTCARDS"
msgstr "GIFTCARDS"
#: models.py:214
msgid "GIFTCARD"
msgstr "GIFTCARD"
#: models.py:218
msgid "DONATIONS"
msgstr "DONATIES"
#: models.py:220
msgid "DONATION"
msgstr "DONATIE"
#: models.py:222
msgid "DONATIONS & GIFTCARDS"
msgstr "DONATIES & GIFTCARDS"
#: models.py:223
msgid "THANK YOU!"
msgstr "BEDANKT!"
#: models.py:237
msgid "Couldn't generate a unique order number."
msgstr "Kon geen unieke order number genereren"
#: serializers.py:43 serializers.py:82
msgid "You cannot modify a Donation that does not have status new."
msgstr "Je kunt geen donatie aanpassen die geen status nieuw heeft."
#: serializers.py:52 serializers.py:91
msgid "Donations must be at least €2."
msgstr "Het minimumbedrag is €5."
#: serializers.py:55 serializers.py:58 serializers.py:94 serializers.py:97
msgid "Donations must be at least €5."
msgstr "Het minimumbedrag is €5."
#: serializers.py:65 serializers.py:104
msgid "You can only donate a project in the campaign phase."
msgstr "Je kunt alleen doneren aan een project in de 'campaign-fase'."
#: serializers.py:110
msgid "Can only Recurring Donations to a Recurring Order."
msgstr "Can only Recurring Donations to a Recurring Order."
#: serializers.py:112
msgid ""
"Can only Recurring Donations to an active Recurring Order (status "
"recurring)."
msgstr "Can only Recurring Donations to an active Recurring Order (status recurring)."
#: serializers.py:132
msgid "You cannot modify a closed Order."
msgstr "Je kunt een closed Order niet aanpassen."
#: views.py:33
msgid "No active order"
msgstr "Niet actief"
#: views.py:91
msgid "You cannot add a donation to a closed Order."
msgstr "Je kunt geen donatie toevoegen aan een closed Order."
#: views.py:339 views.py:343
msgid "Order not found."
msgstr "Betaling niet gevonden."
#: views.py:341
msgid "No order specified."
msgstr "Geen betaling opgegeven"
#: views.py:409
#, python-format
msgid "No %(verbose_name)s found matching the query"
msgstr "Geen %(verbose_name)s gevonden"
#: views.py:415
msgid "Anonymous users are not permitted to create recurring orders."
msgstr "Anonieme gebruikers kunnen geen maandelijkse donatie aanmaken."
#: templates/orders.hbs:13
#, python-format
msgid "Order digital 1%%GIFTCARDS"
msgstr "Bestel 1%%Giftcards"
#: templates/orders.hbs:18
msgid "Switch to donations"
msgstr "Switch naar donaties"
#: templates/orders.hbs:28
msgid "Support"
msgstr ""
#: templates/orders.hbs:46
msgid "Projects"
msgstr "Project"
#: templates/orders.hbs:51
msgid "Details"
msgstr "Details"
#: templates/orders.hbs:56
msgid "Profile"
msgstr "Profiel"
#: templates/orders.hbs:61
msgid "Payment"
msgstr "Betaling"
#: templates/orders.hbs:112
msgid "Choose a project to support"
msgstr "Kies je project om te steunen"
#: templates/orders.hbs:113
msgid ""
"Choose a project and click 'Support this project' to add it to your list"
msgstr "Kies een project en klik op 'Steun dit project' om dit aan je lijst toe te voegen"
#: templates/orders.hbs:121
msgid "Total"
msgstr "Totaal"
#: templates/orders.hbs:127
msgid "Add another project"
msgstr "Voeg project toe"
#: templates/orders.hbs:129
msgid "Add a project"
msgstr "Voeg project toe"
#: templates/orders.hbs:134 templates/orders.hbs.py:136
#: templates/orders.hbs:247 templates/orders.hbs.py:249
#: templates/orders.hbs:455 templates/orders.hbs.py:457
#: templates/orders.hbs:813 templates/orders.hbs.py:815
msgid "Next Step"
msgstr "Volgende"
#: templates/orders.hbs:163 templates/orders.hbs.py:395
msgid "Have an account?"
msgstr "Heb je een profiel?"
#: templates/orders.hbs:163 templates/orders.hbs.py:395
msgid "Log in here"
msgstr "Log hier in"
#: templates/orders.hbs:169
msgid "Great that you are doing another donation!"
msgstr ""
#: templates/orders.hbs:170
msgid "Please verify your details"
msgstr ""
#: templates/orders.hbs:172
msgid "Nice to meet you"
msgstr ""
#: templates/orders.hbs:173
msgid "To process your donation we need some information."
msgstr "Om verder te gaan met je donatie hebben we een paar gegevens nodig."
#: templates/orders.hbs:182 templates/orders.hbs.py:408
msgid "Your full name"
msgstr "Jouw naam"
#: templates/orders.hbs:190 templates/orders.hbs.py:415
#: templates/orders.hbs:915
msgid "Email"
msgstr "E-mail"
#: templates/orders.hbs:201
msgid "Address"
msgstr "Adres"
#: templates/orders.hbs:212
msgid "Postal code"
msgstr "Postcode"
#: templates/orders.hbs:223
msgid "City"
msgstr "Woonplaats"
#: templates/orders.hbs:234
msgid "Country"
msgstr "Land"
#: templates/orders.hbs:285
msgid "is still needed"
msgstr "nog nodig"
#: templates/orders.hbs:290
msgid "I'd like to give"
msgstr "Doneer"
#: templates/orders.hbs:297 templates/orders.hbs.py:955
msgid "Delete"
msgstr "Verwijder"
#: templates/orders.hbs:310 templates/orders.hbs.py:353
#: templates/orders.hbs:479
msgid "You're almost there!"
msgstr "Je bent er bijna!"
#: templates/orders.hbs:311 templates/orders.hbs.py:328
#: templates/orders.hbs:354
msgid ""
"We'll redirect you through our payment provider where you can finish your "
"donation securely."
msgstr "We sturen je door naar onze betaalservice waar je je donatie veilig kan afronden. "
#: templates/orders.hbs:327
msgid "Select your bank below"
msgstr "Kies je bank"
#: templates/orders.hbs:341 templates/orders.hbs.py:357
msgid "Processing payment…"
msgstr ""
#: templates/orders.hbs:342 templates/orders.hbs.py:344
#: templates/orders.hbs:347 templates/orders.hbs.py:358
#: templates/orders.hbs:360
msgid "Proceed with Payment"
msgstr "Ga door met betaling"
#: templates/orders.hbs:381
msgid "We'll keep you up to date!"
msgstr "We houden je op de hoogte!"
#: templates/orders.hbs:382
msgid ""
"You already have an account. Great! We'll keep you updated with the progress"
" of the projects you support"
msgstr "Je hebt al een profiel. Super! We houden je op de hoogte van de voortgang van het project."
#: templates/orders.hbs:387
msgid "Next"
msgstr "Volgende"
#: templates/orders.hbs:401
msgid "Follow the progress?"
msgstr "De voortgang volgen?"
#: templates/orders.hbs:402
msgid ""
"Sign up for an account and we keep you updated on the projects progress"
msgstr "Maak een profiel aan en we houden je op de hoogte van de voortgang van het project."
#: templates/orders.hbs:425
msgid "Password"
msgstr "Wachtwoord"
#: templates/orders.hbs:435
msgid "Password again"
msgstr "Herhaal wachtwoord"
#: templates/orders.hbs:447
#, python-format
msgid "By joining 1%%Club I hereby agree to the "
msgstr "Door mee te doen met 1%%Club verklaar ik het eens te zijn met "
#: templates/orders.hbs:448
#, python-format
msgid "1%%Club Terms of service"
msgstr "1%%Club Servicevoorwaarden"
#: templates/orders.hbs:480
msgid ""
"Add or edit your bank account information and submit to set your monthly "
"donations."
msgstr "Vul je betaalgegevens aan en druk op verzend om je maandelijkse betaling in te stellen."
#: templates/orders.hbs:485
msgid "Account Name"
msgstr "Naam rekeninghouder"
#: templates/orders.hbs:495
msgid "Account City"
msgstr "Plaats bank"
#: templates/orders.hbs:505
msgid "Account Number"
msgstr "Rekeningnummer"
#: templates/orders.hbs:517
#, python-format
msgid "By clicking submit, I authorize 1%%Club to withdraw money every month."
msgstr "Door op verzend te klikken, ga ik akkoord met een maandelijkse afschrijving van mijn rekening door 1%%CLUB."
#: templates/orders.hbs:525
msgid "Updating monthly donation…"
msgstr ""
#: templates/orders.hbs:526 templates/orders.hbs.py:528
#: templates/orders.hbs:531
msgid "Submit"
msgstr "Verzend"
#: templates/orders.hbs:538
msgid "Your monthly donation"
msgstr "Jouw maandelijkse donatie is ingesteld!"
#: templates/orders.hbs:539
#, python-format
msgid ""
"Thank you 1%%Friend! You're about to set your monthly donation amount to "
"€"
msgstr "Bedankt 1%%Friend! Je hebt nu bijna een maandelijkse donatie ingesteld ter hoogte van €"
#: templates/orders.hbs:605
msgid "You supported"
msgstr ""
#: templates/orders.hbs:624
msgid "Did you know that you rock?"
msgstr ""
#: templates/orders.hbs:624
msgid "Well, you rock!"
msgstr ""
#: templates/orders.hbs:626
msgid ""
"Why not share the project with your friends, and encourage them to support "
"as well?"
msgstr ""
#: templates/orders.hbs:627
msgid "Just hit (one of the) share buttons to make even more impact:"
msgstr ""
#: templates/orders.hbs:639
msgid "Thank you!"
msgstr ""
#: templates/orders.hbs:641
msgid ""
"For supporting <strong>€[amount]</strong> to these projects below:"
msgstr ""
#: templates/orders.hbs:655
msgid "Donate monthly"
msgstr ""
#: templates/orders.hbs:656
msgid ""
"Did you know: you support to projects monthly as a monthly member? You'll "
"rock even more!"
msgstr ""
#: templates/orders.hbs:657
msgid "Set up monthly donations"
msgstr ""
#: templates/orders.hbs:659
msgid "Stay updated"
msgstr ""
#: templates/orders.hbs:660
msgid ""
"We’d love to keep you updated on the progress of the projects you just "
"supported. Sign up and receive updates, and our everlasting love."
msgstr ""
#: templates/orders.hbs:661
msgid "Signup now"
msgstr ""
#: templates/orders.hbs:683
msgid "Donation Successful!"
msgstr "Donatie geslaagd!"
#: templates/orders.hbs:685
#, python-format
msgid ""
"\n"
"\t\t\t\t\t\t\tThanks for your support! Your 1%% has brought them one step closer to realise their smart idea! Don't forget to tune in to see how they're doing! \n"
"\t\t\t\t\t\t"
msgstr "\n\t\t\t\t\tBedankt voor je support! Jouw 1%% heeft dit project weer een stapje dichterbij hun doel gebracht! Vergeet niet om af en toe te kijken hoe het met je project gaat! \n\t\t\t\t\t"
#: templates/orders.hbs:689
#, python-format
msgid ""
"\n"
"\t\t\t\t\t\t\tThanks for your support! We'd be happy to keep you posted on the progress of the project(s) you supported. Why? Because it's a fun and personal way to see what's happening with your 1%%. Sounds good? Just become a 1%%Member!\n"
"\t\t\t\t\t\t"
msgstr "\n\t\t\t\t\tBedankt voor je support! Als je wil, houden we je graag op de hoogte van de status van de projecten die jij hebt gesteund. Waarom? Omdat het een makkelijke en leuke manier is om te zien wat er met jouw 1%% gebeurt! \nKlinkt goed toch? Meld je aan als 1%%Lid!\n\t\t\t\t\t"
#: templates/orders.hbs:692
#, python-format
msgid "Become a 1%%Member"
msgstr "Word lid van 1%%Club"
#: templates/orders.hbs:698
msgid "No donation set..."
msgstr "Geen donatie ingesteld....."
#: templates/orders.hbs:700
msgid "Create or enable your monthly donation"
msgstr "Maak je maandelijkse donatie aan"
#: templates/orders.hbs:716
msgid "You just supported these projects"
msgstr "Je hebt bijgedragen aan"
#: templates/orders.hbs:718
msgid "You just supported this project"
msgstr "Je hebt zojuist gesteund"
#: templates/orders.hbs:721
msgid "You just supported the top three projects."
msgstr "Je hebt bijgedragen aan"
#: templates/orders.hbs:746
msgid "Your monthly donation is set"
msgstr "Jouw maandelijkse donatie is ingesteld!"
#: templates/orders.hbs:748
msgid ""
"Your monthly donation will be deducted from your account at the beginning of"
" each month."
msgstr "Je maandelijkse donatie wordt aan het begin van iedere maand ingehouden van je bankrekening."
#: templates/orders.hbs:750
msgid "Monthly donation total:"
msgstr "Maandelijkse donatie totaal:"
#: templates/orders.hbs:796
#, python-format
msgid "1%%GIFTCARDS will be sent out with a total value of"
msgstr "1%%Giftcards worden verstuurd met een totale waarde van"
#: templates/orders.hbs:805
msgid "No gift cards in shopping basket"
msgstr "Geen giftcards in mandje"
#: templates/orders.hbs:826
#, python-format
msgid "Choose value & personalize 1%%GIFTCARD"
msgstr "Kies bedrag & laat een bericht achter op de 1%%Giftcard"
#: templates/orders.hbs:832
msgid "Language"
msgstr "Taal"
#: templates/orders.hbs:837
msgid "English"
msgstr "English"
#: templates/orders.hbs:840
msgid "Dutch"
msgstr "Dutch"
#: templates/orders.hbs:846
msgid "Value"
msgstr "Waarde"
#: templates/orders.hbs:871
msgid "Your name"
msgstr "Naam"
#: templates/orders.hbs:883
msgid "Your email"
msgstr "E-mail"
#: templates/orders.hbs:899
msgid "This gift card is for:"
msgstr "Deze giftcard is voor:"
#: templates/orders.hbs:903
msgid "Name"
msgstr "Naam"
#: templates/orders.hbs:927
msgid "Personal message"
msgstr "Persoonlijk bericht"
#: templates/orders.hbs:940
msgid "Add"
msgstr "Voeg toe"
#: templates/fund/user_orders.html:9
msgid "Order History"
msgstr "Donatie overzicht"
#: templates/fund/user_orders.html:15
msgid "Monthly Donation"
msgstr "Maandelijkse donatie"
#: templates/fund/user_orders.html:15
msgid "Single Donation"
msgstr "Eenmalige donatie"
#: templates/fund/user_orders.html:30
msgid "Loading order history"
msgstr "Donatie geschiedenis laden"
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d5148cb651d1c0d5c976bfcb1e0b2ebe | French Open Data | Open Government | Licence ouverte | 2,005 | Code de l'urbanisme, article R*123-2-1 | LEGI | French | Spoken | 403 | 572 | Lorsque le plan local d'urbanisme doit faire l'objet d'une évaluation environnementale conformément aux articles L. 121-10 et suivants, le rapport de présentation : 1° Expose le diagnostic prévu au premier alinéa de l'article L. 123-1 et décrit l'articulation du plan avec les autres documents d'urbanisme et les plans ou programmes mentionnés à l'article L. 122-4 du code de l'environnement avec lesquels il doit être compatible ou qu'il doit prendre en considération ; 2° Analyse l'état initial de l'environnement et les perspectives de son évolution en exposant, notamment, les caractéristiques des zones susceptibles d'être touchées de manière notable par la mise en oeuvre du plan ; 3° Analyse les incidences notables prévisibles de la mise en oeuvre du plan sur l'environnement et expose les conséquences éventuelles de l'adoption du plan sur la protection des zones revêtant une importance particulière pour l'environnement telles que celles désignées conformément aux articles R. 214-18 à R. 214-22 (1) du code de l'environnement ainsi qu'à l'article 2 du décret n° 2001-1031 du 8 novembre 2001 relatif à la procédure de désignation des sites Natura 2000 ; 4° Explique les choix retenus pour établir le projet d'aménagement et de développement durable, au regard notamment des objectifs de protection de l'environnement établis au niveau international, communautaire ou national, et, le cas échéant, les raisons qui justifient le choix opéré par rapport aux autres solutions envisagées. Il expose les motifs de la délimitation des zones, des règles qui y sont applicables et des orientations d'aménagement. Il justifie l'institution des secteurs des zones urbaines où les constructions ou installations d'une superficie supérieure à un seuil défini par le règlement sont interdites en application du a de l'article L. 123-2 ; 5° Présente les mesures envisagées pour éviter, réduire et, si possible, compenser s'il y a lieu, les conséquences dommageables de la mise en oeuvre du plan sur l'environnement et rappelle que le plan fera l'objet d'une analyse des résultats de son application, notamment en ce qui concerne l'environnement, au plus tard à l'expiration d'un délai de dix ans à compter de son approbation ; 6° Comprend un résumé non technique des éléments précédents et une description de la manière dont l'évaluation a été effectuée. En cas de modification ou de révision, le rapport de présentation est complété par l'exposé des motifs des changements apportés. Le rapport de présentation peut se référer aux renseignements relatifs à l'environnement figurant dans d'autres études, plans et documents. | 42,032 |
https://www.wikidata.org/wiki/Q8036304 | Wikidata | Semantic data | CC0 | null | World Tour | None | Multilingual | Semantic data | 163 | 317 | World Tour
international bodyboarding competition
World Tour official website http://ibaworldtour.com/
World Tour Facebook username apbtour
World Tour Commons category World Tour (bodyboarding)
World Tour Freebase ID /m/0696k3
World Tour instance of recurring sporting event
World Tour sport bodyboarding
APB World Tour
APB World Tour sítio web oficial http://ibaworldtour.com/
APB World Tour identificador no Facebook apbtour
APB World Tour categoria da Commons World Tour (bodyboarding)
APB World Tour identificador Freebase /m/0696k3
APB World Tour instância de evento desportivo recorrente
APB World Tour desporto bodyboard
Gira Mundial de Bodyboard de la APB
Competición organizada por la asociación de Bodyboarders
Gira Mundial de Bodyboard de la APB página web oficial http://ibaworldtour.com/
Gira Mundial de Bodyboard de la APB identificador en Facebook apbtour
Gira Mundial de Bodyboard de la APB categoría en Commons World Tour (bodyboarding)
Gira Mundial de Bodyboard de la APB Identificador Freebase /m/0696k3
Gira Mundial de Bodyboard de la APB instancia de evento deportivo recurrente
Gira Mundial de Bodyboard de la APB deporte Bodyboarding | 6,352 |
US-50555609-A_2 | USPTO | Open Government | Public Domain | 2,009 | None | None | English | Spoken | 6,246 | 7,794 | It may be noted that the data transmission speed on the wire link 56 has to be at least equal to that provided by standard USB2.0 in order to be able to empty the array 26 rapidly without having to make use of a buffer memory.
FIG. 3 represents in a more detailed way the arrangement of the active pixel array 26 and the sequencer 30 on the common substrate 28 of the detector's chip.
The array 26 is linked to a circuit 70 for selection piloting and resetting the rows L₁, L₂, L₃ . . . L_(n) . . . , L_(N) of the array.
A circuit 72 of shift registers controlled by the clock and synchronization signals enables the circuit 70 to be controlled for the successive operations of row selection and resetting.
The array is also connected to an amplification circuit 74 of columns C₁, C₂, C₃ . . . , C_(n) . . . , C_(I) of the array and which multiplexes on an output amplification circuit 76 the image data captured by said array.
A circuit 78 of array column shift registers is provided to control the operation of the circuit 74 and, especially, to pilot the reading of the pixels of each array row.
As stated above, the detector receives several signals from the electronic module 32 and, especially, the signals Clk-x, Clk-y and Sync-y from which all the array's internal signals are derived.
The signal Clk-x is a clock signal, for example, at 12 MHz which acts to pilot the column shift registers and constitutes the principal clock signal from which the sequencer 30 generates all the signals, and especially the array control signals.
The control signal Sync-y acts to initialize the reading of the array.
The signal Clk-y is the control signal of the row shift registers controlling the circuit 72.
The reading of the image data captured by the array is performed as follows.
The signal Sync-y, applied at the same time as the signal Clk-y, initializes the shift registers of the array's rows and causes the selection of the first row of the array.
A first selection signal of the first row of the array, which is generated by the sequencer 30, is tripped, for example, on a rising front of the clock signal Clk-y, and controls the selection of the first row of the array.
The application of the signal Clk-x will cause the appearance of the video signal (output signal) at the detector's output.
The application of only the signal Clk-y will cause the selection of the next row of the array.
This continues until all the rows have been read, and then the combination of the signals Sync-y and Clk-y is applied again to select the first row of the array again.
For the selected row thus considered, the various data values held by each of the row's pixels having been exposed to radiation will undergo a first sampling step, also called reading step, at a rate set by the clock signal Clk-x.
Each value of the pixel's light data is stored in the column amplification circuit 74.
Following a first sampling step of the first row's pixels, a Reset signal is generated by the sequencer in order to reset all the pixels of the relevant row.
This resetting step initializes all the pixels of the selected row to a reference data value specific to each pixel.
This is a data value corresponding to an unlit pixel, also called dark data value.
After initialization of the pixels of the relevant row, a second sampling or reading step of the reference data values held by each pixel is performed, at the rate set by the clock signal Clk-x that selects the various columns of the array.
The sampled reference data values are stored in the column amplification circuit 74 where they are added to the light data values already stored and coming from the first sampling step.
The two types of data values are then multiplexed on two buses respectively, one carrying a read signal S (light data values) and the other carrying a re-initialization signal R (reference data values).
The data coming from these two buses are multiplexed on the output amplification circuit 76 according to a rate set by the clock signal Clk-x which activates the column shift registers.
An S-R output signal is created by the output amplification circuit 76 based on the difference between the read signal S and the re-initialization signal R and a reference signal that is representative of the electronic drifts intrinsic to the detector.
This reference signal comes from an input reference signal “black-in”, which is a DC voltage coming from the module 32 and applied at the detector input. The reference signal “black-ref” is created as shown in FIG. 4.
The circuit of FIG. 4 is representative of the way noise is generated in the detector and the black-in signal applied at this circuit's input undergoes drifts as it goes through the array.
Therefore, this circuit comprises a transistor 71 that acts as buffer memory for the black-in input signal and is also shown schematically in FIG. 3.
A resistor 73 and capacitance 75, whose values are appropriately selected according to the detector, are representative of the detector's intrinsic elements.
An amplifier 77 amplifies the signal obtained after it has undergone the distortions caused by the elements 71, 73 and 75 and the black-ref amplified signal is thus delivered at the detector's output 22.
The signal obtained before going into the amplifier 77 (“non-amplified reference signal”) is supplied to the output amplification circuit 76 where, with the clock signal Clk-x, on one of the rising or falling fronts of the signal Clk-x the strongest value of the S-R signal is selected and, on the other front, the value supplied by the non-amplified reference signal is selected, as illustrated in FIG. 5.
Thus an S-R signal is obtained whose highest values are those of the array read signal and whose lowest values are those of the non-amplified reference signal, these latter values varying over time.
The S-R signal obtained (FIG. 6) is representative of the tooth's image data captured by the detector's pixels.
FIG. 7 a represents the overall rate of the R-S signal of the detector's output (FIG. 3) and the black-ref output reference signal.
As shown in FIG. 3, the analog electrical signal of the detector's S-R output is converted by a signal generator 79 into two differential analog electrical signals V+ and V−.
The generator 79 is a two-output amplifier which subtracts the black-ref signal from the S-R signal and delivers differential signals V+ and V− whose rate is shown in FIG. 7 b.
The superimposition of the difference between the S-R signals and the black-ref output reference signal avoids any drifts due to the detector's construction that are constant over time and that vary from one sensor to another.
By transmitting the image signal from the sensor in differential form, the various disturbances it may be subject to are avoided.
Indeed, as each of the two signals V+ and V− is subject to the same disturbances, by reconstituting a single signal the disturbances found on each of the signals V+ and V− can thus be avoided, which would not be the case if only the image signal were transmitted.
Furthermore, the transmission of a differential image signal also indirectly enables the sensor's signal-to-noise ratio to be improved.
A sampling signal Sample-clk is generated by the sequencer (FIG. 3) and, by construction, is perfectly synchronous with the S-R output signal insofar as the sequencer knows exactly when the data will arrive at the detector's output. The sampling signal is produced by a phase difference suited to the clock signal Clk-x and is shown in FIG. 7 c.
This sampling signal which is in phase with the S-R output signal, and thus with the differential signals V+ and V−, will be transmitted simultaneously with the latter by the cable 34 intended for the electronic module 32.
The simultaneous transmission of in-phase signals will enable, inside the electronic module 32, conversion of the differential analog signals to be performed in the analog-digital conversion circuit 42 at the frequency set by the sampling signal.
By transmitting the signals simultaneously, this enables phase errors arising in the cable to be avoided insofar as a phase error affecting both the differential analog signals and the sampling signal can be compensated for.
In the same way any other disturbances affecting the signals during their transmission are avoided.
As shown in FIG. 2, the differential analog output signals V+ and V− are respectively amplified in the amplification circuits 36 and 38 before being transmitted to the filtering circuit 40.
The signals thus filtered are transmitted to the analog-digital converter 42 where they are summed to produce a single signal and this signal is digitized using the sampling signal Sample-clk (for example on the rising front of the sampling signal, as shown in FIG. 7 d) before reaching the central processing unit 44.
In order to avoid time variation of the dark current, which is defined as being the electric current collected at the detector output when the latter is not exposed to any radiation, a correction signal is generated between two phases of exposure to radiation of the array that are, for example, successive.
It may be noted that the generation of such a signal can be regular or not over time.
Thus aside from the sensor taking a tooth image, a sampling of the data values held by the pixels of the array when this is not exposed to any radiation is carried out. The array reading signal that is generated is a correction signal.
Similarly to the above description for the output signals V+ and V−, the reading signal, in the absence of radiation, is transmitted in differential form in the cable 34 and then amplified in the amplification circuits 36 and 38 before being reconstituted as a single signal by the circuit 40 and digitized in the converter 42.
This digitized signal is introduced into the central unit 44 in which the microprocessor calculates an average value of this digitized signal which is not zero, unlike what should be obtained in the absence of radiation. This average value is injected into the analog digital converter 46 to convert it into an analog correction signal applied to one, 38, of the amplification circuits that is a subtractor circuit.
The application of this correction signal to one of the output analog signals, here the signal V−, enables this signal's amplitude to be offset by adjusting this signal towards the top as shown in FIGS. 7 e and 7 f.
FIG. 7 e shows very schematically the rate of the differential output signals V+ and V− which are each offset in relation to the zero level by the same value.
By measuring an average value (2× offset) on the digitized correction signal and by applying it, after analog digital conversion, to the analog output signal V−, the latter is offset by a corrected value of 2× offset, as shown in FIG. 7 f, to adjust it to the bottom level of the other non-corrected analog output signal V+.
When the signal V+ and the corrected signal V− are filtered and combined, then the compensated analog signal shown in FIG. 7 g is obtained that goes from zero up to a maximum amplitude of 2× (max-offset), where the “max” value designates the maximum amplitude in absolute value of each of the signals V+ and V−.
The compensated analog signal is then digitized in the circuit 42.
Thus variations due to the dark current in the array are avoided.
FIG. 7 h, which shows the number of pixels according to the gray levels presents in the video signal, illustrates this compensation phenomenon by demonstrating the rate of the histogram of the video signal before and after the application of a correction.
It may be noted that it is preferable to convert the correction analog signal rather than applying it directly to one of the output analog signals, as soon as the electronic module 32 receives the correction signal.
Indeed, this would require storing the correction analog signal with all the risks of drifts and/or volatility that this involves.
By performing this correction digitally, these problems are avoided and in addition the analog-digital converter is integrated into the compensation, which avoids affecting the digitizing process with a drift specific to the converter.
Further, it may be noted that a correction analog signal can also be applied to the other output analog signal V+, or even to the two signals V+ and V−.
The application of a correction to the two signals makes the process symmetrical.
The application of a correction to one of the analog output signals or to the single analog signal is adjusted according to the law of variation according to the time of the dark current of the array and the duration of use of this array.
Indeed, knowing these two settings, it is possible to plan at what moment the dark current is liable to vary most and thus to envisage performing a correction to compensate for the drifts due to these variations.
As explained above, at the time of reading the array and, more particularly, after having carried out a first sampling of the pixels of a selected row of the array, a reset signal is applied to the relevant array row by means of the circuits 70 and 72 (FIG. 3) to reinitialize the row's pixel values to the reference data values (dark data values).
However, if the reset signal varies from one row to another, an error is introduced into the data values held by the row's pixels, which results in offsets in relation to zero: the data value held by a pixel after its re-initialization is not zero as it should be in theory, but has an offset in relation to zero and, what is more, this offset can vary from one row to another.
The introduction of an additional error results in a deterioration of the signal-to-noise ratio supplied by the detector.
More especially, with such errors, a “horizontal combing” noise is introduced into the image signal produced on the screen 58 of the computer 54 (FIG. 2).
To remedy this problem, a number m of pixels of each of the array rows is first arranged to be made optically inactive, the optically inactive pixels of the various rows being equal in number (e.g. equal to 3) and arranged in the same array columns.
It may be noted that the pixels made optically inactive are arranged in the first array columns but may well also be found somewhere else, such as in its last columns.
It may be noted that the number m of optically inactive pixels can vary according to the accuracy that is required for the drift compensation introduced with the re-initialization signal.
The number m can also vary according to the size of the array. In the embodiment example illustrated in FIG. 3, the rows L₁, L₂ . . . L_(n) . . . L_(N) each respectively contain three “blind” pixels P_(1.1), P_(1.2), P_(1.3), P_(2.1), P_(2.2), P_(2.3) . . . . P_(n1), P_(n2), P_(n3) . . . P_(N1), P_(N2) and P_(N3).
To make a pixel optically inactive, metallization or serigraphy, for example, is carried out on these pixels.
Then processing of the detector's output signal is performed after digitization by the circuit 42 (FIG. 2).
The processing is applied to the signal by the central processing unit 44 by means of the processor 50 which will execute a series of instructions provided for in the algorithm of FIG. 8 which is stored in the memory 52.
This algorithm includes a first initialization step S1 during which the variable n representative of the array's rows is initialized to the value 1.
During the next step S2, the data values S_(i)(n) of the row n of the array are read for the three blind pixels P_(n1), P_(n2), P_(n3).
These values are read in the digitized output signal.
During the next step S3, the data values S_(i)(n+1) are read respectively from the three optically inactive pixels P_(n+1.1), P_(n+1.2), P_(n+1.3) of the next row n+1 of the array.
After having read the data values from the optically inactive pixels of two consecutive rows n and n+1 of the array, during the next steps S4 and S5, for each of the rows n and n+1 an average data value S(n), S(n+1) is determined that is obtained based on the respective data values S_(i)(n), S_(i)(n+1) of each row.
The higher the number m, the better the accuracy in determining the average value.
The average data value is, for example, obtained by performing arithmetic averaging.
During the step S6, the absolute value of the difference between the two previously determined average values is determined.
The next step S7 is a test that makes a comparison between the average data values S(n) and S(n+1).
In theory, one examines whether the two average values are equal but, in practice, one compares the result obtained in the step S6 with a threshold value ε that takes into account, for example, the order of size of the differences that it is technically possible to detect between the average values.
When no significant difference is found between the average data values S(n) and S(n+1), then the next step S8 is a test during which one checks whether the variable representative of the number of rows n is equal to the total number N of rows in the array.
If yes, the algorithm is stopped.
If not, if array rows remain to be processed, then step S8 is followed by a step S9 during which the variable n is incremented by one unit and then the steps that have just been described are performed again.
When the result of the test made in the step S7 is positive, then it is decided to modify the data values of all the pixels of the row n+1 in the digital output signal as illustrated by the step S10.
During this step, the data value coming from each of the pixels I of the row n+1 and which is noted S_(i)(n+1) is modified by assigning to it the absolute value of the difference determined in step S6, in order to adjust the average data value S(n+1) of the row n+1 to the average data value S(n) of the row n.
The step S10 is then followed by step S8 as described above.
By continuing in this way for each pair of consecutive rows, each of the array rows is corrected, except for the first and thus the image is homogenized row by row in order to suppress the above-mentioned “horizontal combing” noise.
It may be noted that it is also possible to make a comparison, not on two consecutive rows of the array but on three consecutive rows.
In this case, each of the data values from the m optically inactive pixels of a set of three consecutive rows of the array are read and an average data value is determined for each of these rows.
After comparison of the average data values of the three rows, according to the result of the comparison, one then decides to modify or not the data values of all the pixels of the second row in the digital output signal.
FIG. 9 shows the physical embodiment of a dental radiology apparatus according to the invention that includes the intraoral sensor 14, the electronic module 32 integrated in a case, to be described later, the two parts being interlinked by a cable 34, and a connector 80 linked to the module 32 by the cable 56.
The connector 80 is intended to work together with a complementary connector of the processing and display unit 54.
It may be noted that the cable 34 is relatively short insofar as it carries the analog signals that risk being over attenuated if the cable were too long.
This arrangement enables the constraints specific to dental radiology to be taken into account and especially because the intensity of the sensor's output signal 14 is limited by the fact that the x-ray dose going through the patient's tooth is necessarily maintained as low as possible in order not to expose the latter to too great radiation doses.
Therefore, the length l of the cable 34 is generally less than 2 meters.
The reduced length l of the cable 34 thus enables the sensor 14 signal-to-noise ratio not to be deteriorated.
On the other hand, this length l is generally more than 50 cm in order not to cause additional discomfort by placing it too near the patient's mouth.
However, it may be noted that the length L of the cable 56 that transmits the digital signals is not limited and can, for example, equal several meters and, in particular, be between 2 and 5 meters long.
The electronic module 32 includes a detector activation device 100 that is, for example, in the form of a pushbutton.
This device 100 is especially useful for dentists to activate the sensor 14 detector and put it into a state to receive and process x-rays that have passed through the patient's tooth 16, insofar as the module 32 is placed, when in use, within the dentist's sphere of activity.
This means that he/she can then, without having to move, hold the module 32 and press the detector's activation device 100.
This arrangement saves the dentist from moving to the remote unit 54 to click on a computer mouse with the surgical gloves that he/she used to put the sensor 14 into the patient's mouth and which are thus already contaminated, especially by the patient's saliva.
It may be noted that in the prior art, by clicking on the mouse, the intraoral sensor is activated by means of a software interface.
Thus the risks of crossover contamination with another patient are prevented insofar as the mouse is not generally part of the equipment that is disinfected after use.
After activating the sensor using the activation device 100, the dentist starts the x-ray generator 12 using a switch device 102 such as an electrical pushbutton switch (FIG. 10) that he/she has within reach.
Further, as shown in the FIG. 10, at the time of using the dental radiology apparatus according to the invention, the encapsulated electronic module is suspended from the sensor 14 when this is placed in a patient's mouth, which enables it to be within reach of the dentist when he/she is wearing gloves and has just installed the sensor in the patient's mouth.
Indeed it is possible to suspend the electronic module encapsulated in its case at the end of the cable 34 linking it to the sensor insofar as it has been designed so that its weight and dimensions enable this use.
Indeed, too high a weight would risk pulling on the cable 34, and thus exerting a pull on the sensor 14, which would be felt by the patient and cause an additional discomfort.
Furthermore, reasonable dimensions of the encapsulated module are suited to the size of an adult's hand and thus do not cause additional discomfort linked to the size, either for the dentist, or for the patient.
It may also be noted that the activation device 100 of the electronic module 32 or several activation devices can be used to execute other functions.
Insofar as a single activation device 100 is used, these other functions can be implemented by successively pressing on the latter.
Thus, when an image is being taken by the sensor or even after the image capture, it is useful to be able to supply data on the direction of orientation of the image to the image processing software installed in the remote unit 54, for example, according to whether an image of a top tooth is taken, whether the sensor is placed horizontally to take an image of an occlusion, or even whether an image of a bottom tooth is taken.
Thus, by several successive presses on the device 100, one can mark in which position the sensor has been placed by the dentist.
For example, one press on the device 100 switches on the sensor and indicates that this is taking the image of a bottom tooth, two brief presses switch on the sensor and indicate that this is taking the image of an occlusion with the sensor placed horizontally, while three successive presses switches on the sensor and indicates that the image is rotated insofar as a top tooth has been taken vertically.
Other functions such as, for example, the adjustment of image brightness or contrast, can also be controlled by activating the device 100.
As shown in FIG. 11, the electronic module 32 has the form of a printed circuit board 150 with overall shape elongated along a longitudinal axis X.
The printed circuit board 150 here has an overall rectangular shape and has, at each of its two opposite ends 150 a, 150 b that are arranged longitudinally according to the axis X, an axial cut-out 152, 154 having, for example, a rectangular shape open towards the outside of the circuit.
The axial cut-outs 152, 154 are intended to house a metal anti-pull body 156, 158 (FIG. 11) according to the circuit's longitudinal axis.
The electronic module 32 is equipped with two anti-pull devices that are each capable of working together with one of the ends of one of the cables 34 and 56, so as to prevent the removal of the corresponding cable from the electronic module and from the case by a pulling action exerted on said cable.
Each cable has a sheath (sheath 56 a for the cable 56 in FIG. 12) that is coaxial with a bundle of electrical wires (bundle 56 b of the cable 56).
Opposite each end of each cable that is inserted into the case, as will be seen later, the part of the corresponding wire bundle 56 b, opposite the end 56 c of the cable 56, is held solid with the metal anti-pull body 158.
It may be noted that everything that is described for the cable 56 and the metal anti-pull body 158 is valid for the cable 34 and the anti-pull body 156.
Each of the wire bundles (cable braid) is made solid with the corresponding metal anti-pull body by means of a cylindrical drum, marked 160 for the body 156 and 162 for the body 158, which itself is an integral part of said body.
More particularly, the cable, for example the cable 56 of FIG. 12, is stripped at its end 56 c so that the wire bundle 56 b can be introduced inside the drum 162 and, then, a weld of the end part of the wire bundle can be made in the drum.
Thus, the wire bundles are made solid indirectly to the metal anti-pull body by means of the corresponding drum, but one can very well envisage welding the wire bundles directly to the body itself.
As shown in FIG. 11, the metal anti-pull bodies 156 and 158 are introduced into the corresponding longitudinal slots or cut-outs 152 and 154 perpendicularly to the longitudinal axis X of the circuit 150.
This can be explained by the fact that each metal anti-pull body is provided with fitting parts arranged on the opposite sides parallel to the direction of the end part of the wire bundle that is made solid with the body (FIG. 12), a direction that is akin to the longitudinal axis X of the circuit 150 when the metal anti-pull body is in position on said circuit.
More particularly, the fitting parts 158 a and 158 b of the anti-pull body 158 have the form of projections present over the whole height of the body (FIG. 13) and which work together with the complementary fitting parts arranged respectively on the opposite longitudinal edges of the corresponding cut-out.
These complementary fitting parts have the form of transversal notches that are shown in FIG. 11 and, more visibly, in FIG. 12 for the cut-out 152.
These notches 152 a and 152 b work together with the projecting fitting parts of the corresponding body and constitute a mortise-and-tenon type assembly.
The notches 154 a and 154 b of the cut-out 154 by which the metal anti-pull body 58 is introduced are shown in FIG. 11.
It may be noted that the fitting parts of the anti-pull body and the complementary parts arranged in the corresponding cut-out constitute axial holding parts of the anti-pull body, preventing any axial removal of the body in relation to the printed circuit board 150.
These fitting parts also facilitate the installation of the metal anti-pull body by an appropriate guiding in a transversal direction (FIG. 11).
The presence of the anti-pull devices means avoiding the use of electrical connectors, which is particularly advantageous.
Indeed, the use of electrical connectors would risk leading to unwanted disconnections, which is not desirable when the patient has just been exposed to a dose of x-rays and it is then necessary to expose him/her again to this radiation after having re-established the electrical connection at the electronic module.
Besides, the presence of electrical connectors equipped with sophisticated locking systems is not very desirable insofar as this would complicate the apparatus and add weight and volume to the electronic module encapsulated in its case, which is especially to be avoided.
Furthermore, the presence of an electrical connector close to the patient can become problematic for safety raisons in the case of unwanted disconnection or faulty contact.
On the other hand, the case 180 that encloses the electronic module has to be disinfected after each intervention of the dentist. But the presence of a male electrical connector and a female electrical connector requires receptacles for the connector branches and such arrangements create places that can never be sterilized, at least satisfactorily.
Besides, leak tightness problems risk arising during sterilization, which is not acceptable.
Each anti-pull body is also provided, on its two parallel opposite sides that carry the fitting parts, with two transversal end-stop parts arranged either side of one of the fitting parts and that are referenced 158 c, 158 d, for those around the fitting part 158 a, and 158 e and 158 f for those around the fitting part 158 b (FIGS. 12 and 13).
These transversal end-stop parts are shorter than the fitting parts so that, when the fitting parts of each anti-pull body are introduced inside the cut-out's corresponding openings, the transversal end-stop parts come up against the cut-out's longitudinal edges to immobilize the anti-pull body in this position (FIG. 13).
It may be noted that the fitting parts arranged, on the one hand, on the metal anti-pull body and, on the other hand, on the edges of the corresponding cut-out can be reversed, in the sense that the body can be provided with longitudinal grooves and the cut-out with corresponding pins.
Other fitting parts can be envisaged (dovetail joint assembly, several notches on each edge of the cut-out, notches of different shapes, etc.).
It may be noted that the board 150 includes an activation device 100 shown in the form of a pushbutton and that enables the detector to be activated when a tooth image has to be taken.
As shown in FIG. 11, two metal half-shells 164 and 166 are arranged on either side of the printed circuit board 150 and assembled together, by means of a weld bead, to secure said printed circuit board.
These metal shells are assembled after the metal anti-pull bodies are made solid with the cables 34 and 56, after these bodies are positioned in the corresponding cut-outs of the circuit 150 and after the electrical connections 168 with the board (FIG. 12) are put into place.
It may be noted that the metal anti-pull bodies also act as spacers to enable the fixing of the metal half-shells.
The latter fulfill several functions:
- - a first function of these metal half-shells is to ensure electrical continuity across the two cables 34 and 56; - a second function is thus to provide a Faraday cage for electromagnetic compatibility purposes; - a third function of these half-shells is to mechanically protect the electronic module 32.
Two end-sleeves 170 and 172 are provided to enable the routing of the corresponding cables 56, 34 by means of a longitudinal conduit 174 (FIG. 15).
These sleeves, such as the sleeve 172 of FIG. 15, include longitudinal recesses 176, 178 which lend them some flexibility. This flexibility prevents shearing of the cable that could occur following the repeated handling and distortion it undergoes.
These sleeves also ensure the leak tightness of the cable and the case interior.
The case 180 shown in FIG. 16 and which encapsulates the electronic module 32 already protected by the two metal half-shells 164 and 166 has two plastic parts forming a cover 182, 184 (FIG. 14).
These two parts with overall elongated and more particularly oblong shape are assembled together, for example, by gluing or US welding so as to enclose the electronic module 32.
One may note the presence on each of the end sleeves 170 and 172 of a collar 186, 188 (FIGS. 14 and 15) and an opening with at least partially complementary shape made at the ends of each of the parts 182 and 184 forming the cover.
In FIG. 14, the top half-cover 182 has two openings, of which one 190 is shown, and the bottom half-cover 184 has two openings 192 and 194, both shown.
When the two half-covers are assembled on either side of the electronic module 32, the openings of each half-cover slot into the collar and the latter's body to axially hold solid the case and the end-sleeves that extend it.
The openings arranged at the ends of the top and bottom half-covers thus constitute the holding edges of the corresponding sleeves.
One may also note the presence inside the top half-cover 184 of transversal guide walls 196 and 198, which are recessed to enable the positioning of the corresponding cable.
Transversal stiffening ribs 200, 202 and 204 as well as a longitudinal rib 206, of which only one end is visible, are arranged inside the half-cover 184 to stiffen the latter.
A plate 208 is arranged at the bottom of the half-cover 184 to enable correct positioning of the electronic module protected by the two metal half-shells.
It should be noted that the top half-cover 182 has the same arrangements as those described for the half-cover 184.
The detector activation device 100 cannot be directly handled by the user for leak-tightness reasons and it is accessible to the user through a thinned zone 210 provided in the top half-cover 182 and which is designed to be distorted locally and made to press in under the user's finger pressure and return to its initial position when the pressure is no longer exerted.
According to an alternative embodiment, the thinned zone is replaced by an added button created in a flexible material, which the user will have access to and which will be attached to the half-cover 182, for example by gluing, so as to ensure the leak-tightness and not to have zones capable of causing dirt incrustation.
It may be noted that the case 180 enclosing the electronic module 32, and the axial extensions 170 and 172 of this case have external surfaces enabling them to be easily disinfected/sterilized and the forms of this external surface are of a kind not to encourage dirt incrustation.
Furthermore, the external surface of the case and its axial extensions 170, 172 is drip-proof to prevent the case interior from being contaminated.
The dental radiology apparatus according to the invention thus has a particularly simple and reliable design. The video signal supplied to the processing and display unit 54 has very high quality as the detector's signal-to-noise ratio has been considerably improved compared with the prior art.
Other alternative embodiments within the capacity of those skilled in the art can also be envisaged for the various aspects of the invention that have just been described.
1. A dental radiology apparatus comprising an intraoral sensor adapted to receive x-rays that have passed through at least one tooth, the sensor including: an x-ray to visible radiation converter, a detector comprising an active pixel array produced using biCMOS technology on a substrate made of semi-conductor material, and a sequencer capable of generating several control signals to control the active pixel array, the sequencer being integrated on the same substrate as the array.
2. The dental radiology apparatus according to claim 1 wherein the sequencer is capable of receiving at least one signal external to the sensor from which the control signals are generated.
3. The dental radiology apparatus according to claim 1 further comprising an electronic module separate from the sensor and which is capable of generating the at least one signal external to the sensor, from which the control signals are generated.
4. The dental radiology apparatus according to claim 3 further comprising a link between the electronic module and the sensor for the transmission of the at least one external signal.
5. The dental radiology apparatus according to claim 4 wherein the link is a wire link..
| 16,782 |
https://github.com/edenleung/think-admin/blob/master/app/common/service/MenuActionService.php | Github Open Source | Open Source | Apache-2.0 | 2,021 | think-admin | edenleung | PHP | Code | 69 | 248 | <?php
declare(strict_types=1);
/*
* This file is part of TAnt.
* @link https://github.com/edenleung/think-admin
* @document https://www.kancloud.cn/manual/thinkphp6_0
* @contact QQ Group 996887666
* @author Eden Leung [email protected]
* @copyright 2019 Eden Leung
* @license https://github.com/edenleung/think-admin/blob/6.0/LICENSE.txt
*/
namespace app\common\service;
use app\common\model\MenuAction;
class MenuActionService extends \Crud\CrudService
{
/**
* @var MenuAction
*/
protected $model;
protected $pageSize = 10;
public function __construct(MenuAction $model)
{
parent::__construct($model);
}
public function filter($q, $query)
{
}
}
| 5,717 |
https://stackoverflow.com/questions/48227772 | StackExchange | Open Web | CC-By-SA | 2,018 | Stack Exchange | English | Spoken | 208 | 378 | ffmpeg player in discord.py (python) automatically leave
I have created a discord bot that on certain messages either sends back a message or plays a sound (like a soundboard)
The crucial line of code is:
soundboard_player = voice_client.create_ffmpeg_player("doh.mp3")
soundboard_player.start()
await client.send_message(message.channel, "Playing DOH...")
This works absolutely fine but i kept trying to add the line
after=voice_client.disconnect()
I put this inside the ("doh.mp3", * I PUT IT HERE *) brackets.
I wanted the bot to leave after it was done.
When I run the code with the 'after' statement included, the bot joins and I get the error message:
TypeError: disconnect() takes 1 positional argument but 2 were given
I know you can use soundboard_player.is_done() to check the status of the bot but I couldn't figure out a way to check the status without trapping the code in a loop
By trapping the code in the loop I cant execute a STOP command to stop it playing the song (soundbite) half way through.
Any help with the after=voice_client.disconnect() command for the ffmpeg player
or a creative way to periodically check the status without getting trapped in the loop?
run it threadsafe.
I recommend:
loop = voice_client.loop
after=lambda:
asyncio.run_coroutine_threadsafe(voice_client.disconnect(), loop)
you should write it inside a sync function.
good luck.
| 1,564 |
|
https://github.com/keefo/swiftplot/blob/master/Sources/SwiftPlot/Geometry/Size.swift | Github Open Source | Open Source | Apache-2.0 | 2,022 | swiftplot | keefo | Swift | Code | 78 | 157 | public struct Size: Hashable {
public var width: Float
public var height: Float
public init(width: Float, height: Float) {
self.width = width
self.height = height
}
}
extension Size {
public static let zero = Size(width: 0, height: 0)
}
extension Size {
/// Returns a `Size` whose `width` is equal to this size's `height`,
/// and whose `height` is equal to this size's `width`.
///
public func swappingComponents() -> Size {
Size(width: height, height: width)
}
}
| 48,290 |
https://github.com/3mdeb/talos-hostboot/blob/master/src/usr/hdat/hdatmsvpd.C | Github Open Source | Open Source | Apache-2.0 | 2,018 | talos-hostboot | 3mdeb | C | Code | 5,457 | 25,346 | /* IBM_PROLOG_BEGIN_TAG */
/* This is an automatically generated prolog. */
/* */
/* $Source: src/usr/hdat/hdatmsvpd.C $ */
/* */
/* OpenPOWER HostBoot Project */
/* */
/* Contributors Listed Below - COPYRIGHT 2016,2018 */
/* [+] International Business Machines Corp. */
/* */
/* */
/* Licensed under the Apache License, Version 2.0 (the "License"); */
/* you may not use this file except in compliance with the License. */
/* You may obtain a copy of the License at */
/* */
/* http://www.apache.org/licenses/LICENSE-2.0 */
/* */
/* Unless required by applicable law or agreed to in writing, software */
/* distributed under the License is distributed on an "AS IS" BASIS, */
/* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or */
/* implied. See the License for the specific language governing */
/* permissions and limitations under the License. */
/* */
/* IBM_PROLOG_END_TAG */
/**
* @file hdatmsvpd.C
*
* @brief This file contains the implementation of the HdatMsVpd class.
*
*/
/*----------------------------------------------------------------------------*/
/* Includes */
/*----------------------------------------------------------------------------*/
#include "hdatmsvpd.H" // HdatMsVpd class definition
#include "hdathdif.H"
#include <sys/mm.h>
#include <sys/mmio.h>
#include <assert.h>
#include <util/align.H>
#include <limits.h>
namespace HDAT
{
/*----------------------------------------------------------------------------*/
/* Global variables */
/*----------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------*/
/* Macros */
/*----------------------------------------------------------------------------*/
// macro to compute the address of a main store area
#define HDAT_MS_AREA(_i_idx_) *((HdatMsArea **)((char *)iv_msAreaPtrs + \
_i_idx_ * sizeof(HdatMsArea *)))
/** @brief See the prologue in hdatmsvpd.H
*/
HdatMsVpd::HdatMsVpd(errlHndl_t &o_errlHndl,
const hdatMsAddr_t &i_msAddr
):HdatHdif(o_errlHndl,
HDAT_MSVPD_STRUCT_NAME, HDAT_MS_VPD_LAST, HDAT_START_INSTANCE,
HDAT_MS_CHILD_LAST, HDAT_MS_VPD_VERSION),
iv_actMsAreaCnt(0), iv_maxMsAreaCnt(0), iv_msAreaPtrs(NULL),
iv_IMTaddrRangeArray(NULL), iv_maxIMTAddrRngCnt(0),
iv_UEaddrRangeArray(NULL), iv_maxUEAddrRngCnt(0)
{
memcpy(&iv_msAddr, &i_msAddr, sizeof(hdatMsAddr_t));
}
void HdatMsVpd::hdatInit(hdatMsAddr_t &i_maxMsAddr,
hdatMsAddr_t &i_maxMsCcmAddr,
uint32_t i_msSize,
uint32_t i_msAreaCnt,
uint32_t i_MostSigAffinityDomain,
uint32_t i_ueAreaCnt,
uint64_t i_MirrMemStartAddr)
{
iv_maxUEAddrRngCnt = i_ueAreaCnt;
iv_maxMsAreaCnt = i_msAreaCnt;
iv_maxIMTAddrRngCnt = i_msAreaCnt;
memcpy(&iv_maxAddr.hdatMaxAddr, &i_maxMsAddr, sizeof(hdatMsAddr_t));
memcpy(&iv_maxAddr.hdatMaxCcmAddr, &i_maxMsCcmAddr, sizeof(hdatMsAddr_t));
iv_maxAddr.hdatMstSigAffntyDom = i_MostSigAffinityDomain;
memcpy(&iv_maxAddr.hdatMirrMemStartAddr, &i_MirrMemStartAddr,
sizeof(hdatMsAddr_t));
memset(&iv_maxAddr.hdatHRMORstashLoc,0x00,sizeof(hdatMsAddr_t));
iv_maxSize.hdatReserved1 = 0;
iv_maxSize.hdatTotSize = i_msSize;
memset(&iv_mover, 0x00, sizeof(hdatMsVpdPageMover_t));
iv_IMTaddrRngArrayHdr.hdatOffset = sizeof(hdatHDIFDataArray_t);
iv_IMTaddrRngArrayHdr.hdatArrayCnt = 0;
iv_IMTaddrRngArrayHdr.hdatAllocSize = sizeof(hdatMsVpdImtAddrRange_t);
iv_IMTaddrRngArrayHdr.hdatActSize = sizeof(hdatMsVpdImtAddrRange_t);
iv_UEaddrRngArrayHdr.hdatOffset = sizeof(hdatHDIFDataArray_t);
iv_UEaddrRngArrayHdr.hdatArrayCnt = 0;
iv_UEaddrRngArrayHdr.hdatAllocSize = sizeof(hdatMsVpdUEAddrRange_t);
iv_UEaddrRngArrayHdr.hdatActSize = sizeof(hdatMsVpdUEAddrRange_t);
iv_RHBaddrRngArrayHdr.hdatOffset = sizeof(hdatHDIFDataArray_t);
iv_RHBaddrRngArrayHdr.hdatArrayCnt = 0;
iv_RHBaddrRngArrayHdr.hdatAllocSize = sizeof(hdatMsVpdRhbAddrRange_t);
iv_RHBaddrRngArrayHdr.hdatActSize = sizeof(hdatMsVpdRhbAddrRange_t);
iv_maxRHBAddrRngCnt = HDAT_RHB_MAX_RANGE_ENTRIES * hdatGetMaxCecNodes();
// Allocate space for the mainstore area entries and IMT Addr Range array
iv_msAreaPtrs = new HdatMsArea*[iv_maxMsAreaCnt];
iv_IMTaddrRangeArray = new hdatMsVpdImtAddrRange_t[iv_maxIMTAddrRngCnt];
iv_UEaddrRangeArray = new hdatMsVpdUEAddrRange_t[iv_maxUEAddrRngCnt];
// Allocate space for the host boot memory reserve range
iv_RHBaddrRangeArray = new hdatMsVpdRhbAddrRange_t[iv_maxRHBAddrRngCnt];
// Update the base class internal data pointers.
// When the data is written to the file by commit(), it must be done in the
// same order as these addData() calls
this->addData(HDAT_MS_VPD_MAX_ADDR, sizeof(hdatMsVpdAddr_t));
this->addData(HDAT_MS_VPD_MAX_SIZE, sizeof(hdatMsVpdSize_t));
this->addData(HDAT_MS_VPD_PAGE_MOVER, sizeof(hdatMsVpdPageMover_t));
this->addData(HDAT_MS_VPD_IMT_ADDR_RNG, (sizeof(hdatHDIFDataArray_t) +
(iv_maxIMTAddrRngCnt * sizeof(hdatMsVpdImtAddrRange_t))));
this->addData(HDAT_MS_VPD_UE_ADDR_RNG, (sizeof(hdatHDIFDataArray_t) +
(iv_maxUEAddrRngCnt * sizeof(hdatMsVpdUEAddrRange_t))));
this->addData(HDAT_MS_VPD_HB_ADDR_RNG, (sizeof(hdatHDIFDataArray_t) +
(iv_maxRHBAddrRngCnt * sizeof(hdatMsVpdRhbAddrRange_t))));
this->align();
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
HdatMsVpd::~HdatMsVpd()
{
uint32_t l_cnt;
HdatMsArea *l_obj, **l_curPtr;
// Delete mainstore area objects (which in turn delete RAM objects)
l_curPtr = iv_msAreaPtrs;
for (l_cnt = 0; l_cnt < iv_actMsAreaCnt; l_cnt++)
{
l_obj = *l_curPtr;
delete l_obj;
l_curPtr = reinterpret_cast<HdatMsArea**>(reinterpret_cast<char*>
(l_curPtr) + sizeof(HdatMsArea *));
}
delete[] iv_msAreaPtrs;
// Delete IMT Address Range Array
delete[] iv_IMTaddrRangeArray;
// Delete UE Address Range Array
delete[] iv_UEaddrRangeArray;
delete[] iv_RHBaddrRangeArray;
uint64_t l_addr = reinterpret_cast<uint64_t> (iv_virtAddr);
l_addr = ALIGN_PAGE_DOWN(l_addr);
iv_virtAddr = reinterpret_cast<void*>(l_addr);
int rc = mm_block_unmap(iv_virtAddr);
if( rc != 0)
{
errlHndl_t l_errl = NULL;
/*@
* @errortype
* @moduleid HDAT::MOD_MSVPD_DESTRUCTOR
* @reasoncode HDAT::RC_DEV_MAP_FAIL
* @devdesc Unmap a mapped region failed
* @custdesc Firmware encountered an internal error.
*/
hdatBldErrLog(l_errl,
MOD_MSVPD_DESTRUCTOR,
RC_DEV_MAP_FAIL,
0,0,0,0,
ERRORLOG::ERRL_SEV_UNRECOVERABLE,
HDAT_VERSION1,
true);
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
errlHndl_t HdatMsVpd::addIMTAddrRange(hdatMsAddr_t &i_start,
hdatMsAddr_t &i_end)
{
errlHndl_t l_errlHndl = NULL;
hdatMsVpdImtAddrRange_t *l_addr;
if (iv_IMTaddrRngArrayHdr.hdatArrayCnt < iv_maxIMTAddrRngCnt)
{
l_addr = reinterpret_cast<hdatMsVpdImtAddrRange_t*>(reinterpret_cast
<char*>(iv_IMTaddrRangeArray) + (iv_IMTaddrRngArrayHdr.hdatArrayCnt *
sizeof(hdatMsVpdImtAddrRange_t)));
l_addr->hdatImtAddrRngStrAddr = i_start;
l_addr->hdatImtAddrRngEndAddr = i_end;
iv_IMTaddrRngArrayHdr.hdatArrayCnt++;
}
else
{
/*@
* @errortype
* @refcode LIC_REFCODE
* @subsys EPUB_FIRMWARE_SP
* @reasoncode RC_ERC_MAX_EXCEEDED
* @moduleid MOD_ADD_IMT_ADDR_RANGE
* @userdata1 current number of array entries
* @userdata2 maximum number of array entries
* @userdata3 none
* @userdata4 none
* @devdesc Exceeded limit of number of mainstore VPD
* In Memory Trace array entries
*/
hdatBldErrLog(l_errlHndl,
MOD_ADD_IMT_ADDR_RANGE, // SRC module ID
RC_ERC_MAX_EXCEEDED, // SRC extended reference code
iv_IMTaddrRngArrayHdr.hdatArrayCnt, // SRC hex word 1
iv_maxIMTAddrRngCnt); // SRC hex word 2
}
return l_errlHndl;
}
/** @brief See the prologue in hdatmsvpd.H
*/
errlHndl_t HdatMsVpd::addUEAddrRange(hdatMsAddr_t &i_addr)
{
errlHndl_t l_errlHndl = NULL;
hdatMsVpdUEAddrRange_t *l_addr;
if (iv_UEaddrRngArrayHdr.hdatArrayCnt < iv_maxUEAddrRngCnt)
{
l_addr = reinterpret_cast<hdatMsVpdUEAddrRange_t*>(reinterpret_cast
<char*>(iv_UEaddrRangeArray) + (iv_UEaddrRngArrayHdr.hdatArrayCnt *
sizeof(hdatMsVpdUEAddrRange_t)));
l_addr->hdatUEAddr = i_addr;
iv_UEaddrRngArrayHdr.hdatArrayCnt++;
}
else
{
/*@
* @errortype
* @refcode LIC_REFCODE
* @subsys EPUB_FIRMWARE_SP
* @reasoncode RC_ERC_MAX_EXCEEDED
* @moduleid MOD_ADD_UE_ADDR_RANGE
* @userdata1 current number of array entries
* @userdata2 maximum number of array entries
* @userdata3 none
* @userdata4 none
* @devdesc Exceeded limit of number of mainstore
* VPD In Memory Trace array entries
*/
hdatBldErrLog(l_errlHndl,
MOD_ADD_UE_ADDR_RANGE, // SRC module ID
RC_ERC_MAX_EXCEEDED, // SRC extended reference code
iv_UEaddrRngArrayHdr.hdatArrayCnt, // SRC hex word 1
iv_maxUEAddrRngCnt); // SRC hex word 2
}
return l_errlHndl;
}
errlHndl_t HdatMsVpd::addRHBAddrRange(uint32_t i_dbob_id, hdatMsAddr_t &i_start,
hdatMsAddr_t &i_end, uint32_t i_labelSize,
uint8_t* &i_labelStringPtr,
hdatRhbPermType i_permission)
{
errlHndl_t l_errlHndl = NULL;
hdatMsVpdRhbAddrRange_t *l_addr;
if (iv_RHBaddrRngArrayHdr.hdatArrayCnt < iv_maxRHBAddrRngCnt)
{
l_addr = reinterpret_cast<hdatMsVpdRhbAddrRange_t*>(reinterpret_cast
<char*>(iv_RHBaddrRangeArray) + (iv_RHBaddrRngArrayHdr.hdatArrayCnt *
sizeof(hdatMsVpdRhbAddrRange_t)));
l_addr->hdatRhbRngType = HDAT::RHB_TYPE_INVALID;
l_addr->hdatRhbRngId = i_dbob_id;
l_addr->hdatRhbAddrRngStrAddr = i_start;
l_addr->hdatRhbAddrRngEndAddr = i_end;
//TODO : : RTC Story 159684
//Need to verify the correct data for label size and string
if (i_labelSize <= HDAT_MS_RHB_LABEL_LEN)
{
l_addr->hdatRhbLabelSize = i_labelSize;
}
else
{
l_addr->hdatRhbLabelSize = HDAT_MS_RHB_LABEL_LEN;
}
memset(l_addr->hdatRhbLabelString, 0x00, HDAT_MS_RHB_LABEL_LEN);
if (i_labelStringPtr != NULL)
{
for(uint8_t l_idx = 0; l_idx < l_addr->hdatRhbLabelSize; l_idx++)
{
l_addr->hdatRhbLabelString[l_idx] = i_labelStringPtr[l_idx];
}
}
else
{
HDAT_INF("hdatmsvpd:addRHBAddrRange "
"i_labelStringPtr is NULL");
}
l_addr->hdatRhbPermission = i_permission;
iv_RHBaddrRngArrayHdr.hdatArrayCnt++;
}
else
{
/*@
* @errortype
* @refcode LIC_REFCODE
* @subsys EPUB_FIRMWARE_SP
* @reasoncode RC_ERC_MAX_EXCEEDED
* @moduleid MOD_ADD_RES_HB_ADDR_RANGE
* @userdata1 current number of array entries
* @userdata2 maximum number of array entries
* @userdata3 none
* @userdata4 none
* @devdesc Exceeded limit of number of mainstore VPD Reserved
* Hostboot array entries
*/
hdatBldErrLog(l_errlHndl,
MOD_ADD_RES_HB_ADDR_RANGE, // SRC module ID
RC_ERC_MAX_EXCEEDED, // SRC extended reference code
iv_RHBaddrRngArrayHdr.hdatArrayCnt, // SRC hex word 1
iv_maxRHBAddrRngCnt); // SRC hex word 2
}
return l_errlHndl;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setBSR(const hdatMsAddr_t &i_bsrAddr,
hdatBsrMode i_bsrMode)
{
const uint32_t HDAT_BSR_ENABLED = 0x20000000;
iv_mover.hdatFlags |= (HDAT_BSR_ENABLED | i_bsrMode);
memcpy(&iv_mover.hdatBSRAddr, &i_bsrAddr, sizeof(hdatMsAddr_t));
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setXSCOM(const hdatMsAddr_t &i_xscomAddr)
{
const uint32_t HDAT_XSCOM_ENABLED = 0x10000000;
iv_mover.hdatFlags |= HDAT_XSCOM_ENABLED;
memcpy(&iv_mover.hdatXSCOMAddr, &i_xscomAddr, sizeof(hdatMsAddr_t));
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
errlHndl_t HdatMsVpd::addMsAreaFru(uint32_t i_resourceId,
uint32_t i_slcaIndex,
TARGETING::Target * i_target,
uint16_t i_msAreaId,
uint32_t i_ramCnt,
uint32_t i_chipEcCnt,
uint32_t i_addrRngCnt)
{
errlHndl_t l_errlHndl = NULL;
HdatMsArea *l_msArea, *l_prevMsArea, **l_arrayEntry;
uint32_t l_slcaIdx, l_kwdSize, l_resourceId, l_prevIdx;
char *l_kwd;
l_msArea = NULL;
l_kwd = NULL;
l_slcaIdx = i_slcaIndex;
l_kwdSize = 0;
// Ensure we are not over max mainstore areas that we were told this object
// could handle on the constructor.
if (iv_actMsAreaCnt < iv_maxMsAreaCnt)
{
// Determine if the resource ID associated with this mainstore area is
// the same as the resoruce id of the previous mainstore area.If it is,
// we can gain a performance advantage (translates into a smaller IPL
// time for the builddata step) by using the ASCII keyword data we
// already have rather than going to svpd to get it again.
if (iv_actMsAreaCnt > 0)
{
l_prevIdx = iv_actMsAreaCnt - 1;
l_prevMsArea = HDAT_MS_AREA(l_prevIdx);
l_prevMsArea->getKwdInfo(l_resourceId, l_slcaIdx, l_kwdSize, l_kwd);
if (l_resourceId != i_resourceId)
{
l_kwd = NULL;
l_slcaIdx = 0;
l_kwdSize = 0;
}
}
// Create a mainstore area object and add it to the array of objects we
// are managing
l_msArea = new HdatMsArea(l_errlHndl,
i_target,
i_msAreaId,
i_ramCnt,
i_chipEcCnt,
i_addrRngCnt,
i_resourceId,
l_slcaIdx,
l_kwdSize,
l_kwd);
if (NULL == l_errlHndl)
{
l_arrayEntry = reinterpret_cast<HdatMsArea**>(reinterpret_cast
<char*>(iv_msAreaPtrs) + iv_actMsAreaCnt * sizeof(HdatMsArea *));
*l_arrayEntry = l_msArea;
iv_actMsAreaCnt++;
}
else
{
delete l_msArea;
}
}
else
{
/*@
* @errortype
* @refcode LIC_REFCODE
* @subsys EPUB_FIRMWARE_SP
* @reasoncode RC_ERC_MAX_EXCEEDED
* @moduleid MOD_ADD_MS_AREA_FRU
* @userdata1 current array entry count
* @userdata2 maximum array entry count
* @userdata3 ID number of mainstore area that wasn't added
* @userdata4 none
* @devdesc Exceeded limit of number of mainstore area array entries
*/
hdatBldErrLog(l_errlHndl,
MOD_ADD_MS_AREA_FRU, // SRC module ID
RC_ERC_MAX_EXCEEDED, // SRC extended reference code
iv_actMsAreaCnt, // SRC hex word 1
iv_maxMsAreaCnt, // SRC hex word 2
i_msAreaId); // SRC hex word 3
}
return l_errlHndl;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setMsAreaType(uint16_t i_msAreaId,
hdatMemParentType i_type)
{
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_obj->setParentType(i_type);
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setMsAreaStat(uint16_t i_msAreaId,
uint16_t i_status)
{
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_obj->setStatus(i_status);
}
else
{
HDAT_ERR( "hdatmsvpd:setMsAreaStat - invalid i_msAreadId parameter");
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setMsAreaInterleavedId(uint16_t i_msAreaId,
uint16_t i_id)
{
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_obj->setInterleavedId(i_id);
}
else
{
HDAT_ERR( "hdatmsvpd:setMsAreaInterleavedId-invalid i_msAreadId "
"parameter");
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setMsAreaSize(uint16_t i_msAreaId,
uint32_t i_size)
{
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_obj->setSize(i_size);
}
else
{
HDAT_ERR( "hdatmsvpd:setMsAreaSize - invalid i_msAreadId parameter");
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setMsAreaModuleId(uint16_t i_msAreaId,
uint32_t i_moduleId)
{
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_obj->setModuleId(i_moduleId);
}
else
{
HDAT_ERR( "hdatmsvpd:setMsAreaModuleId - invalid i_msAreadId"
" parameter");
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setMsAreaAffinityDomain(uint16_t i_msAreaId,
uint32_t i_affinityDomain)
{
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_obj->setAffinityDomain(i_affinityDomain);
}
else
{
HDAT_ERR("hdatmsvpd:setMsAreaAffinityDomain-invalid "
"i_msAreadId parameter");
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
errlHndl_t HdatMsVpd::addMsAreaAddr(uint16_t i_msAreaId,
hdatMsAddr_t &i_start,
hdatMsAddr_t &i_end,
uint32_t i_procChipId,
bool i_rangeIsMirrorable,
uint8_t i_mirroringAlgorithm,
uint64_t i_startMirrAddr,
uint32_t i_hdatMemCntrlID)
{
errlHndl_t l_errlHndl = NULL;
HdatMsArea *l_obj;
hdatMsAddr_t l_startMirrAddr;
memcpy(&l_startMirrAddr, &i_startMirrAddr, sizeof(hdatMsAddr_t));
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_errlHndl = l_obj->addAddrRange(i_start, i_end, i_procChipId,
i_rangeIsMirrorable, i_mirroringAlgorithm, l_startMirrAddr, i_hdatMemCntrlID);
}
else
{
HDAT_INF( "hdatmsvpd:addMsAreaAddr - invalid i_msAreadId parameter");
}
return l_errlHndl;
}
/** @brief See the prologue in hdatmsvpd.H
*/
errlHndl_t HdatMsVpd::addEcEntry(uint16_t i_msAreaId,
uint32_t i_manfId,
uint32_t i_ecLvl)
{
errlHndl_t l_errlHndl = NULL;
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_errlHndl = l_obj->addEcEntry(i_manfId, i_ecLvl);
}
else
{
HDAT_ERR( "hdatmsvpd:addEcEntry - invalid i_msAreadId parameter");
}
return l_errlHndl;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::setMsaI2cInfo(uint16_t i_msAreaId,
std::vector<hdatI2cData_t>& i_I2cDevEntries)
{
HdatMsArea *l_obj;
if (i_msAreaId < iv_actMsAreaCnt)
{
l_obj = HDAT_MS_AREA(i_msAreaId);
l_obj->setMsaI2cInfo(i_I2cDevEntries);
}
else
{
HDAT_ERR("hdatmsvpd:setMsaI2cInfo - invalid i_msAreadId parametera");
}
}
/** @brief See the prologue in hdatmsvpd.H
*/
errlHndl_t HdatMsVpd::addRamFru(uint16_t i_msAreaId,
TARGETING::Target * i_target,
uint32_t i_resourceId,
uint32_t i_slcaIndex,
uint16_t i_ramId,
uint16_t i_status,
uint32_t i_size,
uint32_t i_dimmId,
uint32_t i_RamCurFreq)
{
errlHndl_t l_errlHndl = NULL;
HdatMsArea *l_msArea;;
HdatRam *l_ram;
// Ensure we are not over the current mainstore area count
if (i_msAreaId < iv_actMsAreaCnt)
{
l_ram = NULL;
l_msArea = HDAT_MS_AREA(i_msAreaId);
// Create a RAM object
l_ram = new HdatRam(l_errlHndl, i_target, i_resourceId,i_slcaIndex);
if (NULL == l_errlHndl)
{
l_ram->iv_ramArea.hdatRamAreaId = i_ramId;
l_ram->iv_ramArea.hdatRamStatus = i_status;
l_ram->iv_ramArea.hdatRamDimmId = i_dimmId;
l_ram->iv_ramArea.hdatRamCurFreq = i_RamCurFreq;
l_ram->iv_ramSize.hdatRamTotalSize = i_size;
// Add the RAM object to the mainstore area object
if (l_msArea)
{
l_errlHndl = l_msArea->addRam(*l_ram);
}
}
if (NULL != l_errlHndl)
{
delete l_ram;
}
}
else
{
/*@
* @errortype
* @refcode LIC_REFCODE
* @subsys EPUB_FIRMWARE_SP
* @reasoncode RC_ERC_NO_PARENT
* @moduleid MOD_ADD_RAM_FRU
* @userdata1 main store area id
* @userdata2 current count of main store areas
* @userdata3 none
* @userdata4 none
* @devdesc Attempted to add a RAM FRU for an invalid mainstore area
*/
HDAT_INF("Attempted to add a RAM FRU for an invalid mainstore area %d",
i_msAreaId);
hdatBldErrLog(l_errlHndl,
MOD_ADD_RAM_FRU, // SRC module ID
RC_ERC_NO_PARENT, // SRC extended reference code
i_msAreaId, // SRC hex word 1
iv_actMsAreaCnt); // SRC hex word 2
}
return l_errlHndl;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::adjustMsAreaObjects()
{
HdatMsArea *l_msEntry;
uint32_t l_idx, l_maxSize, l_tempSize;
bool l_adjust;
l_maxSize = 0;
l_adjust = false;
// Finalize the object size for each MS area object. Also, determine if
// the objects differ in size. If they do, an extra step is needed to make
// them all the same size.
for (l_idx = 0; l_idx < iv_actMsAreaCnt; l_idx++)
{
l_msEntry = *(reinterpret_cast<HdatMsArea**>(reinterpret_cast
<char*>(iv_msAreaPtrs) + l_idx * sizeof(HdatMsArea *)));
l_msEntry->finalizeObjSize(); // Get the MS area sizes updated before
// size() method is used
l_tempSize = l_msEntry->size();
if (l_maxSize != l_tempSize)
{
if (l_maxSize != 0)
{
l_adjust = true;
}
if (l_maxSize < l_tempSize)
{
l_maxSize = l_tempSize;
}
}
}
// Do we need to adjust some of the MS area objects to make them all the
// same size?
if (l_adjust)
{
for (l_idx = 0; l_idx < iv_actMsAreaCnt; l_idx++)
{
l_msEntry = *(reinterpret_cast<HdatMsArea**>(reinterpret_cast
<char*>(iv_msAreaPtrs) + l_idx * sizeof(HdatMsArea *)));
// If too small, adjust its size
if (l_msEntry->size() < l_maxSize)
{
l_msEntry->maxSiblingSize(l_maxSize);
}
}
}
// Tell the base class about child and grandchild structures.
for (l_idx = 0; l_idx < iv_actMsAreaCnt; l_idx++)
{
l_msEntry = *(reinterpret_cast<HdatMsArea**>(reinterpret_cast
<char*>(iv_msAreaPtrs) + l_idx * sizeof(HdatMsArea *)));
this->addChild(HDAT_MS_AREAS, l_msEntry->size(),1);//1st parm is 0 based
this->addGrandChild(l_msEntry->ramObjSizes());
}
return;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::getTotalSize(uint32_t &o_size)
{
HdatMsArea *l_msEntry;
// Since MS area objects could be different sizes at this point (different
// size for the VPD, for example) and since PHYP traverses the MS areas
// as an array, we may need to adjust the MS areas so they are all the same
// size.
this->adjustMsAreaObjects();
o_size = this->getSize();
o_size += sizeof(hdatMsVpdAddr_t);
o_size += sizeof(hdatMsVpdSize_t);
o_size += sizeof(hdatMsVpdPageMover_t);
o_size += sizeof(hdatHDIFDataArray_t);
o_size += (iv_maxIMTAddrRngCnt * sizeof(hdatMsVpdImtAddrRange_t));
o_size += sizeof(hdatHDIFDataArray_t);
o_size += (iv_maxUEAddrRngCnt * sizeof(hdatMsVpdUEAddrRange_t));
o_size += sizeof(hdatHDIFDataArray_t);
o_size += (iv_maxRHBAddrRngCnt * sizeof(hdatMsVpdRhbAddrRange_t));
o_size += this->endCommitSize();
// Write the MS area structures and RAM structures
if (iv_actMsAreaCnt > 0)
{
// All of the mainstore areas must be written first so that can be
// processed as an array of mainstore areas.
uint32_t l_ramSizes = 0;
uint8_t l_cnt = 0;
uint8_t l_currOffset = 0;
while (l_cnt < iv_actMsAreaCnt)
{
l_msEntry = *(reinterpret_cast<HdatMsArea**>(reinterpret_cast
<char*>(iv_msAreaPtrs) + l_cnt * sizeof(HdatMsArea *)));
// Since we don't know what order mainstore areas and RAM
// areas were created, update the offset in the HdatMsArea
// child structure triple so it points to the first RAM area.
l_currOffset = (iv_actMsAreaCnt - l_cnt) * l_msEntry->size()
+ l_ramSizes;
l_msEntry->chgChildOffset(HDAT_MS_AREA_RAM_AREAS, l_currOffset);
o_size += l_msEntry->getMsAreaSize();
// Now compute the size of the RAM areas associated with this
// mainstore area. These will have to be added to the child offset
// for the next mainstore area to skip over them.
l_ramSizes += l_msEntry->ramObjSizes();
l_cnt++;
}
// Now the children (RAM areas) of each mainstore area must be committed
l_cnt = 0;
while (l_cnt < iv_actMsAreaCnt)
{
l_msEntry = *(reinterpret_cast<HdatMsArea**>(reinterpret_cast
<char*>(iv_msAreaPtrs) + l_cnt * sizeof(HdatMsArea *)));
o_size += l_msEntry->getRamAreaSize();
l_cnt++;
}
}
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::prt()
{
uint32_t l_cnt;
HdatMsArea *l_obj;
HDAT_INF(" **** HdatMsVpd start ****");
HDAT_INF(" iv_msAddr = 0X %08X %08X ", iv_msAddr.hi, iv_msAddr.lo);
HDAT_INF(" iv_actMsAreaCnt = %u", iv_actMsAreaCnt);
HDAT_INF(" iv_maxMsAreaCnt = %u", iv_maxMsAreaCnt);
this->print();
HDAT_INF(" **hdatMsVpdAddr_t**");
HDAT_INF(" hdatMaxAddr = 0X %08X %08X ", iv_maxAddr.hdatMaxAddr.hi,
iv_maxAddr.hdatMaxAddr.lo);
HDAT_INF(" hdatMaxCcmAddr = 0X %08X %08X ", iv_maxAddr.hdatMaxCcmAddr.hi,
iv_maxAddr.hdatMaxCcmAddr.lo);
HDAT_INF(" hdatMstSigAffntyDom = 0X %08X ", iv_maxAddr.hdatMstSigAffntyDom);
HDAT_INF(" HRMOR stash loc = 0X %08X %08X \n",
iv_maxAddr.hdatHRMORstashLoc.hi, iv_maxAddr.hdatHRMORstashLoc.lo);
HDAT_INF(" **hdatMsVpdSize_t**");
HDAT_INF(" hdatReserved1 = %u", iv_maxSize.hdatReserved1);
HDAT_INF(" hdatTotSize = %u", iv_maxSize.hdatTotSize);
HDAT_INF(" **hdatMsVpdPageMover_t**");
HDAT_INF(" hdatFlags = %u", iv_mover.hdatFlags);
HDAT_INF(" hdatLockCnt = %u", iv_mover.hdatLockCnt);
HDAT_INF(" hdatLockAddr = 0X %08X %08X ", iv_mover.hdatLockAddr.hi,
iv_mover.hdatLockAddr.lo);
HDAT_INF(" hdatMoverAddr = 0X %08X %08X ", iv_mover.hdatMoverAddr.hi,
iv_mover.hdatMoverAddr.lo);
HDAT_INF(" hdatBSRAddr = 0X %08X %08X ", iv_mover.hdatBSRAddr.hi,
iv_mover.hdatBSRAddr.lo);
HDAT_INF(" **hdatMsVpdImtAddrRange_t**");
hdatPrintHdrs(NULL, NULL, &iv_IMTaddrRngArrayHdr, NULL);
{
hdatMsVpdImtAddrRange_t *l_addr = iv_IMTaddrRangeArray;
for (l_cnt = 0; l_cnt < iv_IMTaddrRngArrayHdr.hdatArrayCnt; l_cnt++)
{
HDAT_INF(" hdatImtAddrRngStrAddr = 0X %08X %08X ",
l_addr->hdatImtAddrRngStrAddr.hi,
l_addr->hdatImtAddrRngStrAddr.lo);
HDAT_INF(" hdatImtAddrRngEndAddr = 0X %08X %08X ",
l_addr->hdatImtAddrRngEndAddr.hi,
l_addr->hdatImtAddrRngEndAddr.lo);
l_addr++;
l_cnt++;
}
}
HDAT_INF(" **hdatMsVpdUEAddrRange_t**");
hdatPrintHdrs(NULL, NULL, &iv_UEaddrRngArrayHdr, NULL);
{
hdatMsVpdUEAddrRange_t *l_addr = iv_UEaddrRangeArray;
for (l_cnt = 0; l_cnt < iv_UEaddrRngArrayHdr.hdatArrayCnt; l_cnt++)
{
HDAT_INF(" hdatUEAddrRngStrAddr = 0X %08X %08X ",
l_addr->hdatUEAddr.hi,
l_addr->hdatUEAddr.lo);
l_addr++;
l_cnt++;
}
}
HDAT_INF(" **hdatMsVpdRhbAddrRange_t**");
hdatPrintHdrs(NULL, NULL, &iv_RHBaddrRngArrayHdr, NULL);
{
hdatMsVpdRhbAddrRange_t *l_addr = iv_RHBaddrRangeArray;
for (l_cnt = 0; l_cnt < iv_RHBaddrRngArrayHdr.hdatArrayCnt; l_cnt++)
{
HDAT_INF(" hdatRhbAddrRngStrAddr = 0X %08X %08X ",
l_addr->hdatRhbAddrRngStrAddr.hi,
l_addr->hdatRhbAddrRngStrAddr.lo);
HDAT_INF(" hdatRhbAddrRngEndAddr = 0X %08X %08X ",
l_addr->hdatRhbAddrRngEndAddr.hi,
l_addr->hdatRhbAddrRngEndAddr.lo);
l_addr++;
l_cnt++;
}
}
HDAT_INF("");;
HDAT_INF(" **** HdatMsVpd end ****");
HDAT_INF(" **main store areas and their associated RAM areas**");
for (l_cnt = 0; l_cnt < iv_actMsAreaCnt; l_cnt++)
{
l_obj = *(HdatMsArea **)((char *)iv_msAreaPtrs + l_cnt *
sizeof(HdatMsArea *));
l_obj->prt();
}
return;
}
/*******************************************************************************
* hdatLoadMsData
*******************************************************************************/
errlHndl_t HdatMsVpd::hdatLoadMsData(uint32_t &o_size, uint32_t &o_count)
{
errlHndl_t l_err = NULL;
HDAT_ENTER();
do
{
//Find the system target
TARGETING::Target *l_pSysTarget = NULL;
(void) TARGETING::targetService().getTopLevelTarget(l_pSysTarget);
assert(l_pSysTarget != NULL);
hdatMsAddr_t l_addr_range;
hdatMsAddr_t l_end;
l_addr_range.hi = 0x0;
l_addr_range.lo = 0x0;
l_end = l_addr_range;
uint32_t l_sizeConfigured = 0;
uint64_t l_maxMsAddr = hdatGetMaxMemConfiguredAddress();
hdatMsAddr_t l_tmpMaxMsAddr;
l_tmpMaxMsAddr.hi = (l_maxMsAddr & 0xFFFFFFFF00000000ull) >> 32;
l_tmpMaxMsAddr.lo = l_maxMsAddr & 0x00000000FFFFFFFFull;
HDAT_INF("MaxMsAddr high:0x%.8X 0x%.8X",
l_tmpMaxMsAddr.hi,l_tmpMaxMsAddr.lo);
uint32_t l_mostSigAffinityDomain_x = 0;
uint32_t l_ueCount = 1;
TARGETING::ATTR_MIRROR_BASE_ADDRESS_type l_mirroringBaseAddress_x =
l_pSysTarget->getAttr<TARGETING::ATTR_MIRROR_BASE_ADDRESS>();
TARGETING::ATTR_MIRROR_BASE_ADDRESS_type l_mirrorBaseAddress_x =
l_mirroringBaseAddress_x;
l_mirroringBaseAddress_x |= HDAT_REAL_ADDRESS_MASK64;
TARGETING::ATTR_MAX_MCS_PER_SYSTEM_type l_maxMsAreas =
l_pSysTarget->getAttr<TARGETING::ATTR_MAX_MCS_PER_SYSTEM>();
// Initialize the MS vpd class
// TODO : RTC Story 166994 to set the maximum number of Ms Area entries
// from new attribute
hdatInit(l_tmpMaxMsAddr,l_tmpMaxMsAddr,l_sizeConfigured,l_maxMsAreas*2,
l_mostSigAffinityDomain_x,l_ueCount,l_mirroringBaseAddress_x);
TARGETING::ATTR_XSCOM_BASE_ADDRESS_type l_xscomAddr =
l_pSysTarget->getAttr<TARGETING::ATTR_XSCOM_BASE_ADDRESS>();
assert(l_xscomAddr != 0);
{
hdatMsAddr_t l_hdatXscomAddr;
l_hdatXscomAddr.hi = (l_xscomAddr & 0xFFFFFFFF00000000ull) >> 32;
l_hdatXscomAddr.lo = l_xscomAddr & 0x00000000FFFFFFFFull;
l_hdatXscomAddr.hi |= HDAT_REAL_ADDRESS_MASK;
setXSCOM(l_hdatXscomAddr);
}
uint32_t l_index = 0;
//for each proc/ memory controller in the system
TARGETING::PredicateCTM l_procPred(TARGETING::CLASS_CHIP,
TARGETING::TYPE_PROC);
TARGETING::PredicateHwas l_predHwasPresent;
l_predHwasPresent.present(true);
TARGETING::PredicateHwas l_predHwasFunc;
l_predHwasFunc.functional(true);
TARGETING::PredicatePostfixExpr l_funcProc;
l_funcProc.push(&l_procPred).push(&l_predHwasFunc).And();
TARGETING::TargetRangeFilter l_procs(
TARGETING::targetService().begin(),
TARGETING::targetService().end(),
&l_funcProc);
uint32_t l_nxtSharingGroupId = 0;
for(;l_procs;++l_procs)
{
TARGETING::Target *l_pProcTarget = *(l_procs);
TARGETING::ATTR_ORDINAL_ID_type l_procChipId
= l_pProcTarget->getAttr<TARGETING::ATTR_ORDINAL_ID>();
//For each MCA
TARGETING::PredicateCTM l_allMca(TARGETING::CLASS_UNIT,
TARGETING::TYPE_MCA);
TARGETING::PredicateHwas l_funcMca;
l_funcMca.functional(true);
TARGETING::PredicatePostfixExpr l_allFuncMca;
l_allFuncMca.push(&l_allMca).push(&l_funcMca).And();
TARGETING::TargetHandleList l_mcaList;
TARGETING::targetService().
getAssociated(l_mcaList, l_pProcTarget,
TARGETING::TargetService::CHILD,
TARGETING::TargetService::ALL, &l_allFuncMca);
TARGETING::ATTR_PROC_MEM_BASES_type l_procMemBases = {0};
assert(l_pProcTarget->
tryGetAttr<TARGETING::ATTR_PROC_MEM_BASES>(l_procMemBases));
//Sharing count for each group
TARGETING::ATTR_MSS_MEM_MC_IN_GROUP_type l_mcaSharingCount = {0};
//Group ID for each group, group id will be assigned only
//if the group is shared
TARGETING::ATTR_MSS_MEM_MC_IN_GROUP_type l_mcsSharingGrpIds = {0};
//Size configured under each group
TARGETING::ATTR_PROC_MEM_SIZES_type l_procMemSizesBytes = {0};
assert(l_pProcTarget->tryGetAttr<TARGETING::ATTR_PROC_MEM_SIZES>
(l_procMemSizesBytes));
for(uint32_t l_mcaIdx = 0; l_mcaIdx<l_mcaList.size();
++l_mcaIdx)
{
uint32_t l_mcaInGrp = 0;
TARGETING::Target *l_pMcaTarget =
l_mcaList[l_mcaIdx];
if(!hdatFindGroupForMc(l_pProcTarget,
l_pMcaTarget,
l_mcaInGrp))
{
//Skip this MCA is not in any group
continue;
}
//Increment sharing count if mem configured under group.
if(l_procMemSizesBytes[l_mcaInGrp] > 0)
{
l_mcaSharingCount[l_mcaInGrp]++;
//Assign sharing group id only if shared
//And only when first instance of sharing is found
if(l_mcaSharingCount[l_mcaInGrp] ==
HDAT_MIN_NUM_FOR_SHARING)
{
l_mcsSharingGrpIds[l_mcaInGrp] =
l_nxtSharingGroupId;
l_nxtSharingGroupId++;
}
}
}
// TODO : RTC Story 159682
// Further CHTM support needs to be added which contains the trace
// array for 24 cores
hdatMsAddr_t l_hdatNhtmStartAddr;
hdatMsAddr_t l_hdatNhtmEndAddr;
TARGETING::ATTR_PROC_NHTM_BAR_BASE_ADDR_type l_nhtmStartAddr =
l_pProcTarget->getAttr<TARGETING::ATTR_PROC_NHTM_BAR_BASE_ADDR>();
TARGETING::ATTR_PROC_NHTM_BAR_SIZE_type l_nhtmSize =
l_pProcTarget->getAttr<TARGETING::ATTR_PROC_NHTM_BAR_SIZE>();
if( 0 != l_nhtmSize )
{
l_hdatNhtmStartAddr.hi =
(l_nhtmStartAddr & 0xFFFFFFFF00000000ull) >> 32;
l_hdatNhtmStartAddr.lo =
l_nhtmStartAddr & 0x00000000FFFFFFFFull;
l_hdatNhtmStartAddr.hi |= HDAT_REAL_ADDRESS_MASK;
auto l_nhtmEndAddr = l_nhtmStartAddr + l_nhtmSize;
l_hdatNhtmEndAddr.hi =
(l_nhtmEndAddr & 0xFFFFFFFF00000000ull) >> 32;
l_hdatNhtmEndAddr.lo = l_nhtmEndAddr & 0x00000000FFFFFFFFull;
l_hdatNhtmEndAddr.hi |= HDAT_REAL_ADDRESS_MASK;
HDAT_INF("hdatNhtmStartAddr = 0x%08X 0x%08X ",
l_hdatNhtmStartAddr.hi, l_hdatNhtmStartAddr.lo);
HDAT_INF("hdatNhtmEndAddr = 0x%08X 0x%08X ",
l_hdatNhtmEndAddr.hi, l_hdatNhtmEndAddr.lo);
addIMTAddrRange(l_hdatNhtmStartAddr, l_hdatNhtmEndAddr);
}
else
{
HDAT_INF("NHTM Bar size value = 0x%016llX",
l_nhtmSize);
}
TARGETING::PredicateCTM l_mcbistPredicate(TARGETING::CLASS_UNIT,
TARGETING::TYPE_MCBIST);
TARGETING::PredicatePostfixExpr l_presentMcbist;
l_presentMcbist.push(&l_mcbistPredicate).
push(&l_predHwasFunc).And();
TARGETING::TargetHandleList l_mcbistList;
// Find Associated MCBIST list
TARGETING::targetService().getAssociated(l_mcbistList,
l_pProcTarget,
TARGETING::TargetService::CHILD_BY_AFFINITY,
TARGETING::TargetService::ALL,
&l_presentMcbist);
//scan all mcbist in this proc
for(uint32_t l_mcbistIdx =0;
l_mcbistIdx < l_mcbistList.size();
++l_mcbistIdx)
{
TARGETING::Target *l_pMcbistTarget = l_mcbistList[l_mcbistIdx];
TARGETING::PredicateCTM l_mcsPredicate(TARGETING::CLASS_UNIT,
TARGETING::TYPE_MCS);
TARGETING::PredicatePostfixExpr l_funcMcs;
l_funcMcs.push(&l_mcsPredicate).push(&l_predHwasFunc).And();
TARGETING::TargetHandleList l_mcsList;
// Find Associated memory controllers
TARGETING::targetService().getAssociated(l_mcsList,
l_pMcbistTarget,
TARGETING::TargetService::CHILD,
TARGETING::TargetService::ALL,
&l_funcMcs);
uint32_t l_memBusFreq = getMemBusFreq(l_pMcbistTarget);
//scan all mcs in this proc to get sharing counit
for(uint32_t l_mcsIdx = 0;l_mcsIdx<l_mcsList.size(); ++l_mcsIdx)
{
TARGETING::Target *l_pMcsTarget = l_mcsList[l_mcsIdx];
//for each MCA connected to this this MCS
TARGETING::PredicateCTM l_mcaPredicate(
TARGETING::CLASS_UNIT, TARGETING::TYPE_MCA);
TARGETING::PredicateHwas l_predMca;
l_predMca.present(true);
TARGETING::PredicatePostfixExpr l_presentMca;
l_presentMca.push(&l_mcaPredicate).push(&l_predMca).And();
TARGETING::TargetHandleList l_mcaList;
// Get associated MCAs
TARGETING::targetService().
getAssociated(l_mcaList, l_pMcsTarget,
TARGETING::TargetService::CHILD_BY_AFFINITY,
TARGETING::TargetService::ALL, &l_presentMca);
for(uint32_t l_mcaIdx = 0; l_mcaIdx<l_mcaList.size();
++l_mcaIdx)
{
TARGETING::Target *l_pMcaTarget =
l_mcaList[l_mcaIdx];
//Group which this MCA is belonging
uint32_t l_mcaInGrp = 0;
if(!hdatFindGroupForMc(l_pProcTarget,
l_pMcaTarget,
l_mcaInGrp))
{
HDAT_INF("No group found for MCA");
//Skip this MCS is not under any group
continue;
}
uint32_t l_mcaFruId = 0;
hdatMemParentType l_parentType= HDAT_MEM_PARENT_CEC_FRU;
std::list<hdatRamArea> l_areas;
l_areas.clear();
uint32_t l_areaSizeInMB = 0;
bool l_areaFunctional = false;
uint32_t l_numDimms =0;
l_err = hdatScanDimms(l_pMcaTarget,
l_pMcsTarget,
l_mcaFruId,
l_areas,
l_areaSizeInMB,
l_numDimms,
l_areaFunctional,
l_parentType);
if(NULL != l_err)
{
HDAT_ERR("Error in calling Scan Dimms");
break;
}
HDAT_INF("l_areaSizeInMB:0x%.8X l_numDimms:0x%.8X "
"l_areas.size():0x%.8X", l_areaSizeInMB, l_numDimms,
l_areas.size());
//Skip if no memory configured under this MCS
if(l_areaSizeInMB == 0)
{
continue;
}
uint32_t l_maxMemBlocks = 0;
l_err =
hdatGetMaxMemoryBlocks(l_pMcsTarget,l_maxMemBlocks);
if(NULL != l_err)
{
HDAT_ERR("Error error in get max blocks");
break;
}
TARGETING::ATTR_SLCA_RID_type l_procRid =
l_pProcTarget->getAttr<TARGETING::ATTR_SLCA_RID>();
TARGETING::ATTR_SLCA_INDEX_type l_procSlcaIndex =
l_pProcTarget->getAttr<TARGETING::ATTR_SLCA_INDEX>();
l_err = addMsAreaFru(l_procRid,
l_procSlcaIndex,
l_pProcTarget,
l_index,
l_numDimms,
MAX_CHIP_EC_CNT_PER_MSAREA,
l_maxMemBlocks);
if(NULL != l_err)
{
HDAT_ERR("Error adding MSArea %d"
"Number of Dimms: %d Max Blocks: %d",
l_index,
l_numDimms,l_maxMemBlocks);
break;
}
uint32_t l_memStatus = 0;
//If group is shared with more than one area
if(l_mcaSharingCount[l_mcaInGrp] >=
HDAT_MIN_NUM_FOR_SHARING)
{
l_memStatus = HDAT_MEM_SHARED;
setMsAreaInterleavedId(l_index,
l_mcsSharingGrpIds[l_mcaInGrp]);
}
setMsAreaType(l_index,l_parentType);
setMsAreaSize(l_index,l_areaSizeInMB);
iv_maxSize.hdatTotSize += l_areaSizeInMB;
l_memStatus |= l_areaFunctional ?
(HDAT_MEM_INSTALLED | HDAT_MEM_FUNCTIONAL) :
HDAT_MEM_INSTALLED;
setMsAreaStat(l_index, l_memStatus);
//Add MCS ec level
uint32_t l_mcsEcLevel = 0;
uint32_t l_mcsChipId = 0;
l_err = hdatGetIdEc(l_pMcsTarget,
l_mcsEcLevel,
l_mcsChipId);
if(NULL != l_err)
{
HDAT_ERR("Error in getting MCS ID "
"and EC HUID:[0x%08X]",
l_pMcsTarget->getAttr<TARGETING::ATTR_HUID>());
break;
}
l_err = addEcEntry(l_index,
l_mcsChipId,
l_mcsEcLevel);
if(NULL != l_err)
{
HDAT_ERR("Error in adding"
" ID[0x%08X] and EC[0x%08X] to ms area"
" HUID:[0x%08X]",l_mcsChipId,
l_mcsEcLevel,
l_pMcsTarget->getAttr<TARGETING::ATTR_HUID>());
break;
}
// Need to get i2c Master data correctly
std::vector<hdatI2cData_t> l_i2cDevEntries;
TARGETING::PredicateCTM l_membufPredicate(
TARGETING::CLASS_CHIP, TARGETING::TYPE_MEMBUF);
TARGETING::PredicatePostfixExpr l_presentMemBuf;
l_presentMemBuf.push(&l_membufPredicate).
push(&l_predHwasPresent).And();
TARGETING::TargetHandleList l_membufList;
// Find Associated membuf
TARGETING::targetService().getAssociated(l_membufList,
l_pMcsTarget,
TARGETING::TargetService::CHILD_BY_AFFINITY,
TARGETING::TargetService::ALL,
&l_presentMemBuf);
//Skip is there is no Membuf attached to this MCS
if(l_membufList.size() > 0)
{
TARGETING::Target *l_pMembufTarget =
l_membufList[0];
if (l_pMembufTarget != NULL)
{
hdatGetI2cDeviceInfo(l_pMembufTarget,
l_i2cDevEntries);
}
}
setMsaI2cInfo(l_index, l_i2cDevEntries);
std::list<hdatRamArea>::iterator l_area =
l_areas.begin();
for (uint32_t l_ramId = 0;
l_area != l_areas.end();
++l_ramId, ++l_area)
{
uint32_t l_status = (l_area)->ivFunctional ?
(HDAT_RAM_INSTALLED | HDAT_RAM_FUNCTIONAL)
: HDAT_RAM_INSTALLED;
TARGETING::Target *l_pDimmTarget =
TARGETING::Target::getTargetFromHuid(l_area->ivHuid);
TARGETING::ATTR_SLCA_RID_type l_dimmRid =
l_pDimmTarget->getAttr<TARGETING::ATTR_SLCA_RID>();
TARGETING::ATTR_SLCA_INDEX_type l_dimmSlcaIndex =
l_pDimmTarget->getAttr<TARGETING::ATTR_SLCA_INDEX>();
uint32_t l_dimmId =
1 << (31 - (l_pDimmTarget->getAttr<TARGETING::ATTR_FAPI_POS>() % MAX_DIMMS_PER_MCBIST));
l_err = addRamFru(l_index,
l_pDimmTarget,
l_dimmRid,
l_dimmSlcaIndex,
l_ramId,
l_status,
(l_area)->ivSize,
l_dimmId,
l_memBusFreq);
if (l_err) // Failed to add ram fru information
{
HDAT_ERR("Error in adding RAM FRU"
"Index:%d Rid:[0x%08X] status:[0x%08X]"
"Size:[0x%08X] RamID:[0x%08X]",
l_index,(l_area)->ivHuid,
l_status,(l_area)->ivSize,l_ramId);
ERRORLOG::errlCommit(l_err,HDAT_COMP_ID);
delete l_err;
l_err = NULL;
continue;
}
}//end of RAM list
l_addr_range.hi = (l_procMemBases[l_mcaInGrp] &
0xFFFFFFFF00000000ull) >> 32;
l_addr_range.lo = l_procMemBases[l_mcaInGrp] &
0x00000000FFFFFFFFull;
l_end = l_addr_range;
//Update the range
l_end.hi += (l_procMemSizesBytes[l_mcaInGrp] &
0xFFFFFFFF00000000ull) >> 32;
l_end.lo += l_procMemSizesBytes[l_mcaInGrp] &
0x00000000FFFFFFFFull;
HDAT_INF("MCS:0x%08X l_addr_range:0x%08X 0x%08X"
" l_end:0x%08X 0x%08X",
l_pMcsTarget->getAttr<TARGETING::ATTR_HUID>(),
l_addr_range.hi, l_addr_range.lo,
l_end.hi,l_end.lo);
uint64_t l_hdatMirrorAddr_x = 0x0ull;
uint64_t l_hdatMirrorAddr = 0x0ull;
uint32_t l_hdatMemcntrlID = 0x0 ;
uint8_t l_hdatMirrorAlogrithm = 0xFF;
bool l_rangeIsMirrorable = false;
TARGETING::ATTR_PROC_MIRROR_BASES_type
l_MirrorAddr = {0};
assert(l_pProcTarget->tryGetAttr<
TARGETING::ATTR_PROC_MIRROR_BASES>(l_MirrorAddr));
TARGETING::ATTR_PROC_MIRROR_SIZES_type
l_MirrorSize = {0};
assert(l_pProcTarget->tryGetAttr<
TARGETING::ATTR_PROC_MIRROR_SIZES>(l_MirrorSize));
uint64_t l_startAddr =
(((uint64_t)(l_addr_range.hi) << 32 )
| (uint64_t)(l_addr_range.lo));
l_hdatMirrorAddr_x =
(l_startAddr / 2) + l_mirrorBaseAddress_x;
TARGETING::ATTR_PAYLOAD_IN_MIRROR_MEM_type
l_payLoadMirrorMem =
l_pSysTarget->getAttr<
TARGETING::ATTR_PAYLOAD_IN_MIRROR_MEM>();
HDAT_INF(
"Start add : 0x%016llX MirrorBase : 0x%016llX"
" MirrorAddr : 0x%016llX PayLoadMirrorMem : 0x%X",
l_startAddr, l_mirrorBaseAddress_x,
l_hdatMirrorAddr_x, l_payLoadMirrorMem);
if ( 0 != l_payLoadMirrorMem )
{
for ( int idx=0 ; idx <
(int)(sizeof(TARGETING::ATTR_PROC_MIRROR_SIZES_type)
/ sizeof(uint64_t)) ; idx++ )
{
HDAT_INF("Mirror size : 0x%016llX"
" MirrorAddr[idx] : 0x%016llX"
" hdatMirrorAddr_x : 0x%016llX",
l_MirrorSize[idx], l_MirrorAddr[idx],
l_hdatMirrorAddr_x);
if( (0 != l_MirrorSize[idx]) &&
(l_MirrorAddr[idx] == l_hdatMirrorAddr_x) )
{
l_rangeIsMirrorable = true;
l_hdatMirrorAddr = l_MirrorAddr[idx]
| HDAT_REAL_ADDRESS_MASK64;
break;
}
}
}
if(l_pProcTarget->getAttr<TARGETING::ATTR_MODEL>() == TARGETING::MODEL_NIMBUS)
{
// Set the memory controller ID
l_hdatMemcntrlID |= 1 << (31 - l_pMcbistTarget->getAttr<TARGETING::ATTR_CHIP_UNIT>());
l_hdatMemcntrlID |= 1 << (31 - (l_pMcsTarget->getAttr<TARGETING::ATTR_CHIP_UNIT>() + 4));
l_hdatMemcntrlID |= 1 << (31 - (l_pMcaTarget->getAttr<TARGETING::ATTR_CHIP_UNIT>() + 8));
}
else if(l_pProcTarget->getAttr<TARGETING::ATTR_MODEL>() == TARGETING::MODEL_CUMULUS)
{
//TODO : MEmory controller ID for cumulus need to be defined.
HDAT_INF("Memory controller ID : 0 since this is Cumulus proc");
}
l_err = addMsAreaAddr(l_index,
l_addr_range,
l_end,
l_procChipId,
l_rangeIsMirrorable,
l_hdatMirrorAlogrithm,
l_hdatMirrorAddr,
l_hdatMemcntrlID);
if(NULL != l_err)
{
HDAT_ERR("Error in adding addMsAreaAddr"
" to ms area index[%d]",
l_index);
break;
}
// TODO : RTC Story 159682
// Further CHTM support needs to be added which contains
// the trace array for 24 cores
// Reinitializing the NHTM size
//Don't re-init NHTM size -- only one HTM region per proc
uint64_t l_end_hi = l_end.hi;
uint64_t l_end_lo = l_end.lo;
uint64_t l_end_addr = ((l_end_hi << 32 ) | l_end_lo);
uint64_t l_addr_range_hi = l_addr_range.hi;
uint64_t l_addr_range_lo = l_addr_range.lo;
uint64_t l_start_addr =((l_addr_range_hi << 32 )| l_addr_range_lo);
uint64_t l_size_bytes = ((uint64_t)l_areaSizeInMB) * l_mcaSharingCount[l_mcaInGrp] * 1024 * 1024;
if((0 != l_nhtmSize) &&
(l_size_bytes != (l_end_addr - l_start_addr)))
{
HDAT_INF("NHTM Bar size = 0x%016llX "
" MS area size = 0x%016llX"
" l_end_addr = 0x%016llX"
" l_start_addr = 0x%016llX",
l_nhtmSize,l_size_bytes, l_end_addr,
l_start_addr);
l_addr_range.lo = l_hdatNhtmStartAddr.lo;
l_addr_range.hi = l_hdatNhtmStartAddr.hi;
l_end.lo = l_hdatNhtmEndAddr.lo;
l_end.hi = l_hdatNhtmEndAddr.hi;
l_err = addMsAreaAddr(l_index,
l_addr_range,
l_end,
l_procChipId,
false, 0, 0);
if(NULL != l_err)
{
HDAT_ERR("Error in adding "
" addMsAreaAddr to ms area index[%d]",
l_index);
break;
}
l_nhtmSize=0; //only add 1 entry
}
l_addr_range = l_end;
l_index++;
} //end of mca list
} //end of MCS list
} //end of MCBIST list
if(l_err)
{
// Error message recorded above
break;
}
} //end of proc list
TARGETING::PredicateCTM l_nodePred(TARGETING::CLASS_ENC,
TARGETING::TYPE_NODE);
TARGETING::PredicateHwas l_predFunctional;
l_predFunctional.functional(true);
TARGETING::PredicatePostfixExpr l_functionalnode;
l_functionalnode.push(&l_nodePred).push(&l_predFunctional).And();
TARGETING::TargetRangeFilter l_nodes(TARGETING::targetService().begin(),
TARGETING::targetService().end(),
&l_functionalnode);
TARGETING::ATTR_HB_RSV_MEM_SIZE_MB_type l_rhbSize =
l_pSysTarget->getAttr<TARGETING::ATTR_HB_RSV_MEM_SIZE_MB>();
if( 0 != l_rhbSize )
{
for(;l_nodes;++l_nodes)
{
TARGETING::ATTR_HB_HRMOR_NODAL_BASE_type l_rhbStartAddr =
l_pSysTarget->getAttr<TARGETING::ATTR_HB_HRMOR_NODAL_BASE>();
TARGETING::Target *l_pNodeTarget = *(l_nodes);
uint32_t l_dbobId =
l_pNodeTarget->getAttr<TARGETING::ATTR_ORDINAL_ID>();
hdatMsAddr_t l_hdatRhbStartAddr;
hdatMsAddr_t l_hdatRhbEndAddr;
l_rhbStartAddr = l_rhbStartAddr * l_dbobId;
TARGETING::ATTR_PAYLOAD_BASE_type l_payLoadBase =
l_pSysTarget->getAttr<TARGETING::ATTR_PAYLOAD_BASE>();
// Since PAYLOAD_BASE is in MB's, converting it to bytes
l_rhbStartAddr |= ((uint64_t)(l_payLoadBase)) << 20;
l_rhbStartAddr &= 0xFFFFFFFF00000000;
if( l_payLoadBase > 0x100 )
{
l_rhbStartAddr = 0x40000000000; //4TB hardcode for now
}
l_hdatRhbStartAddr.hi =
(l_rhbStartAddr & 0xFFFFFFFF00000000ull) >> 32;
l_hdatRhbStartAddr.lo = l_rhbStartAddr & 0x00000000FFFFFFFFull;
l_hdatRhbStartAddr.hi |= HDAT_REAL_ADDRESS_MASK;
// need to store a 64 bit range
uint64_t l_hbSize=0;
// in bytes
uint64_t l_size_bytes = (l_rhbSize * 1024 * 1024) -1;
l_hbSize = l_rhbStartAddr + l_size_bytes;
l_hdatRhbEndAddr.hi = (l_hbSize & 0xFFFFFFFF00000000ull) >> 32;
l_hdatRhbEndAddr.lo = l_hbSize & 0x00000000FFFFFFFFull;
l_hdatRhbEndAddr.hi |= HDAT_REAL_ADDRESS_MASK;
//TODO : : RTC Story 159684
//Need to populate correct label size and label string
uint32_t l_rhbLabelSize = 0;
uint8_t* l_rhbLabelStringPtr = NULL;
addRHBAddrRange(l_dbobId, l_hdatRhbStartAddr,
l_hdatRhbEndAddr, l_rhbLabelSize,
l_rhbLabelStringPtr);
TARGETING::ATTR_HB_RSV_MEM_SIZE_MB_type l_rhbEntries =
l_pSysTarget->getAttr
<TARGETING::ATTR_HDAT_RSV_MEM_NUM_SECTIONS>();
l_dbobId = 0x0;
l_hdatRhbStartAddr.lo = 0x0;
l_hdatRhbStartAddr.hi = 0x0;
l_hdatRhbEndAddr.lo = 0x0;
l_hdatRhbEndAddr.hi = 0x0;
for(uint32_t l_entry=0; l_entry<l_rhbEntries; l_entry++)
{
addRHBAddrRange(l_dbobId, l_hdatRhbStartAddr,
l_hdatRhbEndAddr, l_rhbLabelSize,
l_rhbLabelStringPtr);
}
}
}
else
{
HDAT_INF("Reserve HB mem size 0x%08X",l_rhbSize);
}
if(l_err)
{
// Error message recorded above
break;
}
o_size = 0;
o_count = 1; // Only 1 of these structures is ever built
getTotalSize (o_size);
uint64_t l_base_addr = ((uint64_t) iv_msAddr.hi << 32) | iv_msAddr.lo;
uint64_t l_base_addr_down = ALIGN_PAGE_DOWN(l_base_addr);
iv_virtAddr = mm_block_map ( reinterpret_cast<void*>(l_base_addr_down),
(ALIGN_PAGE(o_size) + PAGESIZE));
uint64_t l_final_addr = reinterpret_cast<uint64_t>(iv_virtAddr);
l_final_addr += l_base_addr - l_base_addr_down;
iv_virtAddr = reinterpret_cast<void *> (l_final_addr);
commit(iv_virtAddr,o_size);
prt();
}
while(0);
HDAT_EXIT();
return l_err;
}
/** @brief See the prologue in hdatmsvpd.H
*/
void HdatMsVpd::commit(void * i_addr,
uint32_t i_size)
{
uint32_t l_cnt,l_currOffset, l_ramSizes;
HdatMsArea *l_msEntry;
UtilMem l_data(i_addr, i_size);
// Start committing the base class data
this->startCommit(l_data);
l_data.write(&iv_maxAddr, sizeof(hdatMsVpdAddr_t));
l_data.write(&iv_maxSize, sizeof(hdatMsVpdSize_t));
// Page mover is called 'Misc Addr Structure' on OPAL but still exists
l_data.write(&iv_mover, sizeof(hdatMsVpdPageMover_t));
l_data.write(&iv_IMTaddrRngArrayHdr,sizeof(hdatHDIFDataArray_t));
l_data.write(iv_IMTaddrRangeArray,
iv_maxIMTAddrRngCnt * sizeof(hdatMsVpdImtAddrRange_t));
l_data.write(&iv_UEaddrRngArrayHdr, sizeof(hdatHDIFDataArray_t));
l_data.write(iv_UEaddrRangeArray,
iv_maxUEAddrRngCnt * sizeof(hdatMsVpdUEAddrRange_t));
l_data.write(&iv_RHBaddrRngArrayHdr,sizeof(hdatHDIFDataArray_t));
l_data.write (iv_RHBaddrRangeArray,iv_maxRHBAddrRngCnt
* sizeof(hdatMsVpdRhbAddrRange_t));
this->endCommit(l_data);
// Write the MS area structures and RAM structures
if (iv_actMsAreaCnt > 0)
{
// All of the mainstore areas must be written first so that can be
// processed as an array of mainstore areas.
l_ramSizes = 0;
l_cnt = 0;
while (l_cnt < iv_actMsAreaCnt)
{
l_msEntry = *(reinterpret_cast<HdatMsArea **>(
reinterpret_cast<char *>(iv_msAreaPtrs) + l_cnt
* sizeof(HdatMsArea *)));
// Since we don't know what order mainstore areas and RAM
// areas were created, update the offset in the HdatMsArea
// child structure triple so it points to the first RAM area.
l_currOffset = (iv_actMsAreaCnt - l_cnt) * l_msEntry->size()
+ l_ramSizes;
l_msEntry->chgChildOffset(HDAT_MS_AREA_RAM_AREAS, l_currOffset);
l_msEntry->commit(l_data);
// Now compute the size of the RAM areas associated with this
// mainstore area. These will have to be added to the child
// offset for the next mainstore area to skip over them.
l_ramSizes += l_msEntry->ramObjSizes();
l_cnt++;
}
// Now the children (RAM areas) of each mainstore area must be committed
l_cnt = 0;
while (l_cnt < iv_actMsAreaCnt)
{
l_msEntry = *(reinterpret_cast<HdatMsArea **>(reinterpret_cast<char *>
(iv_msAreaPtrs) + l_cnt
* sizeof(HdatMsArea *)));
l_msEntry->commitRamAreas(l_data);
l_cnt++;
}
}
}
/*******************************************************************************
* hdatGetMaxMemConfiguredAddress
*******************************************************************************/
uint64_t HdatMsVpd::hdatGetMaxMemConfiguredAddress()
{
//For each processor in the system
TARGETING::PredicateCTM l_procChipPred(TARGETING::CLASS_CHIP,
TARGETING::TYPE_PROC);
TARGETING::PredicateHwas l_predFunctional;
l_predFunctional.functional(true);
TARGETING::PredicatePostfixExpr l_functionalProc;
l_functionalProc.push(&l_procChipPred).push(&l_predFunctional).And();
TARGETING::TargetRangeFilter l_procs(
TARGETING::targetService().begin(),
TARGETING::targetService().end(),
&l_functionalProc);
uint64_t l_maxBase = 0x0ull;
uint64_t l_maxMsAddress = 0x0ull;
bool l_processedAnyGroup = false;
uint64_t l_hdatMaxImtAddr = 0x0ull;
for(;l_procs;++l_procs)
{
TARGETING::Target *l_pProcTarget = (*l_procs);
TARGETING::ATTR_PROC_MEM_BASES_type l_procMemBases = {0};
TARGETING::ATTR_PROC_MEM_SIZES_type l_procMemSizesBytes = {0};
assert(l_pProcTarget->tryGetAttr<TARGETING::ATTR_PROC_MEM_SIZES>
(l_procMemSizesBytes));
assert(l_pProcTarget->
tryGetAttr<TARGETING::ATTR_PROC_MEM_BASES>(l_procMemBases));
//For each MCA
TARGETING::PredicateCTM l_allMca(TARGETING::CLASS_UNIT,
TARGETING::TYPE_MCA);
TARGETING::PredicateHwas l_funcMca;
l_funcMca.functional(true);
TARGETING::PredicatePostfixExpr l_allFuncMca;
l_allFuncMca.push(&l_allMca).push(&l_funcMca).And();
TARGETING::TargetHandleList l_mcaList;
TARGETING::targetService().
getAssociated(l_mcaList, l_pProcTarget,
TARGETING::TargetService::CHILD,
TARGETING::TargetService::ALL, &l_allFuncMca);
for(uint32_t i=0; i < l_mcaList.size(); i++)
{
TARGETING::Target *l_pMcaTarget = l_mcaList[i];
uint32_t l_mcaInGroup = 0;
if(!hdatFindGroupForMc(l_pProcTarget,
l_pMcaTarget,
l_mcaInGroup))
{
HDAT_INF("Input target is not in group,"
" MCA HUID:[0x%08X]",
l_pMcaTarget->getAttr<TARGETING::ATTR_HUID>());
//Skip this MC not part of any group
continue;
}
if(!l_processedAnyGroup ||
(l_procMemBases[l_mcaInGroup] > l_maxBase))
{
l_maxBase = l_procMemBases[l_mcaInGroup];
l_processedAnyGroup = true;
l_maxMsAddress = l_maxBase + l_procMemSizesBytes[l_mcaInGroup];
HDAT_INF("Max MS Addr l_maxMsAddress: = 0x%016llX,"
"l_maxBase= 0x%016llX,"
"l_procMemSizesBytes[l_mcaInGroup]= 0x%016llX",
l_maxMsAddress, l_maxBase, l_procMemSizesBytes[l_mcaInGroup]);
}
}
// TODO : RTC Story 159682
// Further CHTM support needs to be added which contains the trace array
// for 24 cores
hdatMsAddr_t l_hdatNhtmStartAddr;
hdatMsAddr_t l_hdatNhtmEndAddr;
TARGETING::ATTR_PROC_NHTM_BAR_BASE_ADDR_type l_nhtmStartAddr =
l_pProcTarget->getAttr<TARGETING::ATTR_PROC_NHTM_BAR_BASE_ADDR>();
TARGETING::ATTR_PROC_NHTM_BAR_SIZE_type l_nhtmSize =
l_pProcTarget->getAttr<TARGETING::ATTR_PROC_NHTM_BAR_SIZE>();
if( 0 != l_nhtmSize )
{
l_hdatNhtmStartAddr.hi =
(l_nhtmStartAddr & 0xFFFFFFFF00000000ull) >> 32;
l_hdatNhtmStartAddr.lo = l_nhtmStartAddr & 0x00000000FFFFFFFFull;
l_hdatNhtmStartAddr.hi |= HDAT_REAL_ADDRESS_MASK;
l_nhtmSize = l_nhtmStartAddr + l_nhtmSize;
l_hdatNhtmEndAddr.hi =
(l_nhtmSize & 0xFFFFFFFF00000000ull) >> 32;
l_hdatNhtmEndAddr.lo = l_nhtmSize & 0x00000000FFFFFFFFull;
l_hdatNhtmEndAddr.hi |= HDAT_REAL_ADDRESS_MASK;
if( l_hdatMaxImtAddr <
(((uint64_t)l_hdatNhtmEndAddr.hi << 32) |l_hdatNhtmEndAddr.lo))
{
l_hdatMaxImtAddr =
(((uint64_t)l_hdatNhtmEndAddr.hi << 32) |l_hdatNhtmEndAddr.lo);
HDAT_INF("NHTM Max Addr: = 0x%016llX", l_hdatMaxImtAddr);
}
}
else
{
HDAT_INF("NHTM Bar size value = 0x%016llX ", l_nhtmSize);
}
}
// Set MSB to 1 for PHYP
l_maxMsAddress |= HDAT_REAL_ADDRESS_MASK64;
if(l_hdatMaxImtAddr > l_maxMsAddress)
{
l_maxMsAddress = l_hdatMaxImtAddr;
HDAT_INF("IMT Max MS Addr: = 0x%016llX",l_maxMsAddress);
}
// We now have to subtract 1 since the address range starts at 0
if(l_maxMsAddress != 0)
{
l_maxMsAddress -= 1;
}
return l_maxMsAddress;
}
//******************************************************************************
//* hdatFindGroupForMc
//******************************************************************************
bool HdatMsVpd::hdatFindGroupForMc(const TARGETING::Target *i_pProcTarget,
const TARGETING::Target *i_pMcaTarget,
uint32_t& o_groupOfMc)
{
bool l_foundGroup = false;
TARGETING::ATTR_MSS_MEM_MC_IN_GROUP_type l_mcaGroups = {0};
assert(i_pProcTarget != NULL || i_pMcaTarget != NULL);
assert(!(i_pProcTarget->getAttr<TARGETING::ATTR_TYPE>()
!= TARGETING::TYPE_PROC)||
!(i_pProcTarget->getAttr<TARGETING::ATTR_CLASS>()
!= TARGETING::CLASS_CHIP));
assert(i_pProcTarget->
tryGetAttr<TARGETING::ATTR_MSS_MEM_MC_IN_GROUP>(l_mcaGroups));
assert(!(i_pMcaTarget->getAttr<TARGETING::ATTR_TYPE>()
!= TARGETING::TYPE_MCA)||
!(i_pMcaTarget->getAttr<TARGETING::ATTR_CLASS>()
!= TARGETING::CLASS_UNIT));
TARGETING::ATTR_CHIP_UNIT_type l_chipUnit =
i_pMcaTarget->getAttr<TARGETING::ATTR_CHIP_UNIT>();
uint32_t l_sizeOfArray = sizeof(l_mcaGroups)/sizeof(l_mcaGroups[0]);
assert(!(sizeof( l_mcaGroups[0] ) != sizeof(uint8_t)));
assert(!( l_chipUnit >= ( sizeof( l_mcaGroups[0] ) * HDAT_BITS_PER_BYTE )));
const uint8_t MC_IN_GROUP_MCA_0 = 0x80;
for(uint32_t l_idx =0; l_idx < l_sizeOfArray;++l_idx)
{
//Attribute ATTR_MSS_MEM_MC_IN_GROUP is an array of bitmask
//bit 0 of bitmask corresponds to mca 0, bit 7 to mca7
if((l_mcaGroups[l_idx] & (MC_IN_GROUP_MCA_0 >> l_chipUnit)) ==
(MC_IN_GROUP_MCA_0 >> l_chipUnit))
{
HDAT_INF("hdatFindGroupForMc::: Found group : %d",l_idx);
o_groupOfMc = l_idx;
l_foundGroup = true;
break;
}
}
return l_foundGroup;
}
/*******************************************************************************
* hdatScanDimms
*******************************************************************************/
errlHndl_t HdatMsVpd::hdatScanDimms(const TARGETING::Target *i_pTarget,
const TARGETING::Target *i_pMcsTarget,
uint32_t i_mcaFruid,
std::list<hdatRamArea>& o_areas,
uint32_t& o_areaSize,
uint32_t& o_dimmNum,
bool& o_areaFunctional,
hdatMemParentType& o_parentType)
{
errlHndl_t l_err = NULL;
do
{
if(i_pTarget->getAttr<TARGETING::ATTR_TYPE>() != TARGETING::TYPE_MCA)
{
HDAT_ERR("Input Target is type not MCA");
break;
}
if(i_pMcsTarget->getAttr<TARGETING::ATTR_TYPE>() != TARGETING::TYPE_MCS)
{
HDAT_ERR("Input Target is type not MCA");
break;
}
TARGETING::ATTR_EFF_DIMM_SIZE_type l_dimSizes = {{0}};
//Get configured memory size
if(!i_pMcsTarget->
tryGetAttr<TARGETING::ATTR_EFF_DIMM_SIZE>(l_dimSizes))
{
HDAT_ERR("DIMM size should be available with MCS");
}
uint8_t l_mcaPort = 0;
if(!i_pTarget->
tryGetAttr<TARGETING::ATTR_REL_POS>(l_mcaPort))
{
HDAT_ERR("REL_POS not there in MCA port");
}
else
{
l_mcaPort= l_mcaPort%2;
}
//[TODO RTC: 47148]
//for each DIMM connected to this this MCA
TARGETING::PredicateCTM l_dimmPredicate(TARGETING::
CLASS_LOGICAL_CARD,
TARGETING::TYPE_DIMM);
TARGETING::PredicateHwas l_predDimm;
l_predDimm.present(true);
TARGETING::PredicatePostfixExpr l_presentDimm;
l_presentDimm.push(&l_dimmPredicate).push(&l_predDimm).And();
TARGETING::TargetHandleList l_dimmList;
// Get associated dimms
TARGETING::targetService().
getAssociated(l_dimmList, i_pTarget,
TARGETING::TargetService::CHILD_BY_AFFINITY,
TARGETING::TargetService::ALL, &l_presentDimm);
for(uint32_t j=0; j < l_dimmList.size(); ++j)
{
//fetch each dimm
TARGETING::Target *l_pDimmTarget = l_dimmList[j];
uint32_t l_dimmfru = 0;
l_dimmfru = l_pDimmTarget->getAttr<TARGETING::ATTR_FRU_ID>();
uint8_t l_mcaDimm = 0;
TARGETING::ATTR_REL_POS_type l_dimmRelPos = 0;
if(l_pDimmTarget->
tryGetAttr<TARGETING::ATTR_REL_POS>(l_dimmRelPos))
{
l_mcaDimm = l_dimmRelPos%2; //2 DIMMs per MCA
l_dimmRelPos = 0;
if(!i_pTarget->
tryGetAttr<TARGETING::ATTR_REL_POS>(l_dimmRelPos))
{
HDAT_ERR("Attribute REL_POS in MCA is not "
"present");
}
}
else
{
HDAT_ERR("Attribute REL_POS in DIMM "
"is not present");
}
//Convert GB to MB
uint32_t l_dimmSizeInMB =
l_dimSizes[l_mcaPort][l_mcaDimm] * HDAT_MB_PER_GB;
uint32_t l_huid = TARGETING::get_huid(l_pDimmTarget);
bool foundArea = false;
for (std::list<hdatRamArea>::iterator l_area = o_areas.begin();
l_area != o_areas.end();
++l_area)
{
//we do not need to compare each dimm fru id with mca fru id
//to create ram area, by the below logic
//dimms with same fruid will fall into same ram area
//even if they have fru id same with mca
if (l_area->ivfruId == l_dimmfru)//this means soldered dimms
{
foundArea = true;
l_area->ivFunctional = (l_area)->ivFunctional ||
isFunctional(l_pDimmTarget);
(l_area)->ivFunctional = true;
(l_area)->ivSize += l_dimmSizeInMB;
break;
}
}
//Search in the list of RAM Areas if not
//present create a new ram area
if (!foundArea)
{
o_dimmNum++;
o_areas.push_back(hdatRamArea(l_huid,
isFunctional(l_pDimmTarget),
l_dimmSizeInMB,l_dimmfru));
}
o_areaSize += l_dimmSizeInMB;
o_areaFunctional = o_areaFunctional ||
isFunctional(l_pDimmTarget);
}
o_parentType = HDAT_MEM_PARENT_CEC_FRU;
if(l_err != NULL)
{
//break if error
break;
}
}
while(0);
return l_err;
}
/*******************************************************************************
* hdatGetMaxMemoryBlocks
*******************************************************************************/
errlHndl_t HdatMsVpd::hdatGetMaxMemoryBlocks(const TARGETING::Target *i_pTarget,
uint32_t &o_maxMemoryBlocks)
{
errlHndl_t l_err = NULL;
do
{
//One Memctrl connected to only one membuf in P8
o_maxMemoryBlocks = 1;
}
while(0);
return l_err;
}
} //namespace HDAT
| 48,752 |
https://github.com/ryderhanson/RPG/blob/master/Assets/Examples/Colors.meta | Github Open Source | Open Source | MIT | 2,017 | RPG | ryderhanson | Unity3D Asset | Code | 14 | 69 | fileFormatVersion: 2
guid: ce359357daba94346a0ee74acd3f9b4c
folderAsset: yes
timeCreated: 1484579062
licenseType: Free
DefaultImporter:
userData:
assetBundleName:
assetBundleVariant:
| 43,402 |
https://www.wikidata.org/wiki/Q14705022 | Wikidata | Semantic data | CC0 | null | Streeter-Peterson House | None | Multilingual | Semantic data | 209 | 431 | Streeter-Peterson House
historic house in Nebraska, United States
Streeter-Peterson House coordinate location
Streeter-Peterson House country United States of America
Streeter-Peterson House located in the administrative territorial entity Nebraska
Streeter-Peterson House instance of house
Streeter-Peterson House heritage designation National Register of Historic Places listed place, start time 1991, subject named as Streeter--Peterson House, subject has role NRHP building, criterion used C
Streeter-Peterson House NRHP reference number 91001754
Streeter-Peterson House image Streeter-Peterson House from E.JPG
Streeter-Peterson House architectural style Queen Anne style architecture in the United States
Streeter-Peterson House architectural style Neoclassical architecture
Streeter-Peterson House Commons category Streeter-Peterson House
Streeter-Peterson House inception 1900
Streeter-Peterson House Freebase ID /m/0vzs1nl
Streeter-Peterson House
Streeter-Peterson House coordonnées géographiques
Streeter-Peterson House pays États-Unis
Streeter-Peterson House localisation administrative Nebraska
Streeter-Peterson House nature de l’élément maison
Streeter-Peterson House statut patrimonial inscrit au Registre national des lieux historiques, date de début 1991, sous le nom Streeter--Peterson House, rôle du sujet bâtiment au NRHP, critère utilisé C
Streeter-Peterson House identifiant Registre national des lieux historiques 91001754
Streeter-Peterson House image Streeter-Peterson House from E.JPG
Streeter-Peterson House style architectural Architecture de style Queen Anne aux États-Unis
Streeter-Peterson House style architectural architecture néoclassique
Streeter-Peterson House catégorie Commons Streeter-Peterson House
Streeter-Peterson House date de fondation ou de création 1900
Streeter-Peterson House identifiant Freebase /m/0vzs1nl | 28,649 |
https://github.com/jctbog9/forward-progress/blob/master/src/components/Uploader.vue | Github Open Source | Open Source | MIT | 2,020 | forward-progress | jctbog9 | Vue | Code | 115 | 356 | <template>
<div>
<dropzone ref="uploader" id="dropzone" :options="uploaderOptions"></dropzone>
</div>
</template>
<script>
import Dropzone from 'nuxt-dropzone'
import 'nuxt-dropzone/dropzone.css'
export default {
name: 'Uploader',
components: {Dropzone},
mixins: [],
props: {
/*
property: {
type: String|Number|Boolean|Array|Object|Date|Function|Symbol,
default: null,
required: false
},
*/
},
data() {
return {
uploaderOptions: {
url: '/api/newNote',
thumbnailWidth: 150,
maxFilesize: 10
}
}
},
computed: {
// computed properties are cached based on their dependencies
/*
computedProperty() {
return 'value'
},
*/
},
methods: {
// Methods run whenever a re-render happens, their results aren't cached.
/*
onClick() {
this.$emit('click-happened')
},
*/
},
mounted() {
// Invoked when the component loads, good place to fetch data from the API
},
}
</script>
<style lang="stylus" scoped>
</style>
| 40,869 |
https://arxiv.org/abs/1906.00801 | arXiv | Open Science | CC-By-SA | 2,019 | Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks | Hiroshi Iritani | English | Spoken | 45,651 | 209,749 | Global Mirrors and Discrepant Transformations for Toric Deligne–Mumford Stacks
Global Mirrors and Discrepant Transformations
for Toric Deligne–Mumford Stacks††This paper is a contribution to the Special
Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase for his
65th birthday. The full collection is available at
https://www.emis.de/journals/SIGMA/Mulase.html
Hiroshi IRITANI H. Iritani
Department of Mathematics, Graduate School of Science, Kyoto University,
Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan
[email protected] https://www.math.kyoto-u.ac.jp/~iritani/
Received June 13, 2019, in final form March 29, 2020; Published online April
22, 2020
We introduce a global Landau–Ginzburg model which is mirror to several toric
Deligne–Mumford stacks and describe the change of the Gromov–Witten theories
under discrepant transformations. We prove a formal decomposition of the
quantum cohomology D-modules (and of the all-genus Gromov–Witten potentials)
under a discrepant toric wall-crossing. In the case of weighted blowups of
weak-Fano compact toric stacks along toric centres, we show that an analytic
lift of the formal decomposition corresponds, via the
$\widehat{\Gamma}$-integral structure, to an Orlov-type semiorthogonal
decomposition of topological $K$-groups. We state a conjectural functoriality
of Gromov–Witten theories under discrepant transformations in terms of a
Riemann–Hilbert problem.
quantum cohomology; mirror symmetry; toric variety; Landau–Ginzburg model;
Gamma-integral structure
14N35; 14J33; 53D45
###### Contents
1. 1 Introduction
1. 1.1 Quantum cohomology D-modules
2. 1.2 Global Landau–Ginzburg models and toric wall-crossings
3. 1.3 Analytic lift and Orlov’s decomposition
4. 1.4 Related works
2. 2 Preliminaries
1. 2.1 Quantum cohomology
2. 2.2 Kähler moduli space
3. 2.3 Quantum D-module
4. 2.4 $\widehat{\Gamma}$-integral structure
3. 3 Global Landau–Ginzburg mirrors of toric DM stacks
1. 3.1 Toric data
1. 3.1.1 Toric DM stacks
2. 3.1.2 Picard group and second (co)homology
3. 3.1.3 Orbifold cohomology
2. 3.2 Landau–Ginzburg model
3. 3.3 Extended refined fan sequence and extended Mori cone
4. 3.4 Local charts of the LG model
5. 3.5 Co-ordinate system on the local chart
6. 3.6 Examples
1. 3.6.1 $A_{1}$-singularity resolution
2. 3.6.2 Blowup of $\mathbb{C}^{2}$
3. 3.6.3 Cyclic quotient singularity
4. 4 Mirror symmetry
1. 4.1 Brieskorn module
2. 4.2 Completion and mirror isomorphism
3. 4.3 Analytification of the completed Brieskorn module
1. 4.3.1 Analytification of algebras
2. 4.3.2 Analytification of D-modules
3. 4.3.3 The higher residue pairing on the analytified Brieskorn module
4. 4.4 Analytic mirror isomorphism
5. 5 Discrepant wall-crossings
1. 5.1 Discrepant transformation of smooth toric DM stacks
2. 5.2 The LG model along a curve
3. 5.3 Decomposition of the Brieskorn module
4. 5.4 Comparison of quantum D-modules
5. 5.5 Comparison of Gromov–Witten theories in all genera
1. 5.5.1 Ancestor potentials
2. 5.5.2 Givental’s quantization formalism
3. 5.5.3 A relationship between ancestor potentials
4. 5.5.4 Givental’s formula and the proof of Theorem 5.19
6. 6 Formal decomposition and analytic lift
1. 6.1 Hukuhara–Turrittin type result
2. 6.2 Asymptotic basis and marked reflection system
3. 6.3 Sectorial decomposition of the Brieskorn module
1. 6.3.1 Formal decomposition of the Brieskorn module
2. 6.3.2 Brieskorn module over the small quantum cohomology locus
3. 6.3.3 Analytic lift of the formal decomposition
7. 7 Functoriality under toric birational morphisms
1. 7.1 Notation and assumption
2. 7.2 Critical points along a curve
3. 7.3 Identifying $\mathcal{O}$
1. 7.3.1 The structure sheaf of $\mathfrak{X}_{+}$
2. 7.3.2 The structure sheaf of $\mathfrak{X}_{-}$
4. 7.4 Inclusion of the local systems of Lefschetz thimbles
1. 7.4.1 Convergent and divergent critical branches
2. 7.4.2 Local co-ordinate system around $0_{-}=0_{\mathbf{\Sigma}_{-}}$
3. 7.4.3 Sliding out $\mathcal{M}^{\rm sm}$
4. 7.4.4 Kouchnirenko’s condition and a local system of Lefschetz thimbles
5. 7.4.5 Inclusion of the local systems: statement and proof
5. 7.5 Functoriality
6. 7.6 Orlov’s decomposition and analytic lift
1. 7.6.1 Decomposition of the relative homology mirror to Orlov’s decomposition
2. 7.6.2 Orlov’s decomposition as a sectorial decomposition of the quantum D-module
8. 8 Conjecture and discussion
1. 8.1 General conjecture
2. 8.2 Functoriality and Riemann–Hilbert problem
9. A The Brieskorn module in the weak Fano case
1. A.1 Generators and relations
2. A.2 Characteristic variety and coherence
3. A.3 Locally freeness and rank
10. B Proof of Lemma 7.24
1. Acknowledgements
## 1 Introduction
It is a very interesting problem to study how Gromov–Witten invariants (or
quantum cohomology) change under birational transformations. When the
birational transformation is _crepant_ (or a _$K$ -equivalence_), a
conjecture of Yongbin Ruan [92] says that the quantum cohomology of
$K$-equivalent spaces should be related to each other by analytic continuation
in quantum parameters (see, e.g., [20, 30, 32, 77, 80]). In this paper, we are
concerned with _discrepant_ transformations, or more precisely, birational
maps $\varphi\colon\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ between smooth
Deligne–Mumford stacks such that there exist projective birational morphisms
$f_{\pm}\colon\widehat{\mathfrak{X}}\to\mathfrak{X}_{\pm}$ satisfying
$f_{-}=\varphi\circ f_{+}$ and that
$f_{+}^{*}K_{\mathfrak{X}_{+}}-f_{-}^{*}K_{\mathfrak{X}_{-}}$ is a non-zero
effective divisor. In this case, we write
“$K_{\mathfrak{X}_{+}}>K_{\mathfrak{X}_{-}}$” by a slight abuse of notation
$\textstyle{\widehat{\mathfrak{X}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{f_{+}}$$\scriptstyle{f_{-}}$$\textstyle{\mathfrak{X}_{+}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{\varphi}$$\textstyle{\mathfrak{X}_{-}.}$
This includes the case where $\varphi$ is a blowup along a smooth subvariey.
In this case, we do not expect that the quantum cohomology of
$\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ are related by analytic continuation
because their ranks are different. Instead, we expect that the quantum
cohomology of $\mathfrak{X}_{+}$ would contain the quantum cohomology of
$\mathfrak{X}_{-}$ as a _direct summand_ after analytic continuation. This is
analogous to the conjecture that $D^{b}(\mathfrak{X}_{+})$ contains
$D^{b}(\mathfrak{X}_{-})$ as a _semiorthogonal summand_ [9, 13, 71, 72], where
$D^{b}(\mathfrak{X}_{\pm})$ denotes the derived category of coherent sheaves
on $\mathfrak{X}_{\pm}$. In this paper, we describe a decomposition of quantum
cohomology D-modules (and of all genus Gromov–Witten potentials) for toric
Deligne–Mumford stacks under discrepant transformations. Moreover, we show in
special cases that the decomposition of quantum cohomology D-modules is
induced by a semiorthogonal decomposition of derived categories (or more
precisely of topological $K$-groups) via the _$\widehat{\Gamma}$ -integral
structure_ [62, 70]. We also formulate a general conjecture in view of our
results in the toric case.
### 1.1 Quantum cohomology D-modules
Our central objects of study are _quantum $($cohomology$)$ D-modules_. Let
$\mathfrak{X}$ be a smooth Deligne–Mumford stack. The genus-zero Gromov–Witten
invariants define a family of (super)commutative product structures
$\star_{\tau}$ on the orbifold cohomology group $H^{*}_{\rm CR}(\mathfrak{X})$
parametrized by $\tau\in H^{*}_{\rm CR}(\mathfrak{X})$; this is called quantum
cohomology. The product $\star_{\tau}$ then defines a meromorphic flat
connection $\nabla$ called the _quantum connection_ (or _Dubrovin connection_)
on the trivial $H^{*}_{\rm CR}(\mathfrak{X})$-bundle over $H^{*}_{\rm
CR}(\mathfrak{X})\times\mathbb{C}$. It is given by the formulae
$\displaystyle\nabla_{\frac{\partial}{\partial\tau^{i}}}=\frac{\partial}{\partial\tau^{i}}+\frac{1}{z}\phi_{i}\star_{\tau},$
$\displaystyle\nabla_{z\frac{\partial}{\partial z}}=z\frac{\partial}{\partial
z}-\frac{1}{z}E\star_{\tau}+\mu,$
where $(\tau,z)$ represents a point on the base $H^{*}_{\rm
CR}(\mathfrak{X})\times\mathbb{C}$, $\\{\tau^{i}\\}$ are linear co-ordinates
on $H^{*}_{\rm CR}(\mathfrak{X})$ dual to a basis $\\{\phi_{i}\\}$, $E$ is the
so-called Euler vector field, and $\mu$ is the (constant) grading operator.
This connection is self-dual with respect to the pairing $P$ between the
fibres at $(\tau,-z)$ and $(\tau,z)$ induced by the orbifold Poincaré pairing.
The _quantum D-module_ 111Here we assume the convergence and the analyticity
of quantum cohomology (which are true for toric DM stacks); the superscript
“an” means analytic. $\operatorname{QDM}^{\rm an}(\mathfrak{X})$ of
$\mathfrak{X}$ is, roughly speaking, the module of sections of this vector
bundle equipped with the meromorphic flat connection $\nabla$ and the pairing
$P$ (see Sections 2.3 and 6.1 for the details). We also obtain the _formal_
quantum D-module (or more precisely, the quantum D-module _completed in_ $z$)
by restricting $\operatorname{QDM}^{\rm an}(\mathfrak{X})$ to the formal
neighbourhood of $z=0$:
$\overline{\operatorname{QDM}^{\rm an}}(\mathfrak{X})=\operatorname{QDM}^{\rm
an}(\mathfrak{X})\otimes_{\mathcal{O}^{\rm an}[z]}\mathcal{O}^{\rm
an}[\\![z]\\!].$
When a torus $\mathbb{T}$ acts on $\mathfrak{X}$, we can also define the
_$\mathbb{T}$ -equivariant_ quantum D-module $\operatorname{QDM}^{\rm
an}_{\mathbb{T}}(\mathfrak{X})$ and its formal version
$\overline{\operatorname{QDM}^{\rm an}_{\mathbb{T}}}(\mathfrak{X})$; they are
deformation of the non-equivariant quantum D-modules.
### 1.2 Global Landau–Ginzburg models and toric wall-crossings
A smooth semiprojective toric Deligne–Mumford (DM) stack
$\mathfrak{X}_{\mathbf{\Sigma}}$ (in the sense of Borisov–Chen–Smith [14]) can
be defined as the geometric invariant theory (GIT) quotient of a vector space
$\mathbb{C}^{S}$ by a torus
$\mathbb{L}_{\mathbb{C}^{\times}}=\mathbb{L}\otimes\mathbb{C}^{\times}$, where
$\mathbb{L}$ is a free $\mathbb{Z}$-module of finite rank. The torus
$\mathbb{L}_{\mathbb{C}^{\times}}$ acts on $\mathbb{C}^{S}$ via a group
homomorphism $\mathbb{L}_{\mathbb{C}^{\times}}\to(\mathbb{C}^{\times})^{S}$,
and by dualizing it, we get the family
$\operatorname{pr}\colon(\mathbb{C}^{\times})^{S}\to\mathbb{L}^{\star}\otimes\mathbb{C}^{\times}$
of tori equipped with the function $F=\sum\limits_{b\in S}u_{b}$ on
$(\mathbb{C}^{\times})^{S}$, where $u_{b}$ is the $b$th co-ordinate on
$(\mathbb{C}^{\times})^{S}$
$\textstyle{(\mathbb{C}^{\times})^{S}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{F}$$\scriptstyle{\operatorname{pr}}$$\textstyle{\mathbb{C}.}$$\textstyle{\mathbb{L}^{\star}\otimes\mathbb{C}^{\times}}$
This is the Landau–Ginzburg (LG) model mirror to
$\mathfrak{X}_{\mathbf{\Sigma}}$ introduced by Givental [47]. Using the
secondary fan of Gelfand–Kapranov–Zelevinsky [45], we can partially compactify
this LG model to an LG model of the form (see Section 3.2)
$\textstyle{\mathcal{Y}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{F}$$\scriptstyle{\operatorname{pr}}$$\textstyle{\mathbb{C},}$$\textstyle{\mathcal{M}}$
where $\mathcal{Y}$, $\mathcal{M}$ are possibly singular toric DM stacks (in
the sense of Tyomkin [106]). The base $\mathcal{M}$ of this LG model
corresponds to the (extended) Kähler moduli space of
$\mathfrak{X}_{\mathbf{\Sigma}}$ (i.e., the base of the quantum D-module) and
contains a distinguished point $0_{\mathbf{\Sigma}}$ called the _large radius
limit point_ of $\mathfrak{X}_{\mathbf{\Sigma}}$. It also contains,222In fact,
by choosing a suitable presentation of $\mathfrak{X}_{\mathbf{\Sigma}}$ as the
GIT quotient $[\mathbb{C}^{S}/\\!/\mathbb{L}_{\mathbb{C}^{\times}}]$, we can
arrange that the large radius limit point of any given smooth toric DM stack
$\mathfrak{X}_{\mathbf{\Sigma}^{\prime}}$ having the same affinization and the
same generic stabilizer as $\mathfrak{X}_{\mathbf{\Sigma}}$ appears in the
base space $\mathcal{M}$. as torus-fixed points, the large radius limit points
$0_{\mathbf{\Sigma}^{\prime}}$ of several other toric DM stacks
$\mathfrak{X}_{\mathbf{\Sigma}^{\prime}}$ which can be obtained from
$\mathfrak{X}_{\mathbf{\Sigma}}$ by varying the stability condition for the
GIT quotient $[\mathbb{C}^{S}/\\!/\mathbb{L}_{\mathbb{C}^{\times}}]$. Hodge-
theoretic mirror symmetry for toric DM stacks established by Coates–Corti-
Iritani–Tseng [26, 27] implies that, for each smooth toric DM stack
$\mathfrak{X}_{\mathbf{\Sigma}^{\prime}}$ whose large radius limit point
appears in $\mathcal{M}$, we have a mirror map defined on the formal
neighbourhood of $0_{\mathbf{\Sigma}^{\prime}}$
$\operatorname{mir}\colon\
(\mathcal{M},0_{\mathbf{\Sigma}^{\prime}})^{^}\longrightarrow\text{a partial
compactification of $H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}^{\prime}})/2\pi\boldsymbol{\mathrm{i}}H^{2}(\mathfrak{X}_{\mathbf{\Sigma}^{\prime}},\mathbb{Z})$}$
and a mirror isomorphism
$\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}^{\prime}}\cong\operatorname{mir}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\mathbf{\Sigma}^{\prime}}).$
Here $\operatorname{Bri}(F)$ denotes the _Brieskorn module_ associated with
the LG potential $F$ and the sub/superscripts
${}_{\mathbf{\Sigma}^{\prime}}^{^}$ means the completion at the large-radius
limit point $0_{\mathbf{\Sigma}^{\prime}}$ (see Sections 4.1–4.2). Using the
convergence result from [59, 27], we show that this mirror isomorphism can be
extended to a small analytic neighbourhood of $0_{\mathbf{\Sigma}^{\prime}}$
as an isomorphism333The analytified Brieskorn module
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}^{\prime}}$ is
analytic in the $\mathcal{M}$-direction but is still formal in $z$; similarly
the formal quantum D-module $\overline{\operatorname{QDM}}^{\rm
an}(\mathfrak{X}_{\mathbf{\Sigma}^{\prime}})$ is formal in $z$ but is still
analytic in $\tau$, so they can be compared. between a certain _analytified_
Brieskorn module
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}^{\prime}}$ and the
formal quantum $D$-module $\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{\mathbf{\Sigma}^{\prime}})$ (see Theorem 4.34). This
enables us to compare the quantum D-modules of various birational models of
$\mathfrak{X}_{\mathbf{\Sigma}}$ over the mirror moduli space $\mathcal{M}$.
Then we arrive at the following result (in this theorem, we do not assume
compactness of $\mathfrak{X}_{\pm}$ or (semi-)positivity of
$c_{1}(\mathfrak{X}_{\pm})$).
###### Theorem 1.1 (Theorem 5.16).
Let $\varphi\colon\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ be a discrepant
transformation between semiprojective toric DM stacks induced by a single
wall-crossing in the space of GIT stability conditions. Suppose that
$K_{\mathfrak{X}_{+}}>K_{\mathfrak{X}_{-}}$. Then we have a formal
decomposition of the $\mathbb{T}$-equivariant quantum D-modules
$\operatorname{mir}_{+}^{*}\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{+})\cong\operatorname{mir}_{-}^{*}\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{-})\oplus\mathscr{R}$ (1.1)
over a non-empty open subset $\mathcal{U}_{0}^{\prime}$ of
$\mathcal{M}\times\operatorname{Lie}\mathbb{T}$, where
$\operatorname{mir}_{\pm}$ denotes the mirror map for $\mathfrak{X}_{\pm}$ and
$\mathscr{R}$ is a locally free $\mathcal{O}^{\rm
an}_{\mathcal{U}_{0}^{\prime}}[\\![z]\\!]$-module equipped with a meromorphic
flat connection and a pairing.
This theorem is a generalization of the result of González–Woodward [51] who
showed a decomposition of the quantum cohomology _algebras_ under a running of
the toric minimal model programme. In this theorem, we consider analytic
continuation over a neighbourhood of a toric curve
$\mathcal{C}\subset\mathcal{M}$ connecting the large radius limit points
$0_{\pm}$ for $\mathfrak{X}_{\pm}$. When $\varphi$ is an isomorphism in
codimension one (“flip”), the curve $\mathcal{C}$ is asymptotically close,
near the large radius limit points $0_{\pm}$, to the curve in the boundary of
the Kähler moduli space given by the extremal curve class. When $\varphi$ (or
$\varphi^{-1}$) contracts a divisor, the curve $\mathcal{C}$ is asymptotically
close to the curve corresponding to the extremal class near $0_{+}$ (resp.
$0_{-}$) and to the line spanned by a cohomology class of degree greater than
2 near $0_{-}$ (resp. of degree less than 2 near $0_{+}$), see Remark 5.9. In
either case, at least one of the mirror maps $\operatorname{mir}_{\pm}$
involves negative degree variables with respect to the Euler vector field (an
instance of the _generalized_ mirror transformation [28, 61, 69]) and the
formal decomposition occurs over the base of the _big_ quantum cohomology in
general. We also note that the decomposition (1.1) is defined only over the
formal power series ring $\mathbb{C}[\\![z]\\!]$ and the completion in $z$ is
unavoidable. In fact, as Theorem 1.3 below shows, the Stokes structure does
not admit an orthogonal decomposition.
Using the Givental–Teleman formula [19, 49, 104, 109], we obtain a
decomposition for the (all-genus) _ancestor Gromov–Witten potentials_. The
result is stated in terms of Givental’s quantization formalism; we refer to
Section 5.5 for the notation.
###### Theorem 1.2 (Theorem 5.19).
Let $\mathfrak{X}_{\pm}$ be toric DM stacks as in Theorem 1.1. Let
$\mathscr{A}_{\pm,\tau}$ denote the ancestor potentials of
$\mathfrak{X}_{\pm}$ at $\tau\in H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{\pm})$. For
$(q,\chi)\in\mathcal{M}\times\operatorname{Lie}\mathbb{T}$ in a non-empty open
set, we have
$T_{\mathbf{s}}{\widehat{U}}_{q,\chi}\mathscr{A}_{+,\operatorname{mir}_{+}(q,\chi)}=\mathscr{A}_{-,\operatorname{mir}_{-}(q,\chi)}\otimes\mathscr{T}^{\otimes\operatorname{rank}\mathscr{R}},$
where $\chi$ is the $\mathbb{T}$-equivariant parameter,
${\widehat{U}}_{q,\chi}$ is the quantization of a symplectic transformation
associated with the decomposition (1.1), $\mathscr{T}$ is the
Witten–Kontsevich tau-function $($the ancestor potential of a point$)$ and
$T_{\mathbf{s}}$ is a certain shift operator.
### 1.3 Analytic lift and Orlov’s decomposition
The non-equivariant quantum D-module has (in general) irregular singularities
at $z=0$ and the formal quantum D-module misses analytic information such as
the Stokes structure at $z=0$. For a compact toric DM stack, at least in the
non-equivariant limit and over the semisimple locus, the formal structure of
the quantum D-module is very poor444This does not mean that Theorem 1.1 is
trivial. It compares the _equivariant_ quantum D-modules over the open set
$\mathcal{U}_{0}^{\prime}$ that contains the _non-semisimple_ loci. It is also
important that the two quantum D-modules are connected through the explicit
mirror LG model., since it is determined only by eigenvalues of the Euler
multiplication. We will restore the missing information by describing the
_analytic lift_ of the formal decomposition (1.1). By the Hukuhara–Turrittin
theorem (see Section 6.1), the decomposition (1.1) in the non-equivariant
limit can be locally lifted to an analytic isomorphism:555More precisely, the
analytic lift is defined over functions in $z$ which admit asymptotic
expansions along an angular sector (with vertex at $z=0$); such functions form
a sheaf $\mathcal{A}$ over the real oriented blowup of $\mathbb{C}$ at the
origin [95].
$\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})\big{|}_{B\times
I}\cong\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{B\times I}\oplus\mathscr{R}^{\rm an},$ (1.2)
where $B$ is a small open subset of $\mathcal{M}$ and $I$ is an angular sector
$\\{z\colon|\arg(z)-\phi|<\frac{\pi}{2}+\epsilon\\}$ with $\epsilon>0$. We
call it the _analytic lift_ or a _sectorial decomposition_ ; its uniqueness is
ensured by the fact that the angle of the sector is bigger than $\pi$. The
analytic lift induces a decomposition (depending on $B$ and $I$) of the local
system underlying $\operatorname{QDM}^{\rm an}(\mathfrak{X}_{+})$. On the
other hand, the _$\widehat{\Gamma}$ -integral structure_ [62, 70] identifies
the complexified topological $K$-group $K(\mathfrak{X})\otimes\mathbb{C}$ with
the space of multi-valued flat sections of the quantum D-module; for toric
stacks, it corresponds to the integral structure on the GKZ system identified
by Borisov–Horja [15]. We show in some special cases that the decomposition of
the local system given by the analytic lift corresponds to a semiorthogonal
decomposition of the topological $K$-group $K(\mathfrak{X}_{+})$ via the
$\widehat{\Gamma}$-integral structure. An important ingredient here is the
fact [62] that the $\widehat{\Gamma}$-integral structure coincides with the
natural integral structure of the Brieskorn module under mirror symmetry. By
describing the analytic lift in terms of mirror oscillatory integrals and
studying the relationship between the local systems of Lefschetz thimbles (see
Theorems 7.22 and 7.31), we obtain the following result.
###### Theorem 1.3 (Theorems 7.25, 7.31, and 7.33).
Let $\mathfrak{X}_{-}$ be a weak-Fano compact toric stack satisfying a mild
technical assumption as described in Section 7.1 and let
$\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$ be a weighted blowup along
a toric substack $Z\subset\mathfrak{X}_{-}$. We assume that $\mathfrak{X}_{+}$
is also weak-Fano. Then there exist a submersion $f$ from an open set $W$ of
$H^{*}_{\rm CR}(\mathfrak{X}_{+})$ to $H^{*}_{\rm CR}(\mathfrak{X}_{-})$ and
an angular sector $I$ $($of angle greater than $\pi)$ such that we have an
analytic decomposition over the sector
$\operatorname{QDM}^{\rm an}(\mathfrak{X}_{+})\big{|}_{W\times
I}\cong\mathscr{R}^{\rm an}_{-J}\oplus\cdots\oplus\mathscr{R}^{\rm
an}_{-1}\oplus f^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{W\times I},$
which induces, via the $\widehat{\Gamma}$-integral structure, a semiorthogonal
decomposition of the $K$-group
$K(\mathfrak{X}_{+})=K(Z)_{-J}\oplus\cdots\oplus
K(Z)_{-1}\oplus\varphi^{*}K(\mathfrak{X}_{-}),$ (1.3)
where $K(Z)_{k}=\mathcal{O}(-kE)\otimes i_{E_{*}}\varphi_{E}^{*}K(Z)\subset
K(\mathfrak{X}_{+})$. Here $E$ is the exceptional divisor of $\varphi$,
$\varphi_{E}=\varphi|_{E}\colon E\to Z$, $i_{E}\colon E\to\mathfrak{X}_{+}$ is
the inclusion and $J=k_{0}+\cdots+k_{c}-1$ when a fibre of $\varphi_{E}\colon
E\to Z$ is given by the weighted projective space
$\mathbb{P}(k_{0},\dots,k_{c})$.
###### Remark 1.4.
1. (1)
In this theorem, we allow $Z$ to be of codimension one (i.e., a toric
divisor); in this case $\mathfrak{X}_{+}$ is obtained from $\mathfrak{X}_{-}$
by a root construction (see [21]) along $Z$.
2. (2)
When $\mathfrak{X}_{-}$ is a smooth projective variety and
$\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$ is the blowup along a
smooth subvariety $Z$, the decomposition (1.3) is induced by Orlov’s
semiorthogonal decomposition [87] for $D^{b}(\mathfrak{X}_{+})$. In general,
the Orlov-type decomposition (1.3) arises from a sectorial decomposition of
the quantum D-module at a point which is far from the large radius limit
point. On the other hand, we can idenfity explicitly the locus in the mirror
moduli space $\mathcal{M}$ where the analytic lift (1.2) induces the pull-back
$\varphi^{*}\colon K(\mathfrak{X}_{-})\to K(\mathfrak{X}_{+})$ in $K$-theory
(Theorem 7.25).
3. (3)
The result suggests that each residual piece $\mathscr{R}^{\rm an}_{i}$ of the
sectorial decomposition should be related to the quantum D-module of the
blowup centre $Z$; they certainly have the same formal structure, but we do
not know if the Stokes structures are related (although we expect from
homological mirror symmetry that they should be related).
4. (4)
We need the weak-Fano assumption when we apply results from [62]. We hope that
the same result holds without such assumptions, but it may require some
technical advances.
5. (5)
In Section 8, we formulate a general conjecture relating the decomposition of
topological $K$-groups and that of quantum D-modules under discrepant
transformations. Under the conjecture, the decomposition of $K$-groups in
principle determines the relationship between the quantum D-modules of
$\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ (including the map $f$). This
involves solving a Riemann–Hilbert problem; see Proposition 8.5.
### 1.4 Related works
We mention some of the earlier works that are closely related to the present
paper.
The relationship between quantum cohomology and derived category has been
suggested by Dubrovin [39]. Our Theorem 1.3 can be viewed as a variation on
this theme (see also Gamma conjecture [44] or Dubrovin-type conjecture [101]).
Bayer [12] showed that the semisimplicity of quantum cohomology is preserved
under blowup at a point in connection with Dubrovin’s conjecture [39]. His
computation [12, Lemma 3.4.2] for the spectral cover is compatible with the
picture in this paper.
As mentioned earlier, González–Woodward [51] showed a decomposition of toric
quantum cohomology under flips; they used the same LG model mirrors (combined
with the quantum Kirwan map) to analyze the change of quantum cohomology.
Charest–Woodward [22] and Sanda [99, 100] discussed (orthogonal) decomposition
of Fukaya category and of quantum cohomology under flips/blowups. From a
categorical viewpoint, the quantum cohomology (or the formal quantum D-module)
should arise as the Hochschild (resp. negative cyclic) homology of the Fukaya
category, and a decomposition of the Fukaya category should induce a (formal)
decomposition of the quantum cohomology/D-module via the open-closed map.
Acosta–Shoemaker [4, 5] (see also an earlier work of Acosta [3]) studied
discrepant wall-crossings for toric Gromov–Witten theory in the same setting
as ours. They compared the Givental $I$-functions of $\mathfrak{X}_{\pm}$ over
the mirror moduli space $\mathcal{M}$. Writing $I_{\pm}$ for the $I$-functions
of $\mathfrak{X}_{\pm}$, they showed that the asymptotic expansion of $I_{+}$
near the large-radius limit point $0_{-}$ is related to $I_{-}$ by a linear
transformation $L\colon H^{*}_{\rm CR}(\mathfrak{X}_{+})\to H^{*}_{\rm
CR}(\mathfrak{X}_{-})$, i.e., $LI_{+}(q)\sim I_{-}(q)$ as $q\to 0_{-}$ along
some (one-dimensional) angular direction. We expect that their linear
transformation $L$ should correspond to the projection between the quantum
cohomology local systems for $\mathfrak{X}_{\pm}$ associated with an analytic
lift (1.2). They also dealt with the case of complete intersections in toric
stacks (which we do not cover in this paper). More recently, Lee–Lin–Wang [78,
Section 6], [79] have announced a decomposition of quantum D-modules under
flips and showed it for local toric flips. In these approaches [3, 4, 5, 78,
79], they studied irregular singularities on the base $\mathcal{M}$ directly
whereas we studied those on the $z$-plane; the singularities at $z=0$ and
$q=0_{-}$ are closely related, but those at $z=0$ have a simpler structure.
Recently, Clingempeel–Le Floch–Romo [25] compared the hemisphere partition
functions (which in our language correspond to certain solutions of the
quantum D-modules) of the cyclic quotient singularities
$\mathbb{C}^{2}/\mu_{n}$ and their Hirzebruch–Jung resolutions. They discussed
the relation to a semiorthogonal decomposition of the derived categories,
extending the work of Herbst–Hori–Page [56] to the anomalous (discrepant)
case. Their examples are complementary to ours: the Hirzebruch–Jung
resolutions are type (II-ii) discrepant transformations whereas
transformations in Theorem 1.3 are of type (II-i) or (III) (see Remark 5.4 for
these types).
Under homological mirror symmetry, the derived categories of coherent sheaves
for toric stacks correspond to the Fukaya–Seidel categories of the mirror LG
models. Kerr [73], Diemer–Katzarkov–Kerr [36, 35] and
Ballard–Diemer–Favero–Katzarkov–Kerr [8] (see also [9]) studied semiorthogonal
decompositions of the Fukaya–Seidel categories of the LG mirrors under toric
wall-crossings; they conjectured [8, Conjecture 1] that semiorthogonal
decompositions for the Fukaya–Seidel categories and for the derived categories
should match up under mirror symmetry. Theorem 1.3 can be viewed as an
evidence for their conjecture on the level of enumerative mirror symmetry. We
note that they introduced a similar toric compactification of the moduli space
of LG models and studied how the critical values assemble under deformation in
a more general setting than ours (a relevant discussion appears in Section 7.4
in this paper).
After the author finished a draft of this paper, he heard a talk of Kontsevich
[74] who studied (in joint project with Katzarkov and Pantev) the change of
quantum cohomology under blowups from a similar perspective and gave an
application to birational geometry.
The author apologizes for the long delay in preparing the paper since the
original announcement [60] (see also [63]) in June 2008. There were many
technical issues in proving our results in this generality. Advances made in
joint work [26, 27] with Coates, Corti and Tseng and in joint work [44] with
Galkin and Golyshev are essential in this paper.
## 2 Preliminaries
In this section, in order to fix notation, we review quantum cohomology,
quantum D-modules and the Gamma-integral structure. Our main interest in this
paper lies in the case where $\mathfrak{X}$ is a toric DM stack, but all the
materials in this section make sense for a general smooth DM stack
$\mathfrak{X}$ satisfying mild assumptions.
### 2.1 Quantum cohomology
Gromov–Witten theory for smooth Deligne–Mumford stacks (or symplectic
orbifolds) has been developed by Chen–Ruan [23] and Abramovich–Graber–Vistoli
[1, 2]. We use the algebro-geometric approach in [1, 2].
Let $\mathfrak{X}$ be a smooth DM (Deligne–Mumford) stack over $\mathbb{C}$.
We write $X$ for the coarse moduli space of $\mathfrak{X}$. Recall that the
_inertia stack_ $I\mathfrak{X}$ is the fibre product
$\mathfrak{X}\times_{\mathfrak{X}\times\mathfrak{X}}\mathfrak{X}$ of the two
diagonal morphisms $\mathfrak{X}\to\mathfrak{X}\times\mathfrak{X}$. A point on
$I\mathfrak{X}$ is given by a pair $(x,g)$ of a point $x\in\mathfrak{X}$ and a
stabilizer $g\in\operatorname{Aut}(x)$. We write
$I\mathfrak{X}=\bigsqcup\limits_{v\in\operatorname{Box}}\mathfrak{X}_{v}$ for
the decomposition of $I\mathfrak{X}$ into connected components, where
$\operatorname{Box}$ is the index set. We have a distinguished element
$0\in\operatorname{Box}$ that corresponds to the _untwisted sector_
$\mathfrak{X}_{0}\cong\mathfrak{X}$ consisting of points $(x,g=1)$ with the
trivial stabilizer. The _orbifold cohomology_ $H_{\rm CR}^{*}(\mathfrak{X})$
of Chen and Ruan [24] is defined to be
$H_{\rm
CR}^{*}(\mathfrak{X}):=H^{*-2\operatorname{age}}(I\mathfrak{X},\mathbb{C})=\bigoplus_{v\in\operatorname{Box}}H^{*-2\operatorname{age}(v)}(\mathfrak{X}_{v},\mathbb{C}),$
(2.1)
where $\operatorname{age}\colon I\mathfrak{X}\to\mathbb{Q}_{\geq 0}$ is a
locally constant function giving a shift of degrees and we write
$\operatorname{age}(v)=\operatorname{age}|_{\mathfrak{X}_{v}}$ (see Section
3.1.3 for the age in the case of toric DM stacks). The right-hand side means
the cohomology group of the underlying complex analytic space of
$I\mathfrak{X}$ and we use complex coefficients unless otherwise specified. We
also restrict ourselves to cohomology classes of “even parity”, i.e., we only
consider cohomology classes of even degrees666An element $\alpha\in H^{*}_{\rm
CR}(\mathfrak{X})$ having “even parity” does not imply that the degree of
$\alpha$ as an orbifold cohomology class is even; it means that the degree of
$\alpha$ is even _as an element of_ $H^{*}(I\mathfrak{X})$. on
$I\mathfrak{X}$. For toric DM stacks, every orbifold cohomology class has even
parity. When $\mathfrak{X}$ is proper, the orbifold Poincaré pairing on
$H_{\rm CR}^{*}(\mathfrak{X})$ is defined to be
$(\alpha,\beta):=\int_{I\mathfrak{X}}\alpha\cup\operatorname{inv}^{*}\beta,$
(2.2)
where $\operatorname{inv}\colon I\mathfrak{X}\to I\mathfrak{X}$ is the
involution sending $(x,g)$ to $\big{(}x,g^{-1}\big{)}$. For $d\in
H_{2}(\mathfrak{X},\mathbb{Q})$ and $l\in\mathbb{Z}_{\geq 0}$, let
$\mathfrak{X}_{g,l,d}$ denote the moduli stack of genus-$g$ twisted stable
maps to $\mathfrak{X}$ of degree $d$ and with $l$ marked points (this was
denoted by $\mathcal{K}_{g,l}(\mathfrak{X},d)$ in [2]). It carries a virtual
fundamental class $[\mathfrak{X}_{g,l,d}]_{\rm vir}\in
A_{*}(\mathfrak{X}_{g,l,d},\mathbb{Q})$ and the evaluation maps
$\operatorname{ev}_{i}\colon\mathfrak{X}_{g,l,d}\to\overline{I}\mathfrak{X}$,
$i=1,\dots,l$ to the rigidified cyclotomic inertia stack
$\overline{I}\mathfrak{X}$ (see [2, Section 3.4]). When the moduli stack
$\mathfrak{X}_{g,l,d}$ is proper (this happens when $\mathfrak{X}$ has a
projective coarse moduli space), we define _genus-zero descendant
Gromov–Witten invariants_ by
$\big{\langle}\alpha_{1}\psi^{k_{1}},\dots,\alpha_{l}\psi^{k_{l}}\big{\rangle}_{g,l,d}:=\int_{[\mathfrak{X}_{g,l,d}]_{\rm
vir}}\prod_{i=1}^{l}\operatorname{ev}_{i}^{*}(\alpha_{i})\psi_{i}^{k_{i}},$
where $\alpha_{1},\dots,\alpha_{l}\in H^{*}_{\rm CR}(\mathfrak{X})$, $d\in
H_{2}(\mathfrak{X},\mathbb{Q})$ and $\psi_{i}$ denotes the $\psi$-class (see
[2, Section 8.3]) at the $i$th marking. Here note that the rigidified
cyclotomic inertia stack $\overline{I}\mathfrak{X}$ has the same coarse moduli
space as $I\mathfrak{X}$, and thus $\alpha_{i}$ can be regarded as a
cohomology class of $\overline{I}\mathfrak{X}$.
We assume that there exists a finitely generated monoid
$\boldsymbol{\Lambda}_{+}\subset H_{2}(\mathfrak{X},\mathbb{Q})$ such that
$\mathbb{R}_{\geq 0}\boldsymbol{\Lambda}_{+}$ is a strictly convex full-
dimensional cone in $H_{2}(\mathfrak{X},\mathbb{R})$ and that
$\boldsymbol{\Lambda}_{+}$ contains classes of any orbifold stable curves. We
also assume that $\boldsymbol{\Lambda}_{+}$ is saturated, i.e.,
$\boldsymbol{\Lambda}_{+}=\boldsymbol{\Lambda}\cap\mathbb{R}_{\geq
0}\boldsymbol{\Lambda}_{+}$ for
$\boldsymbol{\Lambda}:=\mathbb{Z}\boldsymbol{\Lambda}_{+}$. The monoid
$\boldsymbol{\Lambda}_{+}$ for toric DM stacks will be described in Section
3.3 and will be denoted by $\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}$ there.
For a ring $K$, let $K[\\![\boldsymbol{\Lambda}_{+}]\\!]$ denote the
completion of $K[\boldsymbol{\Lambda}_{+}]$ consisting of all formal sums
$\sum\limits_{d\in\boldsymbol{\Lambda}_{+}}a_{d}Q^{d}$ with $a_{d}\in K$. The
variable $Q$ here is called the _Novikov variable_. We also choose a
homogeneous basis $\\{\phi_{i}\\}_{i=0}^{s}$ of $H^{*}_{\rm CR}(\mathfrak{X})$
and introduce linear co-ordinates $\\{\tau^{i}\\}_{i=0}^{s}$ on $H^{*}_{\rm
CR}(\mathfrak{X})$ as
$\big{(}\tau^{0},\dots,\tau^{s}\big{)}\mapsto\tau=\sum\limits_{i=0}^{s}\tau^{i}\phi_{i}$.
We write $K[\\![\tau]\\!]=K[\\![\tau^{0},\dots,\tau^{s}]\\!]$ for any ring
$K$. The _quantum product_ $\alpha\star\beta$ of classes $\alpha,\beta\in
H^{*}_{\rm CR}(\mathfrak{X})$ is defined so that for every $\gamma\in
H^{*}_{\rm CR}(\mathfrak{X})$, we have
$(\alpha\star\beta,\gamma):=\sum_{d\in\boldsymbol{\Lambda}_{+}}\sum_{l\geq
0}\left\langle\alpha,\beta,\gamma,\tau,\dots,\tau\right\rangle_{0,l+3,d}\frac{Q^{d}}{l!},$
where $\tau=\sum\limits_{i=0}^{s}\tau^{i}\phi_{i}\in H^{*}_{\rm
CR}(\mathfrak{X})$ is a parameter. This definition makes sense when $X$ is
projective and $\alpha\star\beta$ lies in $H^{*}_{\rm
CR}(\mathfrak{X})\otimes\mathbb{C}[\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau]\\!]$.
The quantum product $\star$ is known to be commutative and associative and
defines a commutative ring structure on $H^{*}_{\rm
CR}(\mathfrak{X})\otimes\mathbb{C}[\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau]\\!]$.
When we want to emphasize the dependence of $\star$ on the parameter $\tau$,
we shall write $\alpha\star_{\tau}\beta$ in place of $\alpha\star\beta$.
The Gromov–Witten invariants and the quantum product can be generalized to the
equivariant setting or to a non-projective space $\mathfrak{X}$. Suppose that
an algebraic torus $\mathbb{T}$ acts on $\mathfrak{X}$. The equivariant
orbifold cohomology $H_{{\rm CR},\mathbb{T}}^{*}(\mathfrak{X})$ is defined to
be the $\mathbb{T}$-equivariant cohomology of $I\mathfrak{X}$ with the same
degree shift as before:
$H_{{\rm
CR},\mathbb{T}}^{*}(\mathfrak{X}):=H^{*-2\operatorname{age}}_{\mathbb{T}}(I\mathfrak{X},\mathbb{C})=\bigoplus_{v\in\operatorname{Box}}H^{*-2\operatorname{age}(v)}_{\mathbb{T}}(\mathfrak{X}_{v},\mathbb{C}).$
Let $E\mathbb{T}\to B\mathbb{T}$ denote a universal $\mathbb{T}$-bundle. We
assume that
* (a)
$I\mathfrak{X}$ is equivariantly formal, i.e., the Serre spectral sequence for
$I\mathfrak{X}\times_{\mathbb{T}}E\mathbb{T}\to B\mathbb{T}$ collapses at the
$E^{2}$-term (over $\mathbb{Q}$); this implies that $H_{{\rm
CR},\mathbb{T}}^{*}(\mathfrak{X})$ is a free
$R_{\mathbb{T}}:=H^{*}_{\mathbb{T}}({\operatorname{pt}},\mathbb{C})$-module of
rank $\dim H_{\rm CR}^{*}(\mathfrak{X})$;
* (b)
the $\mathbb{T}$-fixed set of $\mathfrak{X}$ is projective;
* (c)
the evaluation maps
$\operatorname{ev}_{i}\colon\mathfrak{X}_{0,l,d}\to\overline{I}\mathfrak{X}$
are proper.
By the assumption (a), the $\mathbb{C}$-basis $\\{\phi_{i}\\}_{i=0}^{s}\subset
H^{*}_{\rm CR}(\mathfrak{X})$ can be lifted to an $R_{\mathbb{T}}$-basis of
$H^{*}_{{\rm CR},\mathbb{T}}(\mathfrak{X})$, which we denote by the same
symbol. This induces $R_{\mathbb{T}}$-linear co-ordinates
$(\tau^{0},\dots,\tau^{s})\mapsto\tau=\sum\limits_{i=0}^{s}\tau^{i}\phi_{i}$
on $H_{{\rm CR},\mathbb{T}}^{*}(\mathfrak{X})$ as before. Under the assumption
(b), we can define the equivariant orbifold Poincaré pairing and the
equivariant Gromov–Witten invariants via the virtual localization formula
[53]. They take values in the fraction field
$S_{\mathbb{T}}:=\operatorname{Frac}(R_{\mathbb{T}})$ of $R_{\mathbb{T}}$.
Under the assumption (c), we can define the quantum product using the push-
forward by the proper map $\operatorname{ev}_{3}$ as follows:
$\alpha\star\beta=\sum_{d\in\boldsymbol{\Lambda}_{+}}\sum_{l\geq
0}\operatorname{inv}^{*}\operatorname{PD}{\operatorname{ev}_{3}}_{*}\left(\operatorname{ev}_{1}^{*}(\alpha)\operatorname{ev}_{2}^{*}(\beta)\prod_{j=1}^{l}\operatorname{ev}_{3+j}^{*}(\tau)\cap[\mathfrak{X}_{0,l+3,d}]_{\rm
vir}\right)\frac{Q^{d}}{l!},$
where $\operatorname{PD}$ stands for the Poincaré duality on $I\mathfrak{X}$.
Therefore we get the quantum product $\star$ defined on the space $H_{{\rm
CR},\mathbb{T}}^{*}(\mathfrak{X})\otimes_{R_{\mathbb{T}}}R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau]\\!]$
without inverting equivariant parameters, whereas the Gromov–Witten invariants
themselves lie in $S_{\mathbb{T}}$ in general.
###### Remark 2.1.
As remarked in [20], the assumption (c) is satisfied if the coarse moduli
space $X$ is semi-projective, i.e., projective over an affine variety. We will
impose the semi-projectivity assumption on toric DM stacks.
### 2.2 Kähler moduli space
In this section, we specialize the Novikov variable $Q$ to one with the aid of
the divisor equation, and introduce the Kähler moduli space $\mathcal{M}_{\rm
A}(\mathfrak{X})$ parameterizing the quantum product.
As before, let $\phi_{0},\phi_{1},\dots,\phi_{s}$ be a homogeneous basis of
$H^{*}_{\rm CR}(\mathfrak{X})$. We assume that $\phi_{0}=\boldsymbol{1}$ is
the identity class and that $\\{\phi_{1},\dots,\phi_{r}\\}$, $r\leq s$ is a
basis of the degree-two untwisted sector $H^{2}(\mathfrak{X})\subset
H^{2}_{\rm CR}(\mathfrak{X})$. We write $\tau=\sigma+\tau^{\prime}$ with
$\sigma=\sum\limits_{i=1}^{r}\tau^{i}\phi_{i}\in H^{2}(\mathfrak{X})$ and
$\tau^{\prime}=\tau^{0}\phi_{0}+\sum\limits_{i=r+1}^{s}\tau^{i}\phi_{i}$. The
divisor equation [2, Theorem 8.3.1] implies
$(\alpha\star_{\tau}\beta,\gamma)=\sum_{d\in\boldsymbol{\Lambda}_{+}}\sum_{l=0}^{\infty}\left\langle\alpha,\beta,\gamma,\tau^{\prime},\dots,\tau^{\prime}\right\rangle_{0,l+3,d}\frac{Q^{d}e^{\sigma\cdot
d}}{l!}.$
This shows that the quantum product $\star_{\tau}$ depends only on the
equivalence class
$[\tau]\in H^{*}_{\rm
CR}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star},$
where $\boldsymbol{\Lambda}^{\star}\subset H^{2}(\mathfrak{X},\mathbb{Q})$
denotes the dual lattice of
$\boldsymbol{\Lambda}=\mathbb{Z}\boldsymbol{\Lambda}_{+}$. Note that
$d\in\boldsymbol{\Lambda}$ defines a function $q^{d}\colon[\tau]\mapsto
e^{\sigma\cdot d}=\exp\big{(}\sum\limits_{i=1}^{r}\tau^{i}(\phi_{i}\cdot
d)\big{)}$ on $H^{*}_{\rm
CR}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}$,
and that each co-ordinate $\tau^{i}$ with $i\notin\\{1,\dots,r\\}$ also
defines a function on $H^{*}_{\rm
CR}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}$.
These functions define an open embedding of $H^{*}_{\rm
CR}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}$
into the following space:
$\mathcal{M}_{\rm
A}(\mathfrak{X}):=\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}_{+}][\tau^{\prime}]=\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}_{+}]\big{[}\tau^{0},\tau^{r+1},\dots,\tau^{s}\big{]},$
where the element of $\mathbb{C}[\boldsymbol{\Lambda}_{+}]$ corresponding to
$d\in\boldsymbol{\Lambda}_{+}$ represents the function $q^{d}=e^{\sigma\cdot
d}$. The space $\mathcal{M}_{\rm A}(\mathfrak{X})$ gives a partial
compactification of $H_{\rm
CR}^{*}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}$
depending on the choice of the monoid $\boldsymbol{\Lambda}_{+}$. By setting
$Q=1$, we may view $\star_{\tau}$ as a family of products parameterized by the
formal neighbourhood of the “origin” (that is, $q^{d}=0$ for all non-zero
$d\in\boldsymbol{\Lambda}_{+}$ and $\tau^{0}=\tau^{r+1}=\cdots=\tau^{s}=0$) in
$\mathcal{M}_{\rm A}(\mathfrak{X})$. This origin is called the _large radius
limit point_.
Quantum cohomology for smooth DM stacks has the additional symmetry called the
_Galois symmetry_ [62, Section 2.2]. Let $H^{2}(\mathfrak{X},\mathbb{Z})$
denote the sheaf cohomology of the constant sheaf $\mathbb{Z}$ on the
topological stack (orbifold) underlying $\mathfrak{X}$; an element $\xi\in
H^{2}(\mathfrak{X},\mathbb{Z})$ corresponds to a topological orbi-line bundle
$L_{\xi}$ over $\mathfrak{X}$. For a connected component $\mathfrak{X}_{v}$ of
$I\mathfrak{X}$, the stabilizer along $\mathfrak{X}_{v}$ acts on fibres of
$L_{\xi}$ by a constant scalar $\exp(2\pi\boldsymbol{\mathrm{i}}f_{v}(\xi))$
for some $f_{v}(\xi)\in[0,1)\cap\mathbb{Q}$. This number $f_{v}(\xi)$ is
called the _age_ of $L_{\xi}$ along $\mathfrak{X}_{v}$. We define a map
$g(\xi)\colon H_{\rm CR}^{*}(\mathfrak{X})\to H_{\rm CR}^{*}(\mathfrak{X})$ by
$g(\xi)(\tau)=\left(\tau_{0}-2\pi\boldsymbol{\mathrm{i}}\xi\right)\oplus\bigoplus_{v\neq
0}e^{2\pi\boldsymbol{\mathrm{i}}f_{v}(\xi)}\tau_{v},$
where $\tau_{v}$ denotes the $H^{*}(\mathfrak{X}_{v})$-component of $\tau\in
H^{*}_{{\rm CR}}(\mathfrak{X})$ in the decomposition (2.1). Let
$dg(\xi)\in\operatorname{End}(H_{\rm CR}^{*}(\mathfrak{X}))$ denote the
derivative of the map $g(\xi)$; it is given by
$dg(\xi)\tau=\bigoplus\limits_{v\in\operatorname{Box}}e^{2\pi\boldsymbol{\mathrm{i}}f_{v}(\xi)}\tau_{v}$.
Gromov–Witten invariants satisfy (see [62, Proposition 2.3])
$\big{\langle}dg(\xi)(\alpha_{1})\psi^{k_{1}},\dots,dg(\xi)(\alpha_{l})\psi^{k_{l}}\big{\rangle}_{g,l,d}=e^{2\pi\boldsymbol{\mathrm{i}}\xi\cdot
d}\big{\langle}\alpha_{1}\psi^{k_{1}},\dots,\alpha_{l}\psi^{k_{l}}\big{\rangle}_{g,l,d}$
(2.3)
and thus the quantum product satisfies
$dg(\xi)(\alpha\star_{\tau}\beta)=(dg(\xi)\alpha)\star_{g(\xi)(\tau)}(dg(\xi)\beta).$
The map $g(\xi)$ induces the action of
$H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}$ on $H_{\rm
CR}^{*}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}$;
this action naturally extends to the partial compactification
$\mathcal{M}_{\rm A}(\mathfrak{X})$. In view of this symmetry, we can regard
the quantum products $\star_{\tau}$ as a family of products parametrized by
the formal neighbourhood of the origin (large radius limit) of the stack:
$\big{[}\mathcal{M}_{\rm
A}(\mathfrak{X})\big{/}\big{(}H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}\big{)}\big{]}.$
We refer to $\mathcal{M}_{\rm A}(\mathfrak{X})$ or to the quotient stack above
as the _Kähler moduli space_ , where the subscript A stands for the A-model.
The above construction can be adapted to the equivariant quantum cohomology.
We choose a homogeneous $R_{\mathbb{T}}$-basis $\\{\phi_{i}\\}_{i=0}^{s}$ of
$H_{{\rm CR},\mathbb{T}}^{*}(\mathfrak{X})$ such that
$\phi_{0}=\boldsymbol{1}\qquad\text{and}\qquad\\{\phi_{1},\dots,\phi_{r}\\}\subset
H^{2}_{\mathbb{T}}(\mathfrak{X})\qquad\text{with $r=\dim
H^{2}(\mathfrak{X})\leq s$}.$ (2.4)
Then the non-equivariant limits of $\phi_{1},\dots,\phi_{r}$ form a basis of
$H^{2}(\mathfrak{X})$. The basis $\\{\phi_{i}\\}_{i=0}^{s}$ defines
$R_{\mathbb{T}}$-linear co-ordinates $\\{\tau^{i}\\}_{i=0}^{s}$ on $H_{{\rm
CR},\mathbb{T}}^{*}(\mathfrak{X})$ as before. The equivariant Kähler moduli
spaces are given by replacing the ground ring $\mathbb{C}$ with
$R_{\mathbb{T}}$.
$\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}):=\operatorname{Spec}R_{\mathbb{T}}[\boldsymbol{\Lambda}_{+}]\big{[}\tau^{0},\tau^{r+1},\dots,t^{s}\big{]}.$
(2.5)
It is fibred over
$\operatorname{Spec}R_{\mathbb{T}}\cong\operatorname{Lie}\mathbb{T}$. The
group $H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}$ acts on
$\mathcal{M}_{\rm A,\mathbb{T}}(\mathfrak{X})$ through the isomorphism
$\mathcal{M}_{\rm A,\mathbb{T}}(\mathfrak{X})\cong\mathcal{M}_{\rm
A}(\mathfrak{X})\times\operatorname{Spec}R_{\mathbb{T}}$. The
$\mathbb{T}$-equivariant quantum product $\star_{\tau}$ can be viewed as a
family of product structures parameterized by the formal neighbourhood of the
origin in $\big{[}\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})/\big{(}H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}\big{)}\big{]}$.
###### Remark 2.2.
Unlike the non-equivariant case, the _equivariant_ Kähler moduli space
$\mathcal{M}_{\rm A,\mathbb{T}}(\mathfrak{X})$ is _not_ a partial
compactification of $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}$;
we do not even have a natural map $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})\to\mathcal{M}_{\rm A,\mathbb{T}}(\mathfrak{X})$.
If we regard $H^{*}_{{\rm CR},\mathbb{T}}(\mathfrak{X})$ as a locally free
coherent sheaf over $\operatorname{Spec}R_{\mathbb{T}}$ and write
$\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})=\operatorname{Spec}\big{(}\operatorname{Sym}^{\bullet}_{R_{\mathbb{T}}}\big{(}H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})^{\vee}\big{)}\big{)}$ for the total space of the
associated vector bundle (where $(-)^{\vee}$ stands for the dual as an
$R_{\mathbb{T}}$-module), then we have an open dense embedding
$\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}\to\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})$. In this paper, we take the view that the
equivariant quantum product $\star_{\tau}$ is parametrized by points in
$\mathbf{H}_{{\rm CR},\mathbb{T}}(\mathfrak{X})$ rather than by equivariant
cohomology classes. Note that equivariant cohomology classes correspond to
sections of $\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})\to\operatorname{Spec}R_{\mathbb{T}}$.
###### Remark 2.3.
The _equivariant_ Kähler moduli space $\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})$ depends on the choice of a basis
$\phi_{1},\dots,\phi_{r}$. In fact, in the equivariant case, we can replace
the basis $\\{\phi_{i}\\}_{i=0}^{s}$ with a new basis
$\\{\tilde{\phi}_{i}\\}_{i=0}^{s}$ of the form
$\tilde{\phi}_{i}=\begin{cases}\phi_{i}+c_{i}\phi_{0},&i\in\\{1,\dots,r\\},\\\
\phi_{i},&i\notin\\{1,\dots,r\\},\end{cases}$
for some $c_{i}\in H^{2}_{\mathbb{T}}({\operatorname{pt}})$ without violating
the homogeneity. Then the corresponding $0$-th co-ordinate
$\tilde{\tau}^{0}=\tau^{0}-\sum\limits_{i=1}^{r}c_{i}\tau^{i}$ does not lie in
the ring
$R_{\mathbb{T}}[\boldsymbol{\Lambda}_{+}]\big{[}\tau^{0},\tau^{r+1},\dots,\tau^{s}\big{]}$.
In other words, the construction of the equivariant Kähler moduli space
requires the choice of a splitting of the sequence $0\to
H^{2}_{\mathbb{T}}({\operatorname{pt}})\to H^{2}_{\mathbb{T}}(\mathfrak{X})\to
H^{2}(\mathfrak{X})\to 0$.
###### Remark 2.4.
In the above discussion, we considered the specialization $Q=1$ and the
equivalence class of $\tau$ in $H^{*}_{{\rm
CR}}(\mathfrak{X})/2\pi\boldsymbol{\mathrm{i}}\boldsymbol{\Lambda}^{\star}$.
This is equivalent to considering the restriction to
$\tau^{1}=\cdots=\tau^{r}=0$ and the substitution of $q^{d}$ for $Q^{d}$.
###### Remark 2.5.
Henceforth we specialize the Novikov variable $Q$ to one in the quantum
product $\star_{\tau}$, unless otherwise stated.
### 2.3 Quantum D-module
The quantum product defines a meromorphic flat connection on a vector bundle
(with fibre orbifold cohomology) over the Kähler moduli space, called the
_quantum connection_. The quantum connection, the grading and the orbifold
Poincaré pairing constitute the _quantum D-module_ of $\mathfrak{X}$.
We start by explaining the equivariant version; we get the non-equivariant
version by taking non-equivariant limit. As before, we fix a homogeneous
$R_{\mathbb{T}}$-free basis $\\{\phi_{0},\dots,\phi_{s}\\}$ of $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})$ that satisfies (2.4). We use this basis to
construct the equivariant Kähler moduli spaces $\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})$. Consider the vector bundle
$\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})\times_{\operatorname{Spec}R_{\mathbb{T}}}(\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})\times\mathbb{C}_{z})\to\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})\times\mathbb{C}_{z}$ (2.6)
of rank equal to $\dim H_{\rm CR}^{*}(\mathfrak{X})$, where
$\mathbb{C}_{z}:=\operatorname{Spec}\mathbb{C}[z]$ is the complex plane with
co-ordinate $z$ and $\mathbf{H}_{{\rm CR},\mathbb{T}}(\mathfrak{X})$ denotes a
vector bundle over $\operatorname{Spec}R_{\mathbb{T}}$ corresponding to
$H^{*}_{{\rm CR},\mathbb{T}}(\mathfrak{X})$ (see Remark 2.2). The Galois
symmetry in the previous section induces the
$(H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star})$-action on this
vector bundle defined by the map $dg(\xi)\times
g(\xi)\times\operatorname{id}_{\mathbb{C}_{z}}$. By the Galois symmetry, this
vector bundle descends to a vector bundle on the quotient stack
$\big{[}\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})/\big{(}H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}\big{)}\big{]}\times\mathbb{C}_{z}$.
The _quantum connection_ is a meromorphic flat partial connection on this
vector bundle over the formal neighbourhood of the origin in $\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})$ (times $\mathbb{C}_{z}$); it is given by
$\nabla=d+z^{-1}\sum_{i=0}^{s}(\phi_{i}\star_{\tau})d\tau^{i}.$
This connection is partial in the sense that it is defined only in the
$\tau$-direction and not in the $z$-direction or in the direction of
equivariant parameters (the first term $d$ means the relative differential
over $\operatorname{Spec}R_{\mathbb{T}}[z]$). The connection has simple poles
along $z=0$ and has logarithmic singularities along the toric boundary of
$\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}_{+}]$. Note that
$d\tau^{i}$ with $1\leq i\leq r$ defines a logarithmic $1$-form on
$\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}_{+}]$. In a more formal
language, the module
$H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]:=H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})\otimes_{R_{\mathbb{T}}}R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}_{+}]\\!]\big{[}\\!\big{[}\tau^{0},\tau^{r+1},\dots,\tau^{s}\big{]}\\!\big{]}$
(which we regard as the module of sections of the bundle (2.6) over the formal
neighbourhood of the origin in $\mathcal{M}_{\rm A,\mathbb{T}}(\mathfrak{X})$)
is equipped with $s+1$ operators
$\nabla_{\frac{\partial}{\partial\tau^{i}}}=\frac{\partial}{\partial\tau^{i}}+z^{-1}\phi_{i}\star_{\tau}$,
$i=0,1,\dots,s$:
$\nabla_{\frac{\partial}{\partial\tau^{i}}}\colon H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]\to
z^{-1}H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]$
that commute each other:
$\big{[}\nabla_{\frac{\partial}{\partial\tau^{i}}},\nabla_{\frac{\partial}{\partial\tau^{j}}}\big{]}=0$.
Let $\\{\chi_{1},\dots,\chi_{k}\\}$ denote a basis of
$H^{2}_{\mathbb{T}}({\operatorname{pt}},\mathbb{C})$ so that
$R_{\mathbb{T}}=\mathbb{C}[\chi_{1},\dots,\chi_{k}]$. For $\xi\in
H^{2}(\mathfrak{X},\mathbb{C})$, we write $\xi q\frac{\partial}{\partial q}$
for the derivation of $\mathbb{C}[\\![\boldsymbol{\Lambda}_{+}]\\!]$ given by
$\big{(}\xi q\frac{\partial}{\partial q}\big{)}q^{d}=(\xi\cdot d)q^{d}$. The
_Euler vector field_ $\mathcal{E}$ is the following derivation of
$R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]$
$\mathcal{E}=c_{1}(\mathfrak{X})q\frac{\partial}{\partial
q}+\sum_{i\in\\{0,r+1,\dots,s\\}}\left(1-\frac{\deg\phi_{i}}{2}\right)\tau^{i}\frac{\partial}{\partial\tau^{i}}+\sum_{i=1}^{k}\chi_{i}\frac{\partial}{\partial\chi_{i}}.$
(2.7)
The _grading operator_
$\operatorname{Gr}\in\operatorname{End}_{\mathbb{C}}(H_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!])$
is defined to be
$\operatorname{Gr}(f(q,\tau^{\prime},\chi,z)\phi_{i})=\left(\left(\mathcal{E}+z\frac{\partial}{\partial
z}\right)f(q,\tau^{\prime},\chi,z)\right)\phi_{i}+\frac{\deg\phi_{i}}{2}f(q,\tau^{\prime},\chi,z)\phi_{i},$
(2.8)
where $f(q,\tau^{\prime},\chi,z)\in
R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]$.
This is compatible with the quantum connection in the sense that
$\left[\nabla_{\frac{\partial}{\partial\tau^{i}}},\operatorname{Gr}\right]=\left(1-\frac{\deg\phi_{i}}{2}\right)\nabla_{\frac{\partial}{\partial\tau^{i}}}\left(=\nabla_{\big{[}\frac{\partial}{\partial\tau^{i}},\mathcal{E}\big{]}}\right).$
Let $P$ denote the pairing between the fibres of the bundle (2.6) at
$(q,\tau^{\prime},\chi,-z)$ and at $(q,\tau^{\prime},\chi,z)$ induced by the
orbifold Poincaré pairing. This gives the following
$R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]$-bilinear
pairing on the module $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]$:
$P(\alpha,\beta):=(\alpha(-z),\beta(z))\in
S_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!],$
(2.9)
where $(\cdot,\cdot)$ denotes the orbifold Poincaré pairing (2.2). The pairing
$P$ satisfies
$\displaystyle
P(f(q,\tau^{\prime},\chi,-z)\alpha,\beta)=P(\alpha,f(q,\tau^{\prime},\chi,z)\beta)=f(q,\tau^{\prime},\chi,z)P(\alpha,\beta),$
$\displaystyle P(\beta,\alpha)=P(\alpha,\beta)|_{z\to-z}$
for $f(q,\tau^{\prime},\chi,z)\in
R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]$
and the compatibility equations with $\nabla$ and $\mathcal{E}$:
$\displaystyle\frac{\partial}{\partial\tau^{i}}P(\alpha,\beta)=P\big{(}\widetilde{\nabla}_{\frac{\partial}{\partial\tau^{i}}}\alpha,\beta\big{)}+P\big{(}\alpha,\nabla_{\frac{\partial}{\partial\tau^{i}}}\beta\big{)},$
$\displaystyle\left(z\frac{\partial}{\partial
z}+\mathcal{E}\right)P(\alpha,\beta)=P(\operatorname{Gr}\alpha,\beta)+P(\alpha,\operatorname{Gr}\beta)-(\dim\mathfrak{X})P(\alpha,\beta),$
where $\widetilde{\nabla}=\nabla|_{z\to-z}$. The structures $\nabla$,
$\operatorname{Gr}$, $P$ are equivariant with respect to the Galois symmetry
of $H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}$. We call the
$\big{(}H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}\big{)}$-equivariant
quadruple
$\operatorname{QDM}_{\mathbb{T}}(\mathfrak{X}):=\left(H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!],\nabla,\operatorname{Gr},P\right)$
(2.10)
the _$\mathbb{T}$ -equivariant quantum D-module_ of $\mathfrak{X}$.
###### Remark 2.6.
The flat connection $\nabla$ defines on the space $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]$
the structure of a module over the ring of differential operators
$R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!]\left\langle
z\frac{\partial}{\partial\tau^{0}},z\frac{\partial}{\partial\tau^{1}},\dots,z\frac{\partial}{\partial\tau^{s}}\right\rangle,$
where $z\frac{\partial}{\partial\tau^{i}}$ acts by the connection
$z\nabla_{\frac{\partial}{\partial\tau^{i}}}$. This is often called a _$z$
-connection_ [94].
The non-equivariant quantum D-module is the restriction of the equivariant one
to the origin
$0\in\operatorname{Spec}R_{\mathbb{T}}=\operatorname{Lie}\mathbb{T}$. It is a
quadruple
$\operatorname{QDM}(\mathfrak{X}):=\big{(}H^{*}_{\rm
CR}(\mathfrak{X})[z][\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime}]\\!],\nabla,\operatorname{Gr},P\big{)},$
where the pairing $P$ is defined only when $\mathfrak{X}$ is proper. In the
non-equivariant case, we can define the connection in the $z$-direction by
$\nabla_{z\frac{\partial}{\partial
z}}:=\operatorname{Gr}-\nabla_{\mathcal{E}}-\frac{\dim\mathfrak{X}}{2}=z\frac{\partial}{\partial
z}-\frac{1}{z}(E\star_{\tau})+\mu$ (2.11)
and this preserves the pairing $P$. Here $\mathcal{E}$ denotes the non-
equivariant limit of (2.7) (and thus does not contain the term
$\sum\limits_{i=1}^{n}\chi_{i}\frac{\partial}{\partial\chi_{i}}$) and
$E=c_{1}(\mathfrak{X})+\sum_{i\in\\{0,r+1,\dots,s\\}}\left(1-\frac{1}{2}\deg\phi_{i}\right)\tau^{i}\phi_{i}$
is the section of $\operatorname{QDM}(\mathfrak{X})$ corresponding to
$\mathcal{E}$ and $\mu\in\operatorname{End}(H^{*}_{\rm CR}(\mathfrak{X}))$ is
the endomorphism given by
$\mu(\phi_{i})=\big{(}\frac{1}{2}\deg\phi_{i}-\frac{1}{2}\dim\mathfrak{X}\big{)}\phi_{i}$.
### 2.4 $\boldsymbol{\widehat{\Gamma}}$-integral structure
The $\widehat{\Gamma}$-integral structure [62, Section 2.4], [70, Proposition
3.1] is an integral lattice in the space of flat sections of the quantum
D-module. The integral lattice is identified with the topological $K$-group of
$\mathfrak{X}$. We review its definition only in the non-equivariant case (see
[31, Section 3] for the equivariant $\widehat{\Gamma}$-integral structure).
For simplicity, we assume that the quantum product $\star_{\tau}$ is
convergent in a neighbourhood of the large radius limit point. Then the
quantum connection is also analytic in the same neighbourhood; it has no
singularities on the intersection of the open subset $\big{[}H^{*}_{\rm
CR}(\mathfrak{X})/H^{2}(\mathfrak{X},\mathbb{Z})\big{]}$
$\subset\big{[}\mathcal{M}_{\rm
A}(\mathfrak{X})/\big{(}H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star}\big{)}\big{]}$
and the convergence domain of $\star_{\tau}$. Introduce the following
$\operatorname{End}(H^{*}_{\rm CR}(\mathfrak{X}))$-valued function:
$L(\tau,z)\phi_{i}=e^{-\sigma/z}\phi_{i}+\sum_{k=0}^{s}\sum_{\begin{subarray}{c}n\geq
0,\,d\in\boldsymbol{\Lambda}_{+}\\\
(n,d)\neq(0,0)\end{subarray}}\left\langle\phi_{k},\tau^{\prime},\dots,\tau^{\prime},\frac{e^{-\sigma/z}\phi_{i}}{-z-\psi}\right\rangle_{0,l+2,d}\frac{e^{\sigma\cdot
d}}{l!}\phi^{k},$
where we write $\tau=\sigma+\tau^{\prime}\in H^{*}_{\rm CR}(\mathfrak{X})$,
$\sigma=\sum\limits_{i=1}^{r}\tau^{i}\phi_{i}\in H^{2}(\mathfrak{X})$,
$\tau^{\prime}=\tau^{0}\phi_{0}+\sum\limits_{i=r+1}^{s}\tau^{i}\phi_{i}$ as
before, $\\{\phi^{k}\\}$ is the dual basis of $\\{\phi_{k}\\}$ with respect to
the orbifold Poincaré pairing, and $1/(-z-\psi)$ should be expanded in the
series $\sum\limits_{k=0}^{\infty}(-z)^{-k-1}\psi^{k}$. We also set
$z^{-\mu}z^{c_{1}(\mathfrak{X})}:=e^{-\mu\log z}e^{c_{1}(\mathfrak{X})\log
z}.$
Then by [62, Proposition 2.4],
$L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X})}\phi_{i}$, $i=0,\dots,s$ form a basis
of (multi-valued) $\nabla$-flat sections (which are flat also in the
$z$-direction with respect to (2.11)), i.e.,
$L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X})}$ is a fundamental solution of the
quantum connection.
We introduce the Chern character and the $\widehat{\Gamma}$-class for a smooth
DM stack $\mathfrak{X}$. Let $\pi\colon I\mathfrak{X}\to\mathfrak{X}$ denote
the natural projection. Recall the decomposition
$I\mathfrak{X}=\bigsqcup\limits_{v\in\operatorname{Box}}\mathfrak{X}_{v}$ into
twisted sectors. For an orbi-vector bundle $V$ on $\mathfrak{X}$, the
stabilizer along $\mathfrak{X}_{v}$ acts on $(\pi^{*}V)|_{\mathfrak{X}_{v}}$
and decomposes it into the sum of eigenbundles
$\pi^{*}V|_{\mathfrak{X}_{v}}=\bigoplus_{0\leq f<1}V_{v,f},$
where the stabilizer acts on $V_{v,f}$ by
$\exp(2\pi\boldsymbol{\mathrm{i}}f)$. The Chern character of $V$ is defined to
be
$\widetilde{\operatorname{ch}}(V)=\bigoplus_{v\in\operatorname{Box}}\sum_{0\leq
f<1}e^{2\pi\boldsymbol{\mathrm{i}}f}\operatorname{ch}(V_{v,f})\in
H^{*}(I\mathfrak{X}).$
Consider now the tangent bundle $V=T\mathfrak{X}$ and let $\delta_{v,f,j}$,
$j=1,\dots,\operatorname{rank}(V_{v,f})$ denote the Chern roots of
$T\mathfrak{X}_{v,f}$. The $\widehat{\Gamma}$-class of $\mathfrak{X}$ is
defined to be
$\widehat{\Gamma}_{\mathfrak{X}}=\bigoplus_{v\in\operatorname{Box}}\prod_{0\leq
f<1}\prod_{j=1}^{\operatorname{rank}(T\mathfrak{X}_{v,f})}\Gamma(1-f+\delta_{v,f,j})\in
H^{*}(I\mathfrak{X}),$
where in the right-hand side we expand the Euler $\Gamma$-function $\Gamma(z)$
in series at $z=1-f$. This is an algebraic cohomology class defined over
transcendental numbers.
###### Definition 2.7 ([62, Definition 2.9]).
Let $K(\mathfrak{X})$ denote the Grothendieck group of topological orbi-vector
bundles on $\mathfrak{X}$. For $V\in K(\mathfrak{X})$, we define a (multi-
valued) flat section $\mathfrak{s}_{V}(\tau,z)$ of the quantum D-module by
$\mathfrak{s}_{V}(\tau,z)=\frac{1}{(2\pi)^{\dim\mathfrak{X}/2}}L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X})}\big{(}\widehat{\Gamma}_{\mathfrak{X}}\cup(2\pi\boldsymbol{\mathrm{i}})^{\deg_{0}/2}\operatorname{inv}^{*}\widetilde{\operatorname{ch}}(V)\big{)},$
where $\deg_{0}$ denotes the grading operator on $H^{*}(I\mathfrak{X})$
_without age shift_ , i.e., $\deg_{0}(\alpha)=p\alpha$ for $\alpha\in
H^{p}(I\mathfrak{X})$. The map $V\mapsto\mathfrak{s}_{V}$ defines an integral
lattice in the space of flat sections, which we call the _$\widehat{\Gamma}$
-integral structure_.
Important properties of the $\widehat{\Gamma}$-integral structure are as
follows [62, Proposition 2.10]:
* •
it is monodromy-invariant around the large radius limit point: we have
$dg(\xi)^{-1}\mathfrak{s}_{V}(g(\xi)(\tau),z)=\mathfrak{s}_{V\otimes
L_{\xi}}(\tau,z),$ (2.12)
where $L_{\xi}$ is the line bundle corresponding to $\xi\in
H^{2}(\mathfrak{X},\mathbb{Z})$; therefore it defines a $\mathbb{Z}$-local
system underlying the quantum D-module;
* •
it intertwines the Euler pairing with the orbifold Poincaré pairing: if
$V_{1}$, $V_{2}$ are holomorphic orbi-vector bundles on $\mathfrak{X}$, we
have
$\chi(V_{1},V_{2})=\big{(}\mathfrak{s}_{V_{1}}\big{(}\tau,e^{-\pi\boldsymbol{\mathrm{i}}}z\big{)},\mathfrak{s}_{V_{2}}(\tau,z)\big{)},$
(2.13)
where
$\chi(V_{1},V_{2})=\sum\limits_{i=0}^{\dim\mathfrak{X}}(-1)^{i}\dim\operatorname{Ext}^{i}(V_{1},V_{2})$.
When $V_{1}$, $V_{2}$ are $C^{\infty}$ orbi-vector bundles, we can define
$\chi(V_{1},V_{2})$ as the index of a Dirac operator on $V_{1}^{\vee}\otimes
V_{2}\otimes\Omega^{0,\bullet}_{\mathfrak{X}}$ and this formula holds under
mild assumptions, see [62, Remark 2.8]. Note that the right-hand side does not
depend on $(\tau,z)$ since $\mathfrak{s}_{V_{1}}$, $\mathfrak{s}_{V_{2}}$ are
flat sections.
###### Remark 2.8.
The fundamental solution $L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X})}$ is multi-
valued as a function of $(\tau,z)\in\big{[}H^{*}_{\rm
CR}(\mathfrak{X})/H^{2}(\mathfrak{X};\mathbb{Z})\big{]}\times\mathbb{C}^{\times}$,
but it has a standard determination when $\tau$ is the image of a _real_ class
in $H^{*}_{\rm CR}(\mathfrak{X};\mathbb{R})=H^{*}(I\mathfrak{X};\mathbb{R})$
sufficiently close to the large radius limit point and $z$ is _positive real_.
We will sometimes use such a point as a base point.
## 3 Global Landau–Ginzburg mirrors of toric DM stacks
In this section, we construct a global Landau–Ginzburg model (LG model) which
is simultaneously mirror to several smooth toric DM stacks. For background
materials on toric (Deligne–Mumford) stacks, we refer the reader to [14, 34,
42, 66, 67, 106].
### 3.1 Toric data
Throughout the paper, we fix the data $(\mathbf{N},\Pi)$, where
* •
$\mathbf{N}$ is a finitely generated abelian group of rank $n$ (possibly
having torsion) and
* •
$\Pi$ is a full-dimensional, convex, rational polyhedral cone in
$\mathbf{N}_{\mathbb{R}}:=\mathbf{N}\otimes\mathbb{R}$.
We do not require that $\Pi$ is strictly convex; $\Pi$ will be the support of
the fan of a smooth toric DM stack. To construct a mirror family of LG models,
we choose a finite subset $S\subset\mathbf{N}$ such that
* •
$S$ generates the cone $\Pi$ over $\mathbb{R}_{\geq 0}$, i.e.,
$\Pi=\sum\limits_{b\in S}\mathbb{R}_{\geq 0}b$.
The set $S$ specifies the set of monomials appearing in the LG model. We make
the following technical assumption to ensure that the base of the mirror
family has no generic stabilizers, that is, generic LG models have no
automorphisms of diagonal symmetry.
###### Assumption 3.1.
$S$ generates $\mathbf{N}$ as an abelian group, i.e.,
$\mathbf{N}=\mathbb{Z}S$.
This is not an essential restriction. In fact, if $S$ does not satisfy this
assumption, we can first construct the mirror family by taking a bigger set
$S^{\prime}\supset S$ satisfying the assumption, and then restrict the family
to the subspace of the base corresponding to $S$ (then, the subspace has
generic stabilizers).
###### Notation 3.2.
We write $\mathbf{N}_{\rm tor}$ for the torsion part of $\mathbf{N}$ and write
$\overline{\mathbf{N}}=\mathbf{N}/\mathbf{N}_{\rm tor}$ for the torsion-free
quotient. For $v\in\mathbf{N}$, we write $\overline{v}$ for the image of $v$
in $\overline{\mathbf{N}}$. The subscripts $\mathbb{Q}$, $\mathbb{R}$, etc.
means the tensor product with $\mathbb{Q}$, $\mathbb{R}$ over $\mathbb{Z}$,
e.g., $\mathbf{N}_{\mathbb{R}}=\mathbf{N}\otimes_{\mathbb{Z}}\mathbb{R}$. For
subsets $A\subset\mathbf{N}$ and $B\subset\mathbf{N}_{\mathbb{R}}$, we write
$A\cap B:=\\{a\in A\colon\overline{a}\in B\\}$.
###### Definition 3.3.
A _stacky fan adapted to_ $S$ is a triple
$\mathbf{\Sigma}=(\mathbf{N},\Sigma,R)$ such that
* (i)
$\Sigma$ is a rational simplicial fan defined on the vector space
$\mathbf{N}_{\mathbb{R}}$;
* (ii)
the support $|\Sigma|=\bigcup\limits_{\sigma\in\Sigma}\sigma$ of the fan
$\Sigma$ equals $\Pi=\sum\limits_{b\in S}\mathbb{R}_{\geq 0}\overline{b}$;
* (iii)
there exists a strictly convex piecewise linear function
$\eta\colon\Pi\to\mathbb{R}$ which is linear on each cone of $\Sigma$;
* (iv)
$R\subset S$ is a subset such that the map $R\ni b\mapsto\mathbb{R}_{\geq
0}\overline{b}$ gives a bijection between $R$ and the set $\Sigma(1)$ of one-
dimensional cones of $\Sigma$.
The data $(\mathbf{N},\Sigma,R)$ gives a _stacky fan_ in the sense of Borisov,
Chen and Smith [14]. We write $\mathfrak{X}_{\mathbf{\Sigma}}$ for the smooth
toric DM stack (toric stack for short) defined by $\mathbf{\Sigma}$. We also
set $R(\mathbf{\Sigma}):=R$ (“rays”) and $G(\mathbf{\Sigma}):=S\setminus R$
(“ghost rays”). We denote by $\operatorname{\mathfrak{Fan}}(S)$ the set of
stacky fans adapted to $S$.
###### Remark 3.4.
The above conditions (ii), (iii) imply that the corresponding toric DM stack
$\mathfrak{X}_{\mathbf{\Sigma}}$ is _semiprojective_ [34, Section 7.2], that
is, the coarse moduli space $X_{\Sigma}$ of $\mathfrak{X}_{\mathbf{\Sigma}}$
is projective over the affine variety
$\operatorname{Spec}H^{0}(X_{\Sigma},\mathcal{O})$ and has a torus fixed
point. Conversely, any semiprojective toric DM stack arises from some toric
data $(\mathbf{N},\Pi,S,\Sigma,R)$ in this section.
#### 3.1.1 Toric DM stacks
Let $\mathbf{\Sigma}=(\mathbf{N},\Sigma,R)\in\operatorname{\mathfrak{Fan}}(S)$
be a stacky fan adapted to $S$. When we start from the stacky fan
$\mathbf{\Sigma}$, the set $G(\mathbf{\Sigma})=S\setminus R$ can be viewed as
the data of an _extended stacky fan_ in the sense of Jiang [68]. The extended
stacky fan is given by the pair $(\mathbf{\Sigma},G(\mathbf{\Sigma}))$ of the
stacky fan $\mathbf{\Sigma}$ and the finite subset
$G(\mathbf{\Sigma})\subset\mathbf{N}\cap|\Sigma|$. We recall a definition of
the smooth toric DM stack $\mathfrak{X}_{\mathbf{\Sigma}}$ [14, 68] in terms
of the extended stacky fan. The stacky fan $\mathbf{\Sigma}$ defines the _fan
sequence_
$\begin{CD}0@>{}>{}>\mathbb{L}^{\mathbf{\Sigma}}@>{}>{}>\mathbb{Z}^{R(\mathbf{\Sigma})}@>{\beta(\mathbf{\Sigma})}>{}>\mathbf{N},\end{CD}$
(3.1)
where
$\beta(\mathbf{\Sigma})\colon\mathbb{Z}^{R(\mathbf{\Sigma})}\to\mathbf{N}$
sends the basis $e_{b}\in\mathbb{Z}^{R(\mathbf{\Sigma})}$ corresponding to
$b\in R(\mathbf{\Sigma})$ to $b\in\mathbf{N}$ and
$\mathbb{L}^{\mathbf{\Sigma}}:=\operatorname{Ker}(\beta(\mathbf{\Sigma}))$.
The dual sequence
$\begin{CD}0@>{}>{}>\mathbf{M}@>{}>{}>\big{(}\mathbb{Z}^{R(\mathbf{\Sigma})}\big{)}^{\star}@>{}>{}>\big{(}\mathbb{L}^{\mathbf{\Sigma}}\big{)}^{\vee}\end{CD}$
(3.2)
is called the _divisor sequence_ , where
$\big{(}\mathbb{L}^{\mathbf{\Sigma}}\big{)}^{\vee}:=H^{1}(\operatorname{Cone}(\beta(\mathbf{\Sigma}))^{\star})$
is the Gale dual of $\beta(\mathbf{\Sigma})$ (see [14]). The _extended fan
sequence_ is the sequence
$\begin{CD}0@>{}>{}>\mathbb{L}@>{}>{}>\mathbb{Z}^{S}@>{\beta}>{}>\mathbf{N}@>{}>{}>0,\end{CD}$
(3.3)
where the map $\beta\colon\mathbb{Z}^{S}\to\mathbf{N}$ sends the basis
$e_{b}\in\mathbb{Z}^{S}$ corresponding to $b\in S$ to $b\in\mathbf{N}$ and
$\mathbb{L}:=\operatorname{Ker}(\beta)$. Note that $\beta$ is surjective by
Assumption 3.1. The dual sequence
$\begin{CD}0@>{}>{}>\mathbf{M}@>{}>{}>\big{(}\mathbb{Z}^{S}\big{)}^{\star}@>{D}>{}>\mathbb{L}^{\star}\end{CD}$
(3.4)
is called the _extended divisor sequence_ , where
$\mathbf{M}:=\operatorname{Hom}(\mathbf{N},\mathbb{Z})$ and
$D\colon\big{(}\mathbb{Z}^{S}\big{)}^{\star}\to\mathbb{L}^{\star}$ is dual to
$\mathbb{L}\to\mathbb{Z}^{S}$ and
$\operatorname{Cok}(D)\cong\operatorname{Ext}^{1}(\mathbf{N},\mathbb{Z})$. The
torus $\mathbb{L}_{\mathbb{C}^{\times}}:=\mathbb{L}\otimes\mathbb{C}^{\times}$
acts on $\mathbb{C}^{S}$ via the natural map
$\mathbb{L}_{\mathbb{C}^{\times}}\to(\mathbb{C}^{\times})^{S}$ induced by
$\mathbb{L}\to\mathbb{Z}^{S}$. The toric stack
$\mathfrak{X}_{\mathbf{\Sigma}}$ is defined as a GIT quotient of
$\mathbb{C}^{S}$ by the $\mathbb{L}_{\mathbb{C}^{\times}}$-action. Set
$\mathscr{S}_{\mathbf{\Sigma}}:=\\{I\subset R(\mathbf{\Sigma})\colon\text{the
cone spanned by $I$ belongs to $\Sigma$}\\}$
and define the open subset $U_{\mathbf{\Sigma}}\subset\mathbb{C}^{S}$ as
$U_{\mathbf{\Sigma}}=\mathbb{C}^{S}\setminus\bigcup_{I\subset
S,I\notin\mathscr{S}_{\mathbf{\Sigma}}}\mathbb{C}^{S\setminus I},$
where we regard $\mathbb{C}^{I}$ with $I\subset S$ as a co-ordinate subspace
of $\mathbb{C}^{S}$ (we set $\mathbb{C}^{\varnothing}=\\{0\\}$). Since every
element of $\mathscr{S}_{\mathbf{\Sigma}}$ is contained in
$R(\mathbf{\Sigma})$, we may also write
$U_{\mathbf{\Sigma}}=\left(\mathbb{C}^{R(\mathbf{\Sigma})}\setminus\bigcup_{I\subset
R(\mathbf{\Sigma}),I\notin\mathscr{S}_{\mathbf{\Sigma}}}\mathbb{C}^{R(\mathbf{\Sigma})\setminus
I}\right)\times(\mathbb{C}^{\times})^{G(\mathbf{\Sigma})}.$
We define
$\mathfrak{X}_{\mathbf{\Sigma}}:=[U_{\mathbf{\Sigma}}/\mathbb{L}_{\mathbb{C}^{\times}}].$
Since $\mathbb{L}_{\mathbb{C}^{\times}}$ acts on $U_{\mathbf{\Sigma}}$ with at
most finite stabilizers, $\mathfrak{X}_{\mathbf{\Sigma}}$ is a smooth DM
stack. The toric stack $\mathfrak{X}_{\mathbf{\Sigma}}$ depends only on
$\mathbf{\Sigma}=(\mathbf{N},\Sigma,R)$ and does not depend on the choice of
the extension $G(\mathbf{\Sigma})=S\setminus R$ (see [68]). The coarse moduli
space $X_{\Sigma}$ of $\mathfrak{X}_{\mathbf{\Sigma}}$ is the toric variety
associated with the fan $\Sigma$. The $(\mathbb{C}^{\times})^{S}$-action on
$U_{\mathbf{\Sigma}}$ induces the $\mathbb{T}$-action on
$\mathfrak{X}_{\mathbf{\Sigma}}$, where $\mathbb{T}$ is the torus
$\mathbb{T}:=(\mathbb{C}^{\times})^{S}/\operatorname{Im}\big{(}\mathbb{L}_{\mathbb{C}^{\times}}\to(\mathbb{C}^{\times})^{S}\big{)}\cong\mathbf{N}\otimes\mathbb{C}^{\times}.$
#### 3.1.2 Picard group and second (co)homology
A character
$\xi\in\operatorname{Hom}(\mathbb{L}_{\mathbb{C}^{\times}},\mathbb{C}^{\times})=\mathbb{L}^{\star}$
of $\mathbb{L}_{\mathbb{C}^{\times}}$ defines a line bundle
$L_{\xi}=[(U_{\mathbf{\Sigma}}\times\mathbb{C})/\mathbb{L}_{\mathbb{C}^{\times}}]$
over $\mathfrak{X}_{\mathbf{\Sigma}}$, where
$\mathbb{L}_{\mathbb{C}^{\times}}$ acts on the second factor $\mathbb{C}$ by
the character $\xi$. We denote by $D_{b}:=D(e_{b}^{\star})$ the image of the
standard basis $e_{b}^{\star}\in\big{(}\mathbb{Z}^{S}\big{)}^{\star}$ under
$D$. We can see that $D_{b}$ with $b\in G(\mathbf{\Sigma})$ yields the trivial
line bundle on $\mathfrak{X}_{\mathbf{\Sigma}}$, and the correspondence
$\xi\mapsto L_{\xi}$ gives the identification
$\mathbb{L}^{\star}\Big{/}\sum_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}D_{b}\cong\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}}).$
(3.5)
This group is isomorphic to the Gale dual
$\big{(}\mathbb{L}^{\mathbf{\Sigma}}\big{)}^{\vee}$ of
$\beta(\mathbf{\Sigma})$ appearing in (3.2). The torsion free quotient of
$\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})$ can be identified with
the ordinary dual $\big{(}\mathbb{L}^{\mathbf{\Sigma}}\big{)}^{\star}$.
Moreover we have the identifications
$\displaystyle
H^{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Q})\cong\big{(}\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{Q}}\big{)}^{\star},$
$\displaystyle
H^{2}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Q})\cong\big{(}\mathbb{Q}^{R(\mathbf{\Sigma})}\big{)}^{\star},$
$\displaystyle
H^{2}_{\mathbb{T}}({\operatorname{pt}},\mathbb{Q})\cong\mathbf{M}_{\mathbb{Q}},$
(3.6)
so that the divisor sequence (3.2) over $\mathbb{Q}$ is identified with
$\begin{CD}0@>{}>{}>H^{2}_{\mathbb{T}}({\operatorname{pt}},\mathbb{Q})@>{}>{}>H^{2}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Q})@>{}>{}>H^{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Q})@>{}>{}>0.\end{CD}$
We write $\overline{D}_{b}$ for the image of $D_{b}\in\mathbb{L}^{\star}$ in
$\big{(}\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{Q}}\big{)}^{\star}\cong
H^{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Q})$. This is the class of a
toric divisor. We also write
$R_{\mathbb{T}}:=H^{*}_{\mathbb{T}}({\operatorname{pt}},\mathbb{C})\cong\operatorname{Sym}(\mathbf{M}_{\mathbb{C}})$
for the $\mathbb{T}$-equivariant cohomology of a point.
#### 3.1.3 Orbifold cohomology
For a cone $\sigma$ of $\Sigma$, we introduce
$\operatorname{Box}(\sigma)\subset\mathbf{N}$ as
$\operatorname{Box}(\sigma)=\bigg{\\{}v\in\mathbf{N}\colon\text{$\overline{v}$
is of the form $\sum\limits_{b\in\sigma\cap
R(\mathbf{\Sigma})}c_{b}\overline{b}$ for some $c_{b}\in[0,1)$}\bigg{\\}}$
and set
$\operatorname{Box}(\mathbf{\Sigma})=\bigcup\limits_{\sigma\in\Sigma}\operatorname{Box}(\sigma)$.
The set $\operatorname{Box}(\mathbf{\Sigma})$ parametrizes connected
components of the inertia stack $I\mathfrak{X}_{\mathbf{\Sigma}}$ [14]. We
write $\mathfrak{X}_{\mathbf{\Sigma},v}$ for the component of
$I\mathfrak{X}_{\mathbf{\Sigma}}$ corresponding to
$v\in\operatorname{Box}(\mathbf{\Sigma})$. The _age_ of a box element
$v\in\operatorname{Box}(\sigma)$ is given by
$\operatorname{age}(v):=\sum\limits_{b\in R(\mathbf{\Sigma})\cap\sigma}c_{b}$
when we write $\overline{v}=\sum\limits_{b\in
R(\mathbf{\Sigma})\cap\sigma}c_{b}\overline{b}$ with $c_{b}\geq 0$. The
_orbifold cohomology_ $H_{{\rm CR}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$ of
Chen and Ruan [24] is given by (as a graded vector space):
$H_{{\rm
CR}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})=\bigoplus_{v\in\operatorname{Box}(\mathbf{\Sigma})}H^{*-2\operatorname{age}(v)}(\mathfrak{X}_{\mathbf{\Sigma},v},\mathbb{C}).$
(3.7)
As a ring, it is generated by the fundamental classes $\boldsymbol{1}_{v}$ on
$I\mathfrak{X}_{\mathbf{\Sigma},v}$ with
$v\in\operatorname{Box}(\mathbf{\Sigma})$ and the toric divisor classes
$\overline{D}_{b}\in H^{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Q})$ with
$b\in R(\mathbf{\Sigma})$. Here we regard $\overline{D}_{b}$ as a class
supported on the untwisted sector
$\mathfrak{X}_{\mathbf{\Sigma},0}=\mathfrak{X}_{\mathbf{\Sigma}}$. The
$\mathbb{T}$-equivariant orbifold cohomology $H_{{\rm
CR},\mathbb{T}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$ is defined by replacing
each factor in the right-hand side of (3.7) with the $\mathbb{T}$-equivariant
cohomology
$H_{\mathbb{T}}^{*-2\operatorname{age}(v)}(\mathfrak{X}_{\mathbf{\Sigma},v})$.
### 3.2 Landau–Ginzburg model
We construct a global family of mirror LG models which are simultaneously
mirror to all the toric stacks $\mathfrak{X}_{\mathbf{\Sigma}}$ with
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$.
The _uncompactified LG model_ [47, 58, 62] is the family of tori
$\begin{CD}\operatorname{Hom}(\mathbf{N},\mathbb{C}^{\times})@>{}>{}>(\mathbb{C}^{\times})^{S}\\\
@V{}V{\operatorname{pr}}V\\\
\mathbb{L}^{\star}\otimes\mathbb{C}^{\times}\end{CD}$
obtained from the extended fan sequence (3.3) by applying
$\operatorname{Hom}(-,\mathbb{C}^{\times})$, together with the function
$F\colon(\mathbb{C}^{\times})^{S}\to\mathbb{C}$
$F=\sum_{b\in S}u_{b},$
where $u_{b}$ denotes the $\mathbb{C}^{\times}$-valued co-ordinate on
$(\mathbb{C}^{\times})^{S}$ given by the projection to the $b$th factor.
We shall partially compactify this family to include all the large radius
limit points of $\mathfrak{X}_{\mathbf{\Sigma}}$ with
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$. We construct partial
compactifications of $(\mathbb{C}^{\times})^{S}$ and
$\mathbb{L}^{\star}\otimes\mathbb{C}^{\times}$ as possibly _singular_ toric DM
stacks in the sense of Tyomkin [106]. According to Tyomkin [106, Section 4.1],
a singular toric DM stack can be described by _toric stacky data_
$(L,\Xi,\daleth)$ such that:
* •
$L$ is a finitely generated free abelian group;
* •
$\Xi$ is a (not necessarily simplicial) rational fan on
$L_{\mathbb{R}}=L\otimes\mathbb{R}$;
* •
$\daleth\subset|\Xi|$ is a subset in the support $|\Xi|$ of $\Xi$ such that
for each cone $\sigma\in\Xi$, there exists a finite index sublattice
$L(\sigma)\subset L$ such that $\daleth\cap\sigma=L(\sigma)\cap\sigma$. We
call $\daleth$ the _integral structure_ of the toric stacky data.
Note that this is a generalization of a stacky fan $(\mathbf{N},\Sigma,R)$ of
Borisov, Chen and Smith [14] when the group $\mathbf{N}$ has no torsion. For a
given stacky fan $(\mathbf{N},\Sigma,R)$ with free $\mathbf{N}$, we can assign
a toric stacky data $(\mathbf{N},\Sigma,\daleth)$ by taking $\daleth$ to be
the union of the monoids $\sigma_{\mathbb{Z}}=\mathbb{Z}_{\geq
0}(R\cap\sigma)$ for all $\sigma\in\Sigma$. Tyomkin constructed a singular
toric DM stack from $(L,\Xi,\daleth)$ by gluing affine charts; its coarse
moduli space is the toric variety $X_{\Xi}$ associated with the fan $\Xi$. We
refer the reader to [106, Section 4.1] for the details (the construction of
the affine charts in our case will be reviewed in Section 3.4).
###### Notation 3.5.
For $c=(c_{b})_{b\in S}\in\big{(}\mathbb{R}^{S}\big{)}^{\star}$, we define a
convex piecewise linear function $\eta_{c}\colon\Pi\to\mathbb{R}$ by
$\eta_{c}(v):=\max\left\\{\varphi(v)\colon\varphi\in\mathbf{M}_{\mathbb{R}}=\operatorname{Hom}(\mathbf{N}_{\mathbb{R}},\mathbb{R}),\,\varphi(\overline{b})\leq
c_{b}\,(\forall\,b\in S)\right\\}.$
This is well-defined when there exists $\varphi\in\mathbf{M}_{\mathbb{R}}$
such that $\varphi(\overline{b})\leq c_{b}$ for all $b\in S$; in particular if
$c_{b}\geq 0$ for all $b\in S$. The graph of $\eta_{c}$ is the union of “lower
faces” of the convex cone in $\mathbf{N}_{\mathbb{R}}\oplus\mathbb{R}$
generated by $(\overline{b},c_{b})$, $b\in S$ and $(0,1)$.
For a stacky fan $\mathbf{\Sigma}=(\mathbf{N},\Sigma,R)$ adapted to $S$, we
define a full-dimensional strictly-convex cone
$\operatorname{CPL}_{+}(\mathbf{\Sigma})\subset\big{(}\mathbb{R}^{S}\big{)}^{\star}$
by
$\operatorname{CPL}_{+}(\mathbf{\Sigma}):=\left\\{c\in\big{(}\mathbb{R}^{S}\big{)}^{\star}\colon\begin{matrix}\text{$c_{b}\geq
0$ $(\forall\,b\in S)$, $\eta_{c}$ is linear on each cone of $\Sigma$},\\\
\text{$\eta_{c}(\overline{b})=c_{b}$ for $b\in
R(\mathbf{\Sigma})$}\end{matrix}\right\\},$ (3.8)
where $\operatorname{CPL}$ stands for “convex piecewise linear” (notation
borrowed from [86]) and the subscript $+$ means non-negative. Note that
$\eta_{c}$ in the definition is determined only by $\\{c_{b}\colon b\in
R(\mathbf{\Sigma})\\}$. Note also that $c_{b}\geq\eta_{c}(\overline{b})$ for
$b\in G(\mathbf{\Sigma})$. We define the integral structure
$\widetilde{\daleth}\subset\big{(}\mathbb{R}^{S}\big{)}^{\star}$ as
$\widetilde{\daleth}:=\left\\{c\in\big{(}\mathbb{Z}^{S}\big{)}^{\star}\colon\text{$c_{b}\geq
0$ $(\forall\,b\in S)$, and $\eta_{c}(\overline{b})\in\mathbb{Z}$
$(\forall\,b\in\mathbf{N}\cap\Pi)$}\right\\}.$
Note that $\widetilde{\daleth}\cap\operatorname{CPL}_{+}(\mathbf{\Sigma})$
equals the intersection of the following sublattice of
$\big{(}\mathbb{Z}^{S}\big{)}^{\star}$
$\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma}):=\left\\{c\in\big{(}\mathbb{Z}^{S}\big{)}^{\star}\colon\text{$\forall\,\sigma\in\Sigma$,
$\exists\,m_{\sigma}\in\mathbf{M}$ s.t.~{}$m_{\sigma}(b)=c_{b}$
($\forall\,b\in R(\mathbf{\Sigma})\cap\sigma$)}\right\\}$ (3.9)
with the cone $\operatorname{CPL}_{+}(\mathbf{\Sigma})$. We also define
$\operatorname{cpl}(\mathbf{\Sigma}):=D(\operatorname{CPL}_{+}(\mathbf{\Sigma})),\qquad\daleth:=D\big{(}\widetilde{\daleth}\big{)},$
(3.10)
where
$D\colon\big{(}\mathbb{R}^{S}\big{)}^{\star}\to\mathbb{L}^{\star}_{\mathbb{R}}$
is the map appearing in the extended divisor sequence (3.4). The cone
$\operatorname{cpl}(\mathbf{\Sigma})$ consists of convex piecewise linear
functions (with respect to $\mathbf{\Sigma}$) modulo linear functions. It is
easy to check that
$\operatorname{CPL}_{+}(\mathbf{\Sigma})=D^{-1}(\operatorname{cpl}(\mathbf{\Sigma}))\cap(\mathbb{R}_{\geq
0})^{S}$ and that $\daleth\cap\operatorname{cpl}(\mathbf{\Sigma})$ is the
intersection of the finite index sublattice
$\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma}):=\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})/\mathbf{M}$
of $\mathbb{L}^{\star}$ with the cone $\operatorname{cpl}(\mathbf{\Sigma})$.
###### Definition 3.6 (partially compactified LG model).
Let $\widetilde{\Xi}$ be the fan in $\big{(}\mathbb{R}^{S}\big{)}^{\star}$
consisting of the maximal cones $\operatorname{CPL}_{+}(\mathbf{\Sigma})$ with
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ and their faces. Let
$\Xi$ be the fan in $\mathbb{L}^{\star}_{\mathbb{R}}$ consisting of the
maximal cones $\operatorname{cpl}(\mathbf{\Sigma})$ with
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ and their faces.
1. 1.
Define $\mathcal{Y}$ to be the singular toric DM stack corresponding to the
toric stacky data
$\big{(}\big{(}\mathbb{Z}^{S}\big{)}^{\star},\widetilde{\Xi},\widetilde{\daleth}\big{)}$.
We call $\mathcal{Y}$ the _total space_ of the LG model.
2. 2.
Define $\mathcal{M}$ to be the singular toric DM stack corresponding to the
toric stacky data $(\mathbb{L}^{\star},\Xi,\daleth)$. We call $\mathcal{M}$
the _secondary toric stack_.
3. 3.
The map $D\colon\big{(}\mathbb{Z}^{S}\big{)}^{\star}\to\mathbb{L}^{\star}$
defines a map between these toric stacky data, and thus induces a toric
morphism $\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$. Let
$u_{b}\colon\mathcal{Y}\to\mathbb{C}$ with $b\in S$ denote the regular
function defined by $e_{b}\in\mathbb{Z}^{S}$, and define the LG potential to
be $F=\sum\limits_{b\in S}u_{b}$. We call the pair
$(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$ the (partially
compactified) _LG model_ associated to $S$.
###### Definition 3.7.
Each stacky fan $\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ gives
rise to a torus-fixed point $0_{\mathbf{\Sigma}}$ of the secondary toric stack
$\mathcal{M}$. We call $0_{\mathbf{\Sigma}}$ the _large radius limit point_ of
$\mathfrak{X}_{\mathbf{\Sigma}}$.
###### Remark 3.8.
1. (1)
The fan $\Xi$ on $\mathbb{L}^{\star}_{\mathbb{R}}$ defined by the cones
$\operatorname{cpl}(\mathbf{\Sigma})$ is called the _secondary fan_ or the
_GKZ fan_ after the work of Gelfand, Kapranov and Zelevinsky [45] (see also
Oda–Park [86]). The fan $\widetilde{\Xi}$ gives a lift of the secondary fan
$\Xi$ to $\big{(}\mathbb{R}^{S}\big{)}^{\star}$. The support of
$\widetilde{\Xi}$ is the positive orthant $(\mathbb{R}_{\geq 0})^{S}$, and
therefore $\mathcal{Y}$ can be viewed as an iterated weighted blowup of
$\mathbb{C}^{S}$. The fibre of the map
$D\colon|\widetilde{\Xi}|=(\mathbb{R}_{\geq
0})^{S}\to\mathbb{L}_{\mathbb{R}}^{\star}$ at an interior point $\omega$ of
$\operatorname{cpl}(\mathbf{\Sigma})\subset\mathbb{L}^{\star}_{\mathbb{R}}$
can be identified with the image of the moment map $\mu\colon
X_{\Sigma}\to\mathbf{M}_{\mathbb{R}}$ of the $\mathbb{T}$-action on
$X_{\Sigma}$ with respect to the reduced symplectic form associated with
$\omega$. Therefore the fan $\widetilde{\Xi}$ can be viewed as the total space
of the moment polytope fibration over the secondary fan $\Xi$.
2. (2)
Diemer, Katzarkov and Kerr [36] introduced a closely related (but slightly
different) compactification of the LG model in the case where $S$ lies in a
hyperplane of integral distance one from the origin. In this case (i.e., when
$S$ lies in a hyperplane of height one), our space $\mathcal{Y}$ can be
obtained from their _total Lafforgue stack_ [36] by contracting a divisor (the
zero-section), at least on the level of coarse moduli spaces. Their _secondary
stack_ [36] and our secondary toric stack are the same on the level of coarse
moduli spaces (the coarse moduli spaces are the toric variety defined by the
fan $\Xi$), however it is not clear to the author if the stack structures are
the same.
###### Remark 3.9.
Cones of $\widetilde{\Xi}$, $\Xi$ can be described more explicitly as follows.
A _possibly degenerate fan_ [86] on $\mathbf{N}_{\mathbb{R}}$ is a finite
collection $\Sigma$ of convex (but not necessarily strictly convex) rational
polyhedral cones in $\mathbf{N}_{\mathbb{R}}$ such that (1) if
$\sigma\in\Sigma$ and $\tau$ is a face of $\sigma$, then $\tau\in\Sigma$; and
(2) if $\sigma,\tau\in\Sigma$ then the intersection $\sigma\cap\tau$ is a
common face of $\sigma$ and $\tau$. Let $\Sigma$ be a possibly degenerate fan
on $\mathbf{N}_{\mathbb{R}}$. Each cone $\sigma\in\Sigma$ contains the linear
subspace $V=\sigma\cap(-\sigma)$ as a face, and the linear subspace $V$ does
not depend on $\sigma$. When $V=0$, $\Sigma$ is a fan in the usual sense. A
_spanning set_ [86] of $\Sigma$ is a finite subset
$R^{\prime}\subset\mathbf{N}$ such that each cone $\sigma\in\Sigma$ is
generated by a subset of $R^{\prime}$ over $\mathbb{R}_{\geq 0}$. Let
$(\Sigma,R^{\prime},\sigma)$ be a triple such that $\Sigma$ is a possibly
degenerate fan on $\mathbf{N}_{\mathbb{R}}$ with support $|\Sigma|=\Pi$ which
admits a strictly convex piecewise linear function
$\eta\colon\Pi\to\mathbb{R}$ linear on each cone of $\Sigma$,
$R^{\prime}\subset S$ is a spanning set of $\Sigma$, and $\sigma\in\Sigma$ is
a cone. For such a triple, we define the cone
$\operatorname{CPL}_{+}(\Sigma,R^{\prime},\sigma)\subset\big{(}\mathbb{R}^{S}\big{)}^{\star}$
as
$\operatorname{CPL}_{+}(\Sigma,R^{\prime},\sigma)=\left\\{c\in\big{(}\mathbb{R}^{S}\big{)}^{\star}\colon\begin{matrix}c_{b}\geq
0\,(\forall\,b\in S),\ \text{$\eta_{c}$ is linear on each cone of
$\Sigma$,}\\\ \eta_{c}(\overline{b})=c_{b}\,(\forall\,b\in R^{\prime}),\
\eta_{c}|_{\sigma}=0\end{matrix}\right\\}.$
When $\mathbf{\Sigma}=(\mathbf{N},\Sigma,R)$ is a stacky fan adapted to $S$,
$R$ is a spanning set for $\Sigma$ and we have
$\operatorname{CPL}_{+}(\mathbf{\Sigma})=\operatorname{CPL}_{+}(\Sigma,R,\\{0\\})$.
Then the fan $\widetilde{\Xi}$ consists of the cones
$\operatorname{CPL}_{+}(\Sigma,R^{\prime},\sigma)$ and the fan $\Xi$ consists
of the cones
$\operatorname{cpl}(\Sigma,R^{\prime})=D(\operatorname{CPL}_{+}(\Sigma,R^{\prime},\sigma))$
(which are independent of $\sigma$).
### 3.3 Extended refined fan sequence and extended Mori cone
The _refined fan sequence_ [27] is an extension of the fan sequence (3.1) by a
finite group. In this section we describe an extended version of the refined
fan sequence for $\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$
(extended by ghost vectors $G(\mathbf{\Sigma})=S\setminus
R(\mathbf{\Sigma})$). This will be used to describe a local chart of the
global LG model $(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$.
###### Notation 3.10.
Define a function $\Psi^{\mathbf{\Sigma}}\colon\Pi\to(\mathbb{R}_{\geq
0})^{S}$ as follows. For $v\in\Pi$, we take a cone $\sigma\in\Sigma$
containing $v$, and write $v=\sum\limits_{b\in
R(\mathbf{\Sigma})\cap\sigma}c_{b}\overline{b}$. Then
$\Psi^{\mathbf{\Sigma}}(v)=\big{(}\Psi^{\mathbf{\Sigma}}_{b}(v)\big{)}_{b\in
S}$ is given by
$\Psi^{\mathbf{\Sigma}}_{b}(v)=\begin{cases}c_{b},&\text{if $b\in
R(\mathbf{\Sigma})\cap\sigma$},\\\ 0,&\text{otherwise}.\end{cases}$
The map $\Psi^{\mathbf{\Sigma}}$ gives a section of the map
$\beta\colon(\mathbb{R}_{\geq 0})^{S}\to\Pi$, i.e.,
$\beta\circ\Psi^{\mathbf{\Sigma}}=\operatorname{id}_{\Pi}$.
We define $\mathbb{O}(\mathbf{\Sigma})\subset\mathbb{Q}^{S}\oplus\mathbf{N}$
to be the subgroup:
$\mathbb{O}(\mathbf{\Sigma}):=\sum_{v\in\mathbf{N}\cap\Pi}\mathbb{Z}\big{(}\Psi^{\mathbf{\Sigma}}(v),v\big{)}+\sum_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}(e_{b},b)$
and define
$\boldsymbol{\Lambda}(\mathbf{\Sigma})\subset\mathbb{L}_{\mathbb{Q}}$ to be
$\boldsymbol{\Lambda}(\mathbf{\Sigma}):=\big{\\{}\lambda\in\mathbb{Q}^{S}\colon(\lambda,0)\in\mathbb{O}(\mathbf{\Sigma})\big{\\}}.$
Note that $\mathbb{O}(\mathbf{\Sigma})$ is contained in
$\big{\\{}(\lambda,v)\in\mathbb{Q}^{S}\oplus\mathbf{N}\colon\beta(\lambda)=\overline{v}\big{\\}}$.
These groups define the _extended refined fan sequence_ :
$\begin{CD}0@>{}>{}>\boldsymbol{\Lambda}(\mathbf{\Sigma})@>{}>{}>\mathbb{O}(\mathbf{\Sigma})@>{}>{}>\mathbf{N}@>{}>{}>0,\end{CD}$
(3.11)
where the map $\mathbb{O}(\mathbf{\Sigma})\to\mathbf{N}$ is given by the
second projection. This is compatible with the extended fan sequence (3.3)
under the inclusions $\mathbb{L}\subset\boldsymbol{\Lambda}(\mathbf{\Sigma})$,
$\mathbb{Z}^{S}\subset\mathbb{O}(\mathbf{\Sigma})$, where the second inclusion
sends $e_{b}$ to $(e_{b},b)$. This sequence splits because the torsion part of
$\mathbb{O}(\mathbf{\Sigma})$ is isomorphic to the torsion part
$\mathbf{N}_{\rm tor}$ of $\mathbf{N}$. The original _refined fan sequence_ in
[27] corresponds to the case where $G(\mathbf{\Sigma})=\varnothing$; it is the
exact sequence
$\begin{CD}0@>{}>{}>\boldsymbol{\Lambda}^{\mathbf{\Sigma}}@>{}>{}>\mathbb{O}^{\mathbf{\Sigma}}@>{}>{}>\mathbf{N}@>{}>{}>0,\end{CD}$
(3.12)
where
$\displaystyle\mathbb{O}^{\mathbf{\Sigma}}:=\mathbb{O}(\mathbf{\Sigma})\cap\big{(}\mathbb{Q}^{R(\mathbf{\Sigma})}\oplus\mathbf{N}\big{)}=\sum_{v\in\Pi\cap\mathbf{N}}\mathbb{Z}\big{(}\Psi^{\mathbf{\Sigma}}(v),v\big{)},$
$\displaystyle\boldsymbol{\Lambda}^{\mathbf{\Sigma}}:=\boldsymbol{\Lambda}(\mathbf{\Sigma})\cap\mathbb{Q}^{R(\mathbf{\Sigma})}=\big{\\{}\lambda\in\mathbb{Q}^{R(\mathbf{\Sigma})}\colon(\lambda,0)\in\mathbb{O}^{\mathbf{\Sigma}}\big{\\}}.$
Note that $\boldsymbol{\Lambda}^{\mathbf{\Sigma}}$ is a lattice in
$\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{Q}}=\mathbb{L}^{\mathbf{\Sigma}}\otimes\mathbb{Q}$,
where $\mathbb{L}^{\mathbf{\Sigma}}$ is the lattice appearing in the fan
sequence (3.1). For $b\in G(\mathbf{\Sigma})$, we define
$\delta^{\mathbf{\Sigma}}_{b}:=e_{b}-\Psi^{\mathbf{\Sigma}}(b)\in\mathbb{Q}^{S}$.
Then $\delta^{\mathbf{\Sigma}}_{b}$ lies in
$\boldsymbol{\Lambda}(\mathbf{\Sigma})$ and we have the following
decompositions:
$\displaystyle\mathbb{O}(\mathbf{\Sigma})=\mathbb{O}^{\mathbf{\Sigma}}\oplus\bigoplus_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}\delta^{\mathbf{\Sigma}}_{b},\qquad\boldsymbol{\Lambda}(\mathbf{\Sigma})=\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\oplus\bigoplus_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}\delta^{\mathbf{\Sigma}}_{b}.$ (3.13)
###### Remark 3.11 ([27, Section 2.4]).
Under the identification $\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{Q}}\cong
H_{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Q})$ in (3.6), the lattice
$\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\subset\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{Q}}$
contains classes of all orbifold stable maps to
$\mathfrak{X}_{\mathbf{\Sigma}}$. We also have an isomorphism
$\big{(}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\big{)}^{\star}\cong\operatorname{Pic}(X_{\Sigma})$
[27, Lemma 4.8], where $\operatorname{Pic}(X_{\Sigma})$ is the Picard group of
the coarse moduli space $X_{\Sigma}$. On the other hand, we expect that
$\mathbb{O}^{\mathbf{\Sigma}}$ is the set of classes of orbi-discs in
$H_{2}(\mathfrak{X}_{\mathbf{\Sigma}},L;\mathbb{Q})\cong\mathbb{Q}^{R(\mathbf{\Sigma})}$
with boundaries in a Lagrangian torus fibre
$L\subset\mathfrak{X}_{\mathbf{\Sigma}}$. The notation $\mathbb{O}$ indicates
‘open’.
We introduce the (extended) Mori cones and their open analogues. Let
$\Sigma(n)$ denote the set of $n$-dimensional (i.e., maximal) cones of
$\Sigma$. For $\sigma\in\Sigma(n)$, we define
$\displaystyle\widetilde{C}_{\mathbf{\Sigma},\sigma}:=\big{\\{}\lambda\in\mathbb{R}^{S}\colon\beta(\lambda)\in\sigma,\,\lambda_{b}\geq
0\text{ for }b\notin R(\mathbf{\Sigma})\cap\sigma\big{\\}},$ $\displaystyle
C_{\mathbf{\Sigma},\sigma}:=\mathbb{L}_{\mathbb{R}}\cap\widetilde{C}_{\mathbf{\Sigma},\sigma}=\\{\lambda\in\mathbb{L}_{\mathbb{R}}\colon\lambda_{b}\geq
0\text{ for }b\notin R(\mathbf{\Sigma})\cap\sigma\\},$ (3.14)
where $\lambda_{b}$ with $b\in S$ denotes the $b$th component of
$\lambda\in\mathbb{R}^{S}$. We define the _extended Mori cone_
$\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}})$ and its open
analogue (cone of “open” curves)
$\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})$ by
$\displaystyle\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}}):=\sum_{\sigma\in\Sigma(n)}\widetilde{C}_{\mathbf{\Sigma},\sigma},\qquad\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}}):=\sum_{\sigma\in\Sigma(n)}C_{\mathbf{\Sigma},\sigma}=\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})\cap\mathbb{L}_{\mathbb{R}}.$
The unextended versions are given by
$\displaystyle\operatorname{OE}(\mathfrak{X}_{\mathbf{\Sigma}}):=\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})\cap\mathbb{R}^{R(\mathbf{\Sigma})},\qquad\operatorname{NE}(\mathfrak{X}_{\mathbf{\Sigma}}):=\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}})\cap\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{R}}.$
The cone $\operatorname{NE}(\mathfrak{X}_{\mathbf{\Sigma}})$ in
$\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{R}}\cong
H_{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{R})$ is the usual Mori cone, that
is, the cone spanned by effective curves in $\mathfrak{X}_{\mathbf{\Sigma}}$.
The corresponding monoids are given as follows
$\displaystyle\mathbb{O}(\mathbf{\Sigma})_{+}:=\big{\\{}(\lambda,v)\in\mathbb{O}(\mathbf{\Sigma})\colon\lambda\in\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})\big{\\}},$
$\displaystyle\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}:=\boldsymbol{\Lambda}(\mathbf{\Sigma})\cap\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}}).$
(3.15)
Similarly, the unextended versions are given by
$\displaystyle\mathbb{O}^{\mathbf{\Sigma}}_{+}:=\mathbb{O}(\mathbf{\Sigma})_{+}\cap\big{(}\mathbb{Q}^{R(\mathbf{\Sigma})}\oplus\mathbf{N}\big{)}=\big{\\{}(\lambda,v)\in\mathbb{O}^{\mathbf{\Sigma}}\colon\lambda\in\operatorname{OE}(\mathfrak{X}_{\mathbf{\Sigma}})\big{\\}},$
$\displaystyle\boldsymbol{\Lambda}_{+}^{\mathbf{\Sigma}}:=\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}\cap\mathbb{Q}^{R(\mathbf{\Sigma})}=\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\cap\operatorname{NE}(\mathfrak{X}_{\mathbf{\Sigma}}).$
These cones and monoids are compatible with the decompositions in (3.13) (cf.
[62, Lemma 3.2]). It is easy to check that
$\displaystyle\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})=\operatorname{OE}(\mathfrak{X}_{\mathbf{\Sigma}})+\sum_{b\in
G(\mathbf{\Sigma})}\mathbb{R}_{\geq 0}\delta_{b}^{\mathbf{\Sigma}},\qquad$
$\displaystyle\mathbb{O}(\mathbf{\Sigma})_{+}=\mathbb{O}^{\mathbf{\Sigma}}_{+}+\sum_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}_{\geq 0}\delta_{b}^{\mathbf{\Sigma}},$
$\displaystyle\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}})=\operatorname{NE}(\mathfrak{X}_{\mathbf{\Sigma}})+\sum_{b\in
G(\mathbf{\Sigma})}\mathbb{R}_{\geq 0}\delta_{b}^{\mathbf{\Sigma}},\qquad$
$\displaystyle\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}=\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}+\sum_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}_{\geq 0}\delta_{b}^{\mathbf{\Sigma}}.$ (3.16)
The following lemma follows immediately from [27, Lemma 2.7].
###### Lemma 3.12.
Consider a natural map $\mathbb{O}(\mathbf{\Sigma})_{+}\to\mathbf{N}\cap\Pi$
given by the second projection. The fibre of this map at
$v\in\mathbf{N}\cap\Pi$ equals
$\big{(}\Psi^{\mathbf{\Sigma}}(\overline{v}),v\big{)}+\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}$.
We introduce a pairing between $\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}}):=\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}(X_{\Sigma})$
and the lattices $\mathbb{O}(\mathbf{\Sigma})$,
$\boldsymbol{\Lambda}(\mathbf{\Sigma})$, where
$\operatorname{Pic}(X_{\Sigma})$ denotes the Picard group of the coarse moduli
space $X_{\Sigma}$ of $\mathfrak{X}_{\mathbf{\Sigma}}$. This pairing
corresponds to the Galois symmetry for quantum cohomology in Section 2.2. Note
that we have
$\displaystyle\boldsymbol{\Lambda}(\mathbf{\Sigma})/\mathbb{L}\cong\mathbb{O}(\mathbf{\Sigma})/\mathbb{Z}^{S}\cong\mathbb{O}^{\mathbf{\Sigma}}/\mathbb{Z}^{R(\mathbf{\Sigma})},$
(3.17)
where the first isomorphism follows from the comparison of the extended fan
sequence (3.3) and the extended refined fan sequence (3.11); the second
isomorphism follows from the fact that
$\mathbb{O}(\mathbf{\Sigma})=\mathbb{O}^{\mathbf{\Sigma}}\oplus\bigoplus\limits_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}(e_{b},b)$. Recall from (3.5) that
$\operatorname{Pic}(\mathfrak{X})\cong\mathbb{L}^{\star}/\sum\limits_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}D_{b}$. Since we have
$\lambda_{b}=D_{b}\cdot\lambda\in\mathbb{Z}$ for $b\in G(\mathbf{\Sigma})$ and
$\lambda\in\boldsymbol{\Lambda}(\mathbf{\Sigma})$, the natural pairing
$\mathbb{L}^{\star}\times(\mathbb{L}_{\mathbb{Q}}/\mathbb{L})\to\mathbb{Q}/\mathbb{Z}$
induces the pairing
$\operatorname{age}\colon\
\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})\times(\boldsymbol{\Lambda}(\mathbf{\Sigma})/\mathbb{L})\to\mathbb{Q}/\mathbb{Z}.$
Through the identification
$\boldsymbol{\Lambda}(\mathbf{\Sigma})/\mathbb{L}\cong\mathbb{O}^{\mathbf{\Sigma}}/\mathbb{Z}^{R(\mathbf{\Sigma})}$
above, this pairing coincides with the age pairing
$\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})\times\big{(}\mathbb{O}^{\mathbf{\Sigma}}/\mathbb{Z}^{R(\mathbf{\Sigma})}\big{)}\to\mathbb{Q}/\mathbb{Z}$
introduced in [27, Section 4.3]. It follows from [27, Lemma 4.7] that the age
pairing descends to a perfect pairing
$\operatorname{age}\colon\ \operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})\times(\boldsymbol{\Lambda}(\mathbf{\Sigma})/\mathbb{L})\to\mathbb{Q}/\mathbb{Z}.$
Via (3.17), we obtain the following pairings:
$\displaystyle\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})\times\mathbb{O}(\mathbf{\Sigma})\to\mathbb{C}^{\times},\qquad$
$\displaystyle(\xi,x)\mapsto
e^{2\pi\boldsymbol{\mathrm{i}}\operatorname{age}(\xi,x)},$
$\displaystyle\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})\times\boldsymbol{\Lambda}(\mathbf{\Sigma})\to\mathbb{C}^{\times},\qquad$
$\displaystyle(\xi,\lambda)\mapsto
e^{2\pi\boldsymbol{\mathrm{i}}\operatorname{age}(\xi,\lambda)}.$ (3.18)
###### Remark 3.13 ([27, Lemma 4.7]).
For a box element $b\in\operatorname{Box}(\mathbf{\Sigma})$,
$\operatorname{age}\big{(}\xi,\big{(}\Psi^{\mathbf{\Sigma}}(b),b\big{)}\big{)}$
is the _age_ of the line bundle $L_{\xi}$ corresponding to
$\xi\in\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})$ along the sector
corresponding to the box $b$, where
$\big{(}\Psi^{\mathbf{\Sigma}}(b),b\big{)}\in\mathbb{O}^{\mathbf{\Sigma}}$.
### 3.4 Local charts of the LG model
We describe the local charts of $\mathcal{Y}$ and $\mathcal{M}$ corresponding
to $\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$. By definition, the
local chart of $\mathcal{Y}$ corresponding to $\mathbf{\Sigma}$ is given by
(see [106, Section 4.1]):
$\mathcal{Y}_{\mathbf{\Sigma}}=\big{[}\operatorname{Spec}\left(\mathbb{C}[\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}\cap\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}]\right)\big{/}\mathcal{G}_{\mathbf{\Sigma}}\big{]},$
where
* •
$\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}\subset\mathbb{R}^{S}$ is the
dual cone of
$\operatorname{CPL}_{+}(\mathbf{\Sigma})\subset\big{(}\mathbb{R}^{S}\big{)}^{\star}$
(see (3.8)),
* •
$\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}=\operatorname{Hom}(\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma}),\mathbb{Z})\subset\mathbb{Q}^{S}$
is the dual lattice of $\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})$ (see
(3.9));
* •
$\mathcal{G}_{\mathbf{\Sigma}}:=\big{(}\mathbb{Z}^{S}\big{)}^{\star}/\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})$
is a finite group; it acts on
$\mathbb{C}[\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}\cap\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}]$
via the natural pairing
$\big{(}\mathbb{Z}^{S}\big{)}^{\star}\times\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}\to\mathbb{Q}\to\mathbb{Q}/\mathbb{Z}\subset\mathbb{C}^{\times}$.
The coarse moduli space of $\mathcal{Y}_{\mathbf{\Sigma}}$ is
$\operatorname{Spec}\big{(}\mathbb{C}\big{[}\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}\cap\mathbb{Z}^{S}\big{]}\big{)}$.
Similarly, the local chart of $\mathcal{M}$ corresponding to $\mathbf{\Sigma}$
is given by:
$\mathcal{M}_{\mathbf{\Sigma}}=\left[\operatorname{Spec}\left(\mathbb{C}[\operatorname{cpl}(\mathbf{\Sigma})^{\vee}\cap\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}]\right)\big{/}\mathcal{G}_{\mathbf{\Sigma}}^{\prime}\right],$
where
* •
$\operatorname{cpl}(\mathbf{\Sigma})^{\vee}\subset\mathbb{L}_{\mathbb{R}}$ is
the dual cone of $\operatorname{cpl}(\mathbf{\Sigma})$ (see (3.10)),
* •
$\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}\subset\mathbb{L}_{\mathbb{Q}}$
is the dual lattice of
$\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})=\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})/\mathbf{M}$
and
* •
$\mathcal{G}^{\prime}_{\mathbf{\Sigma}}:=\mathbb{L}^{\star}/\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})$
acts on
$\mathbb{C}[\operatorname{cpl}(\mathbf{\Sigma})^{\vee}\cap\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}]$
via the natural pairing
$\mathbb{L}^{\star}\times\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}\to\mathbb{Q}\to\mathbb{Q}/\mathbb{Z}\subset\mathbb{C}^{\times}$.
The coarse moduli space of $\mathcal{M}_{\mathbf{\Sigma}}$ is
$\operatorname{Spec}(\mathbb{C}[\operatorname{cpl}(\mathbf{\Sigma})^{\vee}\cap\mathbb{L}])$.
Comparing the extended divisor sequence (3.4) with the sequence
$0\to\mathbf{M}\to\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})\to\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})\to
0$, we obtain the exact sequence
$\begin{CD}0@>{}>{}>\mathcal{G}_{\mathbf{\Sigma}}@>{}>{}>\mathcal{G}_{\mathbf{\Sigma}}^{\prime}@>{}>{}>\operatorname{Ext}^{1}(\mathbf{N},\mathbb{Z})=\mathbf{N}_{\rm
tor}^{^}@>{}>{}>0,\end{CD}$ (3.19)
where $\mathbf{N}_{\rm tor}^{^}=\operatorname{Hom}(\mathbf{N}_{\rm
tor},\mathbb{C}^{\times})$ denotes the Pontrjagin dual of $\mathbf{N}_{\rm
tor}$. We have
$\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})\cong\mathbb{L}^{\star}/\sum\limits_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}D_{b}$ by (3.5), and that the Picard group
$\operatorname{Pic}(X_{\Sigma})$ of the coarse moduli space is given by
$\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})/\sum\limits_{b\in
G(\mathbf{\Sigma})}\mathbb{Z}D_{b}$ (see [34, Section 4.2]). Therefore
$\mathcal{G}_{\mathbf{\Sigma}}^{\prime}\cong\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})(=\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}(X_{\Sigma}))$
and the above sequence (3.19) identifies $\mathcal{G}_{\mathbf{\Sigma}}$ with
the subgroup of $\operatorname{Pic}^{\rm st}(\mathfrak{X}_{\mathbf{\Sigma}})$
on which the generic stabilizers $\mathbf{N}_{\rm tor}$ of
$\mathfrak{X}_{\mathbf{\Sigma}}$ acts trivially.
We give another description of the local chart
$\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}}$, which shows
that the LG model on this chart is the same as the LG model considered in [27,
Section 4].
###### Lemma 3.14 (duality of cones and lattices).
1. $(1)$
The extended Mori cone $\operatorname{\widehat{NE}}(\mathbf{\Sigma})$ is the
dual cone of $\operatorname{cpl}_{+}(\mathbf{\Sigma})$; similarly
$\operatorname{\widehat{OE}}(\mathbf{\Sigma})$ is the dual cone of
$\operatorname{CPL}_{+}(\mathbf{\Sigma})$.
2. $(2)$
The lattice
$\overline{\mathbb{O}(\mathbf{\Sigma})}:=\mathbb{O}(\mathbf{\Sigma})/\mathbf{N}_{\rm
tor}$ equals the dual lattice
$\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}$; similarly
$\boldsymbol{\Lambda}(\mathbf{\Sigma})\\!=\\!\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}$.
Here we identify $\overline{\mathbb{O}(\mathbf{\Sigma})}$ with the image of
the first projection $\mathbb{O}(\mathbf{\Sigma})\to\mathbb{Q}^{S}$ $($recall
that $\mathbf{N}_{\rm tor}$ is the torsion part of
$\mathbb{O}(\mathbf{\Sigma}))$.
###### Proof.
First we prove the statement on the dual cones. Observe that the cone
$\operatorname{CPL}_{+}(\mathbf{\Sigma})$ can be written as the intersection
of the following simplicial cones $K_{\sigma}$ for all maximal cones
$\sigma\in\Sigma(n)$:
$K_{\sigma}=\left\\{c\in\big{(}\mathbb{R}^{S}\big{)}^{\star}\colon\begin{matrix}\text{$c_{b}\geq
0$ $(\forall\,b\in R(\mathbf{\Sigma})\cap\sigma)$, and the linear function}\\\
\text{$\varphi\colon\mathbf{N}_{\mathbb{R}}\to\mathbb{R}$ defined by
$\varphi(\overline{b})=c_{b}$, $b\in R(\mathbf{\Sigma})\cap\sigma$}\\\
\text{satisfies $\varphi(\overline{b})\leq c_{b}$ for all $b\in
S$.}\end{matrix}\right\\}.$
Recall that $\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})$ is
the sum of the cones $\widetilde{C}_{\mathbf{\Sigma},\sigma}$ defined in
(3.14). Therefore, in order to prove
$\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}=\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})$,
it suffices to show that
$K_{\sigma}^{\vee}=\widetilde{C}_{\mathbf{\Sigma},\sigma}$. For $b\in S$, we
write $\overline{b}=\sum\limits_{b^{\prime}\in
R(\mathbf{\Sigma})\cap\sigma}A_{bb^{\prime}}\overline{b^{\prime}}$ with
$A_{bb^{\prime}}\in\mathbb{Q}$. Then the cone $K_{\sigma}$ is defined by the
linear inequalities:
$c_{b}\geq\begin{cases}0,&\text{if $b\in R(\mathbf{\Sigma})\cap\sigma$},\\\
\displaystyle\sum_{b^{\prime}\in
R(\mathbf{\Sigma})\cap\sigma}A_{bb^{\prime}}c_{b^{\prime}},&\text{if $b\notin
R(\mathbf{\Sigma})\cap\sigma$}.\end{cases}$
On the other hand, for $\lambda\in\mathbb{R}^{S}$ and
$c\in\big{(}\mathbb{R}^{S}\big{)}^{\star}$, we have
$\displaystyle c\cdot\lambda=\sum_{b\in
R(\mathbf{\Sigma})\cap\sigma}c_{b}\bigg{(}\lambda_{b}+\sum_{b^{\prime}\notin
R(\mathbf{\Sigma})\cap\sigma}A_{b^{\prime}b}\lambda_{b^{\prime}}\bigg{)}+\sum_{b^{\prime}\notin
R(\mathbf{\Sigma})\cap\sigma}\bigg{(}c_{b^{\prime}}-\sum_{b\in
R(\mathbf{\Sigma})\cap\sigma}A_{b^{\prime}b}c_{b}\bigg{)}\lambda_{b^{\prime}}.\\!\\!$
(3.20)
Hence the dual cone $K_{\sigma}^{\vee}$ is defined by the inequalities
$\lambda_{b}\geq 0$ for $b\notin R(\mathbf{\Sigma})\cap\sigma$ and
$\lambda_{b}+\sum\limits_{b^{\prime}\notin
R(\mathbf{\Sigma})\cap\sigma}A_{b^{\prime}b}\lambda_{b^{\prime}}\geq 0$ for
$b\in R(\mathbf{\Sigma})\cap\sigma$. The latter inequality is equivalent to
$\beta(\lambda)\in\sigma$, and thus
$K_{\sigma}^{\vee}=\widetilde{C}_{\mathbf{\Sigma},\sigma}$. Hence
$\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}=\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})$.
The equality
$\operatorname{cpl}(\mathbf{\Sigma})^{\vee}=\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}})$
follows from this and
$D(\operatorname{CPL}_{+}(\mathbf{\Sigma}))=\operatorname{cpl}(\mathbf{\Sigma})$,
$\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}})=\operatorname{\widehat{OE}}(\mathfrak{X}_{\mathbf{\Sigma}})\cap\mathbb{L}_{\mathbb{R}}$.
Next we study the dual lattices of
$\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})$,
$\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})$. For
$c\in\big{(}\mathbb{R}^{S}\big{)}^{\star}$ and a maximal cone
$\sigma\in\Sigma(n)$, let $m_{\sigma}(c)\in\mathbf{M}_{\mathbb{R}}$ denote the
unique element satisfying $m_{\sigma}(c)\cdot b=c_{b}$ for all $b\in
R(\mathbf{\Sigma})\cap\sigma$. The lattice
$\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})$ is the intersection of the
following lattices $L_{\sigma}$ for all $\sigma\in\Sigma(n)$:
$\displaystyle
L_{\sigma}=\big{\\{}c\in\big{(}\mathbb{R}^{S}\big{)}^{\star}\colon
m_{\sigma}(c)\in\mathbf{M},\,\text{$c_{b}\in\mathbb{Z}$ for all $b\notin
R(\mathbf{\Sigma})\cap\sigma$}\big{\\}}.$
Therefore
$\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}=\sum\limits_{\sigma\in\Sigma(n)}L_{\sigma}^{\star}$.
For $\lambda\in\mathbb{R}^{S}$ and $c\in\big{(}\mathbb{R}^{S}\big{)}^{\star}$,
equation (3.20) can be rewritten as:
$c\cdot\lambda=m_{\sigma}(c)\cdot\beta(\lambda)+\sum_{b^{\prime}\notin
R(\mathbf{\Sigma})\cap\sigma}(c_{b^{\prime}}-m_{\sigma}(c)\cdot
b^{\prime})\lambda_{b^{\prime}}.$
Therefore we have
$L_{\sigma}^{\star}=\big{\\{}\lambda\in\mathbb{R}^{S}\colon\beta(\lambda)\in\overline{\mathbf{N}}=\mathbf{N}/\mathbf{N}_{\rm
tor},\text{$\lambda_{b}\in\mathbb{Z}$ for all $b\notin
R(\mathbf{\Sigma})\cap\sigma$}\big{\\}}.$
On the other hand,
$\overline{\mathbb{O}(\mathbf{\Sigma})}=\sum\limits_{\sigma\in\Sigma(n)}L_{\sigma}^{\star}$
follows easily from the definition. Thus
$\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}=\overline{\mathbb{O}(\mathbf{\Sigma})}$.
The equality
$\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}=\boldsymbol{\Lambda}(\mathbf{\Sigma})$
follows from this, the extended refined fan sequence (3.11) and
$\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})=\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})/\mathbf{M}$.
∎
###### Proposition 3.15.
The local chart
$\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}}$ has the
following presentation:
$\displaystyle\mathcal{Y}_{\mathbf{\Sigma}}\cong\big{[}\operatorname{Spec}(\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}])/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})\big{]},$
$\displaystyle\mathcal{M}_{\mathbf{\Sigma}}\cong\big{[}\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}])/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})\big{]},$
where $\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})=\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}(X_{\Sigma})$
acts on $\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ and
$\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$ via (3.18).
###### Proof.
By the previous Lemma 3.14, we have
$\mathbb{O}(\mathbf{\Sigma})_{+}/\mathbf{N}_{\rm
tor}=\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}\cap\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}$
and
$\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}=\operatorname{cpl}(\mathbf{\Sigma})^{\vee}\cap\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}$.
Therefore we have the natural maps
$\displaystyle\operatorname{Spec}\mathbb{C}\big{[}\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}\cap\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}\big{]}\hookrightarrow\operatorname{Spec}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}],$
$\displaystyle\operatorname{Spec}\mathbb{C}\big{[}\operatorname{cpl}(\mathbf{\Sigma})^{\vee}\cap\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}\big{]}\cong\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}].$
The first map is the inclusion of a connected component. We can see that the
$\mathcal{G}_{\mathbf{\Sigma}}^{\prime}=\mathbb{L}^{\star}/\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})\cong\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})$ action on
$\mathbb{C}[\operatorname{cpl}(\mathbf{\Sigma})^{\vee}\cap\operatorname{pl}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}]$
and the $\operatorname{Pic}^{\rm st}(\mathfrak{X}_{\mathbf{\Sigma}})$ action
on $\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$ are the same (both
are induced by the pairing
$\mathbb{L}^{\star}\times\mathbb{L}_{\mathbb{Q}}\to\mathbb{Q}$). Also the
$\operatorname{Pic}^{\rm st}(\mathfrak{X}_{\mathbf{\Sigma}})$ action on
$\operatorname{Spec}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ induces a
permutation of its connected components, and the subgroup preserving the
component
$\operatorname{Spec}\mathbb{C}[\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}\cap\operatorname{PL}_{\mathbb{Z}}(\mathbf{\Sigma})^{\star}]$
is identified with $\mathcal{G}_{\mathbf{\Sigma}}$ (via the sequence (3.19)).
The proposition follows. ∎
It follows from the above proposition that the local chart
$\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}}$ is a quotient
(by $\operatorname{Pic}^{\rm st}(\mathfrak{X})$) of the LG model considered in
[27, Section 4]. Indeed, the decompositions (3.16) induce the isomorphisms
$\displaystyle\operatorname{Spec}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]\cong\operatorname{Spec}\mathbb{C}\big{[}\mathbb{O}^{\mathbf{\Sigma}}_{+}\big{]}\times\mathbb{C}^{G(\mathbf{\Sigma})},$
$\displaystyle\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\cong\operatorname{Spec}\mathbb{C}\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\big{]}\times\mathbb{C}^{G(\mathbf{\Sigma})}$
(3.21)
and the structure map
$\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}}$ is induced by
the natural map
$\operatorname{Spec}\mathbb{C}\big{[}\mathbb{O}^{\mathbf{\Sigma}}_{+}\big{]}\to\operatorname{Spec}\mathbb{C}\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\big{]}$.
In [27], the LG model was first introduced on
$\operatorname{Spec}\mathbb{C}\big{[}\mathbb{O}^{\mathbf{\Sigma}}_{+}\big{]}\to\operatorname{Spec}\mathbb{C}\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\big{]}$
and then deformed over the parameter space $\mathbb{C}^{G(\mathbf{\Sigma})}$.
The total deformation family there is identified with the uniformizing chart
of the LG model
$(\operatorname{pr}\colon\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}},F)$
in the present paper. See also the expression (3.22) in explicit co-ordinates
and Remark 3.16 below.
### 3.5 Co-ordinate system on the local chart
Using the presentation in Proposition 3.15, we introduce a convenient co-
ordinate system on the local chart
$\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}}$. For
$(\lambda,v)\in\mathbb{O}(\mathbf{\Sigma})$, we write $u^{(\lambda,v)}$ for
the corresponding element in $\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})]$. We set
$u_{b}:=u^{(e_{b},b)}\in\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}],\qquad
q^{\lambda}:=u^{(\lambda,0)}\in\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})]$
for $b\in S$ and $\lambda\in\boldsymbol{\Lambda}(\mathbf{\Sigma})$. When
$\lambda$ lies in
$\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\subset\boldsymbol{\Lambda}(\mathbf{\Sigma})$,
we also write $\mathtt{q}^{\lambda}$ for $q^{\lambda}$. We choose a splitting
$\varsigma\colon\mathbf{N}\to\mathbb{O}^{\mathbf{\Sigma}}$ of the refined fan
sequence (3.12) of the form $\varsigma(v)=(\overline{\varsigma}(v),v)$, where
$\overline{\varsigma}\colon\mathbf{N}\to\mathbb{Q}^{R(\mathbf{\Sigma})}$
defines a splitting of the fan sequence (3.1) over $\mathbb{Q}$. For
$v\in\mathbf{N}$ and $b\in S$, we define
$\displaystyle
x^{v}:=u^{\varsigma(v)}\in\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})],$
$\displaystyle
t_{b}:=q^{\delta^{\mathbf{\Sigma}}_{b}}=q^{e_{b}-\Psi^{\mathbf{\Sigma}}(b)}=u^{(e_{b}-\Psi^{\mathbf{\Sigma}}(b),0)}\in\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}].$
Note that $x^{v}$ does not necessarily belong to
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ and that $t_{b}=1$ for $b\in
R(\mathbf{\Sigma})$. Then we have for $b\in S$,
$u_{b}=t_{b}\mathtt{q}^{\lambda(b)}x^{b},$
where
$\lambda(b):=\Psi^{\mathbf{\Sigma}}(b)-\overline{\varsigma}(b)\in\boldsymbol{\Lambda}^{\mathbf{\Sigma}}$.
Note that
$\mathtt{q}^{\lambda(b)}x^{b}=u^{(\Psi^{\mathbf{\Sigma}}(b),b)}\in\mathbb{C}\big{[}\mathbb{O}^{\mathbf{\Sigma}}_{+}\big{]}$.
We can regard $q=(\mathtt{q},t)$ as co-ordinates on the base
$\mathcal{M}_{\mathbf{\Sigma}}$ and $x$ as co-ordinates on fibres of
$\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}}$. The LG
potential
$F=\sum_{b\in S}u_{b}=\sum_{b\in
R(\mathbf{\Sigma})}\mathtt{q}^{\lambda(b)}x^{b}+\sum_{b\in
G(\mathbf{\Sigma})}t_{b}\mathtt{q}^{\lambda(b)}x^{b}$ (3.22)
can then be viewed as a family of Laurent polynomials in $x$ with the fixed
set $S$ of exponents. Furthermore, we use the following co-ordinate
expressions when necessary.
* •
Choosing an isomorphism $\mathbf{N}\cong\mathbb{Z}^{n}\times\mathbf{N}_{\rm
tor}$, we write $x^{b}=x_{1}^{b_{1}}\cdots x_{n}^{b_{n}}x^{\zeta}$ when
$b\in\mathbf{N}$ corresponds to
$(b_{1},\dots,b_{n},\zeta)\in\mathbb{Z}^{n}\times\mathbf{N}_{\rm tor}$;
$x_{1},\dots,x_{n}$ can be viewed as co-ordinates along fibres of
$\mathcal{Y}\to\mathcal{M}$ and $x^{\zeta}$ are roots of unity labelling
connected components of the fibre.
* •
Choosing a $\mathbb{Z}$-basis $\lambda_{1},\dots,\lambda_{r}$ of
$\boldsymbol{\Lambda}^{\mathbf{\Sigma}}$, we write
$\mathtt{q}_{i}=\mathtt{q}^{\lambda_{i}}\in\mathbb{C}\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\big{]}$;
then $\mathtt{q}_{1},\dots,\mathtt{q}_{r}$ and $t_{b}$, $b\in
G(\mathbf{\Sigma})$ together form a co-ordinate system $q=(\mathtt{q},t)$ on
the base.
###### Remark 3.16.
We compare the notation of [27, 65] with the present one. In these papers, the
LG potential was given in the form
$F(x;y)=\sum_{b\in S}y_{b}w_{b}=\sum_{b\in S}y_{b}Q^{\lambda(b)}x^{b},$
where $\\{y_{b}\\}_{b\in S}$ are deformation parameters. In the present paper,
we set777In [27, 65], we also wrote $\\{y_{1},\dots,y_{m}\\}$ for
$\\{y_{b}\\}_{b\in R(\mathbf{\Sigma})}$ with $m=|R(\mathbf{\Sigma})|$.
$y_{b}=1$ for all $b\in R(\mathbf{\Sigma})$. The variables $Q$ and the other
variables $y_{b}$, $b\in G(\mathbf{\Sigma})$ correspond to our
$\mathtt{q}_{1},\dots,\mathtt{q}_{r}$ and $t_{b}$ with $b\in
G(\mathbf{\Sigma})$, and $w_{b}$ corresponds to our
$u^{(\Psi^{\mathbf{\Sigma}}(b),b)}=\mathtt{q}^{\lambda(b)}x^{b}$. (Note that
$w_{b}$ _does not_ correspond to $u_{b}$ in the present paper.)
###### Remark 3.17 ([27, Section 4.1]).
By Lemma 3.12, we have
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]=\bigoplus_{v\in\mathbf{N}\cap\Pi}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]u^{(\Psi^{\mathbf{\Sigma}}(\overline{v}),v)}.$
In particular the family $\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$ is
flat. The fact that $\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ is a free
$\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$-module played an
important role in establishing a mirror isomorphism in [27].
### 3.6 Examples
We give examples of partially compactified LG models for surface
singularities.
#### 3.6.1 $\boldsymbol{A_{1}}$-singularity resolution
We take $\mathbf{N}=\mathbb{Z}^{2}$ and $S=\\{(-1,1),(1,1),(0,1)\\}$. There
are two stacky fans $\mathbf{\Sigma}_{1}$, $\mathbf{\Sigma}_{2}$ adapted to
$S$ as shown in Fig. 1. The stacky fan $\mathbf{\Sigma}_{1}$ consists of one
maximal cone and gives rise to the toric stack
$\mathfrak{X}_{1}=\big{[}\mathbb{C}^{2}/\mu_{2}\big{]}$ (the $A_{1}$
singularity) and the fan $\mathbf{\Sigma}_{2}$ consists of two maximal cones
and gives rise to the crepant resolution
$\mathfrak{X}_{2}=\mathcal{O}_{\mathbb{P}^{1}}(-2)$ of
$\mathbb{C}^{2}/\mu_{2}$.
Figure 1: The surface $A_{1}$-singularity (left) and its crepant resolution
(right).
The extended fan sequence is
$\begin{CD}0@>{}>{}>\mathbb{L}=\mathbb{Z}@>{\left(\begin{smallmatrix}-1\\\
-1\\\
2\end{smallmatrix}\right)}>{}>\mathbb{Z}^{3}@>{\left(\begin{smallmatrix}-1&1&0\\\
1&1&1\end{smallmatrix}\right)}>{}>\mathbf{N}=\mathbb{Z}^{2}@>{}>{}>0\end{CD}$
(3.23)
and the extended divisor sequence is its dual
$\begin{CD}0@>{}>{}>\mathbf{M}@>{}>{}>\big{(}\mathbb{Z}^{3}\big{)}^{\star}@>{D=(-1,-1,2)}>{}>\mathbb{L}^{\star}=\mathbb{Z}@>{}>{}>0.\end{CD}$
The fan $\widetilde{\Xi}$ on the vector space
$\big{(}\mathbb{Z}^{3}\big{)}^{\star}\otimes\mathbb{R}$ consists of the two
maximal cones:
$\displaystyle\operatorname{CPL}_{+}(\mathbf{\Sigma}_{1})=\big{\\{}(c_{1},c_{2},c_{3})\in(\mathbb{R}_{\geq
0})^{3}\colon 2c_{3}\geq c_{1}+c_{2}\big{\\}},$
$\displaystyle\operatorname{CPL}_{+}(\mathbf{\Sigma}_{2})=\big{\\{}(c_{1},c_{2},c_{3})\in(\mathbb{R}_{\geq
0})^{3}\colon 2c_{3}\leq c_{1}+c_{2}\big{\\}}$
and the integral structure $\widetilde{\daleth}$ is given by
$\widetilde{\daleth}=\big{\\{}(c_{1},c_{2},c_{3})\in(\mathbb{Z}_{\geq
0})^{3}\colon\min\big{(}c_{3},\textstyle\frac{c_{1}+c_{2}}{2}\big{)}\in\mathbb{Z}\big{\\}}.$
The map $D\colon\big{(}\mathbb{Z}^{3}\big{)}^{\star}\to\mathbb{L}^{\star}$
induces the secondary fan $\Xi$ on
$\mathbb{L}^{\star}_{\mathbb{R}}\cong\mathbb{R}$. The fan $\Xi$ consists of
the two maximal cones
$\operatorname{cpl}(\mathbf{\Sigma}_{1})=\mathbb{R}_{\geq 0}$,
$\operatorname{cpl}(\mathbf{\Sigma}_{2})=\mathbb{R}_{\leq 0}$ and the integral
structure is given by $\daleth=2\mathbb{Z}_{\geq 0}\cup\mathbb{Z}_{\leq 0}$.
See Fig. 2. The extended refined fan sequence (see (3.11)) associated to
$\mathbf{\Sigma}_{1}$ is given by
$\begin{CD}0@>{}>{}>\boldsymbol{\Lambda}(\mathbf{\Sigma}_{1})=\frac{1}{2}\mathbb{Z}@>{\left(\begin{smallmatrix}-1\\\
-1\\\
2\end{smallmatrix}\right)}>{}>\mathbb{O}(\mathbf{\Sigma}_{1})=\mathbb{Z}^{3}+\mathbb{Z}\begin{pmatrix}\frac{1}{2}\\\
\overset{}{\frac{1}{2}}\\\
\overset{}{0}\end{pmatrix}@>{\left(\begin{smallmatrix}-1&1&0\\\
1&1&1\end{smallmatrix}\right)}>{}>\mathbf{N}=\mathbb{Z}^{2}@>{}>{}>0,\end{CD}$
which is a refinement of (3.23). The monoids888Note that
$\mathbb{O}(\mathbf{\Sigma})_{+}=\mathbb{O}(\mathbf{\Sigma})\cap\operatorname{CPL}_{+}(\mathbf{\Sigma})^{\vee}$
and
$\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}=\boldsymbol{\Lambda}(\mathbf{\Sigma})\cap\operatorname{cpl}(\mathbf{\Sigma})^{\vee}$.
corresponding to the (open) Mori cone are given by
$\boldsymbol{\Lambda}(\mathbf{\Sigma}_{1})_{+}=\frac{1}{2}\mathbb{Z}_{\geq 0}$
and $\mathbb{O}(\mathbf{\Sigma}_{1})_{+}=\mathbb{Z}_{\geq
0}\big{\langle}e_{1},e_{2},\frac{1}{2}(e_{1}+e_{2}),\delta_{3}\big{\rangle}$
with $\delta_{3}=\big{(}-\frac{1}{2},-\frac{1}{2},1\big{)}$. By Proposition
3.15, the chart
$\mathcal{Y}_{\mathbf{\Sigma}_{1}}\to\mathcal{M}_{\mathbf{\Sigma}_{1}}$ is
given by
$\textstyle{\mathcal{Y}_{\mathbf{\Sigma}_{1}}=\big{[}\big{\\{}(u_{1},u_{2},v,t)\colon
u_{1}u_{2}=v^{2}\big{\\}}\big{/}\mu_{2}\big{]}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{t}$$\scriptstyle{F=u_{1}+u_{2}+tv\quad}$$\textstyle{\mathbb{C},}$$\textstyle{\mathcal{M}_{\mathbf{\Sigma}_{1}}=[\mathbb{C}/\mu_{2}]}$
where $u_{1}$, $u_{2}$, $v$, $t$ correspond to
$e_{1},e_{2},\frac{1}{2}(e_{1}+e_{2}),\delta_{3}\in\mathbb{O}_{+}(\mathbf{\Sigma}_{1})$
and $\operatorname{Pic}^{{\rm
st}}(\mathfrak{X}_{\mathbf{\Sigma}_{1}})=\mathbb{O}(\mathbf{\Sigma}_{1})/\mathbb{Z}^{3}\cong\mu_{2}$
acts on these variables by $(u_{1},u_{2},v,t)\mapsto(u_{1},u_{2},-v,-t)$. On
the other hand, the extended refined fan sequence for $\mathbf{\Sigma}_{2}$ is
the same as the extended fan sequence (3.23) and one has
$\boldsymbol{\Lambda}(\mathbf{\Sigma}_{2})_{+}=\mathbb{Z}_{\leq 0}$ and
$\mathbb{O}(\mathbf{\Sigma}_{2})_{+}=\mathbb{Z}_{\geq 0}\langle
e_{1},e_{2},e_{3},(1,1,-2)\rangle$. Therefore, the chart
$\mathcal{Y}_{\mathbf{\Sigma}_{2}}\to\mathcal{M}_{\mathbf{\Sigma}_{2}}$ is
given by
| |
---|---|---
$\textstyle{\mathcal{Y}_{\mathbf{\Sigma}_{2}}=\big{\\{}(u_{1},u_{2},u_{3},q)\colon
u_{1}u_{2}=qu_{3}^{2}\big{\\}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{q}$$\scriptstyle{F=u_{1}+u_{2}+u_{3}\quad}$$\textstyle{\mathbb{C},}$$\textstyle{\mathcal{M}_{\mathbf{\Sigma}_{2}}=\mathbb{C}}$
where $u_{1}$, $u_{2}$, $u_{3}$, $q$ correspond respectively to $e_{1}$,
$e_{2}$, $e_{3}$, $(1,1,-2)$. The global LG model
$(\mathcal{Y}\to\mathcal{M},F)$ is given by gluing these charts by $u_{3}=vt$,
$q=t^{-2}$. The base space is given by $\mathcal{M}=\mathbb{P}(1,2)$.
Figure 2: The fans $\widetilde{\Xi}$, $\Xi$ and the map $D$ between them.
#### 3.6.2 Blowup of $\boldsymbol{\mathbb{C}^{2}}$
We take $\mathbf{N}=\mathbb{Z}^{2}$ and $S=\\{(1,0),(0,1),(1,1)\\}$. The
possible fan structures $\mathbf{\Sigma}_{1}$, $\mathbf{\Sigma}_{2}$ are shown
in Fig. 3. The fan $\mathbf{\Sigma}_{1}$ corresponds to $\mathbb{C}^{2}$ and
$\mathbf{\Sigma}_{2}$ corresponds to the blowup
$\operatorname{Bl}_{0}\big{(}\mathbb{C}^{2}\big{)}$ of $\mathbb{C}^{2}$ at the
origin.
Figure 3: $\mathbb{C}^{2}$ and its blowup at the origin.
In this case, the LG model has no orbifold singularities. The chart
$\mathcal{Y}_{\mathbf{\Sigma}_{1}}\to\mathcal{M}_{\mathbf{\Sigma}_{1}}$ is
given by
$\textstyle{\mathcal{Y}_{\mathbf{\Sigma}_{1}}=\\{(u_{1},u_{2},u_{3},t)\colon
tu_{1}u_{2}=u_{3}\\}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{t}$$\scriptstyle{F=u_{1}+u_{2}+u_{3}\quad}$$\textstyle{\mathbb{C}.}$$\textstyle{\mathcal{M}_{\mathbf{\Sigma}_{1}}=\mathbb{C}}$
The chart
$\mathcal{Y}_{\mathbf{\Sigma}_{2}}\to\mathcal{M}_{\mathbf{\Sigma}_{2}}$ is
given by
$\textstyle{\mathcal{Y}_{\mathbf{\Sigma}_{2}}=\\{(u_{1},u_{2},u_{3},q)\colon
u_{1}u_{2}=qu_{3}\\}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{q}$$\scriptstyle{F=u_{1}+u_{2}+u_{3}\quad}$$\textstyle{\mathbb{C}.}$$\textstyle{\mathcal{M}_{\mathbf{\Sigma}_{2}}=\mathbb{C}}$
The two charts are glued by $t=q^{-1}$.
#### 3.6.3 Cyclic quotient singularity
We take $\mathbf{N}=\mathbb{Z}^{2}$ and $S=\\{(0,1),(d,-1),(1,0)\\}$ with
$d\geq 3$. The case $d=1$ was considered in Section 3.6.2 (blowup of
$\mathbb{C}^{2}$) and the case $d=2$ was considered in Section 3.6.1
($A_{1}$-singularity). As before, there are two fan structures
$\mathbf{\Sigma}_{1}$, $\mathbf{\Sigma}_{2}$ (see Fig. 4). The fan
$\mathbf{\Sigma}_{1}$ corresponds to $\big{[}\mathbb{C}^{2}/\mu_{d}\big{]}$
(of type $\frac{1}{d}(1,1)$) and $\mathbf{\Sigma}_{2}$ corresponds to its
minimal resolution (the total space of $\mathcal{O}(-d)$ over
$\mathbb{P}^{1}$).
Figure 4: Cyclic quotient singularity and its resolution.
The chart
$\mathcal{Y}_{\mathbf{\Sigma}_{1}}\to\mathcal{M}_{\mathbf{\Sigma}_{1}}$ is
given by
$\textstyle{\mathcal{Y}_{\mathbf{\Sigma}_{1}}=\big{[}\big{\\{}(u_{1},u_{2},v,t)\colon
u_{1}u_{2}=v^{d}\big{\\}}\big{/}\mu_{d}\big{]}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{t}$$\scriptstyle{F=u_{1}+u_{2}+tv\quad}$$\textstyle{\mathbb{C},}$$\textstyle{\mathcal{M}_{\mathbf{\Sigma}_{1}}=[\mathbb{C}/\mu_{d}]}$
where $\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}_{1}})\cong\mu_{d}$ acts by
$(u_{1},u_{2},v,t)\mapsto(u_{1},u_{2},\zeta v,\zeta^{-1}t)$. The chart
$\mathcal{Y}_{\mathbf{\Sigma}_{2}}\to\mathcal{M}_{\mathbf{\Sigma}_{2}}$ is
given by
$\textstyle{\mathcal{Y}_{\mathbf{\Sigma}_{2}}=\big{\\{}(u_{1},u_{2},u_{3},q)\colon
u_{1}u_{2}=u_{3}^{d}q\big{\\}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{q}$$\scriptstyle{F=u_{1}+u_{2}+u_{3}\quad}$$\textstyle{\mathbb{C}.}$$\textstyle{\mathcal{M}_{\mathbf{\Sigma}_{2}}=\mathbb{C}}$
The two charts are glued by $u_{3}=tv$ and $q=t^{-d}$. After gluing, we get
$\mathcal{M}_{\mathbf{\Sigma}_{1}}\cup\mathcal{M}_{\mathbf{\Sigma}_{2}}=\mathbb{P}(1,d)$.
The pictures of the fans $\Xi$, $\widetilde{\Xi}$ are similar to Fig. 2.
## 4 Mirror symmetry
In this section, we review mirror symmetry for smooth toric DM stacks proved
by Coates–Corti–Iritani–Tseng [26, 27] and discuss its analytification. We
construct various versions (algebraic, completed, analytified) of Brieskorn
modules associated with the Landau–Ginzburg model around the limit point
$0_{\mathbf{\Sigma}}$ and compare them with the quantum cohomology D-module of
the toric stack $\mathfrak{X}_{\mathbf{\Sigma}}$. We fix the data
$(\mathbf{N},\Pi,S)$ from Section 3.1.
### 4.1 Brieskorn module
Let $(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$ be the partially
compactified LG model associated with the data $(\mathbf{N},\Pi,S)$ (see
Definition 3.6). We adapt the construction of the equivariant Brieskorn module
in [27, 65] to our context.
Note that the toric stacks $\mathcal{Y}$, $\mathcal{M}$ have natural log
structures defined by their toric boundaries (see, e.g., [54, Chapter 3]).
With respect to these log structures, the family $\mathcal{Y}\to\mathcal{M}$
is log-smooth. The sheaves of logarithmic one-forms and logarithmic vector
fields on $\mathcal{Y}$ are globally free and given respectively by
$\Omega^{1}_{\mathcal{Y}}=\bigoplus_{b\in
S}\mathcal{O}_{\mathcal{Y}}\frac{du_{b}}{u_{b}},\qquad\Theta_{\mathcal{Y}}=\bigoplus_{b\in
S}\mathcal{O}_{\mathcal{Y}}u_{b}\frac{\partial}{\partial u_{b}}.$
Let $x_{1},\dots,x_{n}$ be the co-ordinates on fibres of
$\mathcal{Y}\to\mathcal{M}$ given by the choice of an isomorphism
$\mathbf{N}\cong\mathbb{Z}^{n}\times\mathbf{N}_{\rm tor}$ (see Section 3.5).
Then the sheaf of relative logarithmic $k$-forms999The relative $k$-forms
$\frac{dx_{i_{1}}}{x_{i_{1}}}\wedge\cdots\wedge\frac{dx_{i_{k}}}{x_{i_{k}}}$
are independent of the choice of a splitting $\varsigma$ in Section 3.5,
although the co-ordinates $x_{i}$ themselves depend on $\varsigma$. are
$\Omega^{k}_{\mathcal{Y}/\mathcal{M}}=\bigoplus_{i_{1}<\cdots<i_{k}}\mathcal{O}_{\mathcal{Y}}\frac{dx_{i_{1}}}{x_{i_{1}}}\wedge\cdots\wedge\frac{dx_{i_{k}}}{x_{i_{k}}}.$
The sheaf $\Theta_{\mathcal{Y}/\mathcal{M}}$ of relative logarithmic vector
fields is generated by $x_{1}\frac{\partial}{\partial
x_{1}},\dots,x_{n}\frac{\partial}{\partial x_{n}}$. Let
$\\{\chi_{1},\dots,\chi_{n}\\}$ denote the basis of $\mathbf{M}$ dual to the
chosen isomorphism $\overline{\mathbf{N}}\cong\mathbb{Z}^{n}$; then the
relative vector field $x_{i}\frac{\partial}{\partial x_{i}}$ acts on functions
(on the chart $\mathcal{Y}_{\mathbf{\Sigma}}$) as
$x_{i}\frac{\partial}{\partial x_{i}}\cdot u^{(\lambda,b)}=(\chi_{i}\cdot
b)u^{(\lambda,b)}\qquad\text{for
$(\lambda,b)\in\mathbb{O}(\mathbf{\Sigma})_{+}$}.$
For $\xi\in\mathbb{L}_{\mathbb{C}}^{\star}$, $\xi q\frac{\partial}{\partial
q}$ denotes a vector field on $\mathcal{M}$ such that
$\xi q\frac{\partial}{\partial q}\cdot
q^{\lambda}=(\xi\cdot\lambda)q^{\lambda}\qquad\text{for
$\lambda\in\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}$}.$
We define a generator $\omega$ of $\Omega^{n}_{\mathcal{Y}/\mathcal{M}}$ by
$\omega:=\frac{1}{|\mathbf{N}_{\rm
tor}|}\frac{dx_{1}}{x_{1}}\wedge\cdots\wedge\frac{dx_{n}}{x_{n}}.$
This is normalized so that the integral over the maximal compact subgroup
$\operatorname{Hom}\big{(}\mathbf{N},S^{1}\big{)}$ of
$\operatorname{Hom}(\mathbf{N},\mathbb{C}^{\times})$ equals
$(2\pi\boldsymbol{\mathrm{i}})^{n}$. Informally speaking, the non-equivariant
Brieskorn module below is a D-module on $\mathcal{M}\times\mathbb{C}_{z}$
consisting of certain cohomology classes of relative differential forms
$f\omega\in\operatorname{pr}_{*}\Omega^{n}_{\mathcal{Y}/\mathcal{M}}$ such
that oscillatory integrals
$[f\omega]\longmapsto\int_{\Gamma\subset\mathcal{Y}_{q}}e^{F/z}f(x,q,z)\omega$
are solutions to the D-module, where
$\mathcal{Y}_{q}:=\operatorname{pr}^{-1}(q)$. In the equivariant case, the
phase function $F$ should be replaced with
$F-\sum\limits_{i=1}^{n}\chi_{i}\log x_{i}$, see Remark 4.4 below.
###### Definition 4.1.
1. (1)
The _equivariant Brieskorn module_ $\operatorname{Bri_{\mathbb{T}}}(F)$ is
defined to be the $\mathcal{O}_{\mathcal{Y}}[z]$-module
$\Omega^{n}_{\mathcal{Y}/\mathcal{M}}[z]=\mathcal{O}_{\mathcal{Y}}[z]\cdot\omega$
equipped with the flat connection
$\nabla\colon\operatorname{Bri_{\mathbb{T}}}(F)\to
z^{-1}\operatorname{Bri_{\mathbb{T}}}(F)\otimes_{\mathcal{O}_{\mathcal{Y}}}\Omega^{1}_{\mathcal{Y}}$
given by
$\nabla_{V}(f\omega)=\big{(}V(f)+z^{-1}V(F)f\big{)}\omega$
for $f\in\mathcal{O}_{\mathcal{Y}}[z]$ and $V\in\Theta_{\mathcal{Y}}$. We call
$\nabla$ the _Gauss–Manin connection_. We let the equivariant parameter
$\chi_{i}\in\mathbf{M}_{\mathbb{C}}\cong
H^{2}_{\mathbb{T}}({\operatorname{pt}},\mathbb{C})$ act on
$\operatorname{Bri_{\mathbb{T}}}(F)$ by
$z\nabla_{x_{i}\frac{\partial}{\partial x_{i}}}$, i.e.,
$\chi_{i}\cdot f\omega:=z\nabla_{x_{i}\frac{\partial}{\partial
x_{i}}}(f\omega)=\left(zx_{i}\frac{\partial f}{\partial x_{i}}+\sum_{b\in
S}(\chi_{i}\cdot b)u_{b}f\right)\omega.$
We shall often regard $\operatorname{Bri_{\mathbb{T}}}(F)$ as a sheaf of
modules over $\mathcal{M}$ by pushing it forward by
$\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$; by abuse of notation we
use the same symbol to denote the pushed-forward sheaf. The action of
$\chi_{i}$ commutes with the $\mathcal{O}_{\mathcal{M}}[z]$-module structure
and thus $\operatorname{Bri_{\mathbb{T}}}(F)$ has the structure of an
$\mathcal{O}_{\mathcal{M}}\otimes R_{\mathbb{T}}[z]$-module with
$R_{\mathbb{T}}=H^{*}_{\mathbb{T}}({\operatorname{pt}},\mathbb{C})\cong\operatorname{Sym}(\mathbf{M}_{\mathbb{C}})$.
The _grading operator_
$\operatorname{Gr}\in\operatorname{End}_{\mathbb{C}}(\operatorname{Bri_{\mathbb{T}}}(F))$
is defined by
$\operatorname{Gr}(f\omega)=\left(z\frac{\partial f}{\partial z}+\sum_{b\in
S}u_{b}\frac{\partial f}{\partial u_{b}}\right)\omega$ (4.1)
for $f\in\mathcal{O}_{\mathcal{Y}}[z]$.
2. (2)
The (non-equivariant) _Brieskorn module_ $\operatorname{Bri}(F)$ is defined to
be the non-equivariant limit
$\operatorname{Bri_{\mathbb{T}}}(F)/\mathbf{M}_{\mathbb{C}}\cdot\operatorname{Bri_{\mathbb{T}}}(F)$
of the equivariant Brieskorn module. This has the structure of an
$\mathcal{O}_{\mathcal{M}}[z]$-module. The flat connection and the grading
operator on $\operatorname{Bri_{\mathbb{T}}}(F)$ descend to a flat connection
$\nabla\colon\operatorname{Bri}(F)\to
z^{-1}\operatorname{Bri}(F)\otimes\Omega_{\mathcal{M}}^{1}$, also called the
_Gauss–Manin connection_ , and an operator
$\operatorname{Gr}\in\operatorname{End}_{\mathbb{C}}(\operatorname{Bri}(F))$.
By definition, $\operatorname{Bri_{\mathbb{T}}}(F)$ is isomorphic to the rank-
one free module $\mathcal{O}_{\mathcal{Y}}[z]$ equipped with the flat
connection $\nabla=d+d(F/z)\wedge$. By pushing it forward by
$\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$ and forgetting the action
of the fibre co-ordinates $x_{1},\dots,x_{n}$, we shall regard
$\operatorname{Bri_{\mathbb{T}}}(F)$ as an $\mathcal{O}_{\mathcal{M}}\otimes
R_{\mathbb{T}}[z]$-module; then $\operatorname{Bri_{\mathbb{T}}}(F)$ is not of
rank one as such.101010This is not coherent as an
$\mathcal{O}_{\mathcal{M}}\otimes R_{\mathbb{T}}[z]$-module in general; we
shall take its completion in the next section so that it has a finite expected
rank. We shall also regard $\operatorname{Bri_{\mathbb{T}}}(F)$ as a flat
connection (i.e., D-module) over $\mathcal{M}$. First we regard it as a module
over the ring of differential operators
$\mathscr{D}=\mathcal{O}_{\mathcal{M}}[z]\left\langle
zu_{b}\frac{\partial}{\partial u_{b}}\colon b\in S\right\rangle,$
where $zu_{b}\frac{\partial}{\partial u_{b}}$ act by
$z\nabla_{u_{b}\frac{\partial}{\partial u_{b}}}$. Note that $\mathscr{D}$
contains $\mathcal{O}_{\mathcal{M}}\otimes R_{\mathbb{T}}[z]$ as its centre
via the map $\mathbf{M}_{\mathbb{C}}\ni\chi_{i}\mapsto
zx_{i}\frac{\partial}{\partial x_{i}}$. By choosing a splitting
$\big{(}\mathbb{C}^{S}\big{)}^{\star}\cong\mathbf{M}_{\mathbb{C}}\oplus\mathbb{L}_{\mathbb{C}}^{\star}$
of the extended divisor sequence (3.4) tensored with $\mathbb{C}$, we can lift
a vector field $\xi q\frac{\partial}{\partial q}$ on $\mathcal{M}$ given by
$\xi\in\mathbb{L}_{\mathbb{C}}^{\star}$ to a vector field
${\hat{\xi}}u\frac{\partial}{\partial u}=\sum\limits_{b\in
S}{\hat{\xi}}_{b}u_{b}\frac{\partial}{\partial u_{b}}$ on $\mathcal{Y}$, where
${\hat{\xi}}=\big{(}{\hat{\xi}}_{b}\big{)}_{b\in
S}\in\big{(}\mathbb{C}^{S}\big{)}^{\star}$ denotes the lift of $\xi$ under the
splitting. By this splitting, we can regard
$\operatorname{Bri_{\mathbb{T}}}(F)$ as a module over
$\mathscr{D}\cong\mathcal{O}_{\mathcal{M}}\otimes
R_{\mathbb{T}}[z]\left\langle z\xi q\frac{\partial}{\partial
q}\colon\xi\in\mathbb{L}^{\star}_{\mathbb{C}}\right\rangle.$
A different choice of splittings shifts the action of $z\xi
q\frac{\partial}{\partial q}\in\Theta_{\mathcal{M}}$ by an element of
$\mathbf{M}_{\mathbb{C}}$. When the choice of a splitting is understood, we
write $z\nabla_{\xi q\frac{\partial}{\partial q}}$ for
$z\nabla_{{\hat{\xi}}u\frac{\partial}{\partial u}}$. The grading operator
$\operatorname{Gr}$ satisfies $[\operatorname{Gr},z\nabla_{\xi
q\frac{\partial}{\partial q}}]=z\nabla_{\xi q\frac{\partial}{\partial q}}$ and
$\displaystyle\operatorname{Gr}(f(q,\chi,z)\Omega)$
$\displaystyle=\left(\left(\mathcal{E}+z\frac{\partial}{\partial
z}\right)f(q,\chi,z)\right)\Omega+f(q,\chi,z)\operatorname{Gr}(\Omega)$
for any $\Omega\in\operatorname{Bri_{\mathbb{T}}}(F)$ and
$f(q,z,\chi)\in\mathcal{O}_{\mathcal{M}}\otimes R_{\mathbb{T}}[z]$, where
$\mathcal{E}$ is the Euler vector field defined by
$\mathcal{E}=\left(\sum_{b\in S}D_{b}\right)q\frac{\partial}{\partial
q}+\sum_{i=1}^{n}\chi_{i}\frac{\partial}{\partial\chi_{i}}.$ (4.2)
Recall here that $D_{b}\in\mathbb{L}^{\star}$ is the image of
$e_{i}^{\star}\in\big{(}\mathbb{Z}^{S}\big{)}^{\star}$ under the map $D$ in
(3.4) and $\\{\chi_{1},\dots,\chi_{n}\\}$ denotes a basis of
$H^{2}_{\mathbb{T}}({\operatorname{pt}})$ so that
$R_{\mathbb{T}}=\mathbb{C}[\chi_{1},\dots,\chi_{n}]$.
###### Remark 4.2.
The Brieskorn modules here were called _Gauss–Manin systems_ in our previous
papers [27, 65]. We changed the name because the Gauss–Manin system usually
refers to the localization of the Brieskorn module by $z$; the Brieskorn
modules were also called _Brieskorn lattices_ in [37, 38, 93, 98].
###### Remark 4.3.
The action of $x_{1},\dots,x_{n}$ forgotten in the above process corresponds
to the Seidel representation (or shift operator) on quantum cohomology. This
defines the structure of a _difference module_ with respect to the
equivariant parameters $\chi_{i}$, i.e., the action of $x_{i}$ shifts
$\chi_{j}$ as $\chi_{j}\mapsto\chi_{j}-\delta_{i,j}z$ (note that we have the
commutation relation $[\chi_{i},x_{j}]=z\delta_{i,j}x_{j}$ as operators acting
on $\operatorname{Bri_{\mathbb{T}}}(F)$). See [65].
###### Remark 4.4.
As done in [27, 65], we can define the equivariant and non-equivariant
Brieskorn modules in terms of the twisted (logarithmic) de Rham complex. We
have
$\displaystyle\operatorname{Bri_{\mathbb{T}}}(F)\cong\operatorname{pr}_{*}H^{n}(\Omega^{\bullet}_{\mathcal{Y}/\mathcal{M}}[z][\chi_{1},\dots,\chi_{n}],zd+dF_{\mathbb{T}}\wedge),$
$\displaystyle\operatorname{Bri}(F)\cong\operatorname{pr}_{*}H^{n}(\Omega^{\bullet}_{\mathcal{Y}/\mathcal{M}}[z],zd+dF\wedge)$
with $F_{\mathbb{T}}=F-\sum\limits_{i=1}^{n}\chi_{i}\log x_{i}$, where
$H^{n}(-)$ means the cohomology sheaf of a complex of sheaves (not the
hypercohomology $R^{n}\operatorname{pr}_{*}$). This definition involves the
choice of co-ordinates $x_{1},\dots,x_{n}$, which corresponds to the choice of
a splitting as above. To see that the first isomorphism holds, note that the
$n$th cohomology is the cokernel of
$zd+dF_{\mathbb{T}}\wedge\colon\Omega^{n-1}_{\mathcal{Y}/\mathcal{M}}[z][\chi]\to\Omega^{n}_{\mathcal{Y}/\mathcal{M}}[z][\chi]$
and the relations given by $\operatorname{Im}(zd+dF_{\mathbb{T}}\wedge)$
define the action of $\chi_{i}$ on $\Omega^{n}_{\mathcal{Y}/\mathcal{M}}[z]$.
The second isomorphism follows from the first.
###### Remark 4.5.
Using the local co-ordinates $\mathtt{q}_{1},\dots,\mathtt{q}_{r}$, $t_{b}$
with $b\in G(\mathbf{\Sigma})$ on $\mathcal{M}$ from Section 3.5 and the
expression (3.22) for $F$, the flat connection $\nabla$ of
$\operatorname{Bri}(F)$ and $\operatorname{Bri_{\mathbb{T}}}(F)$ can be
written as
$\displaystyle\nabla_{\mathtt{q}_{i}\frac{\partial}{\partial\mathtt{q}_{i}}}(f\omega)=\left(\mathtt{q}_{i}\frac{\partial
f}{\partial\mathtt{q}_{i}}+\frac{f}{z}\sum_{b\in
S}t_{b}\lambda(b)_{i}\mathtt{q}^{\lambda(b)}x^{b}\right)\omega\qquad$
$\displaystyle(1\leq i\leq r),$ $\displaystyle\nabla_{\frac{\partial}{\partial
t_{b}}}(f\omega)=\left(\frac{\partial f}{\partial
t_{b}}+\frac{f}{z}\mathtt{q}^{\lambda(b)}x^{b}\right)\omega\qquad$
$\displaystyle(b\in G(\mathbf{\Sigma})),$
where $f\in\mathcal{O}_{\mathcal{Y}}[z]$ and $\lambda(b)_{i}$ denotes the
$i$th component of $\lambda(b)\in\boldsymbol{\Lambda}^{\mathbf{\Sigma}}$ with
respect to the chosen basis of $\boldsymbol{\Lambda}^{\mathbf{\Sigma}}$. Since
$\mathtt{q}^{\lambda(b)}x^{b}=u^{(\Psi^{\mathbf{\Sigma}}(b),b)}\in\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$,
it follows that $\nabla$ has no singularities along the divisor $t_{b}=0$ with
$b\in G(\mathbf{\Sigma})$. Therefore, a “smaller” log structure (than the one
given by toric boundaries) suffices to describe the logarithmic singularities
of $\nabla$. Note that in the equivariant case, the choice of co-ordinates
$\mathtt{q}_{i}$, $t_{b}$, $x_{i}$ determines the splitting of the extended
divisor sequence.
###### Remark 4.6.
In the non-equivariant Brieskorn module, the connection $\nabla$ and the
grading operator $\operatorname{Gr}$ together define the connection
$\nabla_{z\frac{\partial}{\partial
z}}=\operatorname{Gr}-\nabla_{\mathcal{E}}-\dim\mathfrak{X}/2$ in the
$z$-direction as in the case of non-equivariant quantum D-modules, where
$\mathcal{E}=\big{(}\sum\limits_{b\in S}D_{b}\big{)}q\frac{\partial}{\partial
q}$ denotes the non-equivariant Euler vector field. Cf. (2.11).
### 4.2 Completion and mirror isomorphism
We introduce a completion of the Brieskorn module at the large radius limit
point $0_{\mathbf{\Sigma}}\in\mathcal{M}_{\mathbf{\Sigma}}$ of
$\mathfrak{X}_{\mathbf{\Sigma}}$ (see Definition 3.7) and recall a statement
on mirror symmetry from [27].
Let $\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ be a stacky fan
adapted to $S$. Let $\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}$,
$\operatorname{Bri}(F)_{\mathbf{\Sigma}}$ denote the $\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})$-equivariant modules corresponding to
$\operatorname{Bri_{\mathbb{T}}}(F)$, $\operatorname{Bri}(F)$ on the affine
chart $\mathcal{Y}_{\mathbf{\Sigma}}\to\mathcal{M}_{\mathbf{\Sigma}}$ (see
Proposition 3.15):
$\displaystyle\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}:=\mathbb{C}[z][\mathbb{O}(\mathbf{\Sigma})_{+}]\cdot\omega,$
$\displaystyle\operatorname{Bri}(F)_{\mathbf{\Sigma}}:=\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}\big{/}\mathbf{M}_{\mathbb{C}}\cdot\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}.$
Let
$\mathfrak{m}_{\mathbf{\Sigma}}\subset\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$
denote the maximal ideal corresponding to $0_{\mathbf{\Sigma}}$, i.e., the
ideal generated by $q^{\lambda}$ with
$\lambda\in\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}\setminus\\{0\\}$.
###### Definition 4.7.
The _completed $($equivariant and non-equivariant$)$ Brieskorn modules at
$0_{\mathbf{\Sigma}}$_ are defined to be
$\displaystyle\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}:=\varprojlim_{k}\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}/\mathfrak{m}_{\mathbf{\Sigma}}^{k}\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}},$
$\displaystyle\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}:=\varprojlim_{k}\operatorname{Bri}(F)_{\mathbf{\Sigma}}/\mathfrak{m}_{\mathbf{\Sigma}}^{k}\operatorname{Bri}(F)_{\mathbf{\Sigma}}.$
The completed equivariant Brieskorn module
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}$ is a free
$R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module
of rank $\dim H^{*}_{\rm CR}(\mathfrak{X})$ [27, Theorem 4.26].
We write
$\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Spec}R_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$
and let
$\mathcal{M}_{\mathbb{T},\mathbf{\Sigma}}^{^}:=\operatorname{Spf}R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$
denote the formal neighbourhood of
$0_{\mathbf{\Sigma}}\times\operatorname{Spec}R_{\mathbb{T}}$ in
$\mathcal{M}_{\mathbb{T}}$. We regard
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$ as a
$\operatorname{Pic}^{\rm st}(\mathfrak{X})$-equivariant module over
$\mathcal{M}_{\mathbb{T},\mathbf{\Sigma}}^{^}$. We again choose a splitting
$\varsigma\colon\mathbf{N}\to\mathbb{O}^{\mathbf{\Sigma}}$ of the refined fan
sequence (3.12); via the decomposition (3.13), $\varsigma$ induces a splitting
of the extended refined fan sequence (3.11) and that of the extended divisor
sequence (3.4) over $\mathbb{C}$. As explained in the previous section
(Section 4.1), this splitting enables us to regard
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$ as a partial
connection over $\mathcal{M}_{\mathbb{T},\mathbf{\Sigma}}^{^}$. (This partial
connection was explicitly described in Remark 4.5 by choosing co-ordinates
$\mathtt{q}_{i}$, $t_{b}$, $x_{i}$ given by $\varsigma$.)
The splitting $\varsigma$ also defines a splitting
$H^{2}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})\cong
H^{2}(\mathfrak{X}_{\mathbf{\Sigma}})\oplus
H^{2}_{\mathbb{T}}({\operatorname{pt}})$ via the isomorphisms (3.6). We choose
an $R_{\mathbb{T}}$-basis $\\{\phi_{i}\\}_{i=0}^{s}$ of $H_{{\rm
CR},\mathbb{T}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$ so that the condition
(2.4) is satisfied _and_ that the splitting
$H^{2}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})\cong\bigoplus\limits_{i=1}^{r}\mathbb{C}\phi_{i}\oplus
H^{2}_{\mathbb{T}}({\operatorname{pt}})$ given by this basis is the same as
the splitting induced by $\varsigma$. This basis defines the equivariant
Kähler moduli space $\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})$ and the equivariant quantum
D-module $\operatorname{QDM}_{\mathbb{T}}(\mathfrak{X})$ (2.10), see Sections
2.2–2.3. Recall that $\operatorname{QDM}_{\mathbb{T}}(\mathfrak{X})$ is an
$H^{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Z})/\big{(}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\big{)}^{\star}$-equivariant
module over the formal neighbourhood of the origin in $\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})$; we denote this formal
neighbourhood by
$\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})^{^}:=\operatorname{Spf}R_{\mathbb{T}}\big{[}\\!\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\big{]}\\!\big{]}\big{[}\\!\big{[}\tau^{0},\tau^{r+1},\dots,\tau^{s}\big{]}\\!\big{]}.$
We have
$H^{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Z})/\big{(}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\big{)}^{\star}\cong\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})$ because
$H^{2}(\mathfrak{X}_{\mathbf{\Sigma}},\mathbb{Z})\cong\operatorname{Pic}(\mathfrak{X}_{\mathbf{\Sigma}})$
and
$\big{(}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\big{)}^{\star}\cong\operatorname{Pic}(X_{\Sigma})$
by [27, Lemma 4.8].
###### Theorem 4.8 ([27, Theorems 4.28 and 6.11]).
Let $\mathfrak{X}_{\mathbf{\Sigma}}$ be a smooth toric DM stack from
Definition 3.3. There exists a $\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})$-equivariant map $($mirror map$)$
$\operatorname{mir}\colon\mathcal{M}_{\mathbb{T},\mathbf{\Sigma}}^{^}\to\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})^{^}$ over $R_{\mathbb{T}}$ and a
$\operatorname{Pic}^{\rm st}(\mathfrak{X}_{\mathbf{\Sigma}})$-equivariant
isomorphism $($mirror isomorphism$)$
$\operatorname{Mir}\colon\
\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}\cong\operatorname{mir}^{*}\operatorname{QDM}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}}),$
such that
* (1)
$\operatorname{Mir}$ identifies the Gauss–Manin connection on
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$ with the quantum
connection on
$\operatorname{mir}^{*}\operatorname{QDM}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})$;
* (2)
$\operatorname{mir}$ preserves the Euler vector fields
$\operatorname{mir}_{*}(\mathcal{E})=\mathcal{E}$ $($see (2.7), (4.2)$)$ and
$\operatorname{Mir}$ intertwines the grading operators
$\operatorname{Gr}\circ\operatorname{Mir}=\operatorname{Mir}\circ\operatorname{Gr}$
$($see (2.8), (4.1)$)$;
* (3)
$\operatorname{Mir}$ identifies the higher residue pairing $($see [27, Section
6] and Section $\ref{subsubsec:higher_residue})$ with the pairing $P$ (2.9)
induced by the orbifold Poincaré pairing.
###### Remark 4.9.
The mirror map $\operatorname{mir}$ and the mirror isomorphism
$\operatorname{Mir}$ are obtained from those in [27] by the restriction to
$y_{1}=\cdots=y_{m}=1$. See also Remark 3.16.
###### Remark 4.10 ([62, (60)]).
We have
$\mathcal{M}_{\mathbb{T},\mathbf{\Sigma}}^{^}\cong\operatorname{Spf}\big{(}R_{\mathbb{T}}\big{[}\\!\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\big{]}\\!\big{]}\big{)}\times\big{(}\mathbb{C}^{G(\mathbf{\Sigma})},0\big{)}^{^}$
by (3.21). Writing $(\mathtt{q},t=\\{t_{v}\\}_{v\in G(\mathbf{\Sigma})})$ for
the co-ordinates on $\mathcal{M}_{\mathbb{T},\mathbf{\Sigma}}^{^}$ as in
Section 3.5, we have that the mirror map
$(\mathtt{q},t)\mapsto\big{(}\hat{\mathtt{q}},\tau^{\prime}=\tau^{0}\phi_{0}+\sum\limits_{i=r+1}^{s}\tau^{i}\phi_{i}\big{)}$
has the following asymptotic form
$\displaystyle\sum_{i=1}^{r}\phi_{i}\log\hat{\mathtt{q}}_{i}+\tau^{\prime}=\sum_{i=1}^{r}\phi_{i}\log\mathtt{q}_{i}+\sum_{v\in
G(\mathbf{\Sigma})}t_{v}\mathfrak{D}_{v}+O\big{(}\mathtt{q},t^{2}\big{)},$
where
$\displaystyle\mathfrak{D}_{v}=\prod_{b\in
R(\mathbf{\Sigma})}\overline{D}_{b}^{\lfloor\Psi_{b}(v)\rfloor}\boldsymbol{1}_{\langle
v\rangle}\qquad\text{with}\quad\langle v\rangle=v-\sum_{b\in
R(\mathbf{\Sigma})}\lfloor\Psi_{b}(v)\rfloor
b\in\operatorname{Box}(\mathbf{\Sigma}).$
Here we assumed that
$\\{\phi_{i}\\}_{i=1}^{r}\subset\big{(}\mathbb{L}^{\mathbf{\Sigma}}_{\mathbb{C}}\big{)}^{\star}$
is chosen to be a $\mathbb{Z}$-basis of
$\big{(}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\big{)}^{\star}$ and that its
dual basis defines co-ordinates $\mathtt{q}_{i}$, $i=1,\dots,r$ as in Section
3.5; $O\big{(}\mathtt{q},t^{2}\big{)}$ denotes an element of the ideal
generated by $\mathtt{q}^{\lambda}$
$\big{(}\lambda\in\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\setminus\\{0\\}\big{)}$
and $t_{b_{1}}t_{b_{2}}$ ($b_{1},b_{2}\in G(\mathbf{\Sigma})$).
The above mirror isomorphism shows that
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$ is a free
$R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module
of rank $\dim H_{{\rm CR}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$. This fact
shows the following two propositions. The first one proves a non-equivariant
version of Theorem 4.8.
###### Proposition 4.11.
We have an isomorphism
$\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}\cong\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}^{^}/\mathbf{M}_{\mathbb{C}}\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}^{^}.$
In particular, the completed Brieskorn module
$\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}$ is a free module of rank $\dim
H^{*}_{{\rm CR}}(\mathfrak{X})$ over
$\mathbb{C}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$ and we have
a non-equivariant mirror isomorphism
$\operatorname{Mir}|_{\chi=0}\colon\
\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}\cong\operatorname{mir}^{*}\operatorname{QDM}(\mathfrak{X}_{\mathbf{\Sigma}}),$
where $\operatorname{mir}$ denotes the non-equivariant limit of the mirror map
in Theorem 4.8.
###### Proof.
We apply Lemma 4.13 below to
$K=\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$,
$I=\mathfrak{m}_{\mathbf{\Sigma}}$,
$N=\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}^{\oplus n}$,
$M=\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}$ and the map
$f=\bigoplus\limits_{i=1}^{n}\chi_{i}$. Then we find that
$\operatorname{Cok}(f)^{^}=\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}$ is the
$\mathfrak{m}_{\mathbf{\Sigma}}$-adic completion of
$\operatorname{Cok}(\hat{f})=\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}^{^}/\mathbf{M}_{\mathbb{C}}\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}^{^}$.
On the other hand, $\operatorname{Cok}(\hat{f})$ is a free
$\mathbb{C}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module of
finite rank, and in particular $\mathfrak{m}_{\mathbf{\Sigma}}$-adically
complete. This proves the proposition. ∎
###### Proposition 4.12.
We have
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}\cong\varprojlim_{k}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]/\mathfrak{m}_{\mathbf{\Sigma}}^{k}.$
###### Proof.
We apply Lemma 4.13 to
$K=\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$,
$I=\mathfrak{m}_{\mathbf{\Sigma}}$,
$N=M=\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}$ and the map $f=z$.
Then we find that the $\mathfrak{m}_{\mathbf{\Sigma}}$-adic completion of
$\operatorname{Cok}(f)=\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ is
isomorphic to the $\mathfrak{m}_{\mathbf{\Sigma}}$-adic completion of
$\operatorname{Cok}(\hat{f})=\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$.
Here $\operatorname{Cok}(\hat{f})$ is a free
$R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module of
finite rank, and in particular $\mathfrak{m}_{\mathbf{\Sigma}}$-adically
complete. The conclusion follows. ∎
###### Lemma 4.13.
Let $K$ be a ring and $I\subset K$ be a finitely generated ideal. Let $N$, $M$
be $K$-modules and $f\colon N\to M$ be a homomorphism of $K$-modules. Let
$\widehat{N}$, $\widehat{M}$ denote the $I$-adic completions of $N$ and $M$
respectively and let $\hat{f}\colon\widehat{N}\to\widehat{M}$ denote the
induced homomorphism. Then the $I$-adic completion of $\operatorname{Cok}(f)$
is isomorphic to the $I$-adic completion of $\operatorname{Cok}(\hat{f})$.
###### Proof.
Since $I$ is finitely generated, we have $\widehat{N}/I^{k}\widehat{N}\cong
N/I^{k}N$ and $\widehat{M}/I^{k}\widehat{M}\cong M/I^{k}M$ (see [103, Lemma
05GG]). Therefore the exact sequences $N\to M\to\operatorname{Cok}(f)\to 0$
and $\widehat{N}\to\widehat{M}\to\operatorname{Cok}(\hat{f})\to 0$ imply (by
the right-exactness of $\otimes_{K}(K/I^{k})$) that
$\operatorname{Cok}(f)/I^{k}\operatorname{Cok}(f)\cong\operatorname{Cok}(\hat{f})/I^{k}\operatorname{Cok}(\hat{f})$.
The conclusion follows. ∎
###### Remark 4.14 (cf. Remark 4.4).
In [27, 65], the completed Brieskorn modules are described as twisted de Rham
cohomology. We have
$\displaystyle\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}\cong\operatorname{pr}_{*}H^{n}(\Omega^{\bullet}_{\mathcal{Y}/\mathcal{M}}[z]^{^}\
[\chi_{1},\dots,\chi_{n}],zd+dF_{\mathbb{T}}\wedge),$
$\displaystyle\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}\cong\operatorname{pr}_{*}H^{n}(\Omega^{\bullet}_{\mathcal{Y}/\mathcal{M}}[z]^{^}\
,zd+dF\wedge),$
where ^ means the $\mathfrak{m}_{\mathbf{\Sigma}}$-adic completion. These
isomorphisms follow from the same argument as in Remark 4.4. Note that
$(\Omega^{\bullet}_{\mathcal{Y}/\mathcal{M}}[z]^{^}\ ,zd+dF\wedge)$ is the
Koszul complex associated with the action of $\chi_{1},\dots,\chi_{n}$ on
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}=\mathcal{O}_{\mathcal{Y}}[z]^{^}\cdot\omega$.
Since we know that $\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$
is a free
$R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module,
$\chi_{1},\dots,\chi_{n}$ form a regular sequence for the module
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$. Thus we have
$H^{i}(\Omega^{\bullet}_{\mathcal{Y}/\mathcal{M}}[z]^{^}\
,zd+dF\wedge)=0\qquad\text{for $i\neq n$.}$
Therefore, we have $\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}\cong
R^{n}\operatorname{pr}_{*}(\Omega^{\bullet}_{\mathcal{Y}/\mathcal{M}}[z]^{^}\
,zd+dF\wedge)$.
### 4.3 Analytification of the completed Brieskorn module
In this section, we construct an analytification of the completed Brieskorn
module. There is a trade-off111111By the convergence result from [26] reviewed
in Section 4.4, we can make the analytified Brieskorn module fully analytic
both in the $\mathcal{M}_{\mathbb{T}}$-direction and in the $z$-direction; the
full analytification is given by the analytic quantum D-module. This analytic
structure is in general different from that of the original (algebraic)
Brieskorn module; the gauge transformation $(M_{i}^{j}(q,\chi,z))$ (see Part
(b) in Section 4.4) connecting the Brieskorn module and the quantum D-module
is only a formal power series in $z$. This stems from the fact that the
(extended) $I$-function [26] is not necessarily convergent: see [59,
Proposition 5.13] for a relevant statement in the non-weak-Fano case. between
the analyticity along
$\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$ and
that along the $z$-plane: the analytified Brieskorn module is analytic in the
$\mathcal{M}_{\mathbb{T}}$-direction but formal in the variable $z$.
#### 4.3.1 Analytification of algebras
First we study the restriction of $\operatorname{Bri_{\mathbb{T}}}(F)$ to
$z=0$. By definition,
$\operatorname{Bri_{\mathbb{T}}}(F)/z\operatorname{Bri_{\mathbb{T}}}(F)$ is
isomorphic to $\mathcal{O}_{\mathcal{Y}}$ and the
$R_{\mathbb{T}}\otimes\mathcal{O}_{\mathcal{M}}$-module structure on it is
induced by the map
$\widetilde{\operatorname{pr}}:=\left(\operatorname{pr},x_{1}\frac{\partial
F}{\partial x_{1}},\dots,x_{n}\frac{\partial F}{\partial x_{n}}\right)\colon\
\mathcal{Y}\to\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T},$
(4.3)
where $\operatorname{Lie}\mathbb{T}=\operatorname{Spec}R_{\mathbb{T}}$ is
identified with $\mathbb{C}^{n}$ via the basis $\chi_{1},\dots,\chi_{n}$
chosen in Section 4.1. Let
$\tilde{0}=\tilde{0}_{\mathbf{\Sigma}}\in\mathcal{Y}_{\mathbf{\Sigma}}\subset\mathcal{Y}$
denote the (unique) torus-fixed point on the chart
$\mathcal{Y}_{\mathbf{\Sigma}}$ such that
$\operatorname{pr}(\tilde{0}_{\mathbf{\Sigma}})=0_{\mathbf{\Sigma}}$: it is
defined by $u^{(\lambda,v)}=0$ for all non-torsion elements
$(\lambda,v)\in\mathbb{O}(\mathbf{\Sigma})_{+}$. On the uniformizing chart
$\operatorname{Spec}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ of
$\mathcal{Y}_{\mathbf{\Sigma}}$, $\tilde{0}_{\mathbf{\Sigma}}$ corresponds to
$|\mathbf{N}_{\rm tor}|$ many points $\mathbf{N}_{\rm
tor}^{^}\cong\operatorname{Spec}\mathbb{C}[\mathbf{N}_{\rm tor}]$ which form a
single $\operatorname{Pic}^{\rm st}(\mathfrak{X}_{\mathbf{\Sigma}})$-orbit
(recall the sequence (3.19)). We mean by $\tilde{0}_{\mathbf{\Sigma}}$ either
a single point in $\mathcal{Y}_{\mathbf{\Sigma}}$ or the corresponding finite
subset in $\operatorname{Spec}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$
depending on the context. We have
$\widetilde{\operatorname{pr}}(\tilde{0}_{\mathbf{\Sigma}})=(0_{\mathbf{\Sigma}},0)$.
_In order to avoid the heavy notation, in this Section 4.3, we will sometimes
omit the subscript $\mathbf{\Sigma}$ for $0_{\mathbf{\Sigma}}$ and
$\tilde{0}_{\mathbf{\Sigma}}$, writing $0\in\mathcal{M}_{\mathbf{\Sigma}}$ for
$0_{\mathbf{\Sigma}}$ and $\tilde{0}\in\mathcal{Y}_{\mathbf{\Sigma}}$ for
$\tilde{0}_{\mathbf{\Sigma}}$_.
###### Lemma 4.15.
The set-theoretic fibre of $\widetilde{\operatorname{pr}}$ at $(0,0)$ is
$\tilde{0}$, i.e., $\tilde{0}=\widetilde{\operatorname{pr}}^{-1}(0,0)$.
###### Proof.
Note that
$x_{i}\frac{\partial F}{\partial x_{i}}=\sum_{b\in S}(\chi_{i}\cdot
b)u_{b}\in\sum_{b\in R(\mathbf{\Sigma})}(\chi_{i}\cdot
b)u_{b}+\mathfrak{m}_{\mathbf{\Sigma}}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}],$
since $t_{b}\in\mathfrak{m}_{\mathbf{\Sigma}}$ for $b\in G(\mathbf{\Sigma})$
(see (3.22)). Therefore the scheme theoretic fibre at $(0,0)$ is the spectrum
of
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]\Big{/}\bigg{(}\mathfrak{m}_{\mathbf{\Sigma}}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]+\bigg{\langle}\sum\limits_{b\in
R(\mathbf{\Sigma})}(\chi_{i}\cdot b)u_{b}\colon 1\leq i\leq
n\bigg{\rangle}\bigg{)}.$ (4.4)
By Remark 3.17, we have
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]\Big{/}\mathfrak{m}_{\mathbf{\Sigma}}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]\cong\bigoplus_{v\in\mathbf{N}\cap\Pi}\mathbb{C}w_{v}\qquad\text{with
$w_{v}:=\big{[}u^{(\Psi^{\mathbf{\Sigma}}(\overline{v}),v)}\big{]}$},$
where $\Psi^{\mathbf{\Sigma}}$ is given in Notation 3.10 and the product on
the right-hand side is given by
$w_{v_{1}}\cdot w_{v_{2}}=\begin{cases}w_{v_{1}+v_{2}},&\text{if $v_{1}$,
$v_{2}$ lie in the same cone of $\Sigma$},\\\ 0,&\text{otherwise}.\end{cases}$
It follows that the ring (4.4) is precisely the presentation of the orbifold
cohomology ring $H_{{\rm CR}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$ due to
Borisov–Chen–Smith [14]. Since elements in $H_{{\rm
CR}}^{>0}(\mathfrak{X}_{\mathbf{\Sigma}})$ are nilpotent, the set-theoretical
fibre at $(0,0)$ equals $\operatorname{Spec}(H_{\rm
CR}^{0}(\mathfrak{X}_{\mathbf{\Sigma}}))\cong\operatorname{Spec}(\mathbb{C}[\mathbf{N}_{\rm
tor}])=\tilde{0}$. ∎
We use the following elementary lemma on general topology.
###### Lemma 4.16.
Let $X$ and $Y$ be locally compact Hausdorff spaces and let $f\colon X\to Y$
be a continuous map. Let $y_{0}\in Y$ be such that $f^{-1}(y_{0})$ is compact.
Then
* (1)
there exist an open neighbourhood $B$ of $f^{-1}(y_{0})$ and an open
neighbourhood $U$ of $y_{0}$ such that $f(B)\subset U$ and $f|_{B}\colon B\to
U$ is proper;
* (2)
the family of open sets $\\{f^{-1}(V)\cap B\colon\text{$V$ is an open
neighbourhood of $y_{0}$}\\}$ is a fundamental neighbourhood system of
$f^{-1}(y_{0})$.
###### Proof.
Since $X$ is locally compact, we can find a relatively compact open
neighbourhood $C$ of $f^{-1}(y_{0})$. Then $\overline{C}\setminus C$ is
compact and hence $f(\overline{C}\setminus C)$ is a compact set not containing
$y_{0}$. Since $Y$ is Hausdorff, $f(\overline{C}\setminus C)$ is closed; thus
there exists an open neighbourhood $U$ of $y_{0}$ such that $U\cap
f(\overline{C}\setminus C)=\varnothing$. Then one sees easily that
$f^{-1}(U)\cap C=f^{-1}(U)\cap\overline{C}$. For every compact subset $K$ in
$U$, we have that $f^{-1}(K)\cap C=f^{-1}(K)\cap\overline{C}$ is compact. This
shows that $f|_{C\cap f^{-1}(U)}$ is proper. It now suffices to set $B=C\cap
f^{-1}(U)$ to conclude Part (1).
To see Part (2), take an open neighbourhood $W\subset B$ of $f^{-1}(y_{0})$.
Then $B\setminus W$ is closed in $B$. Since proper maps between locally
compact Hausdorff spaces are closed, $f(B\setminus W)$ is closed in $U$ and
does not contain $y_{0}$. Thus there exists an open neighbourhood $V\subset U$
of $y_{0}$ such that $V\cap f(B\setminus W)=\varnothing$. Then $f^{-1}(V)\cap
B\subset W$ and Part (2) follows. ∎
###### Lemma 4.17.
There exist an analytic open neighbourhood $\mathcal{B}$ of $\tilde{0}$ in
$\mathcal{Y}_{\mathbf{\Sigma}}$ and an analytic open neighbourhood
$\mathcal{U}$ of $(0,0)$ in
$\mathcal{M}_{\mathbf{\Sigma}}\times\operatorname{Lie}\mathbb{T}\subset\mathcal{M}_{\mathbb{T}}$
such that $\widetilde{\operatorname{pr}}(\mathcal{B})\subset\mathcal{U}$ and
that the map
$\widetilde{\operatorname{pr}}|_{\mathcal{B}}\colon\mathcal{B}\to\mathcal{U}$
is proper. Moreover, for any sheaf $\mathcal{F}$ on $\mathcal{B}$ $($with
respect to the complex-analytic topology$)$, we have
$(\widetilde{\operatorname{pr}}_{*}\mathcal{F})_{(0,0)}=\mathcal{F}_{\tilde{0}}$,
where $(\widetilde{\operatorname{pr}}_{*}\mathcal{F})_{(0,0)}$ and
$\mathcal{F}_{\tilde{0}}$ denote the stalks respectively at $(0,0)$ and
$\tilde{0}$.
###### Proof.
We apply Lemma 4.16 for $f=\widetilde{\operatorname{pr}}$, $X=\mathcal{Y}$,
$Y=\mathcal{M}_{\mathbb{T}}$ and $y_{0}=(0,0)$. Note that Lemma 4.15 gives
$f^{-1}(y_{0})=\tilde{0}$. The former statement follows from Part (1) of Lemma
4.16 and the latter statement on stalks follows from Part (2). ∎
We will use the notation $\mathcal{O}^{\rm an}$ to denote the complex-analytic
structure sheaf. The following lemma shows that
$\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm an}_{\mathcal{B}}$ (which
is coherent by Grauert’s direct image theorem) gives an analytification of
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$.
###### Lemma 4.18.
Let $\mathcal{B}\subset\mathcal{Y}$ and
$\mathcal{U}\subset\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$
be as in Lemma 4.17. $($They are analytic open neighbourhoods of $\tilde{0}$
and $(0,0)$ respectively.$)$ Let
$(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})_{(0,0)}^{^}$ denote the completion of
$\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm an}_{\mathcal{B}}$ at
$(0,0)\in\mathcal{U}$. We have
$(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})_{(0,0)}^{^}\cong\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}\cong\left(\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}\right)\otimes_{R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]}\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}.$
(4.5)
Here $\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$ is the completion of
$\mathcal{O}^{\rm an}_{\mathcal{U}}$ at $(0,0)$ and
$\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}$ is the completion of
$\mathcal{O}_{\mathcal{Y}}$ at $\tilde{0}$; more explicitly, they are
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}=\widehat{R_{\mathbb{T}}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!],\qquad\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}=\mathbb{C}[\\![\mathbb{O}(\mathbf{\Sigma})_{+}]\\!],$
where $\widehat{R_{\mathbb{T}}}=\mathbb{C}[\\![\chi_{1},\dots,\chi_{n}]\\!]$
is the completion of $R_{\mathbb{T}}=\mathbb{C}[\chi_{1},\dots,\chi_{n}]$, and
for a ring $K$, $K[\\![\mathbb{O}(\mathbf{\Sigma})_{+}]\\!]$ denotes the
completion of $K[\mathbb{O}(\mathbf{\Sigma})_{+}]$ with respect to the ideal
generated by $u^{(\lambda,v)}$ with non-torsion
$(\lambda,v)\in\mathbb{O}(\mathbf{\Sigma})_{+}$.
###### Proof.
We show that the natural maps
$\displaystyle(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})_{(0,0)}^{^}\to\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}},$
(4.6)
$\displaystyle\left(\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}\right)\otimes_{R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]}\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}\to\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}$
(4.7)
are isomorphisms. First we prove that the map (4.6) is an isomorphism. The
left-hand side of (4.6) is the $\mathfrak{m}^{\rm an}_{(0,0)}$-adic completion
of $(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})_{(0,0)}$, where $\mathfrak{m}^{\rm
an}_{(0,0)}\subset\mathcal{O}^{\rm an}_{\mathcal{U},(0,0)}$ is the ideal of
$(0,0)$. Recall from Lemma 4.15 that the set-theoretic fibre of
$\widetilde{\operatorname{pr}}$ at $(0,0)$ is $\tilde{0}$; also from Lemma
4.17 that $(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})_{(0,0)}=\mathcal{O}^{\rm an}_{\mathcal{B},\tilde{0}}$.
Therefore the ideal $\mathfrak{m}^{\rm an}_{\tilde{0}}\subset\mathcal{O}^{\rm
an}_{\mathcal{B},\tilde{0}}$ of $\tilde{0}$ is the radical of the ideal
generated by $\mathfrak{m}^{\rm an}_{(0,0)}$, and the $\mathfrak{m}^{\rm
an}_{(0,0)}$-adic topology on
$(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})_{(0,0)}=\mathcal{O}^{\rm an}_{\mathcal{B},\tilde{0}}$ is
equivalent to the $\mathfrak{m}^{\rm an}_{\tilde{0}}$-adic topology on the
same space. The completion with respect to the latter topology equals
$\widehat{\mathcal{O}}_{\mathcal{B},\tilde{0}}=\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}$.
We prove similarly that the map (4.7) is an isomorphism. Recall that
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$
is a finite free
$R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module by
Theorem 4.8. Also $\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$ is the
completion of
$R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$ with
respect to the ideal $\widehat{\mathfrak{m}}_{(0,0)}$ generated by
$\chi_{1},\dots,\chi_{n}$ and $\mathfrak{m}_{\mathbf{\Sigma}}$. Therefore the
left-hand side of (4.7) is the $\widehat{\mathfrak{m}}_{(0,0)}$-adic
completion of
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$
(see, e.g., [103, Lemma 00MA]). Moreover
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$
is the $\mathfrak{m}_{\mathbf{\Sigma}}$-adic completion of
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ by Proposition 4.12.
Thus121212Here we used the following fact. Let $I\subset J$ be ideals of a
ring $R$, let $M$ be an $R$-module and assume that $I$ is finitely generated.
Let $M^{^}_{I}$ denote the $I$-adic completion of $M$ and let
$(M^{^}_{I})^{^}_{J}$ denote the $J$-adic completion of $M^{^}_{I}$. Then
$(M^{^}_{I})^{^}_{J}\cong M^{^}_{J}$. This follows from
$M^{^}_{I}/J^{k}M^{^}_{I}\cong(M^{^}_{I}/I^{k}M^{^}_{I})/J^{k}(M^{^}_{I}/I^{k}M^{^}_{I})\cong(M/I^{k})/J^{k}(M/I^{k})\cong
M/J^{k}M$ (where we used [103, Lemma 05GG] in the middle step). the left-hand
side of (4.7) is the $\mathfrak{m}_{(0,0)}$-adic completion of
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$, where
$\mathfrak{m}_{(0,0)}:=\mathfrak{m}_{\mathbf{\Sigma}}+(\chi_{1},\dots,\chi_{n})$
is an ideal of $R_{\mathbb{T}}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$.
Again Lemma 4.15 implies that the $\mathfrak{m}_{(0,0)}$-adic completion of
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ equals the
$\mathfrak{m}_{\tilde{0}}$-adic completion of it, where
$\mathfrak{m}_{\tilde{0}}\subset\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$
is the ideal of $\tilde{0}$. This shows that the map (4.7) is an isomorphism.
The lemma is proved. ∎
Because
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}/z\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$
is a free
$R_{\mathbb{T}}[\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module of
rank $\dim H_{{\rm CR}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$ (by Theorem 4.8),
we have the following corollary.
###### Corollary 4.19.
The modules (4.5) are free $\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$-modules
of rank $\dim H_{\rm CR}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$.
###### Corollary 4.20.
Let $\mathcal{B}\subset\mathcal{Y}$ and
$\mathcal{U}\subset\mathcal{M}_{\mathbb{T}}$ be as in Lemma 4.17. By shrinking
$\mathcal{B}$, $\mathcal{U}$ if necessary, we have that
$\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm an}_{\mathcal{B}}$ is a
locally free $\mathcal{O}^{\rm an}_{\mathcal{U}}$-module of rank $\dim H_{{\rm
CR}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$. In particular,
$\widetilde{\operatorname{pr}}\colon\mathcal{B}\to\mathcal{U}$ is a finite
flat morphism.
###### Proof.
Note that $\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}}$ is a coherent $\mathcal{O}^{\rm an}_{\mathcal{U}}$-module
by Grauert’s Direct Image Theorem and Lemma 4.17. Thus it suffices to show
that the stalk $(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})_{(0,0)}$ is a free $\mathcal{O}^{\rm
an}_{\mathcal{U},(0,0)}$-module of rank $\dim H_{{\rm
CR}}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$. By Corollary 4.19, we know that the
completion $(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}})^{^}_{(0,0)}$ is a free
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$-module of rank $\dim H_{\rm
CR}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$. The conclusion follows from the
following (probably) well-known fact: for a Noetherian local ring
$(A,\mathfrak{m})$ and a finite $A$-module $M$, $M$ is a free $A$-module of
rank $r$ if and only if its $\mathfrak{m}$-adic completion
$\widehat{M}=M\otimes_{A}\widehat{A}$ is a free $\widehat{A}$-module of rank
$r$. This follows, for instance, by combining the fact that a finite flat
module over a local ring is free, [82, Theorem 22.4(1)] and
$M/\mathfrak{m}M\cong\widehat{M}/\mathfrak{m}\widehat{M}$. ∎
#### 4.3.2 Analytification of D-modules
Next we construct an extension of the completed Brieskorn module
$\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}^{^}$ to an analytic
neighbourhood of
$(0_{\mathbf{\Sigma}},0)\in\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$.
Let $\mathcal{U}\subset\mathcal{M}_{\mathbb{T}}$ and
$\mathcal{B}\subset\mathcal{Y}$ denote analytic open neighbourhoods of
$(0,0)=(0_{\mathbf{\Sigma}},0)$ and $\tilde{0}=\tilde{0}_{\mathbf{\Sigma}}$
respectively as in Corollary 4.20. Recall that
$\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm an}_{\mathcal{B}}$ is a
locally free $\mathcal{O}^{\rm an}_{\mathcal{U}}$-module by Corollary 4.20.
###### Definition 4.21 (cf. Definition 4.1).
Let $\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ be a stacky fan
adapted to $S$.
1. (1)
The _analytified equivariant Brieskorn module_ around the limit point
$0=0_{\mathbf{\Sigma}}$ is the sheaf over $\mathcal{U}$
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}:=\widetilde{\operatorname{pr}}_{*}\left(\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!]\right)\cdot\omega.$
We equip
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ with an
$\mathcal{O}^{\rm an}_{\mathcal{U}}[\\![z]\\!]$-module structure by the
formula
$\chi_{i}\cdot(f\omega)=\left(x_{i}\frac{\partial F}{\partial
x_{i}}f+zx_{i}\frac{\partial f}{\partial x_{i}}\right)\omega$ (4.8)
for $f\in\widetilde{\operatorname{pr}}_{*}(\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!])$, together with the usual multiplication of
functions in $q$ and $z$ (where $\chi_{i}$ is a co-ordinate on
$\operatorname{Lie}\mathbb{T}$ and $q$ is a co-ordinate on $\mathcal{M}$, see
Sections 3.5 and 4.1). A flat connection $\nabla=d+d(F/z)\wedge$ on
$\mathcal{O}^{\rm an}_{\mathcal{B}}[\\![z]\\!]$ induces, via the choice of a
splitting
$\big{(}\mathbb{C}^{S}\big{)}^{\star}\cong\mathbf{M}_{\mathbb{C}}\oplus\mathbb{L}_{\mathbb{C}}^{\star}$
of the extended divisor sequence (3.4) over $\mathbb{C}$, a partial
(logarithmic) flat connection on
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$
$\nabla\colon\
\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\to
z^{-1}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)\otimes_{\mathcal{O}^{\rm
an}_{\mathcal{U}}}\Omega^{1,\rm
an}_{\mathcal{U}/\operatorname{Lie}\mathbb{T}}$
in the direction of $\mathcal{M}$, see the discussion after Definition 4.1. A
_grading operator_
$\operatorname{Gr}\in\operatorname{End}_{\mathbb{C}}(\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}})$
is defined as before
$\operatorname{Gr}(f\omega)=\left(z\frac{\partial f}{\partial z}+\sum_{b\in
S}u_{b}\frac{\partial f}{\partial u_{b}}\right)\omega.$
2. (2)
The (non-equivariant) _analytified Brieskorn module_
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$ around the limit
point $0$ is defined to be the restriction of
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ to
$\mathcal{V}=(\mathcal{M}\times\\{0\\})\cap\mathcal{U}$. It is equipped with
the flat connection
$\nabla\colon\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\to
z^{-1}\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\otimes\Omega^{1,\rm
an}_{\mathcal{V}}$ (independent of the choice of a splitting) and the grading
operator
$\operatorname{Gr}\in\operatorname{End}_{\mathbb{C}}\big{(}\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}$.
The connection $\nabla$ and $\operatorname{Gr}$ together give a flat
connection in the $z$-direction as in Remark 4.6.
###### Remark 4.22.
The overline for
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$,
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$ indicates that
they are completed in the $z$-adic topology. Note also that these analytified
Brieskorn modules depend on the choice of
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$.
###### Remark 4.23.
The $\mathcal{O}^{\rm an}_{\mathcal{U}}\\![\\![z]\\!]$-module structure on
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ is not
a standard one on $\widetilde{\operatorname{pr}}_{*}\\!(\mathcal{O}^{\rm
an}_{\mathcal{B}}\\![\\![z]\\!])\omega.\\!$ A more precise definition of the
module structure is described as follows: we let a function
$h=h(q,\chi_{1},\dots,\chi_{n},z)\in\mathcal{O}^{\rm
an}_{\mathcal{U}}[\\![z]\\!]$ act on a section $f(q,x,z)\omega$ of
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ as
$h\cdot(f\omega)=\left[h\left(q,x_{1}\frac{\partial F}{\partial
x_{1}}+zx_{1}\frac{\partial}{\partial x_{1}},\dots,x_{n}\frac{\partial
F}{\partial x_{n}}+zx_{n}\frac{\partial}{\partial
x_{n}},z\right)f(q,x,z)\right]\omega,$
where in the right-hand side we expand $h\big{(}q,\textstyle
x_{1}\frac{\partial F}{\partial x_{1}}+zx_{1}\frac{\partial}{\partial
x_{1}},\dots,x_{n}\frac{\partial F}{\partial
x_{n}}+zx_{n}\frac{\partial}{\partial x_{n}},z\big{)}$ in power series of
$zx_{i}\frac{\partial}{\partial x_{i}}$ and apply it to $f$. Note that
$h\big{(}q,x_{1}\frac{\partial F}{\partial x_{1}},\dots,x_{n}\frac{\partial
F}{\partial x_{n}},z\big{)}$ is the pull-back of
$h(q,\chi_{1},\dots,\chi_{n},z)$ under $\widetilde{\operatorname{pr}}$ since
$x_{i}\frac{\partial F}{\partial
x_{i}}=\widetilde{\operatorname{pr}}^{*}(\chi_{i})$. The action is well-
defined, since we allow any formal power series in $z$.
###### Proposition 4.24.
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ is a
locally free $\mathcal{O}^{\rm an}_{\mathcal{U}}[\\![z]\\!]$-module of rank
$\dim H^{*}_{{\rm CR}}(\mathfrak{X}_{\mathbf{\Sigma}})$. In particular
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$ is a locally free
$\mathcal{O}^{\rm an}_{\mathcal{V}}[\\![z]\\!]$-module of the same rank.
###### Proof.
This follows from Corollary 4.20. Recall that the $\mathcal{O}^{\rm
an}_{\mathcal{U}}[\\![z]\\!]$-module structure on
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ equals
the standard one on
$\operatorname{pr}_{*}(\mathcal{O}_{\mathcal{B}}[\\![z]\\!])$ modulo $z$. We
show that any local basis $s_{1},\dots,s_{N}$ of
$\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm an}_{\mathcal{B}}$ over
$\mathcal{O}^{\rm an}_{\mathcal{U}}$ gives rise to a local basis of
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ over
$\mathcal{O}^{\rm an}_{\mathcal{U}}[\\![z]\\!]$. That $s_{1},\dots,s_{N}$
generate $\operatorname{Bri_{\mathbb{T}}}(F)_{\mathbf{\Sigma}}$ over
$\mathcal{O}^{\rm an}_{\mathcal{U}}[\\![z]\\!]$ follows from the following
fact. Let $K$ be a ring with an ideal $\mathfrak{m}$ and let $M$ be a
$K$-module. Suppose that $K$ is $\mathfrak{m}$-adically complete and $M$ is
Hausdorff with respect to the $\mathfrak{m}$-adic topology, that is,
$\bigcap\limits_{i\geq 0}\mathfrak{m}^{i}M=\\{0\\}$. If $s_{1},\dots,s_{N}\in
K$ generate $M/\mathfrak{m}M$ over $K/\mathfrak{m}$, then $s_{1},\dots,s_{N}$
generate $M$ over $K$. See for instance [108, Corollary 2, Section 3, Chapter
VIII]. We apply this fact for $K=\mathcal{O}^{\rm
an}_{\mathcal{U}}[\\![z]\\!]$, $\mathfrak{m}=zK$,
$M=\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$. On
the other hand, suppose we have a relation $\sum\limits_{i=1}^{N}c_{i}s_{i}=0$
with $c_{i}\in\mathcal{O}^{\rm an}_{\mathcal{U}}[\\![z]\\!]$ and
$(c_{1},\dots,c_{N})\neq 0$. Setting
$c_{i}=c_{i,m}z^{m}+O\big{(}z^{m+1}\big{)}$ for some $m\geq 0$ and
$c_{i,m}\in\mathcal{O}^{\rm an}_{\mathcal{U}}$ with
$(c_{1,m},\dots,c_{N,m})\neq 0$, we obtain a non-trivial relation
$\sum\limits_{i=1}^{N}c_{i,m}s_{i}=0$ in
$\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm an}_{\mathcal{B}}$ over
$\mathcal{O}^{\rm an}_{\mathcal{U}}$. This is a contradiction. Thus
$s_{1},\dots,s_{N}$ are linearly independent over $\mathcal{O}^{\rm
an}_{\mathcal{U}}[\\![z]\\!]$. ∎
The next proposition shows that
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ is an
analytification of $\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$
(and thus justifies the name).
###### Proposition 4.25 (cf. Lemma 4.18).
Let
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}_{(0,0)}^{^}$
denote the $\mathfrak{m}^{\rm an}_{(0,0)}$-adic completion of
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}_{(0,0)}$,
where $\mathfrak{m}^{\rm an}_{(0,0)}\subset\mathcal{O}^{\rm
an}_{\mathcal{U},(0,0)}$ is the ideal of $(0,0)$. Then
* (1)
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}_{(0,0)}^{^}$
has the structure of an
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$-module;
* (2)
we have an isomorphism of (finite, free)
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$-modules
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}_{(0,0)}^{^}\cong\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}[\\![z]\\!]\cong\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}\otimes_{R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]}\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!],$
where $\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$ and
$\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}$ are as in Lemma 4.18. In Part
$(2)$, the $\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$-module
structure on $\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}[\\![z]\\!]$ is
defined similarly to Definition 4.21: $\chi_{i}$ acts on it by the formula
(4.8) and functions in $q$ and $z$ act in the usual way $($see also Remark
$\ref{rem:module_structure})$.
###### Proof.
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}^{^}_{(0,0)}$
is naturally a module over the completion $(\mathcal{O}^{\rm
an}_{\mathcal{U}}[\\![z]\\!])^{^}_{(0,0)}$ of $(\mathcal{O}^{\rm
an}_{\mathcal{U}}[\\![z]\\!])_{(0,0)}$ with respect to $\mathfrak{m}^{\rm
an}_{(0,0)}$. Hence Part (1) follows from the fact131313Note however that
$(\mathcal{O}^{\rm an}_{\mathcal{U}}[\\![z]\\!])_{(0,0)}\neq\mathcal{O}^{\rm
an}_{\mathcal{U},(0,0)}[\\![z]\\!]$. that $(\mathcal{O}^{\rm
an}_{\mathcal{U}}[\\![z]\\!])_{(0,0)}^{^}=\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$.
We show that the natural maps
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}^{^}_{(0,0)}\to\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}[\\![z]\\!]\leftarrow\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}\otimes_{R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]}\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$
(4.9)
are isomorphisms, where the first map is induced by the map
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}_{(0,0)}\cong(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!])_{(0,0)}\overset{\text{Lemma
\ref{lem:proper}}}{\cong}(\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!])_{\tilde{0}}\to\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}[\\![z]\\!].$
That the maps in (4.9) are isomorphisms follows from the following two facts:
(a) all three modules in (4.9) are finite and free as
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$-modules, and (b) the
maps in (4.9) are isomorphisms modulo $z$. We already know that (b) holds by
Lemma 4.18. In fact, the maps in (4.9) reduces to the isomorphisms in (4.5)
modulo $z$. Thus we only need to show (a). Proposition 4.24 implies that
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}_{(0,0)}$
is a finite free $(\mathcal{O}_{\mathcal{U}}[\\![z]\\!])_{(0,0)}$-module, and
thus
$\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}^{^}_{(0,0)}$
is a finite free
$(\mathcal{O}_{\mathcal{U}}[\\![z]\\!])^{^}_{(0,0)}=\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$-module.
Also, since $\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$ is a
finite free
$R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]$-module,
the third term in (4.9) is a finite free
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$-module. The finite-freeness of
$\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}[\\![z]\\!]$ follows from a
discussion parallel to the proof of Proposition 4.24. Indeed, we know from
Corollary 4.19 that $\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}$ is a
finite free $\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$-module, and any basis
of $\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}$ over
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}$ gives rise to a basis of
$\widehat{\mathcal{O}}_{\mathcal{Y},\tilde{0}}[\\![z]\\!]$ over
$\widehat{\mathcal{O}}_{\mathcal{U},(0,0)}[\\![z]\\!]$. Part (2) is proved. ∎
By restricting the above isomorphism to
$\mathcal{V}=\mathcal{U}\cap(\mathcal{M}\times\\{0\\})$ and using Proposition
4.11, we have
###### Corollary 4.26.
$\big{(}\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}^{^}_{0}\cong\operatorname{Bri}(F)^{^}_{\mathbf{\Sigma}}\otimes_{\mathbb{C}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]}\widehat{\mathcal{O}}_{\mathcal{V},0}[\\![z]\\!]$.
###### Remark 4.27 (cf. Remarks 4.4 and 4.14).
As before, we can describe the analytified Brieskorn module as a twisted de
Rham cohomology. The complex $\big{(}\Omega^{\bullet,\rm
an}_{\mathcal{B}/\mathcal{M}}[\\![z]\\!],zd+dF\wedge\big{)}$ can be identified
with the Koszul complex associated with the action of
$\chi_{1},\dots,\chi_{n}$ on $\mathcal{O}^{\rm an}_{\mathcal{B}}[\\![z]\\!]$
given by (4.8). Since $\chi_{1},\dots,\chi_{n}$ form a regular sequence for
$\mathcal{O}^{\rm an}_{\mathcal{B}}[\\![z]\\!]$, we have
$H^{i}\big{(}\Omega^{\bullet,\rm
an}_{\mathcal{B}/\mathcal{M}}[\\![z]\\!],zd+dF\wedge\big{)}=\begin{cases}0,&i\neq
n,\\\ \mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!]/(\chi_{1},\dots,\chi_{n})\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!],&i=n,\end{cases}$
where the $n$th cohomology sheaf is supported on
$\widetilde{\operatorname{pr}}^{-1}(\mathcal{M}\times\\{0\\})\cap\mathcal{B}=\big{\\{}u\in\mathcal{B}\colon
x_{1}\frac{\partial F}{\partial x_{1}}(u)=\cdots=x_{n}\frac{\partial
F}{\partial x_{n}}(u)=0\big{\\}}$. Therefore we have
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\cong\operatorname{pr}_{*}H^{n}\big{(}\Omega^{\bullet,\rm
an}_{\mathcal{B}/\mathcal{M}}[\\![z]\\!],zd+dF\wedge\big{)}\cong
R^{n}\operatorname{pr}_{*}\big{(}\Omega^{\bullet,\rm
an}_{\mathcal{B}/\mathcal{M}}[\\![z]\\!],zd+dF\wedge\big{)}.$
Note that the second and the third term is supported on
$\mathcal{V}=\mathcal{U}\cap(\mathcal{M}\times\\{0\\})$.
#### 4.3.3 The higher residue pairing on the analytified Brieskorn module
A version of K. Saito’s higher residue pairing [96] on the completed
equivariant Brieskorn module
$\operatorname{Bri_{\mathbb{T}}}(F)^{^}_{\mathbf{\Sigma}}$ was introduced in
[27, Section 6] via the asymptotic expansions of oscillatory integrals. We
explain that the definition there can be extended to the analytified Brieskorn
module $\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$.
Consider the equivariant potential function (as appeared in Remark 4.4)
$F_{\mathbb{T}}=F_{\mathbb{T}}(x,q)=F(x,q)-\sum_{i=1}^{n}\chi_{i}\log x_{i}.$
This is a multi-valued function on $\mathcal{Y}$ with parameter
$\chi\in\operatorname{Lie}\mathbb{T}$. For a fixed
$(q,\chi)\in\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$,
(logarithmic) critical points of $F_{\mathbb{T}}|_{\operatorname{pr}^{-1}(q)}$
are solution to the equation
$x_{i}\frac{\partial F}{\partial x_{i}}=\chi_{i}.$
Thus we can regard
$\widetilde{\operatorname{pr}}\colon\mathcal{B}\to\mathcal{U}$ (4.3) as a
family141414More precisely, $\mathcal{B}$ is the union of branches of critical
points that tend to $\tilde{0}$ as $q\to 0=0_{\mathbf{\Sigma}}$. of critical
points of $F_{\mathbb{T}}$. It follows from the study [27, Lemma 6.2] of
critical points near $0_{\mathbf{\Sigma}}$ that the fibre of the finite
morphism
$\widetilde{\operatorname{pr}}|_{\mathcal{B}}\colon\mathcal{B}\to\mathcal{U}$
at a generic point consists of $\dim H_{\rm
CR}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$ many reduced points. We write
$\mathcal{U}^{\rm
ss}=\big{\\{}(q,\chi)\in\mathcal{U}\colon\text{$\widetilde{\operatorname{pr}}^{-1}(q,\chi)\cap\mathcal{B}$
consists of only reduced points}\big{\\}}\neq\varnothing,$
where “ss” means semisimplicity. The complement of $\mathcal{U}^{\rm ss}$ in
$\mathcal{U}$ (called _caustic_) is an analytic subvariety in $\mathcal{U}$.
Let
$\phi\cdot\omega\in\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$
be a section over $\mathcal{U}^{\rm ss}$, where
$\phi=\phi(x,q,\chi)\in\widetilde{\operatorname{pr}}_{*}(\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!])$. For $(q,\chi)\in\mathcal{U}^{\rm ss}$ and a
critical point
$p\in\widetilde{\operatorname{pr}}^{-1}(q,\chi)\cap\mathcal{B}$, we can define
the _formal asymptotic expansion_ of the oscillatory integral (see [27,
Section 6.2])
$\int_{\Gamma(p)}e^{F_{\mathbb{T}}/z}\phi(x,q,\chi)\omega\sim
e^{F_{\mathbb{T}}(p)/z}(-2\pi
z)^{n/2}\sum_{n=0}^{\infty}a_{n}(q,\chi)z^{n}\qquad\text{as $z\to 0$.}$
We obtain the right-hand side by expanding the integrand
$e^{F_{\mathbb{T}}/z}\phi(x,q,\chi)$ in Taylor series at $p$ (with respect to
the logarithmic co-ordinates $\log x_{1},\dots,\log x_{n}$) and performing
termwise (Gaussian) integration. More precisely, we have
$\sum_{n=0}^{\infty}a_{n}(q,\chi)z^{n}=\frac{1}{|\mathbf{N}_{\rm
tor}|\sqrt{\det(h_{i,j})}}\Big{[}e^{-\frac{z}{2}\sum_{i,j}h^{i,j}\frac{\partial}{\partial
s_{i}}\frac{\partial}{\partial s_{j}}}e^{F_{\mathbb{T}}^{\geq
3}/z}\phi(pe^{s},q,\chi)\Big{]}_{s=0},$ (4.10)
where $s_{1},\dots,s_{n}$ are the logarithmic co-ordinates centred at $p$ so
that $x_{j}=x_{j}(p)e^{s_{j}}$,
$h_{i,j}=\frac{\partial^{2}F_{\mathbb{T}}}{\partial\log x_{i}\partial\log
x_{j}}(p)$ (4.11)
is the Hessian matrix at $p$, $(h^{i,j})$ are the coefficients of the matrix
inverse to $(h_{i,j})$ and
$F^{\geq 3}_{\mathbb{T}}=\sum_{k\geq
3}\frac{1}{k!}\sum_{i_{1},\dots,i_{k}}\frac{\partial^{k}F_{\mathbb{T}}}{\partial\log
x_{i_{1}}\cdots\partial\log x_{i_{k}}}(p)s_{i_{1}}\cdots s_{i_{k}}$
is the truncated Taylor expansion of $F_{\mathbb{T}}$ at the critical point
$p$.
###### Definition 4.28.
We define $\operatorname{Asym}_{p}(\phi\cdot\omega)$ to be the right-hand side
of (4.10).
###### Remark 4.29.
1. (1)
When the critical point $p$ does not lie in the logarithmic locus of
$\mathcal{Y}$ and $\phi(x,q,\chi)$ is a polynomial, the above _formal_
asymptotic expansion makes sense as an _actual_ asymptotic expansion: for this
we choose the integration cycle
$\Gamma(p)\subset\mathcal{Y}_{q}:=\operatorname{pr}^{-1}(q)$ to be a stable
manifold for the Morse function $x\mapsto\Re(F_{\mathbb{T}}(x,q))$ associated
with $p$ and assume that $z$ approaches zero from the _negative_ real axis.
2. (2)
More precisely, the above formal asymptotic expansion depends on the choice of
the square root of the Hessian. This corresponds to the choice of an
orientation of the Morse cycle $\Gamma(p)$ and a branch of $(-2\pi z)^{n/2}$.
###### Definition 4.30.
The _higher residue pairing_ of two sections
$s_{1},s_{2}\in\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$
are defined as:
$P(s_{1},s_{2})(q,\chi)=\sum_{p\in\widetilde{\operatorname{pr}}^{-1}(q,\chi)}\left[\operatorname{Asym}_{p}(s_{1})\right]_{z\to-z}\cdot\operatorname{Asym}_{p}(s_{2}),$
where $(q,\chi)\in\mathcal{U}^{\rm ss}$.
The higher residue pairing gives a bilinear pairing
$P\colon\
\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\bigr{|}_{\mathcal{U}^{\rm
ss}}\times\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\bigr{|}_{\mathcal{U}^{\rm
ss}}\to\mathcal{O}^{\rm an}_{\mathcal{U}^{\rm ss}}[\\![z]\\!],$
which satisfies the following properties [27, Proposition 6.8]:
* (a)
$P$ is $\mathcal{O}^{\rm an}_{\mathcal{U}^{\rm ss}}$-bilinear, non-degenerate,
$z$-sesquilinear and symmetric:
$\displaystyle P(f(-z)s_{1},s_{2})=P(s_{1},f(z)s_{2})=f(z)P(s_{1},s_{2}),$
$\displaystyle P(s_{2},s_{1})=P(s_{1},s_{2})|_{z\to-z},$
where $f(z)\in\mathcal{O}_{\mathcal{U}^{\rm ss}}[\\![z]\\!]$;
* (b)
$P$ is $\nabla$-flat, i.e., $dP(s_{1},s_{2})=P(\nabla
s_{1},s_{2})+P(s_{1},\nabla s_{2})$;
* (c)
$P$ is homogeneous of degree $-n$ ($n=\dim\mathfrak{X}_{\mathbf{\Sigma}}$),
i.e.,
$\left(z\frac{\partial}{\partial
z}+\mathcal{E}+n\right)P(s_{1},s_{2})=P(\operatorname{Gr}s_{1},s_{2})+P(s_{1},\operatorname{Gr}s_{2}),$
where $\mathcal{E}$ is the Euler vector field (4.2).
* (d)
along $z=0$, $P$ equals the Grothendieck residue pairing.
###### Definition 4.31.
Suppose that $\mathcal{V}^{\rm ss}:=\mathcal{U}^{\rm
ss}\cap(\mathcal{M}\times\\{0\\})$ is nonempty. The non-equivariant higher
residue pairing
$P\colon\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}|_{\mathcal{V}^{\rm
ss}}\times\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}|_{\mathcal{V}^{\rm
ss}}\to\mathcal{O}_{\mathcal{V}^{\rm ss}}[\\![z]\\!]$ is defined to be the
restriction of the above $P$ to $\mathcal{V}^{\rm ss}$. If
$\mathfrak{X}_{\mathbf{\Sigma}}$ is compact, the argument in [62, Proposition
3.10] shows that $\mathcal{V}^{\rm ss}$ is an open dense subset of
$\mathcal{V}$, and hence the non-equivariant higher residue pairing is
defined.
###### Remark 4.32.
The definition of the higher residue pairing in terms of oscillatory integrals
is originally due to Pham [90, 2éme Partie, 4].
###### Remark 4.33.
The higher residue pairing here does not necessarily extend to the caustic
$\mathcal{U}\setminus\mathcal{U}^{\rm ss}$. Under mirror symmetry, the higher
residue pairing corresponds to the Poincaré pairing [27, Theorem 6.11],
therefore it has poles along $\chi=0$ when $\mathfrak{X}_{\mathbf{\Sigma}}$ is
noncompact. When $\mathfrak{X}_{\mathbf{\Sigma}}$ is compact, it extends to a
holomorphic and non-degenerate pairing in a neighbourhood of
$(0_{\mathbf{\Sigma}},0)$.
### 4.4 Analytic mirror isomorphism
Using the convergence result [27, Theorem 7.2] (which generalizes [59, Theorem
1.2]), we show that the mirror isomorphism in Theorem 4.8 extends to a
neighbourhood of $0=0_{\mathbf{\Sigma}}$ as an isomorphism between the
_analytified_ Brieskorn module
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ and the
_analytic_ quantum D-module. Let $\mathcal{U}\subset\mathcal{M}_{\mathbb{T}}$
be an open neighbourhood of $(0_{\mathbf{\Sigma}},0)$ as in Corollary 4.20.
Recall that
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ was
defined on $\mathcal{U}$.
The mirror isomorphism in Theorem 4.8 induces, via the isomorphism in
Proposition 4.25, the following isomorphism
$\widehat{\operatorname{Mir}}\colon\
\big{(}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{)}^{^}_{(0_{\mathbf{\Sigma}},0)}\cong\operatorname{mir}^{*}\operatorname{QDM}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})\otimes_{R_{\mathbb{T}}[z][\\![\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]\\!]}\widehat{\mathcal{O}}_{\mathcal{U},(0_{\mathbf{\Sigma}},0)}[\\![z]\\!].$
(4.12)
This isomorphism extends to an analytic neighbourhood of
$(0_{\mathbf{\Sigma}},0)$. We recall the following facts from [27, Section 7]:
* (a)
the structure constants of the big equivariant quantum product are convergent
and analytic in $q$, $\tau^{\prime}$ and $\chi$ [27, Corollary 7.3] (where $q$
and $\tau^{\prime}$ are parameters of the Kähler moduli space, see Section
2.2, and $\chi$ is the equivariant parameter);
* (b)
choose a $\operatorname{Gr}$-homogeneous basis $\\{\Omega_{i}\\}_{i=0}^{s}$ of
the completed Brieskorn module consisting of algebraic differential forms
(i.e., $\Omega_{i}\in\mathbb{C}[z][\mathbb{O}(\mathbf{\Sigma})_{+}]\omega$)
and let $\\{\phi_{i}\\}_{i=0}^{s}$ be the basis of $H_{\rm
CR}^{*}(\mathfrak{X}_{\mathbf{\Sigma}})$ as in Section 2.1; then the matrix
entries $M_{i}^{j}(q,\chi,z)$ of the mirror isomorphism $\operatorname{Mir}$
given by
$\operatorname{Mir}(\Omega_{i})=\sum_{j=0}^{s}M_{i}^{j}(q,\chi,z)\phi_{j}$
belong to $\mathcal{O}^{\rm an}(\mathcal{U}^{\prime})[\\![z]\\!]$ for some
open neighbourhood $\mathcal{U}^{\prime}$ of $(0_{\mathbf{\Sigma}},0)$ in
$\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$ [27,
Theorem 7.1];
* (c)
the mirror map $\operatorname{mir}$ is also analytic in a neighbourhood of
$(0_{\mathbf{\Sigma}},0)\in\mathcal{M}_{\mathbb{T}}$ (_ibid._).
By Part (a), the equivariant quantum D-module
$\operatorname{QDM}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})$ (see (2.10))
extends to a small analytic neighbourhood $U$ of $q=\tau^{\prime}=\chi=0$ in
the equivariant Kähler moduli space
$\big{[}\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})\big{]}$
(see (2.5)). We denote it by
$\operatorname{QDM}^{\rm
an}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}}):=\big{(}H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})\otimes\mathcal{O}^{\rm
an}_{\widetilde{U}}[z],\nabla,\operatorname{Gr},P\big{)},$
where $\widetilde{U}$ is the preimage of $U$ in $\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})$; $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})\otimes\mathcal{O}^{\rm
an}_{\widetilde{U}}[z]$ is a $\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})$-equivariant sheaf by the Galois symmetry
in Section 2.2, and we regard it as a sheaf on the stack
$U=\big{[}\widetilde{U}/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})\big{]}$. By Part (b),
$\widehat{\operatorname{Mir}}^{-1}(\phi_{i})$ extends to a section of
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ over a
small analytic neighbourhood $\mathcal{U}^{\prime}\subset\mathcal{U}$ of
$(0_{\mathbf{\Sigma}},0)\in\mathcal{M}_{\mathbb{T}}$. By Part (c), by
shrinking $\mathcal{U}^{\prime}$ if necessary, we have an analytic mirror map
$\operatorname{mir}\colon\mathcal{U}^{\prime}\to U$. We now have the following
result.
###### Theorem 4.34.
The isomorphism $\widehat{\operatorname{Mir}}$ in (4.12) extends to an open
neighbourhood $\mathcal{U}^{\prime}\subset\mathcal{U}$ of
$(0_{\mathbf{\Sigma}},0)\in\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$
and yields an isomorphism $\operatorname{Mir}^{\rm an}$ of $\mathcal{O}^{\rm
an}_{\mathcal{U}^{\prime}}[\\![z]\\!]$-modules:
$\operatorname{Mir}^{\rm an}\colon\
\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\bigr{|}_{\mathcal{U}^{\prime}}\cong\operatorname{mir}^{*}\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{\mathbf{\Sigma}}),$
where $\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{\mathbf{\Sigma}})$ denotes the $z$-adic
completion of $\operatorname{QDM}^{\rm
an}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})$, i.e.,
$\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{\mathbf{\Sigma}}):=\operatorname{QDM}^{\rm
an}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})\otimes_{\mathcal{O}^{\rm
an}_{U}[z]}\mathcal{O}^{\rm an}_{U}[\\![z]\\!].$
The analytic mirror isomorphism $\operatorname{Mir}^{\rm an}$ satisfies the
same properties $(1)$–$(3)$ as in Theorem 4.8 $($see Section 4.3.3 for the
higher residue pairing on
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}})$.
###### Remark 4.35.
As explained before Theorem 4.8, in the above theorem, we choose a splitting
$\mathbf{N}\to\mathbb{O}^{\mathbf{\Sigma}}$ of the refined fan sequence
(3.12), which simultaneously defines a partial connection $\nabla$ on
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ and the
equivariant quantum D-module.
###### Remark 4.36.
The analytic mirror theorem above shows that the analytified Brieskorn module
can be further analytified in the $z$-direction (since
$\operatorname{QDM}^{\rm an}_{\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})$ is
analytic in $z$). We can regard this as a solution to the Birkhoff problem
(i.e., finding a normal form of the Gauss–Manin connection) which has been
studied extensively in the construction of K. Saito’s flat structure [11, 37,
38, 93, 97, 98].
## 5 Discrepant wall-crossings
We study the change of quantum cohomology of smooth toric DM stacks under a
“discrepant” wall crossing. We show a decomposition of formal (i.e., completed
in the variable $z$) quantum D-modules under discrepant wall-crossings. We
work in the set-up of Section 3.1 and fix the data $(\mathbf{N},\Pi,S)$ as
usual.
### 5.1 Discrepant transformation of smooth toric DM stacks
We describe birational transformations between smooth toric DM stacks
following [45], [15, Sections 4 and 5], [31, Section 5.1 and 6.3] and [5,
Section 3].
Recall from Section 3.1.1 that the toric stacks
$\mathfrak{X}_{\mathbf{\Sigma}}$ with
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ arise as the GIT
quotients of $\mathbb{C}^{S}$ by the torus $\mathbb{L}_{\mathbb{C}^{\times}}$.
These toric stacks are birational to each other since they contain the
(stacky) torus
$\big{[}(\mathbb{C}^{\times})^{S}/\mathbb{L}_{\mathbb{C}^{\times}}\big{]}$ as
an open dense subset. We can regard $\mathbb{L}^{\star}_{\mathbb{R}}$ as the
space of GIT stability conditions for the
$\mathbb{L}_{\mathbb{C}^{\times}}$-action on $\mathbb{C}^{S}$; if we choose a
stability condition from the interior of the maximal cone
$\operatorname{cpl}(\mathbf{\Sigma})$ of the secondary fan $\Xi$ (see
Definition 3.6), then the corresponding GIT quotient is
$\mathfrak{X}_{\mathbf{\Sigma}}$. We choose two adjacent maximal cones
$\operatorname{cpl}(\mathbf{\Sigma}_{+})$,
$\operatorname{cpl}(\mathbf{\Sigma}_{-})$ of $\Xi$ which are separated by a
hyperplane wall $W\subset\mathbb{L}^{\star}_{\mathbb{R}}$. Here we assume that
$W\cap\operatorname{cpl}(\mathbf{\Sigma}_{+})=W\cap\operatorname{cpl}(\mathbf{\Sigma}_{-})$
is a common codimension-one face of
$\operatorname{cpl}(\mathbf{\Sigma}_{\pm})$. Let $\mathbf{w}\in\mathbb{L}$ be
a primitive integral vector which is perpendicular to the wall
$W\subset\mathbb{L}^{\star}_{\mathbb{R}}$ and is non-negative on the chamber
$\operatorname{cpl}(\mathbf{\Sigma}_{+})$. By the definition of $\mathbb{L}$
(see (3.3)), the vector $\mathbf{w}\in\mathbb{L}$ gives rise to a linear
relation
$\sum_{b\in S}(D_{b}\cdot\mathbf{w})b=0,$ (5.1)
where recall that $D_{b}=D(e_{b}^{\star})$ (see (3.4)). This linear relation
defines a _circuit_ $\\{b\in S:D_{b}\cdot\mathbf{w}\neq 0\\}$ in the
terminology of Gelfand–Kapranov–Zelevinsky [45], where a ‘circuit’ means a
minimal linearly dependent set. The transition between $\mathbf{\Sigma}_{+}$
and $\mathbf{\Sigma}_{-}$ can be described in terms of the circuit
(‘modification along a circuit’ [45]).
Figure 5: Modification along a circuit. The signs $\pm$ mean rays belonging to
$M_{\pm}=\\{b\in S\colon\pm D_{b}\cdot\mathbf{w}>0\\}$.
For $I\subset S$, we write151515Note that $\sigma_{I}$ is a closed cone,
whereas $\angle_{I}$ is a relatively open cone.
$\displaystyle\sigma_{I}:=\sum_{b\in I}\mathbb{R}_{\geq
0}\overline{b}\subset\mathbf{N}_{\mathbb{R}},\qquad\angle_{I}:=\sum_{b\in
I}\mathbb{R}_{>0}D_{b}\subset\mathbb{L}^{\star}_{\mathbb{R}}.$
We also set $\sigma_{\varnothing}=\\{0\\}$, $\angle_{\varnothing}=\\{0\\}$.
Consider the (not necessarily simplicial) fan $\Sigma_{0}$ on the vector space
$\mathbf{N}_{\mathbb{R}}$ given by $\Sigma_{0}:=\\{\sigma_{I}\colon
I\in\mathscr{S}_{0}\\}$, where
$\displaystyle\mathscr{S}_{0}=\\{I\subset S\colon\text{$\angle_{S\setminus I}$
contains the relative interior of
$\operatorname{cpl}(\mathbf{\Sigma}_{+})\cap\operatorname{cpl}(\mathbf{\Sigma}_{-})$}\\}.$
The simplicial fans $\Sigma_{\pm}$ underlying $\mathbf{\Sigma}_{\pm}$ arise as
different subdivisions of $\Sigma_{0}$. Set $M_{\pm}=\\{b\in
S\colon\allowbreak{\pm}D_{b}\cdot\mathbf{w}>0\\}$. We have a decomposition
$\mathscr{S}_{0}=\mathscr{S}_{0}^{\rm simp}\sqcup\mathscr{S}_{0}^{\rm circ}$
(disjoint union), where
$\displaystyle\mathscr{S}_{0}^{\rm simp}=\\{I\in\mathscr{S}_{0}\colon
M_{+}\not\subset I,M_{-}\not\subset I\\},$ $\displaystyle\mathscr{S}_{0}^{\rm
circ}=\\{I\in\mathscr{S}_{0}\colon M_{+}\cup M_{-}\subset I\\},$
such that $\Sigma_{\pm}=\\{\sigma_{I}\colon I\in\mathscr{S}_{\pm}\\}$ with
$\displaystyle\mathscr{S}_{\pm}=\big{\\{}I\colon I\in\mathscr{S}_{0}^{\rm
simp}\big{\\}}\sqcup\big{\\{}I\setminus J\colon I\in\mathscr{S}_{0}^{\rm
circ},\,\varnothing\neq J\subset M_{\pm}\big{\\}}.$
The set of rays of $\mathbf{\Sigma}_{\pm}$ is given by
$R_{\pm}:=R(\mathbf{\Sigma}_{\pm})=\bigcup\limits_{I\in\mathscr{S}_{\pm}}I$.
See [31, Lemma 5.2]161616In [31, Section 5.1], the set of “anti-cones”
$\\{S\setminus I\colon I\in\mathscr{S}_{0}\\}$, $\\{S\setminus I\colon
I\in\mathscr{S}_{0}^{\rm simp}\\}$, $\\{S\setminus I\colon
I\in\mathscr{S}_{0}^{\rm circ}\\}$ are denoted by $\mathcal{A}_{0}$,
$\mathcal{A}_{0}^{\rm thick}$, $\mathcal{A}_{0}^{\rm thin}$ respectively..
Here $I\in\mathscr{S}_{0}^{\rm simp}$ yields a simplicial cone
$\sigma_{I}\in\Sigma_{0}$ belonging to both $\Sigma_{+}$ and $\Sigma_{-}$, and
$I\in\mathscr{S}_{0}^{\rm circ}$ yields a (not necessarily simplicial) cone
$\sigma_{I}\in\Sigma_{0}$ containing the circuit $M_{+}\cup M_{-}$; the cone
$\sigma_{I}$ with $I\in\mathscr{S}_{0}^{\rm circ}$ is subdivided into
simplicial cones $\sigma_{I\setminus\\{v\\}}$, $v\in M_{\pm}$ in the fans
$\Sigma_{\pm}$. See Fig. 5. We also remark that $M_{+}\cup
M_{-}\in\mathscr{S}_{0}^{\rm circ}$ so that $(M_{+}\cup
M_{-})\setminus\\{v\\}\in\mathscr{S}_{\pm}$ for every $v\in M_{\pm}$. (In
particular, $M_{\pm}\subset R_{\mp}$.)
Let $\mathfrak{X}_{\pm}$ denote the toric stack corresponding to
$\mathbf{\Sigma}_{\pm}$. As discussed in [15, Section 5], [31, Section 6.3],
the toric birational map
$\varphi\colon\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ fits into a
commutative diagram
$\textstyle{\widehat{\mathfrak{X}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{f_{+}}$$\scriptstyle{f_{-}}$$\textstyle{\mathfrak{X}_{+}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{\varphi}$$\scriptstyle{g_{+}}$$\textstyle{\mathfrak{X}_{-},\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{g_{-}}$$\textstyle{X_{0}}$
(5.2)
where $X_{0}$ is the toric variety associated with $\Sigma_{0}$,
$\widehat{\mathfrak{X}}$ is another smooth toric DM stack and
$f_{\pm}\colon\widehat{\mathfrak{X}}\to\mathfrak{X}_{\pm}$,
$g_{\pm}\colon\mathfrak{X}_{\pm}\to X_{0}$ are projective birational toric
morphisms. Define ${\hat{b}}\in\mathbf{N}\cap\Pi$ to be the vector:
${\hat{b}}:=\sum_{D_{b}\cdot\mathbf{w}>0}(D_{b}\cdot\mathbf{w})b=-\sum_{D_{b}\cdot\mathbf{w}<0}(D_{b}\cdot\mathbf{w})b.$
The smooth toric DM stack $\widehat{\mathfrak{X}}$ is given by a stacky fan
${\widehat{\mathbf{\Sigma}}}$ adapted to $S\cup\\{{\hat{b}}\\}$ (in the sense
of Definition 3.3): the set of rays of ${\widehat{\mathbf{\Sigma}}}$ is
${\widehat{R}}=(R_{+}\cap R_{-})\cup\\{{\hat{b}}\\}$ where
$R_{\pm}:=R(\mathbf{\Sigma}_{\pm})$; the fan $\widehat{\Sigma}$ underlying
${\widehat{\mathbf{\Sigma}}}$ is a simultaneous subdivision of $\Sigma_{+}$
and $\Sigma_{-}$ given by
$\widehat{\Sigma}=\big{\\{}\sigma_{I}\colon I\in\mathscr{S}_{0}^{\rm
simp}\big{\\}}\sqcup\big{\\{}\sigma_{K}\colon K=I\setminus(J_{+}\cup
J_{-})\cup\\{{\hat{b}}\\},\,I\in\mathscr{S}_{0}^{\rm circ},\,\varnothing\neq
J_{\pm}\subset M_{\pm}\big{\\}}.$
The toric morphisms $f_{\pm}\colon\widehat{\mathfrak{X}}\to\mathfrak{X}_{\pm}$
are induced by natural maps
${\widehat{\mathbf{\Sigma}}}\to\mathbf{\Sigma}_{\pm}$ of stacky fans. We refer
the reader to [31, Section 6.3] for a description of $\widehat{\mathfrak{X}}$
and $f_{\pm}$ in terms of GIT quotients.
###### Lemma 5.1.
Let $K_{\pm}=K_{\mathfrak{X}_{\pm}}$ denote the canonical class of
$\mathfrak{X}_{\pm}$ and $E\subset\widehat{\mathfrak{X}}$ denote the toric
divisor of $\widehat{\mathfrak{X}}$ corresponding to the ray ${\hat{b}}$. Then
we have
$f_{+}^{\star}K_{+}=f_{-}^{\star}K_{-}+\left(\sum_{b\in
S}D_{b}\cdot\mathbf{w}\right)[E].$
###### Proof.
This follows immediately from [31, Proposition 6.21]. ∎
In view of the lemma above, we say that the birational transformation
$\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ is _crepant_ if
$\sum\limits_{b\in S}D_{b}\cdot\mathbf{w}=0$ (i.e., $\sum\limits_{b\in
S}D_{b}$ is on the wall $W$) and _discrepant_ otherwise. We shall restrict
ourselves to the case where the transformation is discrepant. By exchanging
$\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ if necessary, we may assume:
###### Assumption 5.2.
The birational transformation $\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$
satisfies $f_{+}^{\star}K_{+}>f_{-}^{\star}K_{-}$, i.e., $\sum\limits_{b\in
S}D_{b}\cdot\mathbf{w}>0$.
###### Remark 5.3.
Under the above assumption, the dimension of orbifold cohomology decreases:
$\dim H^{*}_{{\rm CR}}(\mathfrak{X}_{+})>\dim H^{*}_{\rm
CR}(\mathfrak{X}_{-})$. We can see this from the change of the fans, and using
the fact that $|\mathbf{N}_{\rm tor}|^{-1}\dim H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ equals the sum of volumes of simplices
spanned by $\\{0\\}\cup\\{\overline{b}\in
R(\mathbf{\Sigma})\colon\allowbreak\overline{b}\in\sigma\\}$ over all maximal
cones $\sigma$ of $\mathbf{\Sigma}$, where we normalize the volume of the
standard simplex to be one (see, e.g., [62, Lemma 3.9]).
###### Remark 5.4.
There are three types of discrepant wall-crossings: (I) $\mathfrak{X}_{+}$ and
$\mathfrak{X}_{-}$ are isomorphic in codimension one (“flip”), (II) the
birational map induces a map (i) $\mathfrak{X}_{+}\to X_{-}$ or (ii)
$\mathfrak{X}_{-}\to X_{+}$ contracting a divisor to a toric subvariety, where
$X_{\pm}$ is the coarse moduli space of $\mathfrak{X}_{\pm}$ (“discrepant
resolution”) and (III) $X_{+}=X_{-}$ but the stack structures of
$\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ differ along a divisor. In terms of
stacky fans, we have
* (I)
$R_{+}=R_{-}$, $\sharp M_{+}\geq 2$ and $\sharp M_{-}\geq 2$ (rays are the
same);
* (II-i)
$R_{+}=R_{-}\sqcup M_{-}$, $\sharp M_{-}=1$ and $\sharp M_{+}\geq 2$ (removing
one ray);
* (II-ii)
$R_{-}=R_{+}\sqcup M_{+}$, $\sharp M_{+}=1$ and $\sharp M_{-}\geq 2$ (adding
one ray);
* (III)
$R_{+}\setminus R_{-}=M_{-}$, $R_{-}\setminus R_{+}=M_{+}$ and $\sharp
M_{-}=\sharp M_{+}=1$ (replace a ray $b_{-}\in R_{+}$ with a shorter and
parallel ray $b_{+}\in R_{-}$, where $M_{\pm}=\\{b_{\pm}\\}$).
This is similar to the classification of crepant transformations given in [31,
Propositions 5.4 and 5.5] and can be shown by a parallel argument.
###### Example 5.5.
Let $a_{1},\dots,a_{k}$, $b_{1},\dots,b_{l}$ be positive integers with
$a_{1}+\cdots+a_{k}<b_{1}+\cdots+b_{l}$. Consider the
$\mathbb{C}^{\times}$-action on $\mathbb{C}^{k+l}$ given by the weights
$(-a_{1},\dots,-a_{k},b_{1},\dots,b_{l})$. The GIT variation gives a
discrepant transformation between the spaces:
$\displaystyle\mathfrak{X}_{+}=\text{the total space of
$\mathcal{O}(-a_{1})\oplus\cdots\oplus\mathcal{O}(-a_{k})$ over
$\mathbb{P}(b_{1},\dots,b_{l})$, and}$
$\displaystyle\mathfrak{X}_{-}=\text{the total space of
$\mathcal{O}(-b_{1})\oplus\cdots\oplus\mathcal{O}(-b_{l})$ over
$\mathbb{P}(a_{1},\dots,a_{k})$.}$
Following the classification in Remark 5.4, we have: (I) if $k,l\geq 2$, this
is a flip; (II-i) if $k=1$ and $l\geq 2$, this is a resolution
$\mathfrak{X}_{+}\to X_{-}=\mathbb{C}^{l}/\mu_{a_{1}}$ with positive
discrepancy; (II-ii) if $k\geq 2$ and $l=1$, this is a resolution
$\mathfrak{X}_{-}\to X_{+}=\mathbb{C}^{k}/\mu_{b_{1}}$ with negative
discrepancy; (III) if $k=l=1$, we have
$\mathfrak{X}_{+}=[\mathbb{C}/\mu_{b_{1}}]$ and
$\mathfrak{X}_{-}=[\mathbb{C}/\mu_{a_{1}}]$; the stack structure at the origin
changes. Note that the example in Section 3.6.3 is a special case of the
current example with $k=2$, $l=1$, $(a_{1},a_{2},b_{1})=(1,1,d)$.
###### Example 5.6.
A blow-up along a toric subvariety is an example of type (II) discrepant
transformation.
###### Example 5.7.
A root construction [21] along a toric divisor is an example of type (III)
discrepant transformation.
### 5.2 The LG model along a curve
Consider the partially compactified LG model
$(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$ from Section 3.2.
Recall that $\mathcal{M}$ is defined in terms of the secondary fan $\Xi$
consisting of maximal cones $\operatorname{cpl}(\mathbf{\Sigma})$,
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$. Let
$\mathcal{C}\subset\mathcal{M}$ denote the 1-dimensional toric substack
corresponding to the codimension-1 cone
$\operatorname{cpl}(\mathbf{\Sigma}_{+})\cap\operatorname{cpl}(\mathbf{\Sigma}_{+})$.
The curve $\mathcal{C}$ lies in the boundary of $\mathcal{M}$ and connects the
large radius limit points $0_{\mathbf{\Sigma}_{+}}$ and
$0_{\mathbf{\Sigma}_{-}}$.
We cover $\mathcal{C}$ by the two open sets
$\mathcal{M}_{\pm}:=\mathcal{M}_{\mathbf{\Sigma}_{\pm}}=\big{[}\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma}_{\pm})_{+}]/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\pm})\big{]}$; in these local charts, the embedding
$\mathcal{C}\subset\mathcal{M}$ is given by the $\mathbb{C}$-algebra
homomorphism:
$\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma}_{\pm})_{+}]\to\mathbb{C}\big{[}q^{\pm\mathbf{w}/e_{\pm}}\big{]},\qquad
q^{\lambda}\mapsto\begin{cases}q^{\lambda},&\text{if $\lambda$ is proportional
to $\mathbf{w}$},\\\ 0,&\text{otherwise},\end{cases}$ (5.3)
where $e_{\pm}\in\mathbb{N}$ is the smallest common denominator of
$\\{c\in\mathbb{Q}\colon
c\mathbf{w}\in\boldsymbol{\Lambda}(\mathbf{\Sigma}_{\pm})\\}$. (Recall that
$\boldsymbol{\Lambda}(\mathbf{\Sigma}_{\pm})_{+}=\boldsymbol{\Lambda}(\mathbf{\Sigma}_{\pm})\cap\operatorname{cpl}(\mathbf{\Sigma}_{\pm})^{\vee}$,
see Lemma 3.14.)
###### Lemma 5.8.
The inverse image $\operatorname{pr}^{-1}(\mathcal{C})$ is covered by two
charts
$\operatorname{pr}^{-1}(\mathcal{C}\cap\mathcal{M}_{\pm})=\big{[}\operatorname{Spec}(A_{\pm})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\pm})\big{]},$
where $A_{\pm}$ is the
$\mathbb{C}\big{[}q^{\pm\mathbf{w}/e_{\pm}}\big{]}$-algebra
$\bigoplus\limits_{v\in\mathbf{N}\cap\Pi}\mathbb{C}\big{[}q^{\pm\mathbf{w}/e_{\pm}}\big{]}w_{v}^{\pm}$
equipped with the product
$w_{v_{1}}^{\pm}w_{v_{2}}^{\pm}=\begin{cases}q^{\Psi^{\pm}(v_{1})+\Psi^{\pm}(v_{2})-\Psi^{\pm}(v_{1}+v_{2})}w_{v_{1}+v_{2}}^{\pm},&\text{if
$v_{1}$, $v_{2}$ lie in the same cone of $\Sigma_{0}$},\\\
0&\text{otherwise},\end{cases}$
where $\Psi^{\pm}(v_{1})+\Psi^{\pm}(v_{2})-\Psi^{\pm}(v_{1}+v_{2})$ is
proportional to $\mathbf{w}$ in the first case, $w_{v}^{\pm}$ is the
restriction of $u^{(\Psi^{\pm}(\overline{v}),v)}$ to
$\operatorname{pr}^{-1}(\mathcal{C}\cap\mathcal{M}_{\pm})$ and
$\Psi^{\pm}:=\Psi^{\mathbf{\Sigma}_{\pm}}$ $($see Notation $\ref{nota:Psi})$.
The two charts are glued by
$w_{v}^{-}=\begin{cases}q^{\Psi^{-}(v)-\Psi^{+}(v)}w_{v}^{+},&\text{if $v$
lies in a cone $\sigma_{I}$ with $I\in\mathscr{S}_{0}^{\rm circ}$},\\\
w_{v}^{+},&\text{otherwise}.\end{cases}$
###### Proof.
The space $\operatorname{pr}^{-1}(\mathcal{C}\cap\mathcal{M}_{\pm})$ is the
base change of
$\mathcal{Y}_{\mathbf{\Sigma}_{\pm}}=\big{[}\operatorname{Spec}\mathbb{C}[\mathbb{O}(\mathbf{\Sigma}_{\pm})_{+}]/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\pm})\big{]}$ via (5.3). The conclusion follows from Remark
3.17 and the description of cones of $\Sigma_{0}$, $\Sigma_{\pm}$ in terms of
the circuit (5.1). ∎
###### Remark 5.9.
We describe how the curve $\mathcal{C}$ looks like in the Kähler moduli space.
Using the equation (5.3) for $\mathcal{C}$ and the asymptotics of the mirror
map (Remark 4.10), we find that the image of $\mathcal{C}$ under the (non-
equivariant) mirror map for $\mathfrak{X}_{+}$ is asymptotically close to,
near the large radius limit point $0_{\mathbf{\Sigma}_{+}}$,
type (I) or (II-i) case:
the curve given by $\tau^{\prime}=0$ and $q^{d}=0$ for all
$d\in\boldsymbol{\Lambda}_{+}^{\mathbf{\Sigma}_{+}}\setminus\mathbb{Q}_{\geq
0}\mathbf{w}$ (i.e., the curve corresponding to the extremal class
$\mathbf{w}\in H_{2}(\mathfrak{X}_{+},\mathbb{Q})$);
type (II-ii) or (III) case:
the curve given by $\tau^{\prime}\in\mathbb{C}\mathfrak{D}_{b_{+}}$ and
$q^{d}=0$ for all
$d\in\boldsymbol{\Lambda}_{+}^{\mathbf{\Sigma}_{+}}\setminus\\{0\\}$, where
$b_{+}$ is the unique element of $M_{+}$ and $\mathfrak{D}_{b_{+}}\in
H^{<2}_{{\rm CR}}(\mathfrak{X}_{+})$ is as in Remark 4.10.
Here we use the notation on the Kähler moduli space from Section 2.2 and the
classification in Remark 5.4. Similarly, near $0_{\mathbf{\Sigma}_{-}}$, the
image of $\mathcal{C}$ under the mirror map for $\mathfrak{X}_{-}$ is
asymptotically close to
type (I) or (II-ii) case:
the curve given by $\tau^{\prime}=0$ and $q^{d}=0$ for all
$d\in\boldsymbol{\Lambda}_{+}^{\mathbf{\Sigma}_{-}}\setminus\mathbb{Q}_{\geq
0}(-\mathbf{w})$ (i.e., the curve corresponding to the extremal class
$-\mathbf{w}\in H_{2}(\mathfrak{X}_{-},\mathbb{Q})$);
type (II-i) or (III) case:
the curve given by $\tau^{\prime}\in\mathbb{C}\mathfrak{D}_{b_{-}}$ and
$q^{d}=0$ for all
$d\in\boldsymbol{\Lambda}_{+}^{\mathbf{\Sigma}_{-}}\setminus\\{0\\}$, where
$b_{-}$ is the unique element of $M_{-}$ and $\mathfrak{D}_{b_{-}}\in
H^{>2}_{\rm CR}(\mathfrak{X}_{-})$ is as in Remark 4.10.
The above classes $\mathfrak{D}_{b_{\pm}}$ are supported on the image of the
exceptional divisor. We note that they can be zero, and in that case we need
to examine the higher-order terms in the mirror map to see the asymptotic
behaviour of $\mathcal{C}$.
###### Remark 5.10.
Note that $\operatorname{pr}^{-1}(\mathcal{C})\subset\mathcal{Y}$ is a
possibly reducible toric substack and its components are in one-to-one
correspondence with maximal cones of the fan $\Sigma_{0}$. The LG potential
restricted to $\operatorname{pr}^{-1}(\mathcal{C})$ is of the form
$F=\sum\limits_{b\in R_{+}\cup R_{-}}u_{b}$ (here $u_{b}$ with $b\in
S\setminus(R_{+}\cup R_{-})$ vanishes on
$\operatorname{pr}^{-1}(\mathcal{C})$).
### 5.3 Decomposition of the Brieskorn module
In this section, we show that the analytified Brieskorn module associated with
$\mathbf{\Sigma}_{-}$ is a direct summand of that associated with
$\mathbf{\Sigma}_{+}$ in a neighbourhood of $\mathcal{C}$. For this, we study
the family (4.3)
$\widetilde{\operatorname{pr}}=\left(\operatorname{pr},x_{1}\frac{\partial
F}{\partial x_{1}},\dots,x_{n}\frac{\partial F}{\partial x_{n}}\right)\colon\
\mathcal{Y}\to\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$
over an analytic neighbourhood of the curve
$\mathcal{C}\times\\{0\\}\subset\mathcal{M}\times\operatorname{Lie}\mathbb{T}$,
where $x_{1},\dots,x_{n}$ are co-ordinates along fibres of
$\mathcal{Y}\to\mathcal{M}$ as in Section 4.1. Recall that this family can be
regarded as the relative critical scheme of $F_{\mathbb{T}}$ (see Section
4.3.3).
The $\mathbb{C}^{\times}$-action generated by the Euler vector field (4.2)
plays an important role in the following discussion. Consider the elements
$\sum\limits_{b\in S}e_{b}^{\star}\in\big{(}\mathbb{Z}^{S}\big{)}^{\star}$ and
$\sum\limits_{b\in S}D_{b}\in\mathbb{L}^{\star}$; they define
$\mathbb{C}^{\times}$-actions, respectively, on $\mathcal{Y}$ and
$\mathcal{M}$ such that $\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$ is
$\mathbb{C}^{\times}$-equivariant. In terms of the co-ordinates $(u_{b})_{b\in
S}$, the $\mathbb{C}^{\times}$-action is given by
$\displaystyle s\cdot u_{b}=su_{b}\qquad\text{with
$s\in\mathbb{C}^{\times}$},$
and the potential function $F=\sum\limits_{b\in S}u_{b}$ is of weight 1 with
respect to the action. Introduce the $\mathbb{C}^{\times}$-action on
$\operatorname{Lie}\mathbb{T}$ given by the scalar multiplication; then the
map
$\widetilde{\operatorname{pr}}\colon\mathcal{Y}\to\mathcal{M}\times\operatorname{Lie}\mathbb{T}$
is $\mathbb{C}^{\times}$-equivariant. Let
$0_{\pm}:=0_{\mathbf{\Sigma}_{\pm}}=\\{q^{\pm\mathbf{w}}=0\\}\in\mathcal{C}$
denote the large radius limit points of $\mathfrak{X}_{\pm}$ (see Definition
3.7) and let
$\tilde{0}_{\pm}=\tilde{0}_{\mathbf{\Sigma}_{\pm}}\in\operatorname{pr}^{-1}(\mathcal{C})$
denote the torus-fixed points such that
$\operatorname{pr}(\tilde{0}_{\pm})=0_{\pm}$ as in Section 4.3.1. The
$\mathbb{C}^{\times}$-action on the family
$\operatorname{pr}^{-1}(\mathcal{C})\to\mathcal{C}$ is given by (with notation
as in Lemma 5.8)
$s\cdot w^{\pm}_{v}=s^{\sum_{b\in S}\Psi^{\pm}_{b}(v)}w^{\pm}_{v},\qquad
s\cdot q^{\mathbf{w}}=s^{\sum_{b\in S}D_{b}\cdot\mathbf{w}}q^{\mathbf{w}}.$
By Assumption 5.2, we have that $\lim\limits_{s\to 0}s\cdot x=0_{+}$,
$\lim\limits_{s\to\infty}s\cdot x=0_{-}$ for every
$x\in\mathcal{C}\setminus\\{0_{+},0_{-}\\}$ and $\lim\limits_{s\to 0}s\cdot
y=\tilde{0}_{+}$ for every
$y\in\operatorname{pr}^{-1}(\mathcal{C}\setminus\\{0_{-}\\})$.
We choose analytic open sets $\mathcal{B}_{\pm}\subset\mathcal{Y}$,
$\mathcal{U}_{\pm}\subset\mathcal{M}_{\mathbb{T}}$ with
$\tilde{0}_{\pm}\in\mathcal{B}_{\pm}$, $(0_{\pm},0)\in\mathcal{U}_{\pm}$ such
that the conclusion of Corollary 4.20 holds. Since
$\widetilde{\operatorname{pr}}$ is $\mathbb{C}^{\times}$-equivariant, even
after replacing $\mathcal{B}_{\pm}$ and $\mathcal{U}_{\pm}$ with
$\bigcup_{s\in\mathbb{C}^{\times}}s\cdot\mathcal{B}_{\pm},\qquad\text{and}\qquad\bigcup_{s\in\mathbb{C}^{\times}}s\cdot\mathcal{U}_{\pm},$
we have that the conclusion of Corollary 4.20 still holds. _We henceforth
assume that $\mathcal{B}_{\pm}$, $\mathcal{U}_{\pm}$ are preserved by the
$\mathbb{C}^{\times}$-action_. Since every point in
$\operatorname{pr}^{-1}(\mathcal{C}\setminus\\{0_{-}\\})$ flows to
$\tilde{0}_{+}$ under the $\mathbb{C}^{\times}$-action and $\mathcal{B}_{+}$
is an open neighbourhood of $\tilde{0}_{+}$, we have that
$\operatorname{pr}^{-1}(\mathcal{C}\setminus\\{0_{-}\\})\subset\mathcal{B}_{+}$.
Similarly we have
$(\mathcal{C}\setminus\\{0_{+},0_{-}\\})\times\\{0\\}\subset\mathcal{U}_{\pm}$.
###### Lemma 5.11.
There exists an analytic open set $\mathcal{U}_{0}$ of
$\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$ such
that
* (1)
$(\mathcal{C}\setminus\\{0_{+},0_{-}\\})\times\\{0\\}\subset\mathcal{U}_{0}\subset\mathcal{U}_{+}\cap\mathcal{U}_{-}$;
* (2)
$\widetilde{\operatorname{pr}}^{-1}(\mathcal{U}_{0})\cap\mathcal{B}_{+}=(\widetilde{\operatorname{pr}}^{-1}(\mathcal{U}_{0})\cap\mathcal{B}_{-})\sqcup\mathcal{R}$
for some open set $\mathcal{R}$ of $\mathcal{Y}$.
###### Proof.
First note that $\mathcal{U}_{+}\cap\mathcal{U}_{-}$ contains
$(\mathcal{C}\setminus\\{0_{+},0_{-}\\})\times\\{0\\}$. Since
$\widetilde{\operatorname{pr}}\colon\mathcal{B}_{-}\to\mathcal{U}_{-}$ is
proper and $\mathcal{B}_{-}\setminus\mathcal{B}_{+}$ is closed in
$\mathcal{B}_{-}$,
$\widetilde{\operatorname{pr}}(\mathcal{B}_{-}\setminus\mathcal{B}_{+})$ is
closed in $\mathcal{U}_{-}$. Define
$\mathcal{U}_{0}:=(\mathcal{U}_{+}\cap\mathcal{U}_{-})\setminus\widetilde{\operatorname{pr}}(\mathcal{B}_{-}\setminus\mathcal{B}_{+})$.
This is an open subset of $\mathcal{U}_{+}\cap\mathcal{U}_{-}$. By definition
we have
$\widetilde{\operatorname{pr}}^{-1}(\mathcal{U}_{0})\cap\mathcal{B}_{-}\subset\widetilde{\operatorname{pr}}^{-1}(\mathcal{U}_{0})\cap\mathcal{B}_{+}$.
Since we have
$\widetilde{\operatorname{pr}}^{-1}((\mathcal{C}\setminus\\{0_{+},0_{-}\\})\times\\{0\\})\subset\operatorname{pr}^{-1}(\mathcal{C}\setminus\\{0_{+},0_{-}\\})\subset\mathcal{B}_{+}$,
we conclude
$(\mathcal{C}\setminus\\{0_{+},0_{-}\\})\times\\{0\\}\subset\mathcal{U}_{0}$.
Finally we show that the complement of
$\widetilde{\operatorname{pr}}^{-1}(\mathcal{U}_{0})\cap\mathcal{B}_{-}$ in
$\widetilde{\operatorname{pr}}^{-1}(\mathcal{U}_{0})\cap\mathcal{B}_{+}$ is
open. Take any point $y$ from the complement, and choose a compact
neighbourhood $K$ of $\widetilde{\operatorname{pr}}(y)$ in $\mathcal{U}_{0}$.
Since $\widetilde{\operatorname{pr}}\colon\mathcal{B}_{-}\to\mathcal{U}_{-}$
is proper, $\widetilde{\operatorname{pr}}^{-1}(K)\cap\mathcal{B}_{-}$ is a
compact set not containing $y$. Let $K^{\circ}$ be the interior of $K$; then
$(\widetilde{\operatorname{pr}}^{-1}(K^{\circ})\cap\mathcal{B}_{+})\setminus(\widetilde{\operatorname{pr}}^{-1}(K)\cap\mathcal{B}_{-})$
is an open neighbourhood of $y$ which does not intersect with
$\widetilde{\operatorname{pr}}^{-1}(\mathcal{U}_{0})\cap\mathcal{B}_{-}$. ∎
We consider the analytified equivariant Brieskorn module
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\pm}:=\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}_{\pm}}$
from Definition 4.21. Note that it is defined over the $\mathcal{U}_{\pm}$
above, since the only properties we need in the construction are those in
Corollary 4.20.
###### Corollary 5.12.
Let $\mathcal{U}_{0},\mathcal{R}$ be as in Lemma 5.11.
* (1)
We have a direct sum decomposition of $\mathcal{O}^{\rm
an}_{\mathcal{U}_{0}}$-algebras:
$(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}_{+}})\big{|}_{\mathcal{U}_{0}}\cong(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{B}_{-}})\big{|}_{\mathcal{U}_{0}}\oplus(\widetilde{\operatorname{pr}}_{*}\mathcal{O}^{\rm
an}_{\mathcal{R}}).$
* (2)
We have a direct sum decomposition of $\mathcal{O}^{\rm
an}_{\mathcal{U}_{0}}[\\![z]\\!]$-modules:
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{+}\big{|}_{\mathcal{U}_{0}}\cong\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{-}\big{|}_{\mathcal{U}_{0}}\oplus\widetilde{\operatorname{pr}}_{*}(\mathcal{O}^{\rm
an}_{\mathcal{R}}[\\![z]\\!]).$
Under this decomposition, the Gauss–Manin connection $\nabla$, the grading
operator $\operatorname{Gr}$ and the higher residue pairing $P$ split into the
direct sum.
###### Definition 5.13.
We define $\mathscr{R}:=\widetilde{\operatorname{pr}}_{*}(\mathcal{O}^{\rm
an}_{\mathcal{R}}[\\![z]\\!])$. Since
$\widetilde{\operatorname{pr}}\colon\mathcal{R}\to\mathcal{U}_{0}$ is a finite
flat morphism, we can define the $\mathcal{O}^{\rm
an}_{\mathcal{U}_{0}}[\\![z]\\!]$-module structure, the Gauss–Manin connection
$\nabla^{\mathscr{R}}$, the grading operator $\operatorname{Gr}^{\mathscr{R}}$
and the higher residue pairing $P^{\mathscr{R}}$ on $\mathscr{R}$ similarly to
Definition 4.21 and Section 4.3.3. By the same argument as in Proposition
4.24, $\mathscr{R}$ is a free $\mathcal{O}^{\rm
an}_{\mathcal{U}_{0}}[\\![z]\\!]$-module of rank $\dim H^{*}_{\rm
CR}(\mathfrak{X}_{+})-\dim H^{*}_{\rm CR}(\mathfrak{X}_{-})$. For a generic
$(q,\chi)\in\mathcal{U}_{0}$,
$\widetilde{\operatorname{pr}}^{-1}(q,\chi)\cap\mathcal{R}$ consists of
finitely many reduced points, and the asymptotic expansion in Definition 4.28
defines an isomorphism
$\operatorname{Asym}\colon\mathscr{R}_{(q,\chi)}\cong\mathbb{C}[\\![z]\\!]^{\oplus\operatorname{rank}\mathscr{R}}$.
###### Remark 5.14.
Since $\operatorname{rank}\widetilde{\operatorname{pr}}_{*}(\mathcal{O}^{\rm
an}_{\mathcal{B}_{+}})=\dim H_{\rm CR}^{*}(\mathfrak{X}_{+})>\dim H_{\rm
CR}^{*}(\mathfrak{X}_{-})=\operatorname{rank}\widetilde{\operatorname{pr}}_{*}(\mathcal{O}^{\rm
an}_{\mathcal{B}_{-}})$ (by Corollary 4.20 and Remark 5.3), $\mathcal{R}$ is
never empty under Assumption 5.2.
Figure 6: Family of critical points. Out of $d$ critical points, $d-2$ points
go to infinity at the large radius limit of $\mathcal{O}_{\mathbb{P}^{1}}(-d)$
($d=5$ in the picture).
###### Example 5.15.
Consider the example of the LG model in Section 3.6.3. This corresponds to a
discrepant transformation between
$\mathfrak{X}_{+}=\big{[}\mathbb{C}^{2}/\mu_{d}\big{]}$ (of type
$\frac{1}{d}(1,1)$) and its minimal resolution
$\mathfrak{X}_{-}=\mathcal{O}_{\mathbb{P}^{1}}(-d)$. The LG model was given by
the potential function
$F=x_{2}+\frac{x_{1}^{d}}{x_{2}}+tx_{1}=\tilde{x}_{2}+q\frac{\tilde{x}_{1}^{d}}{\tilde{x}_{2}}+\tilde{x}_{1},$
where $(x_{1},x_{2},t)$ and $(\tilde{x}_{1},\tilde{x}_{2},q)$ are related by
$\tilde{x}_{1}=tx_{1}$, $\tilde{x}_{2}=x_{2}$, $q=t^{-d}$. Here $q=t^{-d}$ is
a co-ordinate on $\mathcal{M}=\mathbb{P}(1,d)$, $\\{t=0\\}$ is the large
radius limit point of $\mathfrak{X}_{+}$ and $\\{q=0\\}$ is the large radius
limit point of $\mathfrak{X}_{-}$. On the chart near $t=0$ (associated to
$\mathfrak{X}_{+}$), the precise domain of definition of the potential
function $F$ is given by (see Section 3.6.3)
$\mathcal{Y}_{\mathbf{\Sigma}_{+}}=\big{\\{}(x_{1},x_{2},y,t)\in\mathbb{C}^{4}\colon
x_{2}y=x_{1}^{d}\big{\\}},$
where $y$ is identified with the term $x_{1}^{d}/x_{2}$ in $F$. The relative
critical scheme of $F$ on this chart is given by
$\displaystyle\left\\{x_{1}\frac{\partial F}{\partial
x_{1}}=x_{2}\frac{\partial F}{\partial x_{2}}=0\right\\}$
$\displaystyle=\left\\{d\frac{x_{1}^{d}}{x_{2}}+tx_{1}=0,\
x_{2}-\frac{x_{1}^{d}}{x_{2}}=0\right\\}$
$\displaystyle=\big{\\{}(x_{1},x_{2},y,t)\in\mathbb{C}^{4}\colon dy+tx_{1}=0,\
x_{2}-y=0,\ x_{2}y=x_{1}^{d}\big{\\}}$
$\displaystyle=\left\\{\left(x_{1},-\frac{tx_{1}}{d},-\frac{tx_{1}}{d},t\right)\in\mathbb{C}^{4}\colon
x_{1}^{2}\big{(}x_{1}^{d-2}-t^{2}/d^{2}\big{)}=0\right\\}.$
This is schematically depicted in Fig. 6.
### 5.4 Comparison of quantum D-modules
Finally we obtain a comparison result between the quantum D-modules of
$\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ combining Theorem 4.34 and Corollary
5.12.
Recall the analytic quantum D-module $\operatorname{QDM}^{\rm
an}_{\mathbb{T}}(\mathfrak{X}_{\pm})$ of $\mathfrak{X}_{\pm}$ from Section
4.4; it is defined over an open neighbourhood $U_{\pm}$ of the origin in the
equivariant Kähler moduli space
$\big{[}\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\pm})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\pm})\big{]}.$
By Theorem 4.34, we have the analytic mirror isomorphism
$\operatorname{Mir}^{\rm an}_{\pm}\colon\
\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\pm}\big{|}_{\mathcal{U}^{\prime}_{\pm}}\cong\operatorname{mir}_{\pm}^{*}\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{\pm})$ (5.4)
over an open neighbourhood
$\mathcal{U}^{\prime}_{\pm}\subset\mathcal{U}_{\pm}$ of
$(0_{\pm},0)\in\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$,
where $\operatorname{mir}_{\pm}\colon\mathcal{U}^{\prime}_{\pm}\to U_{\pm}$
denotes the mirror map and the overline $\overline{\cdots}$ means the $z$-adic
completion. Let us observe that the analytic mirror isomorphism extends to a
domain which is closed under the $\mathbb{C}^{\times}$-action (as discussed in
Section 5.3). We have already seen in Section 5.3 that
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\pm}$ extends to
$\mathbb{C}^{\times}\mathcal{U}^{\prime}_{\pm}=\bigcup\limits_{s\in\mathbb{C}^{\times}}s\cdot\mathcal{U}^{\prime}_{\pm}$.
Introduce the $\mathbb{C}^{\times}$-action on the equivariant Kähler moduli
space $[\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\pm})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\pm})]$ generated by the Euler vector field (2.7); since the
mirror map $\operatorname{mir}_{\pm}$ preserves the Euler vector fields, it
can be extended to a unique $\mathbb{C}^{\times}$-equivariant map
$\operatorname{mir}_{\pm}\colon\mathbb{C}^{\times}\mathcal{U}^{\prime}_{\pm}\to\mathbb{C}^{\times}U_{\pm}$.
We may assume (by shrinking $\mathcal{U}^{\prime}$ if necessary) that
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\pm}|_{\mathcal{U}^{\prime}}$
is generated by $\operatorname{Gr}$-homogeneous sections
$\Omega_{0}^{\pm},\dots,\Omega_{s}^{\pm}$ over $\mathcal{O}^{\rm
an}_{\mathcal{U}^{\prime}_{\pm}}[\\![z]\\!]$ (see [27, Theorem 4.26] and Part
(b) in Section 4.4). Since $\operatorname{Mir}^{\rm an}$ intertwines the
grading operators as $\operatorname{Mir}^{\rm
an}\circ\operatorname{Gr}=\operatorname{Gr}\circ\operatorname{Mir}^{\rm an}$,
the sections $\operatorname{Mir}^{\rm an}(\Omega_{i}^{\pm})$ extend to
$\mathbb{C}^{\times}\mathcal{U}^{\prime}_{\pm}$, and the mirror isomorphism
$\operatorname{Mir}^{\rm an}$ also extends there.
Henceforth we assume that the open set $\mathcal{U}^{\prime}_{\pm}$ (where the
analytic mirror isomorphism (5.4) is defined) is closed under the
$\mathbb{C}^{\times}$-action. By the same argument as in Section 5.3,
$\mathcal{U}^{\prime}_{+}\cap\mathcal{U}^{\prime}_{-}$ is an open set
containing
$(\mathcal{C}\setminus\\{0_{+},0_{-}\\})\times\\{0\\}\subset\mathcal{M}_{\mathbb{T}}$.
Setting
$\mathcal{U}_{0}^{\prime}=\mathcal{U}_{0}\cap(\mathcal{U}^{\prime}_{+}\cap\mathcal{U}^{\prime}_{-})$
for the open set $\mathcal{U}_{0}$ from Lemma 5.11, we obtain the following
result.
###### Theorem 5.16.
There exist an open subset $\mathcal{U}_{0}^{\prime}$ of
$\mathcal{M}_{\mathbb{T}}$ containing
$(\mathcal{C}\setminus\\{0_{+},0_{-}\\})\times\\{0\\}$ and mirror maps
$\operatorname{mir}_{\pm}\colon\mathcal{U}_{0}^{\prime}\to[\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\pm})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\pm})]$ to the equivariant Kähler moduli spaces of
$\mathfrak{X}_{\pm}$ such that the following decomposition of
$\mathcal{O}^{\rm an}_{\mathcal{U}^{\prime}_{0}}[\\![z]\\!]$-modules holds:
$\operatorname{mir}_{+}^{*}\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{+})\cong\operatorname{mir}_{-}^{*}\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{-})\oplus\mathscr{R}\big{|}_{\mathcal{U}^{\prime}_{0}},$
(5.5)
where $\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{\pm})$ denotes the $z$-adic completion of the
equivariant quantum D-module of $\mathfrak{X}_{\pm}$ $($see Section
$\ref{subsec:an_mirror_isom})$ and $\mathscr{R}$ is as in Definition 5.13.
Under this decomposition, the flat connection, the grading operator and the
pairing split as follows:
* (1)
$\operatorname{mir}_{+}^{*}\nabla^{+}=(\operatorname{mir}_{-}^{*}\nabla^{-}+\alpha\cdot\operatorname{id})\oplus\nabla^{\mathscr{R}}$
for some $1$-form
$\alpha\in\Omega^{1}_{\mathcal{M}_{\mathbb{T}}/\operatorname{Lie}\mathbb{T}}$;
* (2)
$\operatorname{mir}_{+}^{*}\operatorname{Gr}^{+}=\operatorname{mir}_{-}^{*}\operatorname{Gr}^{-}\oplus\operatorname{Gr}^{\mathscr{R}}$;
* (3)
$\operatorname{mir}_{+}^{*}P^{+}=\operatorname{mir}_{-}^{*}P^{-}\oplus
P^{\mathscr{R}}$,
where $\nabla^{\pm}$, $\operatorname{Gr}^{\pm}$, $P^{\pm}$ denote respectively
the quantum connection, the grading operator (2.8) and the pairing (2.9) on
the quantum D-module of $\mathfrak{X}_{\pm}$.
###### Remark 5.17.
The one-form $\alpha$ arises from the difference of the splittings of the
extended divisor sequence (3.4) over $\mathbb{Q}$, one chosen for
$\mathfrak{X}_{+}$ and the other for $\mathfrak{X}_{-}$ (see Remark 4.35). It
is of the form $\alpha(\xi q\frac{\partial}{\partial
q})=\overline{\alpha}(\xi)$ for some
$\overline{\alpha}\in\operatorname{Hom}(\mathbb{L}_{\mathbb{Q}}^{\star},\mathbf{M}_{\mathbb{Q}}^{\star})$;
in particular $\alpha$ vanishes in the non-equivariant limit. Recall that the
Gauss–Manin connection in the equivariant case depends on the choice of a
splitting (see Section 4.1).
###### Remark 5.18.
By construction, the above decomposition (5.5) preserves the additional
structure given by multiplication by the mirror co-ordinates
$x_{1},\dots,x_{n}$. They correspond to the equivariant shift operators
(Seidel representation), see Remark 4.3.
### 5.5 Comparison of Gromov–Witten theories in all genera
Using a formula due to Givental [49, 50] and Teleman [104] for higher genus
Gromov–Witten potentials, we show that the ancestor Gromov–Witten potential of
$\mathfrak{X}_{+}$ is decomposed into the ancestor potential of
$\mathfrak{X}_{-}$ and a product of Witten–Kontsevich tau functions, under the
action of a quantized symplectic operator. We use Givental’s formula for
orbifolds studied by Brini–Cavalieri–Ross [19] and Zong [109].
#### 5.5.1 Ancestor potentials
Let $\mathfrak{X}$ be a smooth DM stack equipped with a $\mathbb{T}$-action
satisfying the assumptions in Section 2.1; we use the notation there. Consider
the forgetful morphism
$p\colon\mathfrak{X}_{g,l+m,d}\to\overline{M}_{g,l+m}\to\overline{M}_{g,l}$
which forgets the map and the last $m$ marked points, and let
$\overline{\psi}_{i}\in H^{2}(\mathfrak{X}_{g,l+m,d})$, $1\leq i\leq l$ denote
the pull-back of the universal cotangent class $\psi_{i}\in
H^{2}(\overline{M}_{g,l})$ by $p$. We define the _ancestor Gromov–Witten
invariants_ as the $\mathbb{T}$-equivariant integral
$\big{\langle}\alpha_{1}\overline{\psi}^{k_{1}},\dots,\alpha_{l}\overline{\psi}^{k_{l}};\beta_{1},\dots,\beta_{m}\big{\rangle}_{g,l+m,d}:=\int_{[\mathfrak{X}_{g,l+m,d}]_{\rm
vir}}\prod_{i=1}^{l}\operatorname{ev}_{i}^{*}(\alpha_{i})\overline{\psi}_{i}^{k_{i}}\cdot\prod_{i=1}^{m}\operatorname{ev}_{i+l}^{*}(\beta_{i}),$
where $\alpha_{i},\beta_{j}\in H^{*}_{{\rm CR},\mathbb{T}}(\mathfrak{X})$.
When the moduli stack $\mathfrak{X}_{g,m+l,d}$ is not proper, the right-hand
side is defined by the virtual localization formula and lies in
$S_{\mathbb{T}}=\operatorname{Frac}(R_{\mathbb{T}})$ as before. We choose a
homogeneous $R_{\mathbb{T}}$-basis $\\{\phi_{i}\\}_{i=0}^{N}$ of $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})$ satisfying (2.4) and introduce the infinite set
$\mathbf{y}=\\{y_{k}^{i}\\}_{k\geq 0,0\leq i\leq s}$ of co-ordinates on
$H^{*}_{{\rm CR},\mathbb{T}}(\mathfrak{X})[\\![z]\\!]$ given by
$\mathbf{y}\mapsto\mathbf{y}(z)=\sum_{k=0}^{\infty}\sum_{i=0}^{s}y_{k}^{i}\phi_{i}z^{k}.$
The _ancestor potential_ of $\mathfrak{X}$ is the following generating
function of the ancestor Gromov–Witten invariants
$\mathscr{A}_{\mathfrak{X},\tau}=\exp\left(\sum_{d\in\boldsymbol{\Lambda}_{+}}\sum_{\begin{subarray}{c}g\geq
0,\,l\geq 0\\\
2g-2+l>0\end{subarray}}\sum_{m=0}^{\infty}\left\langle\mathbf{y}(\overline{\psi}),\dots,\mathbf{y}(\overline{\psi});\tau,\dots,\tau\right\rangle_{g,l+m,d}\hbar^{g-1}\frac{Q^{d}}{l!m!}\right),$
which we regard as a function in the formal neighbourhood of $\mathbf{y}=0$.
Introduce another set of variables $\mathbf{x}=\\{x_{k}^{i}\\}_{k\geq 0,0\leq
i\leq N}$ that are related to $\mathbf{y}$ by the formula (Dilaton shift)
$\mathbf{x}(z)=\mathbf{y}(z)-\phi_{0}z,$
where
$\mathbf{x}(z)=\sum\limits_{k=0}^{\infty}\sum\limits_{i=0}^{N}x_{k}^{i}\phi_{i}z^{k}$.
Using the co-ordinate $\mathbf{x}(z)$, we shall regard
$\mathscr{A}_{\mathfrak{X},\tau}$ as a formal function on the formal
neighbourhood of $\mathbf{x}(z)=-\phi_{0}z$ in $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[\\![z]\\!]$.
As in Section 2.2, we can specialize $Q$ to one in the ancestor potential by
using the divisor equation for $\tau$. We have
$\mathscr{A}_{\mathfrak{X},\tau}=\exp\left(\sum_{d\in\boldsymbol{\Lambda}_{+}}\sum_{\begin{subarray}{c}g\geq
0,\,l\geq 0\\\
2g-2+l>0\end{subarray}}\sum_{m=0}^{\infty}\left\langle\mathbf{y}(\overline{\psi}),\dots,\mathbf{y}(\overline{\psi});\tau^{\prime},\dots,\tau^{\prime}\right\rangle_{g,l+m,d}\hbar^{g-1}\frac{e^{\sigma\cdot
d}Q^{d}}{l!m!}\right),$
when $\tau=\sigma+\tau^{\prime}$ with
$\sigma=\sum\limits_{i=1}^{r}\tau^{i}\phi_{i}\in H^{2}(\mathfrak{X})$ and
$\tau^{\prime}=\tau^{0}\phi_{0}+\sum\limits_{i=r+1}^{s}\tau^{i}\phi_{i}$.
Moreover, the Galois symmetry (2.3) implies
$\mathscr{A}_{\mathfrak{X},g(\xi)\tau}(dg(\xi)\mathbf{x})=\mathscr{A}_{\mathfrak{X},\tau}(\mathbf{x}),\qquad\xi\in
H^{2}(\mathfrak{X},\mathbb{Z}),$
where $g(\xi)$, $dg(\xi)$ are as in Section 2.2 (they act on the equivariant
cohomology $H_{{\rm CR},\mathbb{T}}^{*}(\mathfrak{X})$ via the splitting
$H_{{\rm CR},\mathbb{T}}^{*}(\mathfrak{X})\cong H^{*}_{\rm
CR}(\mathfrak{X})\otimes R_{\mathbb{T}}$ given by the basis $\\{\phi_{i}\\}$).
Therefore the specialization $\mathscr{A}_{\mathfrak{X},\tau}|_{Q=1}$ makes
sense as an element of
$S_{\mathbb{T}}(\\!(\hbar)\\!)[\\![\boldsymbol{\Lambda}_{+}]\\!][\\![\tau^{\prime},\mathbf{y}]\\!]$
– we regard it as an
$(H^{2}(\mathfrak{X},\mathbb{Z})/\boldsymbol{\Lambda}^{\star})$-invariant
function of $(\tau,\mathbf{x})\in\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})\times_{\operatorname{Spec}R_{\mathbb{T}}}\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[\\![z]\\!]$, where $\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})[\\![z]\\!]$ denotes the infinite-dimensional
vector bundle over $\operatorname{Spec}R_{\mathbb{T}}$ associated with the
$R_{\mathbb{T}}$-module $H_{{\rm CR},\mathbb{T}}^{*}(\mathfrak{X})[\\![z]\\!]$
(see Remark 2.2). Henceforth we assume that $Q$ is specialized to one in the
ancestor potential.
#### 5.5.2 Givental’s quantization formalism
We briefly review the quantization formalism of Givental [49]. We also refer
to [29, Section 3], [30, Section 5.1] for the exposition.
Let $V$ be a finite-dimensional $\mathbb{C}$-vector space equipped with a
symmetric non-degenerate pairing $(\cdot,\cdot)_{V}$. Then $V(\\!(z)\\!)$ has
the following symplectic form $\Omega_{V}$:
$\Omega_{V}(f,g)=\mathop{\operatorname{Res}}\limits_{z=0}(f(-z),g(z))_{V}dz.$
Choosing a basis $\\{\phi_{i}\\}$ on $V$, we let
$\mathbf{x}=\\{x_{k}^{i}\\}_{k\geq 0,0\leq i\leq s}$ denote the co-ordinates
on $V[\\![z]\\!]$ given by
$\mathbf{x}\mapsto\mathbf{x}(z)=\sum\limits_{k=0}^{\infty}\sum\limits_{i=0}^{s}x_{k}^{i}\phi_{i}z^{k}$.
Let $W$ be another $\mathbb{C}$-vector space of the same dimension equipped
with a symmetric non-degenerate pairing $(\cdot,\cdot)_{W}$. A
$\mathbb{C}[\\![z]\\!]$-linear operator $U\colon V[\\![z]\\!]\to W[\\![z]\\!]$
is said to be _unitary_ when it satisfies
$(U(-z)v_{1},U(z)v_{2})_{W}=(v_{1},v_{2})_{V}.$ (5.6)
A unitary operator $U$ induces a $\mathbb{C}(\\!(z)\\!)$-linear symplectic
transformation $U\colon V(\\!(z)\\!)\to W(\\!(z)\\!)$. The quantized operator
${\widehat{U}}$ described below sends a certain “tame” (spelled out below)
formal function $\mathscr{A}$ on $V[\\![z]\\!]$ to a tame formal function
${\widehat{U}}\mathscr{A}$ on $W[\\![z]\\!]$. For $\mathbf{D}\in
zV[\\![z]\\!]$, let $\operatorname{\mathfrak{AFock}}(V,\mathbf{D})$ denote the
set of formal power series $\mathscr{A}$ of the form
$\mathscr{A}=\exp\left(\sum_{g=0}^{\infty}\hbar^{g-1}F^{g}(\mathbf{x})\right)$
with $F^{g}$ a formal power series in $\mathbf{x}-\mathbf{D}$ (i.e., a
function in the formal neighbourhood of $\mathbf{x}=\mathbf{D}$ in
$V[\\![z]\\!]$) satisfying the following tameness condition
$\left.\frac{\partial^{m}F^{g}}{\partial x_{k_{1}}^{i_{1}}\cdots\partial
x_{k_{m}}^{i_{m}}}\right|_{\mathbf{x}=\mathbf{D}}=0\qquad\text{if
$k_{1}+\dots+k_{m}>3g-3+m$}$
and $F^{0}|_{\mathbf{x}=\mathbf{D}}=F^{1}|_{\mathbf{x}=\mathbf{D}}=0$ (see
[30, Definition 5.1]). Then ${\widehat{U}}$ defines an operator [30,
Definition 5.7]:
${\widehat{U}}\colon\
\operatorname{\mathfrak{AFock}}(V,\mathbf{D})\to\operatorname{\mathfrak{AFock}}(W,U(\mathbf{D})).$
For $\mathbf{s}\in zV[\\![z]\\!]$, let $T_{\mathbf{s}}$ denote the operator
acting on tame functions on $V[\\![z]\\!]$ which shifts the base point
$\mathbf{D}$ by $\mathbf{s}$ [30, Definition 5.5]; for a tame function
$\mathscr{A}\in\operatorname{\mathfrak{AFock}}(V,\mathbf{D})$,
$T_{\mathbf{s}}\mathscr{A}\in\operatorname{\mathfrak{AFock}}(V,\mathbf{D}+\mathbf{s})$
denotes the Taylor expansion of $e^{-F_{1}(\mathbf{D}+\mathbf{s})}\mathscr{A}$
at the new base point $\mathbf{D}+\mathbf{s}$ (whenever it makes sense). The
tameness condition implies that $T_{\mathbf{s}}\mathscr{A}$ is well-defined
for all $\mathscr{A}\in\operatorname{\mathfrak{AFock}}(V,\mathbf{D})$ if
$\mathbf{s}\in z^{2}V[\\![z]\\!]$; under the additional assumption that
$\mathscr{A}$ is rational [30, Definition 5.2], $T_{\mathbf{s}}\mathscr{A}$ is
well-defined for $\mathbf{s}\in zV[\\![z]\\!]$ [30, Definition 5.5]. All tame
functions appearing in this section are rational, since they are obtained by
the Givental formula [29, Proposition 3.20].
When the ancestor potential $\mathscr{A}_{\mathfrak{X},\tau}$ is convergent
and analytic in the variable $\tau$, it defines an element of
$\operatorname{\mathfrak{AFock}}(\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})_{\chi},-z\phi_{0})$ where $\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})_{\chi}$ denotes the fibre of the vector bundle
$\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})\to\operatorname{Spec}R_{\mathbb{T}}$ (see Remark
2.2) at $\chi$ and $\chi$ is the image of $\tau\in\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X})$ in $\operatorname{Spec}R_{\mathbb{T}}$.
The _Witten–Kontsevich tau-function_ is the ancestor potential for a point. It
is a function on the formal neighbourhood of $-z$ in $\mathbb{C}[\\![z]\\!]$
given by
$\displaystyle\mathscr{T}$
$\displaystyle=\exp\left(\sum_{g=0}^{\infty}\hbar^{g-1}\sum_{l\colon
2g-2+l>0}\frac{1}{l!}\sum_{k_{1},\dots,k_{l}\geq
0}\big{\langle}\psi^{k_{1}},\dots,\psi^{k_{l}}\big{\rangle}_{g,l}y_{k_{1}}\cdots
y_{k_{l}}\right)$
$\displaystyle=(-x_{1})^{-\frac{1}{24}}\exp\left(\sum_{g=0}^{\infty}\hbar^{g-1}\sum_{l\colon
2g-2+l>0}\frac{1}{l!}\sum_{\begin{subarray}{c}k_{1},\dots,k_{l}\geq 0,\\\
k_{j}\neq
1\end{subarray}}\big{\langle}\psi^{k_{1}},\cdots,\psi^{k_{l}}\big{\rangle}_{g,l}\frac{x_{k_{1}}\cdots
x_{k_{l}}}{(-x_{1})^{2g-2+l}}\right),$
where
$\big{\langle}\psi^{k_{1}},\dots,\psi^{k_{l}}\big{\rangle}_{g,l}=\int_{\overline{M}_{g,l}}\psi^{k_{1}}\cdots\psi^{k_{l}},$
$\sum\limits_{k=0}^{\infty}x_{k}z^{k}$ denotes the co-ordinate on
$\mathbb{C}[\\![z]\\!]$ and $y_{k}=x_{k}+\delta_{k,1}$. We used the dilaton
equation [2, Theorem 8.3.1] in the second line. The Witten–Kontsevich tau-
function defines a rational element of
$\operatorname{\mathfrak{AFock}}(\mathbb{C},-z)$.
#### 5.5.3 A relationship between ancestor potentials
We fix a homogeneous $R_{\mathbb{T}}$-basis $\\{\phi_{i}\\}$ of $H^{*}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{\pm})$ satisfying (2.4) as above. Let
$\mathcal{U}_{0}^{\prime}\subset\mathcal{M}_{\mathbb{T}}$ be an open set from
Theorem 5.16. As discussed in Section 4.3.3, there exists an open dense subset
${\mathcal{U}^{\prime}_{0}}^{\rm ss}$ of $\mathcal{U}_{0}^{\prime}$ such that
for each $(q,\chi)\in{\mathcal{U}^{\prime}_{0}}^{\rm ss}$,
$\widetilde{\operatorname{pr}}^{-1}(q,\chi)\cap\mathcal{B}_{+}$ consists of
$\dim H^{*}_{\rm CR}(\mathfrak{X}_{+})$ many reduced points. Choose a point
$(q,\chi)\in{\mathcal{U}^{\prime}_{0}}^{\rm ss}$. Combining the decomposition
(5.5) at $(q,\chi)$ and the isomorphism
$\operatorname{Asym}\colon\mathscr{R}_{(q,\chi)}\cong\mathbb{C}[\\![z]\\!]^{\oplus\operatorname{rank}\mathscr{R}}$
given by the asymptotic expansion (see Definition 5.13), we obtain a
$\mathbb{C}[\\![z]\\!]$-linear isomorphism
$\widetilde{U}_{q,\chi}\colon\ \mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{+})_{\chi}[\\![z]\\!]\xrightarrow{\cong}\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{-})_{\chi}[\\![z]\\!]\oplus\mathbb{C}[\\![z]\\!]^{\oplus\operatorname{rank}\mathscr{R}},$
where $\mathbf{H}_{{\rm CR},\mathbb{T}}(\mathfrak{X}_{\pm})_{\chi}$ denotes
the fibre of the vector bundle $\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{\pm})\to\operatorname{Spec}R_{\mathbb{T}}$ at
$\chi$ (see Remark 2.2). The equivariant orbifold Poincaré pairing (2.2)
defines a $\mathbb{C}$-bilinear pairing on $\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{\pm})_{\chi}$ for a generic $\chi$. With respect
to these pairings and the diagonal pairing on
$\mathbb{C}[\\![z]\\!]^{\oplus\operatorname{rank}\mathscr{R}}$,
$U=\widetilde{U}_{q,\chi}$ satisfies the unitarity (5.6); this follows from
Theorem 5.16 and the definition of the higher residue pairing (see Section
4.3.3). We flip the sign of $z$ and set
$U_{q,\chi}:=\widetilde{U}_{q,\chi}\big{|}_{z\to-z}$.
When functions $\mathscr{A}_{i}$ on $V_{i}[\\![z]\\!]$ $(i=1,\dots,k)$ are
given, we write $\mathscr{A}_{1}\otimes\cdots\otimes\mathscr{A}_{k}$ for the
function on $V_{1}[\\![z]\\!]\times\cdots\times V_{k}[\\![z]\\!]$ given by
$\big{(}\mathbf{x}^{(1)},\dots,\mathbf{x}^{(k)}\big{)}\mapsto\prod\limits_{i=1}^{k}\mathscr{A}_{i}(\mathbf{x}^{(i)})$.
###### Theorem 5.19.
Let $\mathscr{A}_{\pm,\tau}$ denote the ancestor potential of
$\mathfrak{X}_{\pm}$. For $(q,\chi)\in{\mathcal{U}_{0}^{\prime}}^{\rm ss}$, we
have
$T_{\mathbf{s}}{\widehat{U}}_{q,\chi}\mathscr{A}_{+,\operatorname{mir}_{+}(q,\chi)}=\mathscr{A}_{-,\operatorname{mir}_{-}(q,\chi)}\otimes\mathscr{T}^{\otimes\operatorname{rank}\mathscr{R}},$
where
$\mathbf{s}:=(-z\phi_{0},(-z,\dots,-z))+U_{q,\chi}(z\phi_{0})\in\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{-})_{\chi}[\\![z]\\!]\times\mathbb{C}[\\![z]\\!]^{\oplus\operatorname{rank}\mathscr{R}}$.
###### Remark 5.20.
Implicit in the above theorem is the convergence and analyticity of
$\mathscr{A}_{\pm,\tau}$ with respect to $\tau$. This follows from the
Givental formula. We refer to [29, Theorem 1.4, Definition 3.13] for the
discussion on the convergence of ancestor potentials.
###### Remark 5.21.
The ancestor potentials of $\mathfrak{X}_{\pm}$ define sections of the Fock
sheaves [30] associated with the quantum D-modules of $\mathfrak{X}_{\pm}$,
and the above relationship can be interpreted in this language.
###### Remark 5.22.
We can state the relationship between the Gromov–Witten theories of
$\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ in terms of cohomological field
theory (CohFT): _the CohFT of $\mathfrak{X}_{+}$ transforms into the product
of the CohFT of $\mathfrak{X}_{-}$ and the trivial semisimple CohFT under the
Givental action of $U_{q,\chi}$_. We refer the reader to [88, 102, 104] for
the Givental group action on CohFTs.
#### 5.5.4 Givental’s formula and the proof of Theorem 5.19
Teleman’s classification theorem [104] implies that the ancestor potential
$\mathscr{A}$ of a semisimple cohomological field theory on a vector space $H$
lies in the orbit of $\mathscr{T}^{\otimes N}$ ($N=\dim H$) with respect to
the action of symplectic operators (via the Givental quantization). That is,
there exists a unitary operator $R\colon\mathbb{C}[\\![z]\\!]^{\oplus N}\to
H[\\![z]\\!]$ such that
$\mathscr{A}=T_{-ze+R(z,\dots,z)}{\widehat{R}}\mathscr{T}^{\otimes N},$
where $e\in H$ is the identity element of the Frobenius algebra $H$. In our
context, $R$ depends on $\tau\in\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X})$ and gives a formal fundamental solution of the
quantum connection in the $\tau$-direction. It is ambiguous up to the right
multiplication by a constant diagonal matrix [48, Remarks after Proposition
1.1]; as [19, 109] did, the ambiguity can be fixed by Tseng’s orbifold quantum
Riemann-Roch theorem [105].
We state Givental’s formula for a semiprojective toric DM stack in terms of
the mirror LG model. Let $\mathfrak{X}_{\mathbf{\Sigma}}$ be a smooth toric DM
stack with $\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ and let
$(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$ denote the mirror LG
model from Definition 3.6. Let $\mathcal{B}\subset\mathcal{Y}$,
$\mathcal{U}\subset\mathcal{M}_{\mathbb{T}}:=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$
be analytic open neighbourhoods of $\tilde{0}_{\mathbf{\Sigma}}$ and
$(0_{\mathbf{\Sigma}},0)$ respectively such that the conclusion of Corollary
4.20 holds, as usual. Let $\mathcal{U}^{\rm ss}\subset\mathcal{U}$ denote the
open dense subset consisting of $(q,\chi)\in\mathcal{U}$ such that
$\widetilde{\operatorname{pr}}^{-1}(q,\chi)\cap\mathcal{B}$ is reduced
(recall, as discussed in Section 4.3.3, that
$\widetilde{\operatorname{pr}}^{-1}(q,\chi)$ consists of relative critical
points of the equivariant potential
$F_{\mathbb{T}}=F-\sum\limits_{i=1}^{n}\chi_{i}\log x_{i}$). For
$(q,\chi)\in\mathcal{U}^{\rm ss}$, the asymptotic expansion of equivariant
oscillatory integrals (see Definition 4.28) defines an isomorphism
$\operatorname{Asym}\colon\
\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{|}_{(q,\chi)}\to\mathbb{C}[\\![z]\\!]^{\oplus
N},\qquad\operatorname{Asym}:=\bigoplus_{p\in\widetilde{\operatorname{pr}}^{-1}(q,\chi)\cap\mathcal{B}}\operatorname{Asym}_{p},$
where $N=\deg(\widetilde{\operatorname{pr}}|_{\mathcal{B}})=\dim H^{*}_{\rm
CR}(\mathfrak{X})$. Composing the inverse map with the mirror isomorphism from
Theorem 4.34, we obtain a linear map
$\widetilde{R}_{q,\chi}\colon\ \mathbb{C}[\\![z]\\!]^{\oplus
N}\xrightarrow{\operatorname{Asym}^{-1}}\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}\big{|}_{(q,\chi)}\xrightarrow{\operatorname{Mir}^{\rm
an}}\overline{\operatorname{QDM}^{\rm
an}_{\mathbb{T}}}(\mathfrak{X}_{\mathbf{\Sigma}})\big{|}_{\operatorname{mir}(q,\chi)}\cong\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})_{\chi}[\\![z]\\!],$
where $\operatorname{mir}\colon\mathcal{U}\to[\mathcal{M}_{\rm
A,\mathbb{T}}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})]$ is the mirror map. We flip the sign of
$z$ and set $R_{q,\chi}:=\widetilde{R}_{q,\chi}|_{z\to-z}$.
###### Proposition 5.23 (Givental’s formula for toric DM stacks).
The ancestor potential of $\mathfrak{X}_{\mathbf{\Sigma}}$ is given by
$\mathscr{A}_{\mathfrak{X}_{\mathbf{\Sigma}},\operatorname{mir}(q,\chi)}=T_{-z\phi_{0}+R(z,\dots,z)}{\widehat{R}}\mathscr{T}^{\otimes
N}$ with $R=R_{q,\chi}$ above.
###### Proof.
The mirror isomorphism $\operatorname{Mir}^{\rm an}$ identifies the
Gauss–Manin connection with the quantum connection, and it was shown in [27,
Lemma 6.7] that $e^{F_{\mathbb{T}}(p)/z}\operatorname{Asym}_{p}$ gives a
solution to the Gauss–Manin connection for each critical branch $p$ of
$F_{\mathbb{T}}$. Let $\mathbf{U}$ denote the diagonal matrix whose entries
are relative critical values of $F_{\mathbb{T}}$. It follows that
$\widetilde{R}_{q,\chi}e^{-\mathbf{U}/z}$ gives a formal fundamental solution
for $\operatorname{mir}^{*}\nabla$ in the sense of [48, Proposition 1.1],
[109, Theorem 5.1] (our $R_{q,\chi}$ corresponds to $\Psi R$ in [48, 109]; see
also Proposition 6.1 below). We need to flip the sign of $z$ because we use
the sign convention for the quantum connection opposite to [48, 109]. It now
suffices to check that $R_{q,\chi}$ satisfies the classical limit condition at
the large radius limit $q=0_{\mathbf{\Sigma}}$ given in [19, Lemma 6.5,
equation (156), Remark 6.6], [109, Theorem 6.2] (which generalize [49, Theorem
9.1] to the orbifold setting). We can easily check that $R_{q,\chi}$ satisfies
this condition by using the computation in [27, Proposition 6.9]. ∎
###### Remark 5.24.
It has been observed by Givental [49] that the operator $R$ can be constructed
by equivariant mirrors (for Fano toric manifolds).
###### Remark 5.25.
Recall from Remark 4.29 that the asymptotic expansion is ambiguous up to sign.
Therefore $R_{q,\chi}$ is ambiguous up to the right multiplication by a signed
permutation matrix. The right-hand side of the Givental formula is, however,
independent of the choice (see, e.g., [29, Proposition 4.3]).
###### Proof of Theorem 5.19.
Let $R_{q,\chi}^{\pm}$ denote the $R$-operators for $\mathfrak{X}_{\pm}$
introduced above. By the construction of $U_{q,\chi}$ in Section 5.5.3, we
have the following commutative diagram for
$(q,\chi)\in{\mathcal{U}^{\prime}_{0}}^{\rm ss}$ (when we order the critical
points of $F_{\mathbb{T}}$ appropriately):
$\textstyle{\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{+})_{\chi}[\\![z]\\!]\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{U_{q,\chi}\phantom{ABCDE}}$$\textstyle{\mathbf{H}_{{\rm
CR},\mathbb{T}}(\mathfrak{X}_{-})_{\chi}[\\![z]\\!]\oplus\mathbb{C}[\\![z]\\!]^{\oplus\operatorname{rank}\mathscr{R}}}$$\textstyle{\mathbb{C}[\\![z]\\!]^{\oplus
N_{+}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{R_{q,\chi}^{+}}$$\textstyle{\mathbb{C}[\\![z]\\!]^{\oplus
N_{-}}\times\mathbb{C}[\\![z]\\!]^{\oplus\operatorname{rank}\mathscr{R}},\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{R_{q,\chi}^{-}\times\operatorname{id}}$
where $N_{\pm}=\dim H^{*}_{\rm CR}(\mathfrak{X}_{\pm})$. The conclusion
follows by Proposition 5.23 and the ‘chain rule’ of the Givental quantization
(see, e.g., [29, Remark 3.22]). ∎
## 6 Formal decomposition and analytic lift
We discuss the formal decomposition and its analytic lift for quantum
D-modules or Brieskorn modules. This is known as the Hukuhara–Turrittin
theorem for irregular differential equations. For mirrors of the small quantum
cohomology of weak Fano compact toric stacks, the analytic lift is described
explicitly in terms of oscillatory integrals. In this section, we restrict
ourselves to the _non-equivariant_ quantum cohomology and Brieskorn module,
and assume that the toric stacks are compact.
### 6.1 Hukuhara–Turrittin type result
Recall that the non-equivariant quantum connection (or, equivalently, the non-
equivariant Gauss–Manin connection) can be extended in the direction of $z$.
The connection in the $z$-direction is of the form (see (2.11))
$\nabla_{z\frac{\partial}{\partial z}}=z\frac{\partial}{\partial
z}-\frac{1}{z}(E\star_{\tau})+\mu.$
When the quantum product $\star_{\tau}$ is semisimple, $\nabla$ decomposes
over $\mathbb{C}[\\![z]\\!]$ into the sum of rank-one connections
$d+d(\mathbf{u}_{i}/z)$, $i=1,\dots,N$ where
$\mathbf{u}_{1},\dots,\mathbf{u}_{N}$ are eigenvalues of $E\star_{\tau}$.
Moreover this formal decomposition admits an analytic lift over a certain
angular sector: this is an instance of the _Hukuhara–Turrittin theorem_ (see,
e.g., [107, Theorem 12.3], [10, Theorem A], [95, Chapter II, Section 5.d] for
more general statement). We state a version of this theorem following
Hertling–Sevenheck [57, Section 8] and Galkin–Golyshev–Iritani [44, Section
2.5]. We restrict our attention to the quantum cohomology of toric stacks, but
the discussion in this section can be equally applied to a general semisimple
Frobenius manifold [40].
Let $\mathfrak{X}_{\mathbf{\Sigma}}$ be a semiprojective smooth toric DM stack
from Section 3.1.1. In this section (Section 6.1), we assume that
$\mathfrak{X}_{\mathbf{\Sigma}}$ is compact but not necessarily weak Fano. Let
$\mathcal{M}_{\rm A}(\mathfrak{X}_{\mathbf{\Sigma}})$ be the non-equivariant
Kähler moduli space of $\mathfrak{X}_{\mathbf{\Sigma}}$ from Section 2.2. By
the convergence result [27, Corollary 7.3], the non-equivariant quantum
product is analytic over an open neighbourhood $V\subset[\mathcal{M}_{\rm
A}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})]$ of the large radius limit point. This
defines the (non-equivariant) quantum connection $\nabla$ over $V$ and the
_analytic quantum D-module_ (cf. Sections 2.3 and 4.4):
$\operatorname{QDM}^{\rm an}(\mathfrak{X}_{\mathbf{\Sigma}})=(H^{*}_{{\rm
CR}}(\mathfrak{X}_{\mathbf{\Sigma}})\otimes\mathcal{O}^{\rm
an}_{\widetilde{V}}[z],\nabla,P),$ (6.1)
where $\nabla$ is understood as being extended in the $z$-direction by (2.11)
and $\widetilde{V}$ is the preimage of $V$ in $\mathcal{M}_{\rm
A}(\mathfrak{X}_{\mathbf{\Sigma}})$; $H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})\otimes\mathcal{O}^{\rm
an}_{\widetilde{V}}[z]$ is a $\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})$-equivariant sheaf, which shall be
regarded as a sheaf on the stack $V=[\widetilde{V}/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})]$. We omitted the grading operator from
the data because it can be recovered from the other data as
$\operatorname{Gr}=\nabla_{\mathcal{E}}+\nabla_{z\frac{\partial}{\partial
z}}+\frac{1}{2}\dim\mathfrak{X}_{\mathbf{\Sigma}}$. We also write
$\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{\mathbf{\Sigma}})=(H^{*}_{{\rm
CR}}(\mathfrak{X}_{\mathbf{\Sigma}})\otimes\mathcal{O}^{\rm
an}_{\widetilde{V}}[\\![z]\\!],\nabla,P)$ (6.2)
for the quantum D-module completed in $z$. We set
$\displaystyle V^{\times}:=V\cap\big{(}\text{the image of the natural map
$H^{*}_{\rm CR}(\mathfrak{X}_{\mathbf{\Sigma}})\to[\mathcal{M}_{\rm
A}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})]$}\big{)},$ $\displaystyle V^{\rm
ss}:=\big{\\{}\tau\in V^{\times}\colon\text{$(H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}}),\star_{\tau})$ is semisimple as a
ring}\big{\\}}\subset V^{\times}.$
Here recall from Section 2.2 that $\mathcal{M}_{\rm
A}(\mathfrak{X}_{\mathbf{\Sigma}})$ is a partial compactification of
$H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})/2\pi\boldsymbol{\mathrm{i}}\big{(}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}\big{)}^{\star}$
and hence we have a natural map $H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})\to\mathcal{M}_{\rm
A}(\mathfrak{X}_{\mathbf{\Sigma}})\to[\mathcal{M}_{\rm
A}(\mathfrak{X}_{\mathbf{\Sigma}})/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{\mathbf{\Sigma}})]$. When $\mathfrak{X}_{\mathbf{\Sigma}}$
is compact, $V^{\rm ss}$ is open and dense in $V^{\times}$ [27, Remark 7.11].
The following proposition describes a Levelt–Turrittin normal form [95,
Chapter II, Theorem 5.7] of the quantum connection in the semisimple case.
###### Proposition 6.1.
Let $\tau_{0}\in V^{\rm ss}$ be a semisimple point. We have the following
decomposition in an open neighbourhood of $\tau_{0}$:
$\widehat{\Phi}\colon\ \overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{\mathbf{\Sigma}})\overset{\cong}{\longrightarrow}\bigoplus_{i=1}^{N}\left(\mathcal{O}^{\rm
an}[\\![z]\\!],d+d(\mathbf{u}_{i}/z),P_{{\rm std}}\right),$
where $\mathbf{u}_{1},\dots,\mathbf{u}_{N}$ are eigenvalues of $E\star_{\tau}$
with $N=\dim H^{*}_{\rm CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ and $P_{{\rm
std}}$ is the pairing given by the multiplication $P_{{\rm
std}}(f,g)=f(-z)g(z)$ with $f,g\in\mathcal{O}^{\rm an}[\\![z]\\!]$. Once we
fix the ordering of $\mathbf{u}_{1},\dots,\mathbf{u}_{N}$, the isomorphism
$\widehat{\Phi}$ is unique up to a right multiplication by
$\operatorname{diag}(\pm 1,\dots,\pm 1)$.
###### Proof.
When $\mathbf{u}_{1},\dots,\mathbf{u}_{N}$ are mutually distinct, this is
discussed in [40, Lecture 4], [48, Proposition 1.1], [95, Chapter II, Theorem
5.7], [30, Proposition 7.2]. When $\mathbf{u}_{1},\dots,\mathbf{u}_{N}$ are
not mutually distinct (but $\star_{\tau}$ is still semisimple), the existence
of $\widehat{\Phi}$ was shown by Teleman [104, Theorem 8.15] (see also [18,
Section 8]). That $\widehat{\Phi}$ depends analytically on $\tau$ (along the
locus where some of $\mathbf{u}_{1},\dots,\mathbf{u}_{N}$ coalesce) was
discussed in [44, Remark 2.5.7]. The pairing fixes the isomorphism
$\widehat{\Phi}$ up to sign (on each factor), see the argument in [30,
Proposition 7.2]. ∎
###### Remark 6.2.
In this proposition, we do not require that eigenvalues of $E\star_{\tau}$ are
mutually distinct. Note however that $\mathbf{u}_{1},\dots,\mathbf{u}_{N}$
form a co-ordinate system in a neighbourhood of a semisimple point $\tau_{0}$
[40, Lecture 3], and thus they are _generically_ mutually distinct.
###### Remark 6.3.
The isomorphism $\widehat{\Phi}$ modulo $z$ is given by a _normalized
idempotent basis_ of $(H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}}),\star_{\tau})$, i.e., a basis
$\\{\Psi_{1},\dots,\Psi_{N}\\}$ such that $\Psi_{i}\star_{\tau}\Psi_{j}$ is a
non-zero scalar multiple of $\delta_{i,j}\Psi_{i}$ and that
$(\Psi_{i},\Psi_{j})=\delta_{i,j}$.
In plain words, Proposition 6.1 means that the differential equation
$\nabla_{z\frac{\partial}{\partial z}}f=0$ for a cohomology-valued function
$f=f(z)$ admits a formal power series solution
$f=e^{-\mathbf{u}_{i}/z}\big{(}\Psi_{i,0}+\Psi_{i,1}z+\Psi_{i,2}z^{2}+\cdots\big{)}$
(6.3)
with $\Psi_{i,n}\in H^{*}_{\rm CR}(\mathfrak{X}_{\mathbf{\Sigma}})$, where
$\Psi_{i,0}=\Psi_{i}$ is the normalized idempotent in Remark 6.3. These formal
power series are typically divergent. Over an appropriate angular sector in
the $z$-plane, however, we can find an actual analytic solution whose
asymptotic expansion is given by (6.3); moreover the actual solution with
prescribed asymptotics is unique if the angle of the sector is bigger than
$\pi$.
To state this analytic lift in a sheaf-theoretic language, we follow Sabbah
[95] and introduce a sheaf $\mathcal{A}$ of “holomorphic” functions on the
real blowup of $\mathbb{C}$. An (open) _sector_ is a subset of $\mathbb{C}$ of
the form $\\{z\in\mathbb{C}^{\times}\colon\phi_{1}<\arg
z<\phi_{2},|z|<\delta\\}$ for some $\phi_{1},\phi_{2}\in\mathbb{R}$ and
$\delta\in(0,\infty]$. A holomorphic function $f(z)$ on the sector
$I=\\{z\in\mathbb{C}^{\times}\colon\phi_{1}<\arg z<\phi_{2},|z|<\delta\\}$ is
said to have the _asymptotic expansion
$f\sim\sum\limits_{k=0}^{\infty}a_{k}z^{k}$ as $z\to 0$ along $I$_ if for
every $\epsilon>0$ and for every $m\geq 0$, there exists a constant
$C_{\epsilon,m}>0$ such that
$\left|f(z)-\sum_{k=0}^{m}a_{k}z^{k}\right|\leq C_{\epsilon,m}|z|^{m+1}$
for all $z$ with $\phi_{1}+\epsilon\leq\arg z\leq\phi_{2}-\epsilon$ and
$|z|\leq\delta/2$.
###### Definition 6.4 ([95, Chapter II, Section 5.c]).
Let ${\widetilde{\mathbb{C}}}:=[0,\infty)\times S^{1}$ denote the oriented
real blowup of $\mathbb{C}$ at the origin. This is a smooth manifold with
boundary and is equipped with the map
$\pi\colon{\widetilde{\mathbb{C}}}\to\mathbb{C}$,
$\pi\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}=re^{\boldsymbol{\mathrm{i}}\theta}$.
Let $C^{\infty}_{\widetilde{\mathbb{C}}}$ denote the sheaf of complex-valued
$C^{\infty}$-functions on ${\widetilde{\mathbb{C}}}$ and define
$\mathcal{A}_{\widetilde{\mathbb{C}}}$ to be the subsheaf of
$C^{\infty}_{\widetilde{\mathbb{C}}}$ of germs annihilated by the Cauchy-
Riemann operator
$\overline{z}\frac{\partial}{\partial\overline{z}}=\frac{1}{2}\big{(}r\frac{\partial}{\partial
r}+\boldsymbol{\mathrm{i}}\frac{\partial}{\partial\theta}\big{)}$. Sections of
$\mathcal{A}_{\widetilde{\mathbb{C}}}$ over the open set
$\\{(r,e^{\boldsymbol{\mathrm{i}}\theta})\in{\widetilde{\mathbb{C}}}\colon
0\leq r<\delta,\,\phi_{1}<\theta<\phi_{2}\\}$ are precisely those holomorphic
functions $f(z)$ on the sector $\\{z\in\mathbb{C}^{\times}\colon\phi_{1}<\arg
z<\phi_{2},\,|z|<\delta\\}$ which admit asymptotic expansions
$f(z)\sim\sum\limits_{k=0}^{\infty}a_{k}z^{k}$ along this sector.
The same construction works in families: for a complex manifold $M$, we
similarly define the sheaf $\mathcal{A}_{M\times{\widetilde{\mathbb{C}}}}$
over $M\times{\widetilde{\mathbb{C}}}$ to be the subsheaf of
$C^{\infty}_{M\times{\widetilde{\mathbb{C}}}}$ of germs annihilated by the
Cauchy–Riemann operators $\overline{z}\frac{\partial}{\partial\overline{z}}$,
$\overline{\partial}_{M}$.
The asymptotic expansion yields a map
$i_{\xi}^{-1}\mathcal{A}_{M\times{\widetilde{\mathbb{C}}}}\rightarrow\mathcal{O}^{\rm
an}_{M}[\\![z]\\!]$ (6.4)
for any $\xi\in S^{1}$, where $i_{\xi}\colon M\cong
M\times\\{(0,\xi)\\}\hookrightarrow M\times{\widetilde{\mathbb{C}}}$ is the
inclusion. This map is known to be surjective (the Borel–Ritt lemma; see,
e.g., [107]). The natural map $\pi\colon M\times{\widetilde{\mathbb{C}}}\to
M\times\mathbb{C}$ is a map of ringed spaces, i.e., we have a map
$\pi^{-1}\mathcal{O}^{\rm
an}_{M\times\mathbb{C}}\to\mathcal{A}_{M\times{\widetilde{\mathbb{C}}}}$ of
sheaves of rings. In particular, we can define the pull-back of an
$\mathcal{O}^{\rm an}_{M\times\mathbb{C}}$-module $\mathcal{F}$ to be
$\pi^{*}\mathcal{F}:=\pi^{-1}\mathcal{F}\otimes_{\pi^{-1}\mathcal{O}^{\rm
an}_{M\times\mathbb{C}}}\mathcal{A}_{M\times{\widetilde{\mathbb{C}}}}$.
For a multi-set
$\\{\mathbf{u}_{i}\\}=\\{\mathbf{u}_{1},\dots,\mathbf{u}_{N}\\}$ of complex
numbers, we say that a direction $e^{\boldsymbol{\mathrm{i}}\phi}\in S^{1}$ or
a phase $\phi$ is _admissible_ for $\\{\mathbf{u}_{i}\\}$ if
$e^{\boldsymbol{\mathrm{i}}\phi}$ is not parallel to any non-zero difference
$\mathbf{u}_{i}-\mathbf{u}_{j}$, i.e.,
$e^{\boldsymbol{\mathrm{i}}\phi}\notin\mathbb{R}(\mathbf{u}_{i}-\mathbf{u}_{j})$
for all $i$, $j$.
###### Proposition 6.5.
Let $\tau_{0}\in V^{\rm ss}$ be a semisimple point and let
$e^{\boldsymbol{\mathrm{i}}\phi}\in S^{1}$ be an admissible direction for the
spectrum $\big{\\{}\mathbf{u}_{1}^{0},\dots,\mathbf{u}_{N}^{0}\big{\\}}$ of
$E\star_{\tau_{0}}$. Let $\pi\colon V^{\rm
ss}\times{\widetilde{\mathbb{C}}}\to V^{\rm ss}\times\mathbb{C}$ denote the
oriented real blowup along $V^{\rm ss}\times\\{0\\}$. There exist an open
neighbourhood $B$ of $\tau_{0}$ in $V^{\rm ss}$, a positive number
$\epsilon>0$, and an isomorphism
$\Phi_{\phi}\colon\ \pi^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\mathbf{\Sigma}})\big{|}_{B\times
I_{\phi}}\cong\bigoplus_{i=1}^{N}(\mathcal{A}_{B\times
I_{\phi}},d+d(\mathbf{u}_{i}/z))$
over the sector
$I_{\phi}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\colon|\theta-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$
such that $\Phi_{\phi}$ induces, via (6.4), the formal decomposition
$\widehat{\Phi}$ in Proposition 6.1. Here we exclude the data of the pairing
from $\operatorname{QDM}^{\rm an}(\mathfrak{X}_{\mathbf{\Sigma}})$. Moreover
such a $\Phi_{\phi}$ is unique. We call $\Phi_{\phi}$ the _analytic lift_ of
$\widehat{\Phi}$.
###### Proof.
In the case where
$\big{\\{}\mathbf{u}_{1}^{0},\dots,\mathbf{u}_{N}^{0}\big{\\}}$ are pairwise
distinct, similar results are given in [107, Theorem 12.3], [10, Theorem A],
[40, Theorem 4.2], [95, Chapter II, Theorem 5.12]. We closely follow
Hertling–Sevenheck [57, Lemma 8.3] for the formulation. The general case
follows from [44, Proposition 2.5.1], where a fundamental solution matrix
$Y_{\phi}(\tau,z)$ for $\nabla$ with the asymptotics
$Y_{\phi}(\tau,z)e^{-\mathbf{U}/z}\to(\Psi_{1},\dots,\Psi_{N})$ as $z\to 0$
along the sector $I_{\phi}$ is constructed for $\tau\in B$. Here
$\mathbf{U}=\operatorname{diag}[\mathbf{u}_{1},\dots,\mathbf{u}_{N}]$ and
$\Psi_{i}$ is the normalized idempotent in Remark 6.3. ∎
###### Remark 6.6.
The uniqueness of the analytic lift $\Phi_{\phi}$ is ensured by the fact that
the angle of the sector $I_{\phi}$ is bigger than $\pi$: see [10, Remark 1.4].
The lift $\Phi_{\phi}$ depends on $\tau_{0}$ and
$e^{\boldsymbol{\mathrm{i}}\phi}$, and it depends continuously on
$\big{(}\tau_{0},e^{\boldsymbol{\mathrm{i}}\phi}\big{)}$ unless
$\big{(}\tau_{0},e^{\boldsymbol{\mathrm{i}}\phi}\big{)}$ crosses the locus
where $e^{\boldsymbol{\mathrm{i}}\phi}$ is non-admissible for the spectrum of
$E\star_{\tau_{0}}$.
###### Remark 6.7.
The analytic lift $\Phi_{\phi}$ preserves the pairing in the following sense:
consider the analytic lift $\Phi_{\phi+\pi}$ associated with the opposite
direction $-e^{\boldsymbol{\mathrm{i}}\phi}$, then
$P(s_{-},s_{+})(x,z)=\sum_{i=1}^{N}\Phi^{i}_{\phi+\pi}(s_{-})(x,-z)\Phi^{i}_{\phi}(s_{+})(x,z)$
for sections $s_{-}$, $s_{+}$ of $\pi^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\mathbf{\Sigma}})$, respectively, over $B\times
I_{\phi+\pi}$, $B\times I_{\phi}$. This follows from the fact that the
asymptotic expansions of both sides coincide by Proposition 6.5, and that the
pairings are flat.
###### Remark 6.8.
For a thorough discussion on the isomonodromic deformation theory of irregular
differential equations (of Poincaré rank 1) with coalescing eigenvalues
$\mathbf{u}_{1},\dots,\mathbf{u}_{N}$, see Cotti–Dubrovin–Guzzetti [33].
### 6.2 Asymptotic basis and marked reflection system
The sectorial decomposition in Proposition 6.5 gives rise to a linear
algebraic data which we call the _marked reflection system_ [44, Section 4.3];
this notion is equivalent to the central connection matrix together with
canonical co-ordinates in Dubrovin’s theory [40, Lecture 4]. We briefly review
it for our later purposes.
Introduce a pairing $[\cdot,\cdot)$ on the $\mathbb{C}$-vector space
$H^{*}_{\rm CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ by
$[\alpha,\beta):=\frac{1}{(2\pi)^{n}}\big{(}e^{\pi\boldsymbol{\mathrm{i}}\mu}e^{-\pi\boldsymbol{\mathrm{i}}c_{1}(\mathfrak{X}_{\mathbf{\Sigma}})}\alpha,\beta\big{)},$
where $(\cdot,\cdot)$ is the orbifold Poincaré pairing (2.2).
Recall the fundamental solution
$L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X}_{\mathbf{\Sigma}})}$ of the quantum
connection introduced in Section 2.4. The map
$\alpha\mapsto(2\pi)^{-n/2}L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X}_{\mathbf{\Sigma}})}\alpha$
intertwines the pairing $[\cdot,\cdot)$ on $H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ with the orbifold Poincaré pairing in the
sense that
$(s_{1}(\tau,e^{-\boldsymbol{\mathrm{i}}\pi}z),s_{2}(\tau,z))=[\alpha_{1},\alpha_{2}),$
when
$s_{i}(\tau,z)=(2\pi)^{-n/2}L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X}_{\mathbf{\Sigma}})}\alpha_{i}$
(where $n=\dim\mathfrak{X}_{\mathbf{\Sigma}}$ as usual), see [62, (20)]. The
pairing $[\cdot,\cdot)$ is also related to the Euler pairing
$\chi(\cdot,\cdot)$ on the $K$-group by (2.13), i.e.,
$\chi(V_{1},V_{2})=[\alpha_{1},\alpha_{2}),$
when
$\alpha_{i}=\widehat{\Gamma}_{\mathfrak{X}_{\mathbf{\Sigma}}}\cup(2\pi\boldsymbol{\mathrm{i}})^{\deg_{0}/2}\operatorname{inv}^{*}\widetilde{\operatorname{ch}}(V_{i})$
and $V_{i}\in K(\mathfrak{X}_{\mathbf{\Sigma}})$.
Let $\tau_{0}\in V^{\rm ss}$ be a semisimple point and let $\phi$ be an
admissible phase for the eigenvalues of $E\star_{\tau_{0}}$. Let $\Phi_{\phi}$
be the sectorial decomposition associated with $\tau_{0}$ and $\phi$ as in
Proposition 6.5:
$\Phi_{\phi}\colon\ \pi^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\mathbf{\Sigma}})\Big{|}_{B\times
I_{\phi}}\cong\bigoplus_{i=1}^{N}(\mathcal{A}_{B\times
I_{\phi}},d+d(\mathbf{u}_{i}/z)).$
We choose a base point $\tau_{\star}\in V^{\times}$ corresponding to a real
cohomology class and choose a path connecting $\tau_{\star}$ and $\tau_{0}$ in
$V^{\times}$ (see Remark 2.8 for the choice of a base point). Let $s_{i}$ be
the flat section of $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\mathbf{\Sigma}})$ on a neighbourhood of
$\big{(}\tau_{0},e^{\boldsymbol{\mathrm{i}}\phi}\big{)}$ satisfying
$\Phi_{\phi}(s_{i})=e^{-\mathbf{u}_{i}/z}e_{i}$, where $e_{i}$ is the $i$th
standard basis of $\mathcal{A}_{B\times I_{\phi}}^{\oplus N}$. Then we have
vectors $v_{i}\in H^{*}_{\rm CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ such that
$s_{i}(\tau,z)=(2\pi)^{-n/2}L(\tau,z)z^{-\mu}z^{c_{1}(\mathfrak{X}_{\mathbf{\Sigma}})}v_{i},$
where the determination of the fundamental solution is given by $\arg z=\phi$
at $z=e^{\boldsymbol{\mathrm{i}}\phi}$ and the chosen path (see Remark 2.8).
The _marked reflection system_ associated with $\tau_{0}$, $\phi$ (and the
path from $\tau_{\star}$ to $\tau_{0}$) is a tuple $\big{(}H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}}),[\cdot,\cdot),\\{v_{1},\dots,v_{N}\\},m,e^{\boldsymbol{\mathrm{i}}\phi}\big{)}$,
where
* •
$\\{v_{1},\dots,v_{N}\\}$ is the basis of $H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ defined as above, called the _asymptotic
basis_ ;
* •
$m\colon\\{v_{1},\dots,v_{N}\\}\to\mathbb{C}$ is the map given by
$m(v_{i})=\mathbf{u}_{i}$, called the _marking_.
The asymptotic basis satisfies the following semiorthogonality condition [44,
Proposition 2.6.4, Section 4.4]
$[v_{i},v_{j})=\begin{cases}1,&\text{if $i=j$},\\\ 0,&\text{if $i\neq j$ and
$\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{i}\big{)}\leq\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{j}\big{)}$}.\end{cases}$
(6.5)
Because of the ambiguity of $\widehat{\Phi}$ in Proposition 6.1, the
asymptotic basis $\\{v_{1},\dots,v_{n}\\}$ is not a priori ordered and each
$v_{i}$ is determined up to sign $v_{i}\to\pm v_{i}$. On the other hand, given
a phase $\phi$, we can order $\\{v_{i}\\}$ in such a way that
$\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{1}\big{)}\geq\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{2}\big{)}\geq\cdots\geq\Im\big{(}e^{\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{N}\big{)}$;
then the Gram matrix $([v_{i},v_{j}))$ is upper-triangular with diagonal
entries all equal to one, and gives the Stokes matrix of the quantum
connection at the irregular singular point $z=0$ (see [40, Lecture 4], [44,
Proposition 2.6.4]).
When $\tau_{0}$ and $\phi$ vary and cross the locus where the corresponding
eigenvalues $\\{\mathbf{u}_{i}\\}$ become non-admissible for $\phi$, the
corresponding marked reflection system undergoes mutation. We refer to [44,
Section 4.2] for the full details of the deformation theory of marked
reflection systems. We illustrate an example of mutation in Fig. 7; the figure
describes a typical procedure where $\\{\mathbf{u}_{i}\\}$ varies in the
configuration space of $N$ points in $\mathbb{C}$ and crosses the wall of non-
admissible configurations. In the picture, we drew the half-ray
$\mathbf{u}_{j}+\mathbb{R}_{\geq 0}e^{\boldsymbol{\mathrm{i}}\phi}$ from each
$\mathbf{u}_{j}$ to show the direction $e^{\boldsymbol{\mathrm{i}}\phi}$.
Suppose that the asymptotic basis $\\{v_{1},\dots,v_{N}\\}$ is marked by
$\\{\mathbf{u}_{1},\dots,\mathbf{u}_{N}\\}$ in the leftmost picture, i.e.,
$\mathbf{u}_{j}=m(v_{j})$. We assume that the basis is ordered so that
$\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{1}\big{)}>\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{2}\big{)}>\cdots>\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{N}\big{)}$.
After passing through the non-admissible configuration in the middle picture,
the vector $v_{i}$ marked by $\mathbf{u}_{i}$ is transformed into
$v_{i}^{\prime}=v_{i}-[v_{i},v_{i+1})v_{i+1}$ (6.6)
and the other vectors remain the same (i.e., the marking is given by
$v_{i}^{\prime}\mapsto\mathbf{u}_{i}$ and $v_{j}\mapsto\mathbf{u}_{j}$ for
$j\neq i$ in the rightmost picture). This is called the _right mutation_ of
$v_{i}$ with respect to $v_{i+1}$. The inverse procedure is the _left
mutation_ of $v_{i}^{\prime}$ with respect to $v_{i+1}$:
$v_{i}=v_{i}^{\prime}-[v_{i+1},v_{i}^{\prime})v_{i+1}.$ (6.7)
The two operations (6.6), (6.7) are inverse to each other because of the
semiorthogonality condition (6.5).
###### Remark 6.9.
The result [62, Theorem 4.11] implies that the asymptotic basis
$\\{v_{1},\dots,v_{N}\\}$ for the quantum cohomology of weak-Fano, compact
toric stacks $\mathfrak{X}_{\mathbf{\Sigma}}$ is of the form
$v_{i}=\widehat{\Gamma}_{\mathfrak{X}_{\mathbf{\Sigma}}}\cup(2\pi\boldsymbol{\mathrm{i}})^{\deg_{0}/2}\operatorname{inv}^{*}\widetilde{\operatorname{ch}}(V_{i})$
for some classes $V_{i}\in K(\mathfrak{X}_{\mathbf{\Sigma}})$ in the
$K$-group, i.e., the corresponding flat section $s_{i}$ lies in the
$\widehat{\Gamma}$-integral structure (see also Proposition 7.8). The Gamma
conjecture II [44, Section 4.6] (recently proved by [41] for Fano toric
manifolds) says that $V_{i}$ comes from a full exceptional collection in the
derived category of coherent sheaves. In this situation, mutation of
asymptotic basis corresponds to that of full exceptional collections.
Figure 7: Right mutation: the “wall-crossing” from the left picture to the
right one in the configuration space yields a right mutation of $v_{i}$.
### 6.3 Sectorial decomposition of the Brieskorn module
In this section, we describe the Hukuhara–Turrittin sectorial decomposition
(Propositions 6.1 and 6.5) explicitly for the non-equivariant Brieskorn
modules. First we observe that the analytified Brieskorn module
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$ (Definition 4.21)
admits a formal decomposition over the locus where $F$ has only non-degenerate
critical points, via the formal asymptotic expansion in Section 4.3.3. When a
toric stack $\mathfrak{X}_{\mathbf{\Sigma}}$ is _weak Fano_ , the Brieskorn
module $\operatorname{Bri}(F)$ over the small quantum cohomology locus of
$\mathfrak{X}_{\mathbf{\Sigma}}$ has the expected rank equal to $\dim
H^{*}_{\rm CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ and gives a fully analytic
(i.e., analytic both in the $\mathcal{M}$ direction and in the $z$-direction)
D-module mirror to the small quantum D-module of
$\mathfrak{X}_{\mathbf{\Sigma}}$. In this case, we can describe the analytic
lift of the formal decomposition using oscillatory integrals.
#### 6.3.1 Formal decomposition of the Brieskorn module
Let $\mathfrak{X}_{\mathbf{\Sigma}}$ be a toric stack with
$\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$ and let
$(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$ denote the LG model
from Definition 3.6. Let $\mathcal{B}\subset\mathcal{Y}$,
$\mathcal{U}\subset\mathcal{M}_{\mathbb{T}}=\mathcal{M}\times\operatorname{Lie}\mathbb{T}$
be open neighbourhoods of (respectively) $\tilde{0}_{\mathbf{\Sigma}}$ and
$(0_{\mathbf{\Sigma}},0)$ as in Corollary 4.20. Recall that the analytified
equivariant Brieskorn module
$\overline{\operatorname{Bri_{\mathbb{T}}^{an}}}(F)_{\mathbf{\Sigma}}$ is
defined over $\mathcal{U}$ and its non-equivariant version
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$ is defined over
$\mathcal{V}=\mathcal{U}\cap(\mathcal{M}\times\\{0\\})$ (see Definition 4.21).
When $\mathfrak{X}_{\mathbf{\Sigma}}$ is compact, the family of relative
critical points of the LG potential $F$
$\operatorname{Cr}:=\left\\{p\in\mathcal{B}\colon x_{1}\frac{\partial
F}{\partial x_{1}}(p)=\cdots=x_{n}\frac{\partial F}{\partial
x_{n}}(p)=0\right\\}\xrightarrow{\operatorname{pr}}\mathcal{V}$
is a finite morphism whose generic fibre is reduced (see [62, Proposition
3.10]), i.e., there exists an open dense subset $\mathcal{V}^{\rm ss}$ of
$\mathcal{V}$ such that for any $q\in\mathcal{V}^{\rm ss}$,
$F|_{\mathcal{B}\cap\operatorname{pr}^{-1}(q)}$ has only non-degenerate
critical points. We set $\operatorname{Cr}^{\rm
ss}:=\operatorname{Cr}\cap\operatorname{pr}^{-1}(\mathcal{V}^{\rm ss})$. By
definition, $\operatorname{pr}\colon\operatorname{Cr}^{\rm
ss}\to\mathcal{V}^{\rm ss}$ is a finite covering. The following result
describes a formal decomposition parallel to Proposition 6.1 for the
analytified Brieskorn module.
###### Proposition 6.10.
The formal asymptotic expansion $\operatorname{Asym}$ in Definition 4.28
defines an isomorphism
$\operatorname{Asym}\colon\
\left.\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\right|_{\mathcal{V}^{\rm
ss}}\cong\operatorname{pr}_{*}\left(\mathcal{O}^{\rm
an}_{\operatorname{Cr}^{\rm
ss}}[\\![z]\\!]\otimes\operatorname{\mathsf{ori}}\right),$
where $\operatorname{\mathsf{ori}}$ is the $\mu_{2}$-local system over
$\operatorname{Cr}^{\rm ss}$ defined by the monodromy of the square root
$\sqrt{\det(h_{i,j})}$ of the logarithmic Hessian of $F$ $($see (4.11) for
$h_{i,j})$. This map identifies the Gauss–Manin connection $\nabla$ with
$d+d(F|_{\operatorname{Cr}^{\rm ss}}/z)\wedge$ and the higher residue pairing
with the diagonal pairing:
$P_{{\rm
std}}(f,g)(x)=\sum_{p\in\operatorname{pr}^{-1}(x)\cap\operatorname{Cr}^{\rm
ss}}f(p,-z)g(p,z),$
where $f=f(x,z),g=g(x,z)\in\operatorname{pr}_{*}(\mathcal{O}^{\rm
an}_{\operatorname{Cr}^{\rm ss}}[\\![z]\\!])$.
###### Proof.
As we remarked in Remark 4.29, we need to choose a square root of the Hessian
when defining the formal asymptotic expansion; hence we need the
$\mu_{2}$-local system $\operatorname{\mathsf{ori}}$. Along $z=0$, the map
$\operatorname{Asym}$ is given by
$\phi\cdot\omega\mapsto\phi|_{\operatorname{Cr}^{\rm ss}}/(|\mathbf{N}_{\rm
tor}|\sqrt{\det(h_{i,j})})$. On the other hand,
$\displaystyle\left.\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\right|_{z=0}$
$\displaystyle\cong\operatorname{pr}_{*}\left(\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!]/(\chi_{1},\dots,\chi_{n},z)\mathcal{O}^{\rm
an}_{\mathcal{B}}[\\![z]\\!]\right)$
$\displaystyle\cong\operatorname{pr}_{*}\left(\mathcal{O}^{\rm
an}_{\mathcal{B}}\Big{/}\left(x_{1}\frac{\partial F}{\partial
x_{1}},\dots,x_{n}\frac{\partial F}{\partial
x_{n}}\right)\right)\cong\operatorname{pr}_{*}\mathcal{O}^{\rm
an}_{\operatorname{Cr}},$
where $\chi_{i}$ acts on $\mathcal{O}^{\rm an}_{\mathcal{B}}[\\![z]\\!]$ as in
(4.8). Hence $\operatorname{Asym}$ is an isomorphism along $z=0$. Since both
sides are locally free $\mathcal{O}_{\mathcal{V}^{\rm
ss}}[\\![z]\\!]$-modules, $\operatorname{Asym}$ is an isomorphism. That
$\operatorname{Asym}$ identifies the connections follows from [27, Lemma 6.7].
That $\operatorname{Asym}$ identifies the pairings is obvious from Definition
4.30. ∎
###### Remark 6.11.
The eigenvalues $\mathbf{u}_{1},\dots,\mathbf{u}_{N}$ of $E\star_{\tau}$ in
Proposition 6.1 correspond to critical values of $F$.
#### 6.3.2 Brieskorn module over the small quantum cohomology locus
To discuss an analytic lift of the above formal decomposition, we restrict the
Brieskorn module to the small quantum cohomology locus. We assume that
$\mathfrak{X}_{\mathbf{\Sigma}}$ is a _weak Fano_ (i.e.,
$-K_{\mathfrak{X}_{\mathbf{\Sigma}}}$ is nef) and _compact_ toric stack.
Furthermore, we assume that
$\text{$S_{-}:=S\cap\Delta=\\{b\in S\colon\overline{b}\in\Delta\\}$ generates
$\mathbf{N}$ as a group},$ (6.8)
where $\Delta\subset\mathbf{N}_{\mathbb{R}}$ denotes the convex hull of ray
vectors $\\{\overline{b}\colon b\in R(\mathbf{\Sigma})\\}$. The compactness
implies that $\Delta$ contains the origin in its interior and the weak-Fano
condition implies that all rays $b\in R(\mathbf{\Sigma})$ lie in the boundary
of $\Delta$. By replacing $S$ with $S_{-}=S\cap\Delta$ in the construction of
the (partially compactified) LG model in Section 3.2, we obtain an LG model
$\begin{CD}\mathcal{Y}^{\rm sm}@>{F}>{}>\mathbb{C},\\\
@V{\operatorname{pr}}V{}V\\\ \mathcal{M}^{\rm sm}\end{CD}$ (6.9)
which we call _the LG model mirror to the small quantum cohomology of
$\mathfrak{X}_{\mathbf{\Sigma}}$_. We also call $\mathcal{M}^{\rm sm}$ the
_small quantum cohomology locus_ of $\mathfrak{X}_{\mathbf{\Sigma}}$. Under
the mirror map, $\mathcal{M}^{\rm sm}$ maps to $H^{\leq 2}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})$.
###### Lemma 6.12.
The total space $\mathcal{Y}^{\rm sm}$ is a closed toric substack of
$\mathcal{Y}$ corresponding to the cone $(\mathbb{R}_{\geq 0})^{S\setminus
S_{-}}$ of $\widetilde{\Xi}$; similarly $\mathcal{M}^{\rm sm}$ is a closed
toric substack of $\mathcal{M}$ corresponding to the cone
$D\big{(}(\mathbb{R}_{\geq 0})^{S\setminus S_{-}}\big{)}\in\Xi$. Moreover, we
have the pull-back diagram:
$\textstyle{\mathcal{Y}^{\rm
sm}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\mathcal{Y}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\mathcal{M}^{\rm
sm}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\mathcal{M}.}$
(6.10)
###### Proof.
Let $\widetilde{\Xi}_{-}$ denote the fan defining $\mathcal{Y}^{\rm sm}$.
Recall that maximal cones of $\widetilde{\Xi}$ are in one-to-one
correspondence with stacky fans adapted to $S$; likewise, maximal cones of
$\widetilde{\Xi}_{-}$ are in one-to-one correspondence with stacky fans
adapted to $S_{-}$. Thus the set of maximal cones of $\widetilde{\Xi}_{-}$ can
be identified with a subset of the set of maximal cones of $\widetilde{\Xi}$.
We can see that this subset consists of maximal cones
$\operatorname{CPL}_{+}(\mathbf{\Sigma})$ of $\widetilde{\Xi}$ that contain
$(\mathbb{R}_{\geq 0})^{S\setminus S_{-}}$ as a face; moreover the
corresponding maximal cone of $\widetilde{\Xi}_{-}$ is given by the image of
$\operatorname{CPL}_{+}(\mathbf{\Sigma})$ under the projection
$\big{(}\mathbb{R}^{S}\big{)}^{\star}\to\big{(}\mathbb{R}^{S_{-}}\big{)}^{\star}$.
Therefore $\widetilde{\Xi}_{-}$ is a fan obtained as the star of the cone
$(\mathbb{R}_{\geq 0})^{S\setminus S_{-}}$ in $\widetilde{\Xi}$. This shows
the first statement. A similar argument shows that $\mathcal{M}^{\rm sm}$ is a
closed toric substack corresponding to $D\big{(}(\mathbb{R}_{\geq
0})^{S\setminus S_{-}}\big{)}$. To see the pull-back diagram, we recall the
description of the uniformizing chart in (3.21). When $\mathbf{\Sigma}$ is
adapted to $S_{-}$, $G(\mathbf{\Sigma})$ contains $S\setminus S_{-}$. In the
local chart associated with $\mathbf{\Sigma}$, the diagram (6.10) is of the
form
$\textstyle{\operatorname{Spec}\mathbb{C}\big{[}\mathbb{O}^{\mathbf{\Sigma}}_{+}\big{]}\times\mathbb{C}^{G(\mathbf{\Sigma})\setminus(S\setminus
S_{-})}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\operatorname{Spec}\mathbb{C}\big{[}\mathbb{O}^{\mathbf{\Sigma}}_{+}\big{]}\times\mathbb{C}^{G(\mathbf{\Sigma})}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\operatorname{Spec}\mathbb{C}\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\big{]}\times\mathbb{C}^{G(\mathbf{\Sigma})\setminus(S\setminus
S_{-})}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\operatorname{Spec}\mathbb{C}\big{[}\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}\big{]}\times\mathbb{C}^{G(\mathbf{\Sigma})},}$
which is clearly a pull-back diagram. ∎
###### Remark 6.13.
The small quantum cohomology locus $\mathcal{M}^{\rm sm}\subset\mathcal{M}$
depends on the choice of $\mathbf{\Sigma}\in\operatorname{\mathfrak{Fan}}(S)$.
###### Remark 6.14.
The condition (6.8) ensures that Assumption 3.1 holds for $S_{-}=S\cap\Delta$.
This condition is, however, not necessary at this point; we can define
$\mathcal{Y}^{\rm sm}$ (or $\mathcal{M}^{\rm sm}$) as the substack
corresponding to $(\mathbb{R}_{\geq 0})^{S\setminus S_{-}}$ (resp. to
$D\big{(}(\mathbb{R}_{\geq 0})^{S\setminus S_{-}}\big{)}$). We shall need this
condition later when we apply the results on the $\widehat{\Gamma}$-integral
structure for toric stacks in [62] (see Section 3.1.4 _ibid_ where the same
assumption was made).
We observe that the non-equivariant Brieskorn module $\operatorname{Bri}(F)$
over $\mathcal{M}^{\rm sm}$ already has the expected rank; hence the
completion and the analytification studied in Sections 4.2–4.3 are unnecessary
over $\mathcal{M}^{\rm sm}$ in the weak-Fano case.
###### Proposition 6.15.
Let $\mathfrak{X}_{\mathbf{\Sigma}}$ be a weak Fano compact toric stack
satisfying (6.8). There exists a Zariski-open subset $\mathcal{M}^{\rm sm,lf}$
of $\mathcal{M}^{\rm sm}$ containing $0_{\mathbf{\Sigma}}$ such that the non-
equivariant Brieskorn module $\operatorname{Bri}(F)|_{\mathcal{M}^{\rm
sm,lf}}$ is a locally free $\mathcal{O}_{\mathcal{M}^{\rm
sm,lf}\times\mathbb{C}_{z}}$-module of rank $\dim H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})$.
###### Proof.
This essentially follows from a result of Mann-Reichelt [81, Theorem 4.10] on
the GKZ system; we give a proof of a more general statement (including the
equivariant case and without assumption (6.8)) in Appendix A. ∎
Let $\mathcal{V}\subset\mathcal{M}$ denote the base of the analytified
Brieskorn module $\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$
as before. This is an analytic open neighbourhood of $0_{\mathbf{\Sigma}}$.
###### Proposition 6.16.
1. $(1)$
Set $\mathcal{V}^{\rm sm}=\mathcal{V}\cap\mathcal{M}^{\rm sm,lf}$. The natural
map
$\operatorname{Bri}(F)\otimes_{\mathcal{O}^{\rm an}_{\mathcal{V}^{\rm
sm}\times\mathbb{C}_{z}}}\mathcal{O}^{\rm an}_{\mathcal{V}^{\rm
sm}}[\\![z]\\!]\to\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$
is an isomorphism.
2. $(2)$
The mirror isomorphism $\operatorname{Mir}|_{\chi=0}$ in Proposition 4.11
extends to an isomorphism
$\operatorname{Bri}(F)|_{{\mathcal{V}^{\rm
sm}}^{\prime}}\cong\operatorname{mir}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X})$
over an open neighbourhood ${\mathcal{V}^{\rm
sm}}^{\prime}\subset\mathcal{V}^{\rm sm}$ of $0_{\mathbf{\Sigma}}$, where
$\operatorname{mir}\colon{\mathcal{V}^{\rm sm}}^{\prime}\to V$ is the analytic
mirror map $($see Section 4.4 for the convergence of the mirror map$)$.
###### Proof.
For Part (1), it suffices to show that the map is an isomorphism along $z=0$.
As discussed in the proof of Proposition 6.10, the analytified Brieskorn
module along $z=0$ is isomorphic to $\operatorname{pr}_{*}\mathcal{O}^{\rm
an}_{\operatorname{Cr}}$. Thus the natural map in (1) is surjective along
$z=0$; it is an isomorphism since the ranks are the same. Part (2) follows
from the convergence of the $I$-function in the weak-Fano case, see, e.g.,
[62, Proposition 4.8]. ∎
#### 6.3.3 Analytic lift of the formal decomposition
We continue to assume that $\mathfrak{X}_{\mathbf{\Sigma}}$ is a compact,
weak-Fano toric stack and that the condition (6.8) holds. Consider the LG
model (6.9) over $\mathcal{M}^{\rm sm}$. As a toric stack, $\mathcal{M}^{\rm
sm}$ contains the open dense torus orbit171717The following discussion works
if we replace $\mathcal{M}^{\rm sm,\times}$ with the slightly bigger subspace
$\\{q\in\mathcal{M}^{\rm
sm}_{\mathbf{\Sigma}}\colon\allowbreak\text{$q^{\lambda}\neq 0$ for all
$\lambda\in\boldsymbol{\Lambda}^{\mathbf{\Sigma}}_{+}$}\\}$: this bigger space
parametrizes Laurent polynomials with Newton polytope $\Delta$.
$\mathcal{M}^{\rm
sm,\times}=(\mathbb{L}^{\prime})^{\star}\otimes\mathbb{C}^{\times}\subset\mathcal{M}^{\rm
sm},$
where
$\mathbb{L}^{\prime}=\operatorname{Ker}(\mathbb{Z}^{S_{-}}\to\mathbf{N})$ is
the lattice appearing in the leftmost term of the extended fan sequence (3.3)
with $S$ replaced with $S_{-}=S\cap\Delta$. The fibre of
$\operatorname{pr}\colon\mathcal{Y}^{\rm sm}\to\mathcal{M}^{\rm sm}$ at a
point $q\in\mathcal{M}^{\rm sm,\times}$ is isomorphic to
$\operatorname{Hom}(\mathbf{N},\mathbb{C}^{\times})$ (i.e., the fibre of the
uncompactified LG model, see Section 3.2). In fact, since $\Delta$ contains
the origin in its interior, we have a linear relation $\sum\limits_{b\in
S_{-}}\lambda_{b}b=0$ with $\lambda_{b}\in\mathbb{Z}_{>0}$; this shows that
$\prod\limits_{b\in S_{-}}u_{b}^{\lambda_{b}}=q^{\lambda}\neq 0$ on the fibre
at $q\in\mathcal{M}^{\rm sm,\times}$ and in particular that $u_{b}\neq 0$ for
all $b\in S_{-}$.
The locally freeness of $\operatorname{Bri}(F)|_{\mathcal{M}^{\rm sm,lf}}$ in
Proposition 6.15 implies (by the restriction to $z=0$) that the family of
relative critical points of $F$
$\operatorname{Cr}^{\rm sm}:=\left\\{p\in\mathcal{Y}^{\rm sm}\colon
x_{1}\frac{\partial F}{\partial x_{1}}(p)=\cdots=x_{n}\frac{\partial
F}{\partial
x_{n}}(p)=0\right\\}\xrightarrow{\operatorname{pr}}\mathcal{M}^{\rm sm}$
(6.11)
is finite flat of degree $N=\dim H^{*}_{\rm
CR}(\mathfrak{X}_{\mathbf{\Sigma}})$ over the base $\mathcal{M}^{\rm sm,lf}$.
The generic fibre of the family $\operatorname{Cr}^{\rm sm}\to\mathcal{M}^{\rm
sm}$ is reduced [62, Proposition 3.10], and thus
$\mathcal{M}^{\rm sm,ss}=\big{\\{}q\in\mathcal{M}^{\rm
sm,\times}\cap\mathcal{M}^{\rm
sm,lf}\colon\text{$F|_{\operatorname{pr}^{-1}(q)}$ has only non-degenerate
critical points}\big{\\}}$
is a non-empty Zariski open subset, where “ss” means semisimplicity.
For $q\in\mathcal{M}^{\rm sm,ss}$, let $\\{c_{1},\dots c_{N}\\}$ be the set of
(mutually distinct) critical points of
$F_{q}:=F|_{\operatorname{pr}^{-1}(q)}$, and let $\mathbf{u}_{i}=F_{q}(c_{i})$
be the critical value. For an admissible phase $\phi$ for
$\\{\mathbf{u}_{1},\dots,\mathbf{u}_{N}\\}$, let
$\Gamma_{i}^{\phi}\subset\operatorname{pr}^{-1}(q)$ denote the Lefschetz
thimble of $F_{q}$ emanating from the critical point $c_{i}$ whose image under
$F_{q}$ is the half-line $\mathbf{u}_{i}-\mathbb{R}_{\geq
0}e^{\boldsymbol{\mathrm{i}}\phi}$; it is given as the stable manifold of the
Morse function
$\Re\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}F_{q}\big{)}\colon\operatorname{pr}^{-1}(q)\to\mathbb{R}$:
$\Gamma_{i}^{\phi}=\big{\\{}x\in\operatorname{pr}^{-1}(q)\colon\lim\limits_{t\to\infty}\varphi_{t}(x)=c_{i}\big{\\}}\cong\mathbb{R}^{n},$
(6.12)
where $\varphi_{t}$ is the upward gradient flow181818The gradient flow of
$\Re\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}F_{q}\big{)}$ equals the
Hamiltonian flow of $\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}F_{q}\big{)}$
and thus preserves $\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}F_{q}\big{)}$.
of $\Re\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}F_{q}\big{)}$ with respect to
the complete Kähler metric
$\frac{\boldsymbol{\mathrm{i}}}{2}\sum\limits_{j=1}^{n}d\log x_{j}\wedge
d\overline{\log x_{j}}$ on $\operatorname{pr}^{-1}(q)$. The cycles
$\Gamma_{1}^{\phi},\dots,\Gamma_{N}^{\phi}$ form a basis of the relative
homology
$H_{n}\big{(}\operatorname{pr}^{-1}(q),\\{\Re(e^{-\boldsymbol{\mathrm{i}}\phi}F_{q})\leq-M\\};\mathbb{Z}\big{)}$
for sufficiently large $M$, see [62, Section 3.3.1] for more details (see also
Section 7.4.4).
Figure 8: The images of the Lefschetz thimbles $\Gamma_{i}^{\phi}$ by
$F_{q}=F|_{\operatorname{pr}^{-1}(q)}$.
###### Remark 6.17.
For a non-admissible phase $\phi$, the Lefschetz thimble $\Gamma_{i}^{\phi}$
is not always defined because $\Gamma_{i}^{\phi}$ may hit other critical
points $c_{j}$ with
$\mathbf{u}_{j}\in\mathbf{u}_{i}-\mathbb{R}_{>0}e^{\boldsymbol{\mathrm{i}}\phi}$.
On the other hand, when some of the critical values
$\mathbf{u}_{1},\dots,\mathbf{u}_{N}$ coalesce at $q_{0}\in\mathcal{M}^{\rm
sm,ss}$ and $\phi$ is an admissible phase for the critical values of
$F_{q_{0}}$, the Lefschetz thimbles
$\Gamma_{1}^{\phi},\dots,\Gamma_{N}^{\phi}$ are well-defined in a
neighbourhood of $q=q_{0}$ despite the possibility that $\phi$ can be non-
admissible at a nearby point. This is because different Lefschetz thimbles
associated with the same critical value do not intersect each other, and no
non-trivial Picard–Lefschetz transformations occur among these thimbles around
$q=q_{0}$.
###### Proposition 6.18.
Let $q_{0}$ be a point in $\mathcal{M}^{\rm sm,ss}$. Choose an admissible
phase $\phi$ for the critical values
$\\{\mathbf{u}_{1,0},\dots,\mathbf{u}_{N,0}\\}$ of $F_{q_{0}}$. Choose a
sufficiently small open neighbourhood $B\subset\mathcal{M}^{\rm sm,ss}$ of
$q_{0}$ and a sufficiently small number $\epsilon>0$ such that
$e^{-\boldsymbol{\mathrm{i}}\phi^{\prime}}(\mathbf{u}_{i}-\mathbf{u}_{j})\notin\mathbb{R}$
whenever $q\in B$, $|\phi-\phi^{\prime}|<\epsilon$ and
$\mathbf{u}_{i,0}\neq\mathbf{u}_{j,0}$. Let $\pi\colon\mathcal{M}^{\rm
sm,ss}\times{\widetilde{\mathbb{C}}}\to\mathcal{M}^{\rm
sm,ss}\times\mathbb{C}$ denote the oriented real blowup along
$\mathcal{M}^{\rm sm,ss}\times\\{0\\}$. Define the map
$\Phi_{\phi}\colon\ \pi^{*}\operatorname{Bri}(F)\big{|}_{B\times
I_{\phi}}\to\mathcal{A}_{B\times I_{\phi}}^{\oplus N}$
by
$\Phi_{\phi}(s)(q,z)=\left((-2\pi
z)^{-n/2}e^{-\mathbf{u}_{i}/z}\int_{\Gamma_{i}^{\phi+\delta}}e^{F_{q}/z}s\right)_{i=1}^{N},\qquad(q,z)\in
B\times I_{\phi},$ (6.13)
where
$I_{\phi}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\colon|\theta-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$
and we choose $\delta\in(-\epsilon,\epsilon)$ depending on the argument of $z$
so that the integral converges. Then $\Phi_{\phi}$ is an isomorphism that
identifies the Gauss–Manin connection $\nabla$ with
$\bigoplus\limits_{i=1}^{N}(d+d(\mathbf{u}_{i}/z))$ and induces the formal
decomposition in Proposition 6.10 $($combined with Proposition
$\ref{prop:Bri_weak_Fano_cor})$ if $B\subset\mathcal{V}^{\rm ss}$:
$\operatorname{Asym}\colon\ \operatorname{Bri}(F)\otimes_{\mathcal{O}^{\rm
an}_{B\times\mathbb{C}_{z}}}\mathcal{O}^{\rm
an}_{B}[\\![z]\\!]\cong\mathcal{O}^{\rm an}_{B}[\\![z]\\!]^{\oplus N}.$
###### Proof.
First observe that the oscillatory integral $\Phi_{\phi}(s)$ converges for a
suitable choice of $\delta\in(-\epsilon,\epsilon)$, and does not depend on
$\delta$ as far as it converges. If $|\arg(z)-\phi|<\frac{\pi}{2}$, we can
choose $\delta=0$ because $\Re(F_{q}/z)\to-\infty$ in the end of
$\Gamma_{i}^{\phi}$; if not we can choose a suitable $\delta$ so that
$\Re(F_{q}/z)\to-\infty$ in the end of $\Gamma_{i}^{\phi+\delta}$. The fact
that $\Phi_{\phi}$ identifies the connections follows from the definition of
the Gauss–Manin connection, see [62, equation (54), Lemma 3.15]. Note that the
shift of the connection $\nabla_{z\frac{\partial}{\partial z}}$ by $n/2$ in
Remark 4.6 is compensated by the prefactor $(-2\pi z)^{-n/2}$. The last
statement follows from the fact that $\operatorname{Asym}_{c_{i}}(s)$ gives
the asymptotic expansion of the $i$th component of $\Phi_{\phi}(s)$ along the
sector $I_{\phi}$. ∎
###### Remark 6.19.
The choice of an orientation of $\Gamma_{i}^{\phi+\delta}$ and the choice of a
branch of $(-2\pi z)^{-n/2}$ in (6.13) together give rise to a section of the
$\mu_{2}$-local system $\operatorname{\mathsf{ori}}$ in Proposition 6.10.
## 7 Functoriality under toric birational morphisms
We study the analytic lift of the formal decomposition of the quantum
D-modules in Theorem 5.16 in the case where the birational map
$\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ extends to a _morphism_. We show
that the analytic lift associated with a certain deformation parameter
$\tau_{+}$ and a phase is induced by the pull-back between the $K$-groups via
the $\widehat{\Gamma}$-integral structure. Moreover, the sectorial
decomposition of the quantum D-module of $\mathfrak{X}_{+}$ at some $\tau_{+}$
corresponds to an Orlov-type semiorthogonal decomposition of the $K$-group. We
assume that both $\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ are compact weak-
Fano smooth toric DM stacks and restrict ourselves to the non-equivariant
quantum D-modules.
### 7.1 Notation and assumption
Consider a discrepant transformation
$\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ arising from a codimension-one
wall crossing as in Section 5.1. Let $\mathbf{\Sigma}_{\pm}$ be the stacky fan
of $\mathfrak{X}_{\pm}$. We assume that
$\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ extends to a birational morphism
$\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$. In this case, the common
blowup $\widehat{\mathfrak{X}}$ in (5.2) is isomorphic to $\mathfrak{X}_{+}$,
and $\varphi$ is necessarily a type (II-i) or (III) discrepant transformation
in the classification of Remark 5.4, i.e., $\varphi$ is a divisorial
contraction or a root construction. We further assume that
* •
$\mathfrak{X}_{+}$ and $\mathfrak{X}_{-}$ are compact weak Fano toric stacks;
we write $\Delta_{\pm}\subset\mathbf{N}_{\mathbb{R}}$ for the fan polytopes of
$\mathfrak{X}_{\pm}$; they are convex polytopes containing the origin in their
interiors and we have $\Delta_{-}\subset\Delta_{+}$;
* •
$S_{-}:=S\cap\Delta_{-}=\\{b\in\mathbf{N}\colon\overline{b}\in\Delta_{-}\\}$
generates $\mathbf{N}$ over $\mathbb{Z}$.
Here the fan polytope $\Delta_{\pm}$ means the convex hull of ray vectors of
the stacky fan $\mathbf{\Sigma}_{\pm}$ and $S$ is a finite subset of
$\mathbf{N}$ as in Section 3.1 such that both $\mathbf{\Sigma}_{+}$ and
$\mathbf{\Sigma}_{-}$ are adapted to $S$ in the sense of Definition 3.3. We
need these assumptions so that we can apply the results [62] on the
$\widehat{\Gamma}$-integral structure for toric stacks, where the same
assumptions were made (see Section 3.1.4 _ibid_).
Figure 9: The change of fans associated with
$\mathfrak{X}_{+}\to\mathfrak{X}_{-}$. The sign $+$ means ray vectors from
$M_{+}\subset R_{-}=R(\mathbf{\Sigma}_{-})$ and ${\hat{b}}$ is a positive
integral linear combination of $\\{v\colon v\in M_{+}\\}$.
As in Section 5.1, let $W$ denote the hyperplane wall between the maximal
cones $\operatorname{cpl}(\mathbf{\Sigma}_{+})$ and
$\operatorname{cpl}(\mathbf{\Sigma}_{-})$ of the secondary fan $\Xi$, and let
$\mathbf{w}\in\mathbb{L}$ denote the primitive normal vector of the wall $W$
pointing towards $\operatorname{cpl}(\mathbf{\Sigma}_{+})$. Set
$M_{\pm}=\\{b\in S\colon\pm D_{b}\cdot\mathbf{w}>0\\}$ as before. When the
wall-crossing induces a morphism $\mathfrak{X}_{+}\to\mathfrak{X}_{-}$,
$M_{-}$ is a singleton $\\{{\hat{b}}\\}$ with
$D_{{\hat{b}}}\cdot\mathbf{w}=-1$ and the corresponding circuit is (see (5.1))
${\hat{b}}=\sum_{b\in M_{+}}k_{b}b\qquad\text{with
$k_{b}:=D_{b}\cdot\mathbf{w}$}.$
Assumption 5.2 gives $\sum\limits_{b\in M_{+}}k_{b}>1$. In the type (II-i)
case, we have $\sharp M_{+}\geq 2$ and the stacky fan $\mathbf{\Sigma}_{+}$ is
obtained from $\mathbf{\Sigma}_{-}$ by adding the new ray ${\hat{b}}$; the
cone $\sigma_{M_{+}}=\sum\limits_{b\in M_{+}}\mathbb{R}_{\geq 0}\overline{b}$
of $\mathbf{\Sigma}_{-}$ is subdivided into cones
$\sigma_{M_{+}\cup\\{{\hat{b}}\\}\setminus\\{v\\}}$ with $v\in M_{+}$. In the
type (III) case, $M_{+}$ is also a singleton $\\{\check{b}\\}$ and
$\mathbf{\Sigma}_{+}$ is obtained from $\mathbf{\Sigma}_{-}$ by replacing
$\check{b}$ with ${\hat{b}}=k_{\check{b}}\check{b}$: see Fig. 9. We write
$R_{\pm}=R(\mathbf{\Sigma}_{\pm})$ for the set of rays. Then
$R_{+}=R_{-}\sqcup\\{{\hat{b}}\\}$ in the type (II-i) case and
$R_{+}\sqcup\\{\check{b}\\}=R_{-}\sqcup\\{{\hat{b}}\\}$ in the type (III)
case, where $\sqcup$ denotes disjoint union. We also note that $M_{+}\subset
R_{-}$. For simplicity of notation, we assume that $S$ is chosen to be a
minimal extension of $S_{-}$:
* •
$S=S_{-}\cup\\{{\hat{b}}\\}$.
We do not lose any generality by this assumption: the base $\mathcal{M}$ of
the LG model for a larger $S$ always contains the locus corresponding to
$S_{-}\cup\\{{\hat{b}}\\}$.
The smooth toric DM stacks $\mathfrak{X}_{+}$, $\mathfrak{X}_{-}$ are the GIT
quotients of $\mathbb{C}^{S}$. The toric birational morphism
$\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$ is induced by the self-map
$\big{(}z_{\hat{b}},(z_{v})_{v\in
S\setminus\\{{\hat{b}}\\}}\big{)}\longmapsto\big{(}1,\big{(}z_{\hat{b}}^{k_{v}}z_{v}\big{)}_{v\in
S\setminus\\{{\hat{b}}\\}}\big{)}$ (7.1)
on
$\mathbb{C}^{S}\cong\mathbb{C}^{\\{{\hat{b}}\\}}\times\mathbb{C}^{S\setminus\\{{\hat{b}}\\}}$,
where note that $k_{v}\geq 0$ for $v\neq{\hat{b}}$. It is easy to check that
this sends the stable locus for $\operatorname{cpl}(\mathbf{\Sigma}_{+})$ to
the stable locus for $\operatorname{cpl}(\mathbf{\Sigma}_{-})$. The map
$\varphi$ contracts the divisor $\\{z_{{\hat{b}}}=0\\}$ onto the toric
substack $Z=\bigcap\limits_{v\in M_{+}}\\{z_{v}=0\\}$. In the type (II-i)
case, $\varphi$ is a weighted blowup along the codimension $\geq 2$ substack
$Z$; in the type (III) case where $M_{+}$ is a singleton $\\{\check{b}\\}$,
$\varphi$ exhibits $\mathfrak{X}_{+}$ as a root stack of $\mathfrak{X}_{-}$
with respect to the divisor $Z=\\{z_{\check{b}}=0\\}$.
We write $(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$,
$(\operatorname{pr}\colon\mathcal{Y}^{\rm sm}\to\mathcal{M}^{\rm sm},F)$ for
the LG models associated with $S$ and $S_{-}=S\cap\Delta_{-}$ respectively
(see Definition 3.6). These two LG models are related by the pull-back (Lemma
6.12):
$\textstyle{\mathcal{Y}^{\rm
sm}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\mathcal{Y}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{F}$$\textstyle{\mathbb{C}}$$\textstyle{\mathcal{M}^{\rm
sm}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\textstyle{\mathcal{M}.}$
We write $\operatorname{Bri}(F)$, $\operatorname{Bri}^{\rm sm}(F)$ for the
non-equivariant Brieskorn modules (Definition 4.1) associated with the LG
models $(\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M},F)$,
$(\operatorname{pr}\colon\mathcal{Y}^{\rm sm}\to\mathcal{M}^{\rm sm},F)$
respectively. On the affine chart associated with $\mathbf{\Sigma}_{-}$,
$\mathcal{M}^{\rm sm}$ is cut out from $\mathcal{M}$ by the equation
$t_{\hat{b}}=0$, where
$t_{\hat{b}}=q^{\delta_{\hat{b}}^{\mathbf{\Sigma}_{-}}}$ is the co-ordinate
introduced in Section 3.5. We have $t_{{\hat{b}}}=q^{-\mathbf{w}}$ since
$\delta_{\hat{b}}^{\mathbf{\Sigma}_{-}}=e_{{\hat{b}}}-\Psi_{-}({\hat{b}})=e_{{\hat{b}}}-\sum\limits_{b\in
M_{+}}k_{b}e_{b}=-\mathbf{w}\in\mathbb{L}$, where
$\Psi_{-}=\Psi^{\mathbf{\Sigma}_{-}}$ (see Notation 3.10).
In this section, we fix an isomorphism
$\mathbf{N}\cong\mathbb{Z}^{n}\times\mathbf{N}_{\rm tor}$ and a splitting
$\varsigma\colon\mathbf{N}\to\mathbb{O}^{\mathbf{\Sigma}_{-}}$ of the refined
fan sequence (3.12) for $\mathbf{\Sigma}_{-}$ and use the associated co-
ordinates $x_{1},\dots,x_{n}$ along the fibres of the LG model as introduced
in Section 3.5.
###### Caution 7.1.
Under our assumption $S=S_{-}\cup\\{{\hat{b}}\\}$, $\mathcal{M}$ is the small
quantum cohomology locus $($see $Section~{}\ref{subsubsec:Bri_sm})$ of
$\mathfrak{X}_{+}$ and $\mathcal{M}^{\rm sm}$ is the small quantum cohomology
locus of $\mathfrak{X}_{-}$.
### 7.2 Critical points along a curve
Consider the 1-dimensional toric substack $\mathcal{C}$ of $\mathcal{M}$
corresponding to
$W\cap\operatorname{cpl}(\mathbf{\Sigma}_{+})=W\cap\operatorname{cpl}(\mathbf{\Sigma}_{-})$.
Recall that uniformizing affine charts of $\mathcal{C}$ and
$\operatorname{pr}^{-1}(\mathcal{C})$ have been described explicitly in
Section 5.2: $q^{-\mathbf{w}/e}=t_{\hat{b}}^{1/e}$ gives a rational co-
ordinate of $\mathcal{C}\cap\mathcal{M}_{\mathbf{\Sigma}_{-}}$, where
$e=e_{-}\in\mathbb{N}$ is the smallest common denominator of
$\\{c\in\mathbb{Q}\colon
c\mathbf{w}\in\boldsymbol{\Lambda}(\mathbf{\Sigma}_{-})\\}$, and
$w_{v}=w_{v}^{-}=u^{(\Psi_{-}(v),v)}$ with $v\in\mathbf{N}$ generate the co-
ordinate ring
$A=\bigoplus\limits_{v\in\mathbf{N}}\mathbb{C}[t_{\hat{b}}^{1/e}]w_{v}$ of
$\operatorname{pr}^{-1}(\mathcal{C})\cap\mathcal{Y}_{\mathbf{\Sigma}_{-}}$
(see Lemma 5.8). Recall also that $F=\sum\limits_{b\in R_{+}\cup R_{-}}u_{b}$
on $\operatorname{pr}^{-1}(\mathcal{C})$. We study the family of relative
critical points
$x_{1}\frac{\partial F}{\partial x_{1}}=\cdots=x_{n}\frac{\partial F}{\partial
x_{n}}=0$ (7.2)
over the curve $\mathcal{C}$.
###### Proposition 7.2.
A relative critical point of the LG potential $F$ over $\mathcal{C}$ is given
by an assignment of a complex number $w_{v}$ to every $v\in\mathbf{N}$
satisfying $w_{0}=1$,
$\displaystyle w_{v_{1}}w_{v_{2}}=w_{v_{1}+v_{2}}\qquad\text{if
$\overline{v_{1}},\overline{v_{2}}\in\sigma_{M_{+}}$}\qquad\text{and}\qquad
w_{v}=\begin{cases}0,&\text{if $\overline{v}\notin\sigma_{M_{+}}$},\\\
k_{v}\gamma,&\text{if $v\in M_{+}$},\end{cases}$
where $k_{v}=D_{v}\cdot\mathbf{w}$ for $v\in S$ and
$\gamma=0\qquad\text{or}\qquad\gamma=\left(-\frac{1}{Kt_{\hat{b}}}\right)^{1/J}\qquad\text{when
$t_{\hat{b}}\neq 0$}$
with $J:=\big{(}\sum\limits_{b\in M_{+}}k_{b}\big{)}-1>0$ and
$K:=\prod\limits_{b\in M_{+}}k_{b}^{k_{b}}$. The corresponding critical value
of $F$ is given by $J\gamma$.
###### Proof.
Take a relative critical point and let $w_{v}$ denote the value of the
function $w_{v}$ at that point. We have $w_{0}=1$. The equation (7.2) for
relative critical points reads
$\sum_{b\in R_{+}\cup R_{-}}u_{b}\overline{b}=0\qquad\text{in
$\mathbf{N}_{\mathbb{R}}$.}$ (7.3)
Note that $R_{+}\cup R_{-}=R_{-}\sqcup\\{{\hat{b}}\\}$, $u_{b}=w_{b}$ for
$b\in R_{-}$ and $u_{\hat{b}}=t_{\hat{b}}w_{\hat{b}}$. By Lemma 5.8, we have
$w_{v}\cdot w_{v^{\prime}}=\begin{cases}w_{v+v^{\prime}},&\text{if
$\overline{v}$ and $\overline{v^{\prime}}$ belong to a common cone of
$\Sigma_{-}=\Sigma_{0}$},\\\ 0,&\text{otherwise},\end{cases}$
where note that $\Sigma_{0}$ in Lemma 5.8 coincides with the underlying fan
$\Sigma_{-}$ of $\mathbf{\Sigma}_{-}$ in the current setting. Therefore there
exists a cone $\sigma\in\Sigma_{-}$ such that $\\{\overline{v}\colon w_{v}\neq
0\\}=\mathbf{N}\cap\sigma$. Then equation (7.3) implies that
$(R_{-}\cup\\{{\hat{b}}\\})\cap\sigma$ is linearly dependent. Therefore we
have either $(R_{-}\cup\\{{\hat{b}}\\})\cap\sigma=\varnothing$ or
$\overline{{\hat{b}}}\in\sigma$. In the former case, we have $\sigma=0$; this
corresponds to the case where $\gamma=0$ in the proposition. In the latter
case, we have $\sigma\supset\sigma_{M_{+}}$; the linear relation
${\hat{b}}=\sum\limits_{b\in M_{+}}k_{b}b$ together with (7.3) implies
$\begin{cases}w_{b}+k_{b}t_{\hat{b}}w_{{\hat{b}}}=0&\text{for $b\in
M_{+}$},\\\ w_{b}=0&\text{for $b\in(R_{-}\setminus
M_{+})\cap\sigma$},\end{cases}\qquad\text{and}\qquad w_{{\hat{b}}}=\prod_{b\in
M_{+}}w_{b}^{k_{b}}.$
Since $w_{b}\neq 0$ for $\overline{b}\in\sigma$, we have $(R_{-}\setminus
M_{+})\cap\sigma=\varnothing$ and thus $\sigma=\sigma_{M_{+}}$. Setting
$\gamma=w_{b}/k_{b}=-t_{\hat{b}}w_{\hat{b}}$ (with $b\in M_{+}$), we find that
$\gamma$ satisfies
$-\gamma/t_{\hat{b}}=\prod_{b\in M_{+}}(k_{b}\gamma)^{k_{b}}\
\Longleftrightarrow\ -1/(Kt_{\hat{b}})=\gamma^{J}.$
This proves the proposition. ∎
###### Remark 7.3.
Proposition 7.2 implies that the critical values of $F$ along $\mathcal{C}$ do
not belong to $\mathbb{R}_{>0}$ when $t_{\hat{b}}>0$. This phenomenon is
closely related to the Conjecture $\mathcal{O}$ [44, Conjecture 3.1.2].
### 7.3 Identifying $\mathcal{O}$
Recall from Section 2.4 that the $\widehat{\Gamma}$-integral structure
identifies the $K$-group of a smooth DM stack with a lattice of flat sections
of the quantum D-module. In this section, we introduce a ‘positive real’
Lefschetz thimble $\Gamma_{\mathbb{R}}$ defined along a ‘positive real’ locus
$\mathcal{M}_{\mathbb{R}}$ (or $\mathcal{M}^{\rm sm}_{\mathbb{R}}$). The flat
section $\mathfrak{s}_{\mathcal{O}}$ given by the structure sheaf
$\mathcal{O}$ corresponds to $\Gamma_{\mathbb{R}}$ under mirror symmetry, and
thus spans a component of the analytic lift of the formal decomposition (as
discussed in Propositions 6.5 and 6.18) associated with the so-called conifold
point. The content in this section is essentially an adaptation of the main
result of [62] to the current setting.
#### 7.3.1 The structure sheaf of $\boldsymbol{\mathfrak{X}_{+}}$
By definition (see Section 3.4), $\mathcal{M}$ and $\mathcal{Y}$ contain open
dense tori
$\mathcal{M}^{\times}=\mathbb{L}^{\star}\otimes\mathbb{C}^{\times}$,
$\mathcal{Y}^{\times}=(\mathbb{C}^{\times})^{S}$ respectively. We define the
positive real loci $\mathcal{M}_{\mathbb{R}}\subset\mathcal{M}^{\times}$,
$\mathcal{Y}_{\mathbb{R}}\subset\mathcal{Y}^{\times}$ to be
$\displaystyle\mathcal{M}_{\mathbb{R}}:=\mathbb{L}^{\star}\otimes\mathbb{R}_{>0},\qquad\mathcal{Y}_{\mathbb{R}}:=(\mathbb{R}_{>0})^{S}.$
We write $\mathcal{Y}_{q}$ for the fibre of
$\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$ at $q\in\mathcal{M}$; and
$\Gamma_{\mathbb{R}}=\Gamma_{\mathbb{R}}(q)$ for the fibre of
$\mathcal{Y}_{\mathbb{R}}\to\mathcal{M}_{\mathbb{R}}$ at
$q\in\mathcal{M}_{\mathbb{R}}$:
$\Gamma_{\mathbb{R}}(q)=\mathcal{Y}_{q}\cap\mathcal{Y}_{\mathbb{R}}\cong\operatorname{Hom}(\mathbf{N},\mathbb{R}_{>0})\cong(\mathbb{R}_{>0})^{n}.$
Consider the restriction of $F_{q}=F|_{\mathcal{Y}_{q}}$ to the real positive
locus $\Gamma_{\mathbb{R}}$. Then
* •
it is a strictly convex function since the Hessian
$\frac{\partial^{2}F_{q}}{\partial\log x_{i}\partial\log
x_{j}}=\sum\limits_{b\in S}u_{b}b_{i}b_{j}$ is positive definite on
$\Gamma_{\mathbb{R}}$ (where $b_{i}\in\mathbb{Z}$ is the $i$th entry of
$\overline{b}\in\overline{\mathbf{N}}\cong\mathbb{Z}^{n}$);
* •
it is proper and bounded from below since $0$ is in the interior of the convex
hull $\Delta_{+}$ of $\\{\overline{b}\colon b\in S\\}$.
Therefore, $F_{q}|_{\Gamma_{\mathbb{R}}}$ attains a global minimum at a unique
critical point
$\operatorname{cr}_{\mathbb{R}}=\operatorname{cr}_{\mathbb{R}}(q)\in\Gamma_{\mathbb{R}}(q)$;
the point $\operatorname{cr}_{\mathbb{R}}$ is called the _conifold point_ [43,
44]. Since $\Gamma_{\mathbb{R}}$ is preserved by the gradient flow of
$\Re(F_{q})$ (with respect to the Kähler metric
$\frac{\boldsymbol{\mathrm{i}}}{2}\sum\limits_{i=1}^{n}d\log x_{i}\wedge
d\overline{\log x_{i}}$) on $\mathcal{Y}_{q}=\operatorname{pr}^{-1}(q)$, we
have the following:
###### Lemma 7.4.
The positive real locus $\Gamma_{\mathbb{R}}$ of $\mathcal{Y}_{q}$ is the
Lefschetz thimble (6.12) of $F_{q}$ associated with the conifold point
$\operatorname{cr}_{\mathbb{R}}$ and the phase $\phi=\pi$.
By Proposition 6.16, there exist an analytic neighbourhood $\mathcal{V}_{+}$
of $0_{+}:=0_{\mathbf{\Sigma}_{+}}\in\mathcal{M}$, a mirror map
$\operatorname{mir}_{+}\colon\mathcal{V}_{+}\to[\mathcal{M}_{\rm
A}(\mathfrak{X}_{+})/\operatorname{Pic}^{\rm st}(\mathfrak{X}_{+})]$ and an
isomorphism
$\operatorname{Mir}_{+}\colon\
\operatorname{Bri}(F)|_{\mathcal{V}_{+}}\cong\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+}),$
where $\operatorname{QDM}^{\rm an}(\mathfrak{X}_{+})$ denotes the analytic
quantum D-module as in (6.1). The following result says that
$\Gamma_{\mathbb{R}}(q)$ corresponds to the flat section
$\mathfrak{s}_{\mathcal{O}}$ under mirror symmetry:
###### Theorem 7.5 ([62, Theorems 4.11 and 4.14, Section 4.3.1]).
Let $P(\alpha,\beta)=(\alpha(-z),\beta(z))$ denote the pairing (2.9) of the
quantum D-module induced by the orbifold Poincaré pairing. We write
$\Omega=\Omega_{q,z}$ for a local section of $\operatorname{Bri}(F)$.
* (1)
For $q\in\mathcal{V}_{+}\cap\mathcal{M}_{\mathbb{R}}$, we have an isomorphism
$H_{n}(\mathcal{Y}_{q},\\{\Re(-F_{q})\ll 0\\};\mathbb{Z})\cong
K(\mathfrak{X}_{+}),\qquad\Gamma\mapsto V(\Gamma),$
which varies locally constantly in $q$ such that
$(2\pi
z)^{-n/2}\int_{\Gamma}e^{-F_{q}/z}\Omega_{q,-z}=P\left(\operatorname{Mir}_{+}(\Omega),\mathfrak{s}_{V(\Gamma)}(\operatorname{mir}_{+}(q),z)\right)$
for $\Gamma\in H_{n}(\mathcal{Y}_{q},\\{\Re(-F_{q})\ll 0\\};\mathbb{Z})$,
$\Omega\in\operatorname{Bri}(F)$ and $z>0$, where $\mathfrak{s}_{V}(\tau,z)$
is the flat section of the $\widehat{\Gamma}$-integral structure $($see
Definition $\ref{def:s})$.
* (2)
In (1), $V(\Gamma_{\mathbb{R}}(q))$ is given by the structure sheaf
$\mathcal{O}$ of $\mathfrak{X}_{+}$.
In other words, the integral structure of the Brieskorn module
$\operatorname{Bri}(F)$ dual to the lattice
$H_{n}(\mathcal{Y}_{q},\\{\Re(F_{q}/z)\ll 0\\};\mathbb{Z})$
corresponds to the $\widehat{\Gamma}$-integral structure of the quantum
D-module under the mirror isomorphism.
###### Remark 7.6 ([62, Section 4.3]).
Since the mirror isomorphism $\operatorname{Mir}_{+}$ preserves the pairing,
the map $\Gamma\mapsto V(\Gamma)$ above satisfies
$(-1)^{n(n-1)/2}\\#\big{(}e^{-\pi\boldsymbol{\mathrm{i}}}\Gamma_{1}\cdot\Gamma_{2}\big{)}=\chi(V(\Gamma_{1}),V(\Gamma_{2}))$
for $\Gamma_{1},\Gamma_{2}\in H_{n}(\mathcal{Y}_{q},\\{\Re(-F_{q})\ll
0\\};\mathbb{Z})$, where $\chi(V_{1},V_{2})$ is the Euler pairing,
$e^{-\pi\boldsymbol{\mathrm{i}}}\Gamma_{1}\in
H_{n}\big{(}\mathcal{Y}_{q_{*}},\\{\Re(F_{q_{*}})\ll 0\\};\mathbb{Z}\big{)}$
is the parallel translate of $\Gamma_{1}$ in the local system
$\bigcup_{\theta\in[0,\pi]}H_{n}\big{(}\mathcal{Y}_{q_{*}},\big{\\{}\Re\big{(}{-}e^{\boldsymbol{\mathrm{i}}\theta}F_{q_{*}}\big{)}\ll
0\big{\\}};\mathbb{Z}\big{)}$
from $\theta=0$ to $\theta=\pi$, and
$\\#\big{(}e^{-\pi\boldsymbol{\mathrm{i}}}\Gamma_{1}\cdot\Gamma_{2}\big{)}$
denotes the algebraic intersection number. Here we use the fact that the
higher residue pairing corresponds to the intersection pairing on relative
homology (see [62, Sections 3.3.1–3.3.2]); note however that the sign factor
$(-1)^{n(n-1)/2}$ was missing in [62], see [64, footnote (16)] for the
correction.
###### Remark 7.7 (cf. Remark 2.8).
We need to specify a branch of the multi-valued section $\mathfrak{s}_{V}$ in
the above theorem. We have a standard choice for the branch of
$\mathfrak{s}_{V}(\operatorname{mir}_{+}(q),z)$ with $V\in
K(\mathfrak{X}_{+})$ when $q\in\mathcal{M}_{\mathbb{R}}$, and the above
theorem holds for this choice. By the argument preceding [62, Proposition
4.8], the fundamental solution $L(\operatorname{mir}(q),z)$ can be obtained
from the $I$-function via the Birkhoff factorization; the $I$-function has a
standard determination on the positive real locus (by requiring $\log
q_{a}\in\mathbb{R}$ in the formula [62, (59)] of the $I$-function). We also
have a standard determination of $z^{-\mu}z^{c_{1}(\mathfrak{X})}$ given by
$\log z\in\mathbb{R}$ for $z>0$. Hence we obtain a standard identification of
the space of flat sections of $\operatorname{Bri}(F)$ over
$(q,z)\in(\mathcal{M}_{\mathbb{R}}\cap\mathcal{V}_{+})\times\mathbb{R}_{>0}$
with the $K$-group $K(\mathfrak{X}_{+})\otimes\mathbb{C}$.
Introduce the following subsets of $\mathcal{V}_{+}\subset\mathcal{M}$:
$\displaystyle\mathcal{V}^{\rm
ss}_{+}:=\\{q\in\mathcal{V}_{+}\cap\mathcal{M}^{\times}\colon\text{$F_{q}=F|_{\mathcal{Y}_{q}}$
has only non-degenerate critical points}\\},$ $\displaystyle\mathcal{V}^{\rm
ss}_{+,\mathbb{R}}:=\mathcal{V}^{\rm ss}_{+}\cap\mathcal{M}_{\mathbb{R}}.$
Note that $\mathcal{V}^{\rm ss}_{+}$ is the intersection of $\mathcal{V}_{+}$
and a non-empty Zariski-open subset of $\mathcal{M}$ by the discussion in
Section 6.3.3; hence $\mathcal{V}^{\rm ss}_{+}$ is open dense in
$\mathcal{V}_{+}$, and $\mathcal{V}^{\rm ss}_{+,\mathbb{R}}$ is open dense in
$\mathcal{V}_{+}\cap\mathcal{M}_{\mathbb{R}}$.
Choose $q_{0}\in\mathcal{V}^{\rm ss}_{+,\mathbb{R}}$ and let
$\operatorname{cr}_{1}(q),\dots,\operatorname{cr}_{N_{+}}(q)$ denote all
branches of critical points of $F_{q}$ near $q=q_{0}$, where $N_{+}=\dim
H^{*}_{\rm CR}(\mathfrak{X}_{+})$. We may assume that
$\operatorname{cr}_{1}(q_{0})$ is the conifold point
$\operatorname{cr}_{\mathbb{R}}(q_{0})$. Let
$\mathbf{u}_{i}(q)=F_{q}(\operatorname{cr}_{i}(q))$ be the corresponding
critical value. Suppose that $\phi\in\mathbb{R}$ is an admissible phase for
$\\{\mathbf{u}_{1}(q_{0}),\dots,\mathbf{u}_{N_{+}}(q_{0})\\}$. By Proposition
6.18, there exist an open neighbourhood $B$ of $q_{0}$ in $\mathcal{V}^{\rm
ss}_{+}$, a sector
$I_{\phi}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\in{\widetilde{\mathbb{C}}}\colon|\theta-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$
(with small $\epsilon>0$) and an isomorphism (analytic lift)
$\Phi^{+}_{\phi}\colon\ \pi^{*}\operatorname{Bri}(F)\big{|}_{B\times
I_{\phi}}\cong\bigoplus_{i=1}^{N_{+}}\left(\mathcal{A}_{B\times
I_{\phi}},d+d(\mathbf{u}_{i}(q)/z)\right)$
that induces the formal decomposition
$\operatorname{Asym}\colon\operatorname{Bri}(F)\otimes_{\mathcal{O}^{\rm
an}_{B\times\mathbb{C}_{z}}}\mathcal{O}^{\rm
an}_{B}[\\![z]\\!]\cong\mathcal{O}^{\rm an}_{B}[\\![z]\\!]^{\oplus N_{+}}$,
where $\pi\colon\mathcal{V}^{\rm
ss}_{+}\times{\widetilde{\mathbb{C}}}\to\mathcal{V}^{\rm
ss}_{+}\times\mathbb{C}$ is the oriented real blow-up. Composing this with the
mirror isomorphism, we also get the analytic lift of the formal decomposition
of the quantum D-module (cf. Proposition 6.5):
$\widetilde{\Phi}_{\phi}^{+}\colon\
\pi^{*}\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})\big{|}_{B\times
I_{\phi}}\cong\bigoplus_{i=1}^{N_{+}}\left(\mathcal{A}_{B\times
I_{\phi}},d+d(\mathbf{u}_{i}(q)/z)\right),$
where
$\widetilde{\Phi}_{\phi}^{+}=\Phi_{\phi}^{+}\circ\operatorname{Mir}_{+}^{-1}$.
###### Proposition 7.8.
For $q_{0}\in\mathcal{V}^{\rm ss}_{+,\mathbb{R}}$, there exists
$\alpha_{0}\in(0,\pi/2)$ such that the following holds. For every admissible
phase $\phi\in(-\alpha_{0},\alpha_{0})$ for
$\\{\mathbf{u}_{1}(q_{0}),\dots,\mathbf{u}_{N_{+}}(q_{0})\\}$, there exists a
basis $\\{V_{i}\\}_{i=1}^{N_{+}}$ of $K(\mathfrak{X}_{+})$ with $V_{1}$ being
the structure sheaf $\mathcal{O}$ of $\mathfrak{X}_{+}$, such that the
corresponding flat section
$s_{i}=\mathfrak{s}_{V_{i}}(\operatorname{mir}_{+}(q),z)$ satisfies
$\widetilde{\Phi}^{+}_{\phi}\big{(}e^{\mathbf{u}_{i}(q)/z}s_{i}\big{)}=e_{i}$,
where $e_{i}$ denotes the $i$th standard basis of $\mathcal{A}_{B\times
I_{\phi}}^{\oplus N_{+}}$.
###### Proof.
Let $\Gamma^{\phi}_{i}(q)$ denote the Lefschetz thimble (6.12) of $F_{q}$
associated with the critical point $\operatorname{cr}_{i}(q)$ and phase
$\phi$. By Lemma 7.4, $\Gamma_{1}^{\pi}(q_{0})=\Gamma_{\mathbb{R}}(q_{0})$.
Since there are no critical points of $F_{q_{0}}$ on
$\Gamma_{\mathbb{R}}(q_{0})$ other than the conifold point
$\operatorname{cr}_{\mathbb{R}}(q_{0})$, $\Gamma^{\pi+\phi}_{1}(q)$ varies
continuously in a neighbourhood of $(q,\phi)=(q_{0},0)$. Let
$\alpha_{0}\in(0,\pi/2)$ be such that $\Gamma_{1}^{\pi+\phi}(q)$ depends
continuously on $(q,\phi)$ as $(q,\phi)$ varies in a neighbourhood of
$\\{q_{0}\\}\times(-\alpha_{0},\alpha_{0})$ in $\mathcal{V}^{\rm
ss}_{+}\times\mathbb{R}$.
Choose an admissible phase $\phi\in(-\alpha_{0},\alpha_{0})$ for
$\\{\mathbf{u}_{1}(q_{0}),\dots,\mathbf{u}_{N_{+}}(q_{0})\\}$ and let
$\Phi^{+}_{\phi}$, $\widetilde{\Phi}^{+}_{\phi}$ be the associated analytic
lifts over a neighbourhood $B\times I_{\phi}$ of
$\big{(}q_{0},\big{(}0,e^{\boldsymbol{\mathrm{i}}\phi}\big{)}\big{)}$ as
above. Let $\varphi_{i}$ denote a section of
$\pi^{*}\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})|_{B\times I_{\phi}}$ such that
$\widetilde{\Phi}_{\phi}^{+}(\varphi_{i})=e_{i}$. Take a local section
$\Omega=\Omega_{q,z}$ of $\operatorname{Bri}(F)$ near $q=q_{0}$. By the
definition (6.13) of $\Phi_{\phi}^{+}$, for $q\in B$ and
$z\in\mathbb{C}^{\times}$ with $|\arg(z)-\phi|<\pi/2$, we have191919Recall
from Proposition 6.18 that $B$ is chosen sufficiently small so that
$\Gamma_{i}^{\phi+\pi}(q)$ deforms continuously as $q$ varies in $B$.
$\displaystyle(2\pi
z)^{-n/2}e^{\mathbf{u}_{i}(q)/z}\int_{\Gamma_{i}^{\phi+\pi}(q)}e^{-F_{q}/z}\Omega_{q,-z}$
$\displaystyle=\Phi_{\phi+\pi}^{i}(\Omega)(q,-z)$ $\displaystyle=P_{\rm
std}(\Phi_{\phi+\pi}(\Omega),e_{i})(q,z)$ $\displaystyle=P_{\rm
std}\big{(}\widetilde{\Phi}_{\phi+\pi}(\operatorname{Mir}_{+}(\Omega)),\widetilde{\Phi}_{\phi}(\varphi_{i})\big{)}(q,z)$
$\displaystyle=P(\operatorname{Mir}_{+}(\Omega),\varphi_{i})(q,z),$
where $P_{\rm std}$ is the diagonal pairing as in Proposition 6.10 and we used
Remark 6.7 in the last step. By Theorem 7.5(1), the left-hand side of the
above equation equals
$e^{\mathbf{u}_{i}(q)/z}P(\operatorname{Mir}_{+}(\Omega),\mathfrak{s}_{V_{i}}(\operatorname{mir}_{+}(q),z))\qquad\text{with
$V_{i}=V\big{(}\Gamma^{\phi+\pi}_{i}(q)\big{)}$}.$
Since the above equation holds for all $\Omega$, we have
$\varphi_{i}=e^{\mathbf{u}_{i}(q)/z}\mathfrak{s}_{V_{i}}(\operatorname{mir}_{+}(q),z)$.
We now set $i=1$. By the choice of $\alpha_{0}$ and $\phi$, the cycle
$\Gamma_{1}^{\phi+\pi}(q_{0})$ (and hence $\Gamma_{1}^{\phi+\pi}(q)$ with
$q\in B$) is a continuous deformation of
$\Gamma_{1}^{\pi}(q_{0})=\Gamma_{\mathbb{R}}(q_{0})$. Thus we get
$V_{1}=V_{1}(\Gamma_{\mathbb{R}}(q_{0}))=\mathcal{O}$ by Theorem 7.5(2). ∎
###### Remark 7.9.
Recall from Propositions 6.1 and 6.10 that the formal decomposition and its
analytic lift $\Phi^{+}_{\phi}$ are ambiguous up to multiplication by
$\operatorname{diag}(\pm 1,\dots,\pm 1)$, and this ambiguity is fixed once we
give a local trivialization of the $\mu_{2}$-local system
$\operatorname{\mathsf{ori}}$. We note that there is a standard trivialization
of $\operatorname{\mathsf{ori}}$ at the conifold point
$\operatorname{cr}_{\mathbb{R}}$ since the Hessian of $F_{q}$ at
$\operatorname{cr}_{\mathbb{R}}$ is positive-definite; hence the component of
the analytic lift $\Phi^{+}_{\phi}$ corresponding to
$\operatorname{cr}_{\mathbb{R}}(q)$ (which is the first component) is
unambiguous.
###### Remark 7.10.
Proposition 7.8 says that $\mathfrak{s}_{\mathcal{O}}$ is characterized by the
exponential asymptotics $\mathfrak{s}_{\mathcal{O}}\sim
e^{-\mathbf{u}_{1}(q)/z}\Psi_{\mathbb{R}}(q)$ as $z\to 0$ along the sector
$\arg z\in(-\frac{\pi}{2}-\alpha_{0},\frac{\pi}{2}+\alpha_{0})$ when $q$ lies
in a neighbourhood of the positive real locus, where $\Psi_{\mathbb{R}}(q)$ is
the normalized idempotent (see Remark 6.3) corresponding to the conifold point
$\operatorname{cr}_{\mathbb{R}}(q)$. In terms of the marked reflection system
in Section 6.2, it also says that
$\widehat{\Gamma}_{\mathfrak{X}_{+}}\cup(2\pi\boldsymbol{\mathrm{i}})^{\deg_{0}/2}\operatorname{inv}^{*}\widetilde{\operatorname{ch}}(V_{i}^{+})$,
$1\leq i\leq N_{+}$ give the asymptotic basis at $q_{0}$ and $\phi$.
###### Remark 7.11.
At various places in Section 7, we work around for the fact that
$u_{1}(q)+\mathbb{R}_{\geq 0}$ may contain other critical values; the argument
would become much simpler if otherwise.
#### 7.3.2 The structure sheaf of $\mathfrak{X}_{-}$
We repeat the same discussion for $\mathfrak{X}_{-}$. The difference is that
we consider the analytic lift over a region $\mathcal{V}_{-}$ which protrudes
from the small quantum cohomology locus $\mathcal{M}^{\rm sm}$ of
$\mathfrak{X}_{-}$.
Let $\mathcal{M}^{\rm
sm,\times}:=\mathbb{L}^{\prime\star}\otimes\mathbb{C}^{\times}$,
$\mathcal{Y}^{\rm sm,\times}:=(\mathbb{C}^{\times})^{S_{-}}$ denote the open
dense tori in $\mathcal{M}^{\rm sm}$ and $\mathcal{Y}^{\rm sm}$ respectively
and set:
$\displaystyle\mathcal{M}^{\rm
sm}_{\mathbb{R}}:=\mathbb{L}^{\prime\star}\otimes\mathbb{R}_{>0}\subset\mathcal{M}^{\rm
sm,\times},$ $\displaystyle\mathcal{Y}^{\rm
sm}_{\mathbb{R}}:=(\mathbb{R}_{>0})^{S_{-}}\subset\mathcal{Y}^{\rm
sm,\times},$
$\displaystyle\Gamma_{\mathbb{R}}=\Gamma_{\mathbb{R}}(q):=\text{the fibre of
$\mathcal{Y}^{\rm sm}_{\mathbb{R}}\to\mathcal{M}^{\rm sm}_{\mathbb{R}}$ at
$q\in\mathcal{M}^{\rm sm}_{\mathbb{R}}$ (as defined before)},$
where
$\mathbb{L}^{\prime}=\operatorname{Ker}\big{(}\mathbb{Z}^{S_{-}}\to\mathbf{N}\big{)}$
is the lattice as in Section 6.3.3. For $q\in\mathcal{M}^{\rm
sm}_{\mathbb{R}}$, $\Gamma_{\mathbb{R}}(q)$ is the Lefschetz thimble of
$F_{q}$ associated with the conifold point $\operatorname{cr}_{\mathbb{R}}(q)$
and the phase $\pi$ as in Lemma 7.4. The analytified Brieskorn module
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}$ is defined over an
analytic open neighbourhood $\mathcal{V}_{-}$ of
$0_{-}:=0_{\mathbf{\Sigma}_{-}}$ in $\mathcal{M}$ (see Definition 4.21). By
the non-equivariant limit of Theorem 4.34, by shrinking $\mathcal{V}_{-}$ if
necessary, we have a mirror map
$\operatorname{mir}_{-}\colon\mathcal{V}_{-}\to[\mathcal{M}_{\rm
A}(\mathfrak{X}_{-})/\operatorname{Pic}^{\rm st}(\mathfrak{X}_{-})]$ and a
mirror isomorphism
$\operatorname{Mir}_{-}\colon\
\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}}\cong\operatorname{mir}_{-}^{*}\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{-}).$ (7.4)
By Proposition 6.16, by shrinking $\mathcal{V}_{-}$ further if necessary, this
mirror isomorphism can be lifted to a fully analytic mirror isomorphism over
$\mathcal{V}^{\rm sm}_{-}=\mathcal{V}_{-}\cap\mathcal{M}^{\rm sm}$
$\operatorname{Mir}_{-}\colon\ \operatorname{Bri}^{\rm
sm}(F)|_{\mathcal{V}^{\rm
sm}_{-}}\cong\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-}).$ (7.5)
###### Theorem 7.12 ([62, Theorems 4.11 and 4.14, Section 4.3.1]).
The conclusions of Theorem 7.5 hold true even when $\mathfrak{X}_{+}$,
$\mathcal{V}_{+}$, $\operatorname{Mir}_{+}$, $\operatorname{mir}_{+}$,
$\mathcal{M}_{\mathbb{R}}$ there are replaced with $\mathfrak{X}_{-}$,
$\mathcal{V}_{-}$, $\operatorname{Mir}_{-}$, $\operatorname{mir}_{-}$,
$\mathcal{M}^{\rm sm}_{\mathbb{R}}$ respectively.
By the construction of
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}_{-}}$ in Section
4.3, we have an open neighbourhood $\mathcal{B}_{-}$ of
$\tilde{0}_{-}:=\tilde{0}_{\mathbf{\Sigma}_{-}}\in\mathcal{Y}$ such that the
family
$\operatorname{Cr}_{-}:=\mathcal{B}_{-}\cap\widetilde{\operatorname{pr}}^{-1}(\mathcal{V}_{-}\times\\{0\\})\xrightarrow{\operatorname{pr}}\mathcal{V}_{-}$
of relative critical points (of $F$) in $\mathcal{B}_{-}$ is a finite flat
morphism of degree $N_{-}=\dim H^{*}_{\rm CR}(\mathfrak{X}_{-})$ (see also the
discussion in Section 6.3.1), where $\widetilde{\operatorname{pr}}$ is the map
in (4.3). Along the small quantum cohomology locus $\mathcal{V}^{\rm
sm}_{-}=\mathcal{V}_{-}\cap\mathcal{M}^{\rm sm}$, this family contains all
relative critical points, i.e.,
$\mathcal{B}_{-}\cap\widetilde{\operatorname{pr}}^{-1}(\mathcal{V}^{\rm
sm}_{-}\times\\{0\\})=\widetilde{\operatorname{pr}}^{-1}(\mathcal{V}^{\rm
sm}_{-}\times\\{0\\})$ (since the Brieskorn module $\operatorname{Bri}^{\rm
sm}(F)$ has the rank $N_{-}$ by Proposition 6.15). We define
$\displaystyle\mathcal{V}^{\rm ss}_{-}:=\\{q\in\mathcal{V}_{-}\colon\text{the
fibre of $\operatorname{Cr}_{-}\to\mathcal{V}_{-}$ at $q\in\mathcal{V}_{-}$ is
reduced}\\},$ $\displaystyle\mathcal{V}^{\rm sm,ss}_{-}:=\mathcal{V}^{\rm
ss}_{-}\cap\mathcal{M}^{\rm sm},$ $\displaystyle\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}:=\mathcal{V}^{\rm sm,ss}_{-}\cap\mathcal{M}^{\rm
sm}_{\mathbb{R}},$
where $\mathcal{V}^{\rm ss}_{-}$ is open dense in $\mathcal{V}_{-}$,
$\mathcal{V}^{\rm sm,ss}_{-}$ is open dense in $\mathcal{V}^{\rm sm}_{-}$ and
$\mathcal{V}^{\rm sm,ss}_{-,\mathbb{R}}$ is open dense in $\mathcal{V}^{\rm
sm}_{-}\cap\mathcal{M}^{\rm sm}_{\mathbb{R}}$.
Choose $q_{0}\in\mathcal{V}^{\rm sm,ss}_{-,\mathbb{R}}$. Let
$\operatorname{cr}_{1}(q),\dots,\operatorname{cr}_{N_{-}}(q)$ be all branches
of critical points of $F_{q}$ contained in $\mathcal{B}_{-}$ and defined in a
neighbourhood of $q=q_{0}$ in $\mathcal{V}^{\rm ss}_{-}$. We may assume that
$\operatorname{cr}_{1}(q_{0})=\operatorname{cr}_{\mathbb{R}}(q_{0})$ and write
$\mathbf{u}_{i}(q)=F_{q}(\operatorname{cr}_{i}(q))$ as before. By combining
the mirror isomorphism (7.4) and the formal decomposition of the analytified
Brieskorn module in Proposition 6.10, we obtain a formal decomposition
$\widehat{\Phi}\colon\
\operatorname{mir}_{-}^{*}\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{-})\cong\bigoplus_{i=1}^{N_{-}}\left(\mathcal{O}^{\rm
an}[\\![z]\\!],d+d(\mathbf{u}_{i}/z)\right)$
over a neighbourhood of $q_{0}$ in $\mathcal{V}^{\rm ss}_{-}$. By Proposition
6.5, for an admissible phase $\phi$ for
$\\{\mathbf{u}_{1}(q_{0}),\dots,\allowbreak\mathbf{u}_{N_{-}}(q_{0})\\}$, we
have a connected open neighbourhood $B$ of $q_{0}$ in $\mathcal{V}^{\rm
ss}_{-}$, a sector
$I_{\phi}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\colon\allowbreak|\theta-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$
(with small $\epsilon>0$) and an analytic lift of $\widehat{\Phi}$:
$\widetilde{\Phi}^{-}_{\phi}\colon\
\pi^{*}\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\Big{|}_{B\times
I_{\phi}}\cong\bigoplus_{i=1}^{N_{-}}\left(\mathcal{A}_{B\times
I_{\phi}},d+d(\mathbf{u}_{i}/z)\right),$
where $\pi\colon\mathcal{V}^{\rm
ss}_{-}\times{\widetilde{\mathbb{C}}}\to\mathcal{V}^{\rm
ss}_{-}\times\mathbb{C}$ is the oriented real blow-up. By the uniqueness of
the analytic lift, this coincides with the analytic lift of the Brieskorn
module from Proposition 6.18 over the small quantum cohomology locus
$B\cap\mathcal{M}^{\rm sm}$, via the mirror isomorphism (7.5). Each component
of $\widehat{\Phi}$, $\widetilde{\Phi}^{-}_{\phi}$ is ambiguous up to sign,
but recall from Remark 7.9 that the sign of the _first_ component
(corresponding to the conifold point $\operatorname{cr}_{\mathbb{R}}(q)$) is
determined canonically. We have the following result for $\mathfrak{X}_{-}$
parallel to Proposition 7.8:
###### Proposition 7.13.
For $q_{0}\in\mathcal{V}^{\rm sm,ss}_{-,\mathbb{R}}$, there exists
$\alpha_{0}\in(0,\pi/2)$ such that the following holds. For every admissible
phase $\phi\in(-\alpha_{0},\alpha_{0})$ for
$\\{\mathbf{u}_{1}(q_{0}),\dots,\mathbf{u}_{N_{-}}(q_{0})\\}$, there exists a
basis $\\{V_{i}\\}_{i=1}^{N_{-}}$ of $K(\mathfrak{X}_{-})$ with $V_{1}$ being
the structure sheaf $\mathcal{O}$ of $\mathfrak{X}_{-}$, such that the
corresponding flat section
$s_{i}=\mathfrak{s}_{V_{i}}(\operatorname{mir}_{-}(q),z)$ satisfies
$\widetilde{\Phi}^{-}_{\phi}(e^{\mathbf{u}_{i}(q)/z}s_{i})=e_{i}$.
###### Proof.
The same argument as Proposition 7.13 (using Theorem 7.12 in place of Theorem
7.5) shows that there exist $V_{i}\in K(\mathfrak{X}_{-})$, $i=1,\dots,N_{-}$
with $V_{1}=\mathcal{O}$ such that
$\widetilde{\Phi}^{-}_{\phi}\big{(}e^{\mathbf{u}_{i}(q)/z}s_{i}\big{)}=e_{i}$
over $B\cap\mathcal{M}^{\rm sm}$, where
$s_{i}=\mathfrak{s}_{V_{i}}(\operatorname{mir}_{-}(q),z)$. It follows from the
flatness of $s_{i}$ and $e^{-\mathbf{u}_{i}(q)/z}e_{i}$ that
$\widetilde{\Phi}^{-}_{\phi}\big{(}e^{\mathbf{u}_{i}(q)/z}s_{i}\big{)}=e_{i}$
holds over the whole $B$. ∎
### 7.4 Inclusion of the local systems of Lefschetz thimbles
The Brieskorn module over the small quantum cohomology locus is underlain by a
local system of Lefschetz thimbles. In this section, we observe an inclusion
of the local system over $\mathcal{M}^{\rm sm}$ in a neighbourhood of
$0_{-}=0_{\mathbf{\Sigma}_{-}}$ (mirror to $\mathfrak{X}_{-}$) to the local
system over $\mathcal{M}$ (mirror to $\mathfrak{X}_{+}$) under a slide in the
‘positive real’ direction. The inclusion shall be identified with the pull-
back $\varphi^{*}\colon K(\mathfrak{X}_{-})\to K(\mathfrak{X}_{+})$ in
$K$-theory in Section 7.5.
#### 7.4.1 Convergent and divergent critical branches
Let $\mathcal{V}_{\pm}$ be (sufficiently small) analytic open neighbourhoods
of $0_{\pm}\in\mathcal{M}$ as in the previous Section 7.3. Recall the
$\mathbb{C}^{\times}$-action on
$\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$ generated by the Euler
vector field considered in Sections 5.3–5.4. As discussed there, we may assume
that $\mathcal{V}_{\pm}$ is $\mathbb{C}^{\times}$-invariant, because the
mirror map $\operatorname{mir}_{\pm}$, the mirror isomorphism
$\operatorname{Mir}_{\pm}$ and the analytified Brieskorn module can be
extended to the orbit $\mathbb{C}^{\times}\mathcal{V}_{\pm}$
($\mathcal{V}_{\pm}$ is the intersection of
$\mathcal{U}_{\pm}\subset\mathcal{M}\times\operatorname{Lie}\mathbb{T}$ in
Section 5.4 with $\mathcal{M}\times\\{0\\}$). Let
$\operatorname{Cr}_{\pm}\to\mathcal{V}_{\pm}$ denote the (finite, flat) family
of relative critical points over $\mathcal{V}_{\pm}$:
$\displaystyle\operatorname{Cr}_{+}=\left\\{p\in\operatorname{pr}^{-1}(\mathcal{V}_{+})\colon
x_{i}\frac{\partial F}{\partial
x_{i}}(p)=0\,(\forall\,i)\right\\}=\widetilde{\operatorname{pr}}^{-1}(\mathcal{V}_{+}\times\\{0\\}),$
$\displaystyle\operatorname{Cr}_{-}=\left\\{p\in\mathcal{B}_{-}\cap\operatorname{pr}^{-1}(\mathcal{V}_{-})\colon
x_{i}\frac{\partial F}{\partial
x_{i}}(p)=0\,(\forall\,i)\right\\}=\widetilde{\operatorname{pr}}^{-1}(\mathcal{V}_{-}\times\\{0\\})\cap\mathcal{B}_{-},$
where $\mathcal{B}_{-}$ is the subset of $\mathcal{Y}$ appearing in the
construction of
$\overline{\operatorname{{Bri}^{an}}}(F)_{\mathbf{\Sigma}_{-}}$ in Section 4.3
and $\widetilde{\operatorname{pr}}$ is the map in (4.3). Since all the
relative critical points over $\mathcal{V}_{+}$ are contained in
$\mathcal{B}_{+}$, we do not need to take the intersection with
$\mathcal{B}_{+}$ in the first formula. By Lemma 5.11, we have an open subset
$\mathcal{V}_{0}=\mathcal{U}_{0}\cap(\mathcal{M}\times\\{0\\})\subset\mathcal{V}_{+}\cap\mathcal{V}_{-}$
containing $\mathcal{C}\setminus\\{0_{+},0_{-}\\}$ such that the ramified
covering $\operatorname{Cr}_{+}|_{\mathcal{V}_{0}}\to\mathcal{V}_{0}$
decomposes as:
$\operatorname{Cr}_{+}|_{\mathcal{V}_{0}}=\operatorname{Cr}_{-}|_{\mathcal{V}_{0}}\sqcup\mathcal{D},$
where $\mathcal{D}\subset\operatorname{Cr}_{+}$ is an open subset giving a
subcover of $\operatorname{Cr}_{+}|_{\mathcal{V}_{0}}$. By taking the
$\mathbb{C}^{\times}$-orbit, we may assume that $\mathcal{V}_{0}$ is also
$\mathbb{C}^{\times}$-invariant. The subcover $\mathcal{D}\to\mathcal{V}_{0}$
consists of branches of critical points that diverge at $0_{-}$. We call
critical points corresponding to $\mathcal{D}$ _divergent_ and those
corresponding to $\operatorname{Cr}_{-}$ _convergent_. Among the critical
points over $\mathcal{C}$ described in Proposition 7.2, those corresponding to
$\gamma\neq 0$ are divergent.
#### 7.4.2 Local co-ordinate system around
$\boldsymbol{0_{-}=0_{\mathbf{\Sigma}_{-}}}$
Recall from Proposition 3.15 that the local chart of $\mathcal{M}$ around
$0_{-}$ is given by
$\mathcal{M}_{-}=\big{[}\widetilde{\mathcal{M}}_{-}/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{-})\big{]}\qquad\text{with}\quad\widetilde{\mathcal{M}}_{-}=\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma}_{-})_{+}])$
Set $R_{-}=R(\mathbf{\Sigma}_{-})$. By the decomposition (3.16), we have
$\boldsymbol{\Lambda}(\mathbf{\Sigma}_{-})_{+}\cong\boldsymbol{\Lambda}^{\mathbf{\Sigma}_{-}}_{+}\times(\mathbb{Z}_{\geq
0})^{S\setminus R_{-}}$. Let
$\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}\cong\boldsymbol{\Lambda}^{\mathbf{\Sigma}_{-}}_{+}\times(\mathbb{Z}_{\geq
0})^{S_{-}\setminus R_{-}}$ denote the monoid that we obtain from
$\boldsymbol{\Lambda}(\mathbf{\Sigma}_{-})_{+}$ by replacing $S$ with $S_{-}$.
Then we can decompose $\widetilde{\mathcal{M}}_{-}$ as
$\widetilde{\mathcal{M}}_{-}=\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}])\times\mathbb{C}^{\\{{\hat{b}}\\}}.$
(7.6)
We denote by $(q,t)=(q,t_{\hat{b}})$ a point on $\widetilde{\mathcal{M}}_{-}$,
where
$q\in\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}])$.
Note that the local chart of $\mathcal{M}^{\rm sm}$ around $0_{-}$ is the
substack $\\{t=0\\}$ of $\mathcal{M}_{-}$:
$\mathcal{M}^{\rm sm}_{-}=\big{[}{\widetilde{\mathcal{M}}}^{\rm
sm}_{-}/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{-})\big{]}\qquad\text{with}\quad{\widetilde{\mathcal{M}}}^{\rm
sm}_{-}=\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}]).$
Recall that $\operatorname{Pic}^{\rm st}(\mathfrak{X}_{-})$ acts on the chart
$\widetilde{\mathcal{M}}_{-}$ (7.6) by the age pairing (3.18); since
$t_{\hat{b}}=q^{-\mathbf{w}}$ and $\mathbf{w}\in\mathbb{L}$,
$\operatorname{Pic}^{\rm st}(\mathfrak{X}_{-})$ acts trivially on the last co-
ordinate $t_{\hat{b}}$.
On the chart (7.6), the $\mathbb{C}^{\times}$-action generated by the Euler
vector field is given by
$s\cdot(q,t)=\big{(}s\cdot q,s^{-J}t\big{)},$ (7.7)
where $J=\big{(}\sum\limits_{b\in M_{+}}D_{b}\cdot\mathbf{w}\big{)}-1$ (as in
Proposition 7.2). Note that the $\mathbb{C}^{\times}$-weight of the co-
ordinate $q^{\lambda}$ with
$\lambda\in\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}$ is non-
negative by Lemma A.5.
#### 7.4.3 Sliding out $\boldsymbol{\mathcal{M}^{\rm sm}}$
Let $\mathcal{C}\subset\mathcal{M}$ be the toric curve connecting $0_{-}$ and
$0_{+}$ as in Section 7.2; in the above chart $\widetilde{\mathcal{M}}_{-}$,
$\mathcal{C}$ consists of points $(0,t)$. By Proposition 7.2, we can choose a
closed polydisc
$\widetilde{\mathbb{D}}\subset\\{t_{\hat{b}}=1\\}\subset\widetilde{\mathcal{M}}_{-}$
of radius $0<\varepsilon<1$ centred at $(0,1)\in\mathcal{C}$ such that
* •
$\widetilde{\mathbb{D}}=\widetilde{\mathbb{D}}_{\rm sm}\times\\{1\\}$ with
$\widetilde{\mathbb{D}}_{\rm sm}\subset{\widetilde{\mathcal{M}}}^{\rm
sm}_{-}=\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}])$
a neighbourhood of $0_{-}$ given by
$\widetilde{\mathbb{D}}_{\rm
sm}:=\big{\\{}q\colon\big{|}q^{\lambda}\big{|}\leq\varepsilon,\,\forall\,\lambda\in\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}\setminus\\{0\\}\big{\\}};$
* •
$\mathbb{D}:=\widetilde{\mathbb{D}}/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{-})$ is contained in $\mathcal{V}_{0}$;
* •
$\mathbb{D}_{\rm sm}:=\widetilde{\mathbb{D}}_{\rm sm}/\operatorname{Pic}^{\rm
st}(\mathfrak{X}_{-})$ is contained in $\mathcal{V}_{-}$ (when regarded as a
subset of $\mathcal{M}^{\rm sm}_{-}$);
* •
$F\big{(}\operatorname{Cr}_{-}\cap\operatorname{pr}^{-1}(\mathbb{D})\big{)}\subset
B_{\rho_{0}}(0)$;
* •
$F\big{(}\mathcal{D}\cap\operatorname{pr}^{-1}(\mathbb{D})\big{)}\subset\bigcup\limits_{k=1}^{J}B_{\rho_{1}}\big{(}3\rho_{0}e^{(2k-1)\pi\boldsymbol{\mathrm{i}}/J}\big{)}$,
where $\rho_{0}:=\frac{1}{3}K^{-1/J}$,
$\rho_{1}:=\min\big{(}1,3\sin\big{(}\frac{\pi}{2J}\big{)}\big{)}\rho_{0}$,
$B_{\rho}(z)$ denotes the open disc of radius $\rho$ centred at
$z\in\mathbb{C}$, and $K$, $J$ are as in Proposition 7.2. The last two
conditions imply that convergent critical values over $\mathbb{D}$ are
contained in $\\{|\mathbf{u}|<\rho_{0}\\}$ and divergent critical values over
$\mathbb{D}$ are contained in $\\{|\mathbf{u}|>2\rho_{0}\\}$ and away from the
sector $-\frac{\pi}{2J}\leq\arg(\mathbf{u})\leq\frac{\pi}{2J}$ with vertex at
the origin, see Fig. 10. See also Fig. 11.
Figure 10: Distribution of critical values over $\mathbb{D}$ for $J=5$:
convergent critical values are in the shaded disc of radius $\rho_{0}$ in the
centre; divergent critical values are in the ‘satellite’ discs. Figure 11: The
base space $\mathcal{M}$ of the LG model and the discs $\mathbb{D}$,
$\mathbb{D}_{\rm sm}$: the vertical $t$-axis is the curve $\mathcal{C}$
connecting $0_{+}$ and $0_{-}$; the thin curve denotes the negative Euler flow
(the flow as $s\to 0$ in (7.7)).
###### Definition 7.14.
Define the _sliding map_ $\operatorname{\mathtt{s}}_{t}\colon\mathbb{D}_{\rm
sm}\to\mathcal{M}_{-}$ with $0\leq t\leq 1$ by
$\operatorname{\mathtt{s}}_{t}(q)=(q,t)$. Note that the map
$\tilde{\operatorname{\mathtt{s}}}_{t}\colon\widetilde{\mathbb{D}}_{\rm
sm}\to\widetilde{\mathcal{M}}_{-}$, $q\mapsto(q,t)$ between the uniformizing
charts is $\operatorname{Pic}^{\rm st}(\mathfrak{X}_{-})$-equivariant and thus
descends to the map $\operatorname{\mathtt{s}}_{t}$. Note also that
$\operatorname{\mathtt{s}}_{0}=\operatorname{id}_{\mathbb{D}_{\rm sm}}$.
###### Lemma 7.15.
1. (1)
For $0<t\leq 1$ and $q\in\mathbb{D}_{\rm sm}^{\times}:=\mathbb{D}_{\rm
sm}\cap\mathcal{M}^{\rm sm,\times}$, we have
$\operatorname{\mathtt{s}}_{t}(q)\in\mathcal{M}^{\times}$.
2. (2)
For $0<t\leq 1$, we have
$\operatorname{Im}(\operatorname{\mathtt{s}}_{t})\subset
t^{-1/J}\cdot\mathbb{D}\subset\mathcal{V}_{0}$, where $t^{-1/J}\cdot(-)$
denotes the $\mathbb{C}^{\times}$-action generated by the Euler vector field.
3. (3)
There exists a constant $\rho_{2}>0$ such that convergent critical values over
$\operatorname{Im}(\operatorname{\mathtt{s}}_{t})$ are contained in
$B_{\rho_{2}}(0)\cap t^{-1/J}\cdot B_{\rho_{0}}(0)$ and divergent critical
values over $\operatorname{Im}(\operatorname{\mathtt{s}}_{t})$ are contained
in $\bigcup\limits_{k=1}^{J}t^{-1/J}\cdot
B_{\rho_{1}}\big{(}3\rho_{0}e^{(2k-1)\pi\boldsymbol{\mathrm{i}}/J}\big{)}$.
###### Proof.
Part (1) is obvious. By (7.7),
$t^{1/J}\cdot\operatorname{Im}(\operatorname{\mathtt{s}}_{t})$ consists of
points $\big{(}t^{1/J}\cdot q,1\big{)}$ with $q\in\widetilde{\mathbb{D}}_{\rm
sm}$. Since $0<t\leq 1$ and the $\mathbb{C}^{\times}$-weights on
$\mathbb{C}[\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}]$ are non-
negative, $\big{|}\big{(}t^{1/J}\cdot
q\big{)}^{\lambda}\big{|}\leq\big{|}q^{\lambda}\big{|}\leq\varepsilon$ for
$q\in\widetilde{\mathbb{D}}_{\rm sm}$ and
$\lambda\in\boldsymbol{\Lambda}^{\prime}(\mathbf{\Sigma}_{-})_{+}$. Hence
$t^{1/J}\cdot\operatorname{Im}(\operatorname{\mathtt{s}}_{t})\subset\mathbb{D}$.
Part (2) follows. Part (2) and the fact that the action of $t^{-1/J}$ scales
the critical values by $t^{-1/J}$ imply that convergent critical values over
$\operatorname{Im}(\operatorname{\mathtt{s}}_{t})$ are contained in
$t^{-1/J}\cdot B_{\rho_{0}}(0)$ and divergent ones over
$\operatorname{Im}(\operatorname{\mathtt{s}}_{t})$ are contained in
$\bigcup\limits_{k=1}^{J}t^{-1/J}\cdot
B_{\rho_{1}}\big{(}3\rho_{0}e^{(2k-1)\pi\boldsymbol{\mathrm{i}}/J}\big{)}$.
Because the convergent critical branches form a proper family
$\operatorname{Cr}_{-}\to\mathcal{V}_{-}$, the corresponding critical values
are uniformly bounded in a neighbourhood of $\mathbb{D}_{\rm
sm}=\operatorname{Im}(\operatorname{\mathtt{s}}_{0})$. Part (3) follows. ∎
#### 7.4.4 Kouchnirenko’s condition and a local system of Lefschetz thimbles
Let $(q,t)=(q,t_{\hat{b}})$ be the local co-ordinates on $\mathcal{M}_{-}$ in
Section 7.4.2. By abuse of notation, we mean by $q$ (resp. $(q,t)$) either a
point on the uniformizing chart ${\widetilde{\mathcal{M}}}^{\rm sm}_{-}$
(resp. $\widetilde{\mathcal{M}}_{-}$) or its image in $\mathcal{M}^{\rm
sm}_{-}$ (resp. $\mathcal{M}_{-}$) depending on the context. We write
$\mathcal{Y}_{q,t}:=\operatorname{pr}^{-1}(q,t)\subset\mathcal{Y}$,
$\mathcal{Y}^{\rm sm}_{q}:=\operatorname{pr}^{-1}(q)\subset\mathcal{Y}^{\rm
sm}$ for the fibres of the LG model; note that $\mathcal{Y}^{\rm
sm}_{q}=\mathcal{Y}_{q,0}$. The LG potential $F_{q,t}=F|_{\mathcal{Y}_{q,t}}$
with $q\in\mathcal{M}^{\rm sm,\times}$ is a Laurent polynomial of the form
(cf. (3.22))
$F_{q,t}=\sum_{b\in S}u_{b}=\left(\sum_{b\in
S_{-}}q^{\ell_{b}}x^{b}\right)+tq^{\hat{\ell}}x^{{\hat{b}}}.$ (7.8)
Following Kouchnirenko [75, Définition 1.19], we make the following
definition:
###### Definition 7.16 ([75]).
Let $T\subset\mathbf{N}$ be a finite set and let $f(x)=\sum\limits_{b\in
T}c_{b}x^{b}$ be a Laurent polynomial function on
$\operatorname{Hom}(\mathbf{N},\mathbb{C}^{\times})$. Suppose that $c_{b}\neq
0$ for all $b\in T$ and that the Newton polytope $\Delta$ of $f$, i.e., the
convex hull of $\\{\overline{b}\colon b\in T\\}$ in $\mathbf{N}_{\mathbb{R}}$,
contains the origin in its interior. We say that $f$ is (Newton) _non-
degenerate_ if for every proper face $\diamondsuit$ of $\Delta$ (of any
dimension), $f_{\diamondsuit}(x):=\sum\limits_{b\in
T\cap\diamondsuit}c_{b}x^{b}$ has no critical points on
$\operatorname{Hom}(\mathbf{N},\mathbb{C}^{\times})$.
We are interested in the case where $T$ is $S$ or $S_{-}$, and $f$ is
$F_{q,t}$ with $(q,t)\in\mathcal{M}^{\times}$ or $F_{q,0}$ with
$q\in\mathcal{M}^{\rm sm,\times}$. The compactness of $\mathfrak{X}_{\pm}$
implies that the Newton polytope contains the origin in its interior in these
cases. We define
$\displaystyle\mathcal{M}^{\rm sm,nd}:=\\{q\in\mathcal{M}^{\rm
sm,\times}\colon\text{$F_{q,0}$ is Newton non-degenerate}\\},$
$\displaystyle\mathcal{M}^{\rm
nd}:=\\{(q,t)\in\mathcal{M}^{\times}\colon\text{$F_{q,t}$ is Newton non-
degenerate}\\}.$
###### Proposition 7.17.
1. (1)
$\mathcal{M}^{\rm sm,nd}$ is Zariski-open and dense in $\mathcal{M}^{\rm
sm,\times}$.
2. (2)
There exists a neighbourhood $B$ of $0_{-}$ in $\mathcal{M}^{\rm sm}$ such
that $\mathcal{M}^{\rm sm,nd}$ contains $B\cap\mathcal{M}^{\rm sm,\times}$.
3. (3)
The same conclusions as (1), (2) hold for $\mathcal{M}^{\rm nd}$ when we
replace $\mathcal{M}^{\rm sm,\times}$ with $\mathcal{M}^{\times}$ and $0_{-}$
with $0_{+}$.
###### Proof.
Part (1) is due to Kouchnirenko [75, Théorème 6.1]. Part (2) follows from the
proof of [62, Lemma 3.8]; there we stated and proved a similar result using a
particular co-ordinate system $\mathbb{C}^{r}\to\mathcal{M}^{\rm sm}_{-}$, but
the argument works verbatim for the possibly singular base $\mathcal{M}^{\rm
sm}_{-}$. ∎
###### Remark 7.18.
In view of Proposition 7.17(2), after shrinking the open sets
$\mathcal{V}_{\pm}$ in Section 7.4.1 if necessary, we may assume that
$\mathcal{V}_{+}\cap\mathcal{M}^{\times}\subset\mathcal{M}^{\rm nd}$ and
$\mathcal{V}_{-}\cap\mathcal{M}^{\rm sm,\times}\subset\mathcal{M}^{\rm
sm,nd}$. This is possible because $\mathcal{V}_{\pm}$ was given as the
$\mathbb{C}^{\times}$-orbit of an arbitrarily small neighbourhood of
$0_{\pm}$, and the non-degenerate loci $\mathcal{M}^{\rm sm,nd}$,
$\mathcal{M}^{\rm nd}$ are $\mathbb{C}^{\times}$-invariant.
We define a function $H(x)$ of
$(x_{1},\dots,x_{n})\in(\mathbb{C}^{\times})^{n}$ as
$H(x):=\sqrt{\sum_{b\in S_{-}}|x^{b}|^{2}}.$ (7.9)
Since the convex hull $\Delta_{-}$ of $\\{\overline{b}\colon b\in S_{-}\\}$
contains the origin in its interior, $H(x)$ is proper and bounded from below.
By the splitting $\varsigma$ chosen at the end of Section 7.1, we can regard
$x_{1},\dots,x_{n}$ and $H(x)$ as functions on the preimage of $\\{(q,t)\colon
q\in\mathcal{M}^{\rm sm,\times}\\}\subset\mathcal{M}_{-}$ under
$\operatorname{pr}\colon\mathcal{Y}\to\mathcal{M}$.
###### Proposition 7.19.
1. (1)
For every compact set $K\subset\mathcal{M}^{\rm sm,nd}$, there exist a compact
set $B\subset\operatorname{pr}^{-1}(K)$ and $\epsilon>0$ such that
$\|dF_{q,0}(x)\|\geq\epsilon H(x)\qquad\text{for all $q\in K$ and
$x\in\mathcal{Y}^{\rm sm}_{q}\setminus B$},$
where $\|\cdot\|$ is the norm with respect to the Kähler metric
$\frac{\boldsymbol{\mathrm{i}}}{2}\sum\limits_{j=1}^{n}d\log x_{j}\wedge
d\overline{\log x_{j}}$, i.e.,
$\|dF_{q,0}(x)\|=\big{(}\sum\limits_{j=1}^{n}|\partial F_{q,0}/\partial\log
x_{j}|^{2}\big{)}^{1/2}$.
2. (2)
The same estimate holds for $\|dF_{q,t}\|$ by replacing $\mathcal{M}^{\rm
sm,nd}$ with $\mathcal{M}^{\rm nd}$, $\mathcal{Y}^{\rm sm}$ with
$\mathcal{Y}$, and $H(x)$ with $\big{(}\sum\limits_{b\in
S}|x^{b}|^{2}\big{)}^{1/2}$.
###### Proof.
This is a refinement of [62, Lemma 3.11], which says that $\|dF_{q,0}(x)\|$ is
proper on $\operatorname{pr}^{-1}(K)$. In fact, a slight modification of the
argument there yields a proof of the proposition.
It suffices to show that there exists $\epsilon>0$ such that
$\big{\\{}x\in\operatorname{pr}^{-1}(K)\colon\|dF_{q,0}(x)\|\leq\epsilon
H(x)\big{\\}}$ is compact. Suppose on the contrary that
$\big{\\{}x\in\operatorname{pr}^{-1}(K)\colon\|dF_{q,0}(x)\|\leq
H(x)/k\big{\\}}$ is non-compact for all $k\geq 1$. Then we can find $q(k)\in
K$ and $x(k)\in\mathcal{Y}^{\rm sm}_{q(k)}$ such that
$\|dF_{q(k),0}(x(k))\|\leq H(x(k))/k$ and $H(x(k))\geq k$. Passing to a
subsequence we may assume that $q(k)$ converges in $K$; we may also assume
that we can label elements of $S_{-}$ as $\\{b(1),b(2),\dots,b(m)\\}$ so that
$\big{|}x(k)^{b(1)}\big{|}\geq\big{|}x(k)^{b(2)}\big{|}\geq\cdots\geq\big{|}x(k)^{b(m)}\big{|}$
holds for all $k$. Since $H(x(k))\leq\sqrt{m}\big{|}x(k)^{b(1)}\big{|}$, we
have $\lim\limits_{k\to\infty}\big{|}x(k)^{b(1)}\big{|}=\infty$ and
$\lim_{k\to\infty}\frac{\|dF_{q(k),0}(x(k))\|}{|x(k)^{b(1)}|}=0.$
Now the argument after the second displayed equation in [62, Section A.2]
yields a contradiction. The proposition follows. ∎
###### Remark 7.20.
Proposition 7.19 shows that the relative critical set of $F$ is proper over
the non-degenerate loci $\mathcal{M}^{\rm sm,nd}$, $\mathcal{M}^{\rm nd}$.
###### Corollary 7.21.
1. (1)
The family $\big{\\{}F_{q,0}^{-1}(\mathbf{u})\subset\mathcal{Y}^{\rm
sm}_{q}\big{\\}}_{q,\mathbf{u}}$ of affine varieties is a locally trivial
family of $C^{\infty}$ manifolds over $\\{(q,\mathbf{u})\colon
q\in\mathcal{M}^{\rm sm,nd},\text{$\mathbf{u}$ is a regular value of
$F_{q,0}$}\\}$.
2. (2)
The same conclusion holds for
$F_{q,t}^{-1}(\mathbf{u})\subset\mathcal{Y}_{q,t}$ when we replace
$\mathcal{M}^{\rm sm,nd}$ with $\mathcal{M}^{\rm nd}$.
###### Proof.
Take $(q_{0},\mathbf{u}_{0})$ such that $q_{0}\in\mathcal{M}^{\rm sm,nd}$ and
$\mathbf{u}_{0}$ is a regular value of $F_{q_{0},0}$. Choose a sufficiently
small co-ordinate neighbourhood $\big{(}B;q^{1},\dots,q^{r},\mathbf{u}\big{)}$
of $(q_{0},\mathbf{u}_{0})$ which does not intersect the discriminant locus.
The ambient family $\bigcup\limits_{(q,\mathbf{u})\in B}\mathcal{Y}^{\rm
sm}_{q}$ is trivial over $B$, and is identified with
$B\times\operatorname{Hom}(\mathbf{N},\mathbb{C}^{\times})$ through the co-
ordinates $x_{1},\dots,x_{n}$. It suffices to shows that the co-ordinate
vector fields202020Here we identify (real) vector fields of a complex manifold
with $(1,0)$ vector fields. $\alpha\partial/\partial q^{i}$,
$\alpha\partial/\partial\mathbf{u}$ with $\alpha\in\mathbb{C}$ on $B$ can be
lifted to integrable vector fields tangent to the family
$\bigcup\limits_{(q,u)\in B}F_{q,0}^{-1}(\mathbf{u})$. Lifts of
$\alpha\partial/\partial q^{i}$, $\alpha\partial/\partial\mathbf{u}$ are given
under the trivialization $\bigcup\limits_{(q,\mathbf{u})\in B}\mathcal{Y}^{\rm
sm}_{q}\cong B\times\operatorname{Hom}(\mathbf{N},\mathbb{C}^{\times})$ by
$\left(\alpha\frac{\partial}{\partial q^{i}},-\alpha\frac{\partial
F_{q,0}}{\partial
q^{i}}\frac{\operatorname{grad}F_{q,0}}{\|dF_{q,0}\|^{2}}\right),\qquad\left(\alpha\frac{\partial}{\partial\mathbf{u}},\alpha\frac{\operatorname{grad}F_{q,0}}{\|dF_{q,0}\|^{2}}\right)$
where
$\operatorname{grad}F_{q,0}:=\sum_{j=1}^{n}\overline{\frac{\partial
F_{q,0}}{\partial\log x_{j}}}\frac{\partial}{\partial\log x_{j}}.$
Since the potential $F_{q,0}$ is of the form (7.8), we have $|\partial
F_{q,0}/\partial q^{i}|\leq C\cdot H(x)$ for some constant $C>0$ over $B$.
Thus the estimate in Proposition 7.19 shows that these lifts are bounded on
the family $\bigcup\limits_{(q,\mathbf{u})\in B}F_{q,0}^{-1}(\mathbf{u})$.
Therefore the flows of these vector fields exist as long as the corresponding
flows on the base $B$ exists. ∎
Proposition 7.19 implies that the improper function $\Re(F_{q,0}(x))$
satisfies the so-called Palais–Smale condition212121$\|dF_{q,0}(x)\|$ is
bounded away from zero outside a neighbourhood of the critical set. when
$q\in\mathcal{M}^{\rm sm,nd}$, and hence the usual Morse theory can be applied
to it. It follows (see [62, Section 3.3.1]) that the relative homology group
$H_{n}\big{(}\mathcal{Y}^{\rm sm}_{q},\\{x\colon\Re(F_{q,0}(x))\geq
M\\};\mathbb{Z}\big{)}$ is a free $\mathbb{Z}$-module of rank $\dim H^{*}_{\rm
CR}(\mathfrak{X}_{-})$ when $M$ is large enough so that all critical values of
$F_{q,0}$ are contained in $\\{\Re(z)<M\\}$. This group is independent of the
choice of sufficiently large $M$, and we denote it by
$H_{n}\big{(}\mathcal{Y}^{\rm sm}_{q},\\{x\colon\Re(F_{q,0}(x))\gg
0\\};\mathbb{Z}\big{)}$. By the local triviality in Corollary 7.21, we have
$\displaystyle\operatorname{\mathsf{Lef}}^{\rm
sm}_{q}:=H_{n}\big{(}\mathcal{Y}^{\rm sm}_{q},\\{x\colon\Re(F_{q,0}(x))\gg
0\\};\mathbb{Z}\big{)}\cong H_{n}\big{(}\mathcal{Y}^{\rm
sm}_{q},F_{q,0}^{-1}(\mathbf{u});\mathbb{Z}\big{)}$
for any $\mathbf{u}>0$ such that all critical values of $F_{q,0}$ are
contained in $\\{z\colon\Re(z)<\mathbf{u}\\}$, and this forms a local system
over $\mathcal{M}^{\rm sm,nd}$. Similarly, the relative homology groups
$\operatorname{\mathsf{Lef}}_{q,t}:=H_{n}\big{(}\mathcal{Y}_{q,t},\\{x\colon\Re(F_{q,t}(x))\gg
0\\};\mathbb{Z}\big{)}\cong
H_{n}\big{(}\mathcal{Y}_{q,t},F_{q,t}^{-1}(\mathbf{u});\mathbb{Z}\big{)}$
(7.10)
form a local system of rank $\dim H^{*}_{\rm CR}(\mathfrak{X}_{+})$ over
$\mathcal{M}^{\rm nd}$, where $\mathbf{u}>0$ is such that all critical values
of $F_{q,t}$ are contained in $\\{z\colon\Re(z)<\mathbf{u}\\}$. These two
local systems have different ranks and we will relate them below.
#### 7.4.5 Inclusion of the local systems: statement and proof
Let $\operatorname{\mathtt{s}}_{t}$ be the sliding map in Definition 7.14 and
set $\mathbb{D}_{\rm sm}^{\times}:=\mathbb{D}_{\rm sm}\cap\mathcal{M}^{\rm
sm,\times}$. Let $\operatorname{\mathtt{s}}_{>0}$ denote the map
$(0,1]\times\mathbb{D}_{\rm sm}^{\times}\to\mathcal{M}^{\rm nd}$ given by
$\operatorname{\mathtt{s}}_{>0}(t,q)=\operatorname{\mathtt{s}}_{t}(q)$. Since
$(0,1]$ is contractible, we have
$\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}\cong\mathtt{p}^{-1}\big{(}\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}|_{\mathbb{D}_{\rm
sm}^{\times}}\big{)}\qquad\forall\,t\in(0,1],$
where $\mathtt{p}\colon(0,1]\times\mathbb{D}_{\rm
sm}^{\times}\to\mathbb{D}_{\rm sm}^{\times}$ is the projection to the second
factor. Let $\mathtt{j}\colon(0,1]\times\mathbb{D}_{\rm
sm}^{\times}\rightarrow[0,1]\times\mathbb{D}_{\rm sm}^{\times}$ and
$\mathtt{i}\colon\mathbb{D}_{\rm sm}^{\times}\cong\\{0\\}\times\mathbb{D}_{\rm
sm}^{\times}\to[0,1]\times\mathbb{D}_{\rm sm}^{\times}$ denote the inclusions.
Then we have
$\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}\cong\mathtt{i}^{-1}\mathtt{j}_{*}\mathtt{p}^{-1}\big{(}\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}|_{\mathbb{D}_{\rm
sm}^{\times}}\big{)}\cong\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}|_{\mathbb{D}_{\rm
sm}^{\times}}.$
###### Theorem 7.22.
We have an inclusion of the local systems:
$\iota\colon\ \operatorname{\mathsf{Lef}}^{\rm sm}|_{\mathbb{D}_{\rm
sm}^{\times}}\to\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}\cong\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}|_{\mathbb{D}_{\rm
sm}^{\times}},\qquad t\in(0,1].$
The map $\iota$ maps the positive real Lefschetz thimble $($introduced in
Section $\ref{subsec:identifying_O})$ to the positive real one, i.e.,
$\iota(\Gamma_{\mathbb{R}}(q))=\Gamma_{\mathbb{R}}(\operatorname{\mathtt{s}}_{t}(q))$
when $q\in\mathbb{D}_{\rm sm}^{\times}\cap\mathcal{M}^{\rm sm}_{\mathbb{R}}$.
###### Remark 7.23.
By Remark 7.18, we may assume that
$\mathcal{V}_{+}\cap\mathcal{M}^{\times}\subset\mathcal{M}^{\rm nd}$ and
$\mathcal{V}_{-}\cap\mathcal{M}^{\rm sm,\times}\subset\mathcal{M}^{\rm
sm,nd}$. Then by the choice of $\mathbb{D}_{\rm sm}$, $\mathbb{D}$ in Section
7.4.3 and Lemma 7.15, we have that $\mathbb{D}_{\rm
sm}^{\times}\subset\mathcal{M}^{\rm sm,nd}$ and
$\operatorname{\mathtt{s}}_{t}(\mathbb{D}_{\rm
sm}^{\times})\subset\mathcal{V}_{0}\cap\mathcal{M}^{\times}\subset\mathcal{V}_{+}\cap\mathcal{M}^{\times}\subset\mathcal{M}^{\rm
nd}$ for $t>0$. Hence $\operatorname{\mathsf{Lef}}^{\rm sm}$ and
$\operatorname{\mathsf{Lef}}$ are local systems over $\mathbb{D}_{\rm
sm}^{\times}$ and $\operatorname{Im}(\operatorname{\mathtt{s}}_{t})$ (with
$0<t\leq 1$) respectively, and the statement of Theorem 7.22 makes sense.
For $(q,t)\in\mathcal{M}_{-}$ and $\eta>0$, we set
$A_{q,t}(\eta):=\mathcal{Y}_{q,t}\cap\\{H(x)\leq\eta\\},$
where $H(x)$ is as in (7.9). When $\eta>\min_{x\in\mathcal{Y}_{q,t}}H(x)$,
$A_{q,t}(\eta)$ is a compact region such that the inclusion
$A_{q,t}(\eta)\hookrightarrow\mathcal{Y}_{q,t}$ is a homotopy equivalence.
Indeed, via the $\operatorname{Hom}\big{(}\mathbf{N},S^{1}\big{)}$-action, we
have
$A_{q,t}(\eta)\cong\operatorname{Hom}\big{(}\mathbf{N},S^{1}\big{)}\times\big{\\{}(x_{1},\dots,x_{n})\in(\mathbb{R}_{>0})^{n}\colon
H(x)\leq\eta\big{\\}}$
and the second factor is contractible since $H|_{(\mathbb{R}_{>0})^{n}}$ is
strictly convex. For any $(q,\mathbf{u})\in\mathcal{M}^{\rm
sm,\times}\times\mathbb{C}$, the real algebraic function $H(x)^{2}$ restricted
to $F_{q,0}^{-1}(\mathbf{u})$ has finitely many critical values by [84,
Corollary 2.8], and thus there exists $\eta_{0}>0$ such that
$F_{q,0}^{-1}(\mathbf{u})$ and $\partial A_{q,0}(\eta)$ intersect
transversally for all $\eta$ with $\eta\geq\eta_{0}$. We will show in the
following lemma that such an $\eta_{0}$ can be chosen independently of
$(q,\mathbf{u})$ as far as $(q,\mathbf{u})$ varies in a compact subset of
$\mathcal{M}^{\rm sm,nd}\times\mathbb{C}$. We note that Nemethi–Zaharia [85]
and Parusinski [89] have obtained analogous results for a single polynomial
function on $\mathbb{C}^{n}$ (and the proof is similar).
###### Lemma 7.24.
1. (1)
For a compact subset $K\subset\mathcal{M}^{\rm sm,nd}\times\mathbb{C}$, there
exists $\eta_{0}$ such that for all $\eta\geq\eta_{0}$ and all
$(q,\mathbf{u})\in K$, $F_{q,0}^{-1}(\mathbf{u})$ and $\partial A_{q,0}(\eta)$
intersect transversally.
2. (2)
The same result on the transversality of $F_{q,t}^{-1}(\mathbf{u})$ and
$\partial A_{q,t}(\eta)$ holds when we replace $\mathcal{M}^{\rm sm,nd}$ with
$\mathcal{M}^{\rm nd}$.
The proof of Lemma 7.24 will be given in Appendix B. In the situation of Lemma
7.24(1), $A_{q,0}(\eta)\cap F_{q,0}^{-1}(\mathbf{u})$ is a deformation retract
of $F_{q,0}^{-1}(\mathbf{u})$ for $\eta\geq\eta_{0}$; we can see this using
the Morse flow for the function $H(x)$ on $F_{q,0}^{-1}(\mathbf{u})$. In
particular, the inclusion of pairs
$\big{(}A_{q,0}(\eta),F_{q,0}^{-1}(\mathbf{u})\cap
A_{q,0}(\eta)\big{)}\rightarrow\big{(}\mathcal{Y}^{\rm
sm}_{q},F_{q,0}^{-1}(\mathbf{u})\big{)}$
induces an isomorphism of relative homology. This fact will be used in the
following proof.
###### Proof of Theorem 7.22.
We shall construct an inclusion of local systems:
$\iota\colon\ \operatorname{\mathsf{Lef}}^{\rm sm}|_{\mathbb{D}_{\rm
sm}^{\times}}\to\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}.$
Note that the stalk of
$\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}$
at $q_{0}\in\mathbb{D}_{\rm sm}^{\times}$ consists of a Gauss–Manin flat
family of relative homology classes in
$\operatorname{\mathsf{Lef}}_{\operatorname{\mathtt{s}}_{t}(q)}$ with $t>0$
sufficiently small and $q$ in a small contractible neighbourhood of $q_{0}$ in
$\mathcal{M}^{\rm sm,nd}$. The construction of $\iota$ will be done in the
following 5 steps.
(1) Construction of $\iota$ on the stalk at $q_{0}\in\mathbb{D}_{\rm
sm}^{\times}$. Let $\rho_{2}>0$ be the constant in Lemma 7.15(3) and let
$\mathbf{u}_{0}>\rho_{2}$ be such that all critical values of $F_{q_{0},0}$
are contained in $\\{\mathbf{u}\colon\Re(\mathbf{u})<\mathbf{u}_{0}\\}$. By
Lemma 7.24, there exists $\eta_{0}>0$ such that
$F_{q,0}^{-1}(\mathbf{u})\pitchfork\partial A_{q,0}(\eta)$ for all
$\eta\geq\eta_{0}$ and $(q,\mathbf{u})$ in a neighbourhood of
$(q_{0},\mathbf{u}_{0})$. Then by the remark preceding the proof, the
inclusion induces an isomorphism of relative homology (we use $\mathbb{Z}$
coefficients unless otherwise mentioned):
$H_{n}\big{(}A_{q_{0},0}(\eta_{0}),F_{q_{0},0}^{-1}(\mathbf{u}_{0})\cap
A_{q_{0},0}(\eta_{0})\big{)}\xrightarrow{\cong}H_{n}\big{(}\mathcal{Y}^{\rm
sm}_{q_{0}},F_{q_{0},0}^{-1}(\mathbf{u}_{0})\big{)}\cong\operatorname{\mathsf{Lef}}^{\rm
sm}_{q_{0}}.$ (7.11)
Since $\\{\partial A_{q,t}(\eta_{0})\\}_{q,t}$ is a proper family,
$F_{q,t}^{-1}(\mathbf{u}_{0})$ and $\partial A_{q,t}(\eta_{0})$ intersect
transversally for $(q,t)$ in a sufficiently small contractible neighbourhood
$B$ of $(q_{0},0)$ in $\mathcal{M}_{-}$. The Ehresmann fibration theorem
implies that $F^{-1}_{q,t}(\mathbf{u}_{0})\cap A_{q,t}(\eta_{0})$ is a trivial
family of $C^{\infty}$-manifolds (with boundary) when $(q,t)$ varies in $B$.
Therefore, whenever $\operatorname{\mathtt{s}}_{t}(q)$ lies in $B$, the
inclusion of pairs
$\big{(}A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0}),F^{-1}_{\operatorname{\mathtt{s}}_{t}(q)}(\mathbf{u}_{0})\cap
A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0})\big{)}\hookrightarrow\big{(}A_{B}(\eta_{0}),F^{-1}(\mathbf{u}_{0})\cap
A_{B}(\eta_{0})\big{)}$
induces an isomorphism of relative homology, where we set
$A_{B}(\eta_{0}):=\bigcup\limits_{(q,t)\in B}A_{q,t}(\eta_{0})$. Thus we
obtain a Gauss–Manin flat isomorphism
$\textstyle{H_{n}\big{(}A_{B}(\eta_{0}),F^{-1}(\mathbf{u}_{0})\cap
A_{B}(\eta_{0})\big{)}}$$\textstyle{H_{n}\big{(}A_{q_{0},0}(\eta_{0}),F_{q_{0},0}^{-1}(\mathbf{u}_{0})\cap
A_{q_{0},0}(\eta_{0})\big{)}\phantom{ABCDE}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{\cong}$$\textstyle{\ignorespaces\ignorespaces\ignorespaces\ignorespaces\phantom{ABCDE}H_{n}\big{(}A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0}),F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{0})\cap
A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0})\big{)}}$$\scriptstyle{\cong}$
(7.12)
for $t>0$ sufficiently small and $q$ in a small neighbourhood of $q_{0}$.
Composing (7.11), (7.12) and the natural map induced by the inclusion:
$H_{n}\big{(}A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0}),F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{0})\cap
A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0})\big{)}\longrightarrow
H_{n}\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q)},F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{0})\big{)}$
we obtain
$\operatorname{\mathsf{Lef}}^{\rm sm}_{q_{0}}\longrightarrow
H_{n}\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q)},F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{0})\big{)}.$
(7.13)
Now recall from Lemma 7.15(3) that there are no critical values of
$F_{\operatorname{\mathtt{s}}_{t}(q)}$ in the region
$\big{\\{}\mathbf{u}\in\mathbb{C}\colon\allowbreak|\mathbf{u}|\geq\rho_{2},\,\arg(\mathbf{u})\in\big{[}{-}\frac{\pi}{2J},\frac{\pi}{2J}\big{]}\big{\\}}$.
Since $\mathbf{u}_{0}>\rho_{2}$, the parallel transportation along a straight
path defines a canonical isomorphism
$H_{n}\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q)},F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{0})\big{)}\cong
H_{n}\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q)},F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{1})\big{)}$
for all $\mathbf{u}_{1}>\mathbf{u}_{0}$. Thus (7.13) gives a map
$\operatorname{\mathsf{Lef}}^{\rm
sm}_{q_{0}}\to\operatorname{\mathsf{Lef}}_{\operatorname{\mathtt{s}}_{t}(q)}$
for $t>0$ sufficiently small and $q$ in a small neighbourhood of $q_{0}$. This
map is Gauss–Manin flat as $(t,q)$ varies and defines the map $\iota_{q_{0}}$
on the stalks.
(2) Independence of the choice of $\eta_{0}$, $\mathbf{u}_{0}$. We show that
the map $\iota_{q_{0}}$ is independent of the choices made. That replacing
$\eta_{0}$ with a bigger $\eta_{1}>\eta_{0}$ does not change the map
$\iota_{q_{0}}$ follows from the commutative diagram:
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0.0pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern 3.0pt\raise
0.0pt\hbox{$\textstyle{}$}}}}}}}{\hbox{\kern 27.0pt\raise
0.0pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern 3.0pt\raise
0.0pt\hbox{$\textstyle{\big{(}A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0}),F^{-1}_{\operatorname{\mathtt{s}}_{t}(q)}(\mathbf{u}_{0})\cap
A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0})\big{)}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$}}}}}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces{\hbox{\kern
3.0pt\raise 0.0pt\hbox{\hbox{\kern 0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces{\hbox{\kern
90.2181pt\raise-30.5pt\hbox{\hbox{\kern 0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces{}\ignorespaces\ignorespaces{\hbox{\lx@xy@drawline@}}\ignorespaces{\hbox{\kern
179.68153pt\raise-30.5pt\hbox{\hbox{\kern 0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}\ignorespaces\ignorespaces{\hbox{\lx@xy@drawline@}}\ignorespaces{\hbox{\lx@xy@drawline@}}{\hbox{\kern
211.86122pt\raise 0.0pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern
3.0pt\raise
0.0pt\hbox{$\textstyle{}$}}}}}}}{\hbox{\kern-3.0pt\raise-42.5pt\hbox{\hbox{\kern
0.0pt\raise 0.0pt\hbox{\hbox{\kern 3.0pt\raise
0.0pt\hbox{$\textstyle{}$}}}}}}}{\hbox{\kern
27.0pt\raise-42.5pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern
3.0pt\raise
0.0pt\hbox{$\textstyle{\big{(}A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{1}),F^{-1}_{\operatorname{\mathtt{s}}_{t}(q)}(\mathbf{u}_{0})\cap
A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{1})\big{)}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$}}}}}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces{\hbox{\kern
3.0pt\raise-42.5pt\hbox{\hbox{\kern 0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces{\hbox{\kern
177.43619pt\raise-42.5pt\hbox{\hbox{\kern 0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}{\hbox{\kern
177.43619pt\raise-42.5pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern
3.0pt\raise
0.0pt\hbox{$\textstyle{\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q)},F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{0})\big{)}.}$}}}}}}}\ignorespaces}}}}\ignorespaces$
Next we show that the map is independent of $\mathbf{u}_{0}$. Suppose that we
choose $\mathbf{u}_{1}>\mathbf{u}_{0}$ in place of $\mathbf{u}_{0}$. By Lemma
7.24 again, we can choose $\eta_{0}>0$ such that
$F_{q,0}^{-1}(\mathbf{u})\pitchfork\partial A_{q,0}(\eta)$ for all
$\eta\geq\eta_{0}$, all $q$ in a neighbourhood of $q_{0}$ and all $\mathbf{u}$
in the interval $[\mathbf{u}_{0},\mathbf{u}_{1}]$. Then the family of
$C^{\infty}$-manifolds $F_{q,t}^{-1}(\mathbf{u})\cap A_{q,t}(\eta_{0})$ is
trivial as $\mathbf{u}$ varies in $[\mathbf{u}_{0},\mathbf{u}_{1}]$ and
$(q,t)$ varies in a contractible neighbourhood $B$ of $(q_{0},0)$. The various
maps in the construction of $\iota_{q_{0}}$ can be compared with the following
sequence of maps:
$\displaystyle\big{(}\mathcal{Y}^{\rm
sm}_{q_{0}}\times[\mathbf{u}_{0},\mathbf{u}_{1}],F^{-1}_{q_{0},0}[\mathbf{u}_{0},\mathbf{u}_{1}]\big{)}$
$\displaystyle\qquad{}\leftarrow\big{(}A_{q_{0},0}(\eta_{0})\times[\mathbf{u}_{0},\mathbf{u}_{1}],F^{-1}_{q_{0},0}[\mathbf{u}_{0},\mathbf{u}_{1}]\cap(A_{q_{0},0}(\eta_{0})\times[\mathbf{u}_{0},\mathbf{u}_{1}])\big{)}$
$\displaystyle\qquad{}\rightarrow\big{(}A_{B}(\eta_{0})\times[\mathbf{u}_{0},\mathbf{u}_{1}],F^{-1}[\mathbf{u}_{0},\mathbf{u}_{1}]\cap(A_{B}(\eta_{0})\times[\mathbf{u}_{0},\mathbf{u}_{1}])\big{)}$
$\displaystyle\qquad{}\leftarrow\big{(}A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0})\times[\mathbf{u}_{0},\mathbf{u}_{1}],F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}[\mathbf{u}_{0},\mathbf{u}_{1}]\cap(A_{\operatorname{\mathtt{s}}_{t}(q)}(\eta_{0})\times[\mathbf{u}_{0},\mathbf{u}_{1}])\big{)}$
$\displaystyle\qquad{}\rightarrow\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q)}\times[\mathbf{u}_{0},\mathbf{u}_{1}],F^{-1}_{\operatorname{\mathtt{s}}_{t}(q)}[\mathbf{u}_{0},\mathbf{u}_{1}]\big{)},$
where $F_{q,t}^{-1}[\mathbf{u}_{0},\mathbf{u}_{1}]$ is regarded as a subset of
$\mathcal{Y}_{q,t}\times[\mathbf{u}_{0},\mathbf{u}_{1}]$ via
$x\mapsto(x,F_{q,t}(x))$ and the maps between the first four pairs induce
isomorphisms in relative homology. It follows that the different choices
$\mathbf{u}_{0}$, $\mathbf{u}_{1}$ give the same map $\iota_{q_{0}}$.
(3) Gauss–Manin flatness of $\iota$. This is obvious from the construction in
(1); note that $q_{0}$ there can vary in a small open subset of
$\mathbb{D}_{\rm sm}^{\times}$.
(4) Injectivity of $\iota$.. Choose $q_{0}\in\mathbb{D}_{\rm
sm}^{\times}\cap\mathcal{V}^{\rm sm,ss}_{-}$, where $\mathcal{V}^{\rm
sm,ss}_{-}$ is an open dense subset of $\mathcal{V}^{\rm sm}_{-}$ appearing in
Section 7.3.2, so that all critical points
$\operatorname{cr}_{1},\dots,\operatorname{cr}_{N_{-}}$ of $F_{q_{0},0}$ are
non-degenerate. It suffices to show that $\iota_{q_{0}}$ is injective. Let
$\mathbf{u}_{0}>0$ be as in (1). In this case, a basis of
$\operatorname{\mathsf{Lef}}^{\rm sm}_{q_{0}}$ is given by Lefschetz thimbles:
setting $\mathbf{u}_{i}=F_{q_{0},0}(\operatorname{cr}_{i})$ with $1\leq i\leq
N_{-}$ and choosing a system of mutually non-intersecting paths $\gamma_{i}$
connecting $\mathbf{u}_{i}$ and $\mathbf{u}_{0}$, we have finite Lefschetz
thimbles $\Gamma_{i}\cong D^{n}$ emanating from the critical point
$\operatorname{cr}_{i}$ and fibred over the path $\gamma_{i}$; then
$\Gamma_{1},\dots,\Gamma_{N_{-}}$ define relative cycles in the pair
$\big{(}\mathcal{Y}^{\rm sm}_{q_{0}},F_{q_{0},0}^{-1}(\mathbf{u}_{0})\big{)}$
and form a basis of $\operatorname{\mathsf{Lef}}^{\rm sm}_{q_{0}}$. We choose
$\eta_{0}>0$ big enough so that $\Gamma_{i}$ are contained in
$A_{q_{0},0}(\eta_{0})$ and that the conditions in (1) are satisfied. The
critical points $\operatorname{cr}_{i}$ belong to convergent critical
branches, and as such, vary continuously in a neighbourhood of $(q_{0},0)$ in
$\mathcal{M}_{-}$; the path $\gamma_{i}$ can be also continuously deformed to
a family of paths $\gamma_{i}(q,t)$ connecting the critical value
$F_{q,t}(\operatorname{cr}_{i})$ and $\mathbf{u}_{0}$. Due to the compactness,
the finite thimble $\Gamma_{i}$ can be continuously deformed222222Away from
the critical point, we use a symplectic connection to deform the thimble;
around the critical point we use a family version of the Morse lemma. to a
finite thimble $\Gamma_{i}(q,t)\subset A_{q,t}(\eta_{0})$ for $F_{q,t}$ fibred
over $\gamma_{i}(q,t)$ when $(q,t)$ is sufficiently close to $(q_{0},0)$;
$\Gamma_{i}(q,t)$ gives a relative cycle of
$\big{(}A_{q,t}(\eta_{0}),F_{q,t}^{-1}(\mathbf{u}_{0})\cap
A_{q,t}(\eta_{0})\big{)}$. As relative cycles in
$\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q)},F_{\operatorname{\mathtt{s}}_{t}(q)}^{-1}(\mathbf{u}_{0})\big{)}$,
$\Gamma_{1}(\operatorname{\mathtt{s}}_{t}(q)),\dots,\Gamma_{N_{-}}(\operatorname{\mathtt{s}}_{t}(q))$
form part of a basis of the $n$th relative homology (corresponding to the
convergent critical points) when $t>0$ is sufficiently small and $q$ is
sufficiently close to $q_{0}$. Thus $\iota_{q_{0}}$ sends a basis to part of a
basis, and is injective.
(5) That $\iota$ maps $\Gamma_{\mathbb{R}}$ to $\Gamma_{\mathbb{R}}$ along
$\mathbb{D}_{\rm sm}^{\times}\cap\mathcal{M}^{\rm sm}_{\mathbb{R}}$. The
positive real Lefschetz thimble $\Gamma_{\mathbb{R}}$ (see Section 7.3)
defines a global section of $\operatorname{\mathsf{Lef}}^{\rm sm}$ over
$\mathbb{D}_{\rm sm}^{\times}\cap\mathcal{M}^{\rm sm}_{\mathbb{R}}$ and a
global section of
$\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}$ over
$(0,1]\times(\mathbb{D}_{\rm sm}^{\times}\cap\mathcal{M}^{\rm
sm}_{\mathbb{R}})$. It is obvious from the construction that the map
$\iota_{q_{0}}$ with $q_{0}\in\mathbb{D}_{\rm sm}^{\times}\cap\mathcal{M}^{\rm
sm}_{\mathbb{R}}$ sends $\Gamma_{\mathbb{R}}(q_{0})$ to the germ in
$\big{(}\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}\big{)}_{q_{0}}$
given by
$\\{\Gamma_{\mathbb{R}}(\operatorname{\mathtt{s}}_{t}(q))\\}_{t>0,q}$. ∎
### 7.5 Functoriality
Let $\mathcal{V}_{0}$ be an open neighbourhood of
$\mathcal{C}\setminus\\{0_{+},0_{-}\\}$ as in Section 7.4.1. We consider the
open dense subset $\mathcal{V}^{\rm ss}_{0}$ of $\mathcal{V}_{0}$:
$\mathcal{V}^{\rm
ss}_{0}:=\\{q\in\mathcal{V}_{0}\cap\mathcal{M}^{\times}\colon\text{$F_{q}=F|_{\operatorname{pr}^{-1}(q)}$
has only non-degenerate critical points}\\}.$
Take $q_{0}\in\mathcal{V}^{\rm ss}_{0}$ and choose an admissible phase $\phi$
for the critical values of $F_{q_{0}}$. By composing the formal decomposition
of the analytified Brieskorn module in Proposition 6.10 and (the non-
equivariant version of) the mirror isomorphism in Theorem 4.34, we get formal
decompositions of the pulled-back quantum D-modules over an analytic open
neighbourhood $B$ of $q_{0}$:
$\operatorname{mir}_{\pm}^{*}\overline{\operatorname{QDM}}^{\rm
an}(\mathfrak{X}_{\pm})\big{|}_{B}\cong\bigoplus_{i=1}^{N_{\pm}}(\mathcal{O}_{B}[\\![z]\\!],d+d(\mathbf{u}_{i}/z),P_{\rm
std}),$
where $N_{\pm}=\dim H^{*}_{\rm CR}(\mathfrak{X}_{\pm})$ and $\mathbf{u}_{i}$
are relative critical values of $F$. By Proposition 6.5, by shrinking $B$ if
necessary, we have analytic lifts of these formal decompositions over $B\times
I_{\phi}$, where
$I_{\phi}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\in{\widetilde{\mathbb{C}}}\colon|\theta-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$
(for some small $\epsilon>0$):
$\pi^{*}\operatorname{mir}_{\pm}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\pm})\big{|}_{B\times
I_{\phi}}\cong\bigoplus_{i=1}^{N_{\pm}}(\mathcal{A}_{B\times
I_{\phi}},d+d(\mathbf{u}_{i}/z)),$ (7.14)
where
$\pi\colon\mathcal{M}^{\times}\times{\widetilde{\mathbb{C}}}\to\mathcal{M}^{\times}\times\mathbb{C}$
denotes the oriented real blowup along $\mathcal{M}\times\\{0\\}$. Summands of
this sectorial decomposition are indexed by relative critical points of $F$;
those for $\mathfrak{X}_{+}$ are indexed by all critical points and those for
$\mathfrak{X}_{-}$ are indexed by the subset of convergent critical points.
Combining these two decompositions, we get a sectorial decomposition:
$\pi^{*}\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})\big{|}_{B\times
I_{\phi}}\cong\pi^{*}\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{B\times I_{\phi}}\oplus\mathcal{A}_{B\times
I_{\phi}}^{\oplus(N_{+}-N_{-})}.$ (7.15)
This gives an analytic lift of the formal decomposition in Theorem 5.16. We
consider the inclusion
$\pi^{*}\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{B\times
I_{\phi}}\hookrightarrow\pi^{*}\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})\big{|}_{B\times I_{\phi}}$ (7.16)
induced by (7.15). Note that the maps (7.15), (7.16) are associated with a
semisimple point $q_{0}$ and an admissible direction
$e^{\boldsymbol{\mathrm{i}}\phi}$.
###### Theorem 7.25.
Let $\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$ be a toric birational
morphism as in Section 7.1. For each point $q_{*}\in\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm
sm}^{\times\circ}\subset\mathcal{M}^{\rm sm}_{\mathbb{R}}$, there exists a
contractible open neighbourhood $W_{*}$ of $q_{*}$ in $\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm sm}^{\times\circ}$ and positive
numbers $t_{*}\in(0,1)$, $\alpha_{0}\in\big{(}0,\frac{\pi}{2J}\big{)}$ such
that the following holds. For each
$q_{0}\in\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})\cap\mathcal{V}^{\rm
ss}_{0}$ and each $\phi\in(-\alpha_{0},\alpha_{0})$ that is admissible for the
critical values of $F_{q_{0}}$, the inclusion (7.16) associated with $q_{0}$
and $e^{\boldsymbol{\mathrm{i}}\phi}$ is induced by the pull-back in
$K$-theory via the $\widehat{\Gamma}$-integral structure, i.e., it sends
$\mathfrak{s}_{V}$ to $\mathfrak{s}_{\varphi^{*}V}$ for $V\in
K(\mathfrak{X}_{-})$.
Recall from Section 7.3.2 that $\mathcal{V}^{\rm sm,ss}_{-,\mathbb{R}}$ is the
intersection of the semisimple locus $\mathcal{V}^{\rm ss}_{-}$ of
$\mathcal{V}_{-}$ and the real positive locus $\mathcal{M}^{\rm
sm}_{\mathbb{R}}$ of $\mathcal{M}^{\rm sm}$. Also, $\mathbb{D}_{\rm
sm}^{\times\circ}$ denotes the interior of $\mathbb{D}_{\rm
sm}^{\times}=\mathbb{D}_{\rm sm}\cap\mathcal{M}^{\rm sm,\times}$ as a subset
of $\mathcal{M}^{\rm sm}$. Recall that $\operatorname{\mathtt{s}}_{t}$ is the
sliding map from Definition 7.14 and $J\geq 1$ is the natural number in
Proposition 7.2. Note that
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})\cap\mathcal{V}^{\rm
ss}_{0}$ is non-empty because $\mathcal{V}^{\rm
ss}_{0}\cap\mathcal{M}_{\mathbb{R}}$ is open dense in
$\mathcal{V}_{0}\cap\mathcal{M}_{\mathbb{R}}$ and
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$ is an open
subset of $\mathcal{V}_{0}\cap\mathcal{M}_{\mathbb{R}}$ by Lemma 7.15(2).
###### Remark 7.26.
As we explained in Remark 7.7, we have a standard identification between
$K$-classes of $\mathfrak{X}_{+}$ (resp. $\mathfrak{X}_{-}$) and flat sections
over $(\mathcal{M}_{\mathbb{R}}\cap\mathcal{V}_{+})\times\mathbb{R}_{>0}$
(resp. $(\mathcal{M}^{\rm
sm}_{\mathbb{R}}\cap\mathcal{V}_{-})\times\mathbb{R}_{>0}$). We use these
identifications in the above theorem; we also use the analytic continuation
along the sliding homotopy $\operatorname{\mathtt{s}}_{t}$ for
$\mathfrak{X}_{-}$.
###### Remark 7.27.
By the duality of the analytic lift discussed in Remark 6.7, if the inclusion
(7.16) corresponds to the pull-back $\varphi^{*}\colon K(\mathfrak{X}_{-})\to
K(\mathfrak{X}_{+})$ in $K$-theory, the projection associated with the
opposite direction
$-e^{\boldsymbol{\mathrm{i}}\phi}=e^{\boldsymbol{\mathrm{i}}(\phi+\pi)}$
$\pi^{*}\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})\big{|}_{B\times
I_{\phi+\pi}}\twoheadrightarrow\pi^{*}\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{B\times I_{\phi+\pi}}$
corresponds to the push-forward $\varphi_{*}\colon K(\mathfrak{X}_{+})\to
K(\mathfrak{X}_{-})$ in $K$-theory.
###### Lemma 7.28.
Let $q_{*}$ be a point in $\mathcal{M}^{\rm
sm}_{\mathbb{R}}\cap\mathbb{D}_{\rm sm}^{\times}$. We have a commutative
diagram
$\begin{aligned} \lx@xy@svg{\hbox{\raise 0.0pt\hbox{\kern
16.1764pt\hbox{\ignorespaces\ignorespaces\ignorespaces\hbox{\vtop{\kern
0.0pt\offinterlineskip\halign{\entry@#!@&&\entry@@#!@\cr&\\\&\crcr}}}\ignorespaces{\hbox{\kern-13.31279pt\raise
0.0pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern 3.0pt\raise
0.0pt\hbox{$\textstyle{\operatorname{\mathsf{Lef}}^{\rm
sm}_{q_{*}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$}}}}}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces{\hbox{\kern
18.13472pt\raise 4.50694pt\hbox{{}\hbox{\kern 0.0pt\raise
0.0pt\hbox{\hbox{\kern 3.0pt\hbox{\hbox{\kern
0.0pt\raise-1.50694pt\hbox{$\scriptstyle{\iota}$}}}\kern
3.0pt}}}}}}\ignorespaces{\hbox{\kern 40.1764pt\raise 0.0pt\hbox{\hbox{\kern
0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces{\hbox{\kern
0.0pt\raise-20.5pt\hbox{{}\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern
3.0pt\hbox{\hbox{\kern 0.0pt\raise-1.75pt\hbox{$\scriptstyle{\cong}$}}}\kern
3.0pt}}}}}}\ignorespaces{\hbox{\kern 0.0pt\raise-30.5pt\hbox{\hbox{\kern
0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}{\hbox{\kern
40.1764pt\raise 0.0pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern
3.0pt\raise
0.0pt\hbox{$\textstyle{\big{(}\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}\big{)}_{q_{*}}\cong\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}_{q_{*}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$}}}}}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces{\hbox{\kern
89.49396pt\raise-20.5pt\hbox{{}\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern
3.0pt\hbox{\hbox{\kern 0.0pt\raise-1.75pt\hbox{$\scriptstyle{\cong}$}}}\kern
3.0pt}}}}}}\ignorespaces{\hbox{\kern 89.49396pt\raise-30.5pt\hbox{\hbox{\kern
0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}{\hbox{\kern-16.1764pt\raise-41.0pt\hbox{\hbox{\kern
0.0pt\raise 0.0pt\hbox{\hbox{\kern 3.0pt\raise
0.0pt\hbox{$\textstyle{K(\mathfrak{X}_{-})\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$}}}}}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces{}{\hbox{\lx@xy@droprule}}\ignorespaces\ignorespaces\ignorespaces{\hbox{\kern
38.4574pt\raise-35.34723pt\hbox{{}\hbox{\kern 0.0pt\raise
0.0pt\hbox{\hbox{\kern 3.0pt\hbox{\hbox{\kern
0.0pt\raise-1.29167pt\hbox{$\scriptstyle{\varphi^{*}}$}}}\kern
3.0pt}}}}}}\ignorespaces{\hbox{\kern 72.0731pt\raise-41.0pt\hbox{\hbox{\kern
0.0pt\raise
0.0pt\hbox{\lx@xy@tip{1}\lx@xy@tip{-1}}}}}}{\hbox{\lx@xy@droprule}}{\hbox{\lx@xy@droprule}}{\hbox{\kern
72.0731pt\raise-41.0pt\hbox{\hbox{\kern 0.0pt\raise 0.0pt\hbox{\hbox{\kern
3.0pt\raise
0.0pt\hbox{$\textstyle{K(\mathfrak{X}_{+})}$}}}}}}}\ignorespaces}}}}\ignorespaces\end{aligned}\qquad\text{with
$t\in(0,1]$},$ (7.17)
where the vertical arrows are induced by the isomorphisms in Theorems 7.5 and
7.12, the top horizontal arrow is the inclusion in Theorem 7.22.
###### Proof.
Note that the left vertical arrow is induced, via the
$\widehat{\Gamma}$-integral structure, by the isomorphism of local systems
over $\mathbb{D}_{\rm sm}^{\times}$:
$\operatorname{\mathsf{Lef}}^{\rm sm}\otimes\mathbb{C}\big{|}_{\mathbb{D}_{\rm
sm}^{\times}}\cong\big{(}\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})|_{\mathbb{D}_{\rm
sm}^{\times}\times\\{1\\}}\big{)}^{\nabla}$ (7.18)
sending a class $[\Gamma]\in H_{n}(\mathcal{Y}_{q},\\{\Re(F_{q})\gg 0\\})$ to
a flat section $s_{\Gamma}$ of
$\operatorname{mir}_{-}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})|_{\mathbb{D}_{\rm sm}^{\times}\times\\{1\\}}$ satisfying
$\frac{1}{(2\pi)^{n/2}}\int_{\Gamma}e^{-F_{q}}\Omega_{q,-1}=P(\operatorname{Mir}(\Omega),s_{\Gamma})$
for every local section $\Omega_{q,z}$ of $\operatorname{Bri}^{\rm sm}(F)$.
Here $(\cdots)^{\nabla}$ denotes the local system defined by the kernel of
$\nabla$. Also, the right vertical arrow in (7.17) is induced by the
isomorphism of local systems over
$\operatorname{Im}(\operatorname{\mathtt{s}}_{>0})$:
$\operatorname{\mathsf{Lef}}\otimes\mathbb{C}\big{|}_{\operatorname{Im}(\operatorname{\mathtt{s}}_{>0})}\cong\big{(}\operatorname{mir}_{+}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})|_{\operatorname{Im}(\operatorname{\mathtt{s}}_{>0})\times\\{1\\}}\big{)}^{\nabla},$
(7.19)
which is defined similarly. We conclude the lemma by studying the monodromy of
these local systems. Let
$\mathbb{L}^{\prime}=\operatorname{Ker}\big{(}\mathbb{Z}^{S_{-}}\to\mathbf{N}\big{)}$
be as in Section 6.3.3. The inclusion $\mathbb{D}_{\rm
sm}^{\times}\subset\mathcal{M}^{\rm
sm,\times}=(\mathbb{L}^{\prime})^{\star}\otimes\mathbb{C}^{\times}$ induces an
isomorphism $\pi_{1}(\mathbb{D}_{\rm
sm}^{\times})\cong(\mathbb{L}^{\prime})^{\star}$; an element
$\xi\in(\mathbb{L}^{\prime})^{\star}$ corresponds to the loop
$[0,2\pi]\ni\theta\mapsto e^{\boldsymbol{\mathrm{i}}\theta\xi}\cdot q_{*}$
based at $q_{*}\in\mathbb{D}_{\rm sm}^{\times}$. We claim that the monodromy
of $\operatorname{\mathsf{Lef}}^{\rm sm}$ around the loop
$e^{\boldsymbol{\mathrm{i}}\theta\xi}\cdot q_{*}$ corresponds to tensoring by
$L_{\xi}^{-1}$ in $K(\mathfrak{X}_{-})$ on the $\widehat{\Gamma}$-integral
structure under the isomorphism (7.18), where $L_{\xi}$ denotes the orbi-line
bundle as in Section 3.1.2. We also claim that the monodromy of
$\operatorname{\mathsf{Lef}}$ around
$\operatorname{\mathtt{s}}_{t}(e^{\boldsymbol{\mathrm{i}}\theta\xi}\cdot
q_{*})=(e^{\boldsymbol{\mathrm{i}}\theta\xi}\cdot q_{*},t)$ corresponds to
tensoring by $\varphi^{*}L_{\xi}^{-1}$ in $K(\mathfrak{X}_{+})$ under the
isomorphism (7.19). These two claims prove the lemma. In fact, since the map
$\iota$ is monodromy-equivariant, the composition
$K(\mathfrak{X}_{-})\cong\operatorname{\mathsf{Lef}}^{\rm
sm}_{q_{*}}\overset{\iota}{\longrightarrow}\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}_{q_{*}}\cong
K(\mathfrak{X}_{+})$ (7.20)
identifies tensoring by $L_{\xi}$ with tensoring by $\varphi^{*}L_{\xi}$; also
this map (7.20) sends the structure sheaf to the structure sheaf since $\iota$
sends the positive real Lefschetz thimble $\Gamma_{\mathbb{R}}(q_{*})$ to the
positive-real one $\Gamma_{\mathbb{R}}(\operatorname{\mathtt{s}}_{t}(q_{*}))$
(see Theorem 7.22); since $K(\mathfrak{X}_{-})$ is generated by line bundles
[16], we conclude that the map (7.20) equals $\varphi^{*}$.
It remains to prove the above two claims. Let $[\xi]$ denote the class in
$\operatorname{Pic}(\mathfrak{X}_{-})$ of $L_{\xi}$. By [62, (61)], the mirror
map satisfies
$\operatorname{mir}_{-}\big{(}e^{2\pi\boldsymbol{\mathrm{i}}\xi}\cdot
q_{*}\big{)}=g(-[\xi])\operatorname{mir}_{-}(q_{*})$
(see Section 2.2 for $g(-[\xi])$) and hence the flat section
$\mathfrak{s}_{V}(\operatorname{mir}_{-}(q_{*}),z=1)$ is analytically
continued, along the path $\theta\mapsto
e^{\boldsymbol{\mathrm{i}}\theta\xi}\cdot q_{*}$, to
$\mathfrak{s}_{V}(g(-[\xi])\operatorname{mir}_{-}(q_{*}),1)$, which is
identified with
$dg(-[\xi])^{-1}\mathfrak{s}_{V}(g(-[\xi])\operatorname{mir}_{-}(q_{*}),1)=\mathfrak{s}_{V\otimes
L_{\xi}^{-1}}(\operatorname{mir}_{-}(q_{*}),1)$ by the Galois action in
Section 2.3; here we used the formula (2.12). This proves the first claim. To
prove the second claim, it suffices to show that the homotopy class
${\hat{\xi}}\in\mathbb{L}^{\star}\cong\pi_{1}(\mathcal{M}^{\times})$ of the
loop $\operatorname{\mathtt{s}}_{t}(e^{\boldsymbol{\mathrm{i}}\theta\xi}\cdot
q_{*})$ defines a line bundle $L_{\hat{\xi}}$ isomorphic to
$\varphi^{*}L_{\xi}$. Observe that we have a direct sum decomposition
$\mathbb{L}=\mathbb{L}^{\prime}\oplus\mathbb{Z}\delta_{\hat{b}}^{\mathbf{\Sigma}_{-}},$
(7.21)
where
$\delta_{\hat{b}}^{\mathbf{\Sigma}_{-}}=e_{\hat{b}}-\Psi_{-}({\hat{b}})=-\mathbf{w}$
is an element introduced in Section 3.3 (see also Section 7.1) which
corresponds to the co-ordinate $t=t_{\hat{b}}$. The class
${\hat{\xi}}\in\mathbb{L}^{\star}$ is a unique lift of
$\xi\in(\mathbb{L}^{\prime})^{\star}$ such that
${\hat{\xi}}\cdot\delta_{\hat{b}}^{\mathbf{\Sigma}_{-}}=0$. The map (7.1)
inducing the birational morphism
$\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$ is equivariant with respect
to the homomorphism
$\mathbb{L}\otimes\mathbb{C}^{\times}\to\mathbb{L}^{\prime}\otimes\mathbb{C}^{\times}$,
$\exp(\lambda)\mapsto\exp(\lambda+(D_{\hat{b}}\cdot\lambda)\mathbf{w})$ (where
$\lambda\in\mathbb{L}_{\mathbb{C}}$), which is dual to the above lift
$(\mathbb{L}^{\prime})^{\star}\to\mathbb{L}^{\star}$, $\xi\mapsto{\hat{\xi}}$.
In view of the definition of $L_{\hat{\xi}}$ in Section 3.1.2, we see that
$L_{\hat{\xi}}\cong\varphi^{*}L_{\xi}$. The lemma is proved. ∎
We show that $\alpha_{0}$ appearing in Proposition 7.8 can be chosen
independently of $q_{0}\in\mathcal{V}^{\rm ss}_{+,\mathbb{R}}$ if $q_{0}$ is
close to a given point $q_{*}$ in $\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm sm}^{\times\circ}$.
###### Lemma 7.29.
Let $q_{*}$ be a point in $\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm sm}^{\times\circ}$. There exist a
contractible open neighbourhood $W_{*}$ of $q_{*}$ in $\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm sm}^{\times\circ}$ and positive
numbers $t_{*}\in(0,1)$, $\alpha_{0}\in\big{(}0,\frac{\pi}{2J}\big{)}$ such
that the conclusion of Proposition 7.8 holds for all
$q_{0}\in\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})\cap\mathcal{V}^{\rm
ss}_{0}\subset\mathcal{V}^{\rm ss}_{+,\mathbb{R}}$ with this same
$\alpha_{0}$.
###### Proof.
Let $\operatorname{cr}_{1}(q),\dots,\operatorname{cr}_{N_{-}}(q)$ be branches
of “convergent” critical points of $F_{q}$ contained in $\mathcal{B}_{-}$ and
defined in a neighbourhood of $q=q_{*}$ in $\mathcal{V}^{\rm ss}_{-}$. We
assume that
$\operatorname{cr}_{1}(q_{*})=\operatorname{cr}_{\mathbb{R}}(q_{*})$ and write
$\mathbf{u}_{i}(q)=F_{q}(\operatorname{cr}_{i}(q))$ as before. We may also
assume that $\mathbf{u}_{i}(q_{*})\in\mathbf{u}_{1}(q_{*})+\mathbb{R}_{\geq
0}$ if and only if $1\leq i\leq k$. Choose
$\alpha_{0}\in\big{(}0,\frac{\pi}{2J}\big{)}$ so that the closed sector
$I_{*}:=\mathbf{u}_{1}(q_{*})+\big{\\{}re^{\boldsymbol{\mathrm{i}}\theta}\colon
r\geq 0,|\theta|\leq\alpha_{0}\big{\\}}$ with vertex at
$\mathbf{u}_{1}(q_{*})$ does not contain critical values other than
$\mathbf{u}_{1}(q_{*}),\dots,\mathbf{u}_{k}(q_{*})$, see Fig. 12. We can find
a contractible open neighbourhood $W_{*}$ of $q_{*}$ in $\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm sm}^{\times\circ}$, $0<t_{*}<1$, and
$\epsilon>0$ such that for all $q\in\bigcup\limits_{0\leq
t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$,
$\mathbf{u}_{i}(q)\in-\epsilon+I_{*}$ if and only if $1\leq i\leq k$. Note
that $W_{*}\subset\mathcal{V}^{\rm sm,ss}_{-}\subset\mathcal{M}^{\rm sm,nd}$
and
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})\subset\mathcal{V}_{0}\subset\mathcal{M}^{\rm
nd}$ by Lemma 7.15 and Remark 7.18.
Figure 12: Critical values at $q_{*}$: only
$\mathbf{u}_{1},\dots,\mathbf{u}_{k}$ (critical values on the half-line
$\mathbf{u}_{1}+\mathbb{R}_{\geq 0}$) lie in the sector
$-\alpha_{0}\leq\arg(\mathbf{u}-\mathbf{u}_{1})\leq\alpha_{0}$ ($k=5$).
We also have divergent critical points over
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$; let
$\operatorname{cr}_{j}(q)$, $j=N_{-}+1,\dots,N_{+}$ denote divergent critical
branches over $\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$
(they can be ramified and may not be single-valued). By taking smaller
$t_{*}>0$ if necessary, by Lemma 7.15(3), we may assume that the divergent
critical values $\mathbf{u}_{j}(q)=F_{q}(\operatorname{cr}_{j}(q))$,
$N_{-}+1\leq j\leq N_{+}$ do not lie in the sector $-\epsilon+I_{*}$ as long
as $q\in\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$.
Let $\Gamma^{\phi}_{i}(q)$ denote the Lefschetz thimble (6.12) of $F_{q}$
associated with the critical point $\operatorname{cr}_{i}(q)$ and the phase
$\phi$. Here $q$ can be either in $W_{*}$ or in
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$ – we have
$1\leq i\leq N_{-}$ in the former case and $1\leq i\leq N_{+}$ in the latter
case. In view of the proof of Proposition 7.8, it suffices to show that the
relative homology class
$\big{[}\Gamma_{1}^{\pi+\phi}(q)\big{]}\in
H_{n}\big{(}\mathcal{Y}_{q},\\{\Re(F_{q})\gg 0\\};\mathbb{Z}\big{)}$
represented by the thimble $\Gamma_{1}^{\pi+\phi}(q)$ is constant as
$(q,\phi)$ varies in
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})\times(-\alpha_{0},\alpha_{0})$.
The homology class $\big{[}\Gamma_{1}^{\pi+\phi}(q)\big{]}$ can jump by the
Picard–Lefschetz transformation as $(q,\phi)$ varies (see, e.g., [7, Chapter
I]). By our choice of $W_{*}$, $t_{*}$ and $\alpha_{0}$, it suffices to check
that the intersection numbers of vanishing cycles at
$\operatorname{cr}_{1}(q)$ and $\operatorname{cr}_{i}(q)$ (with $2\leq i\leq
k$) are zero at some
$q\in\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$; here we
consider vanishing cycles associated with paths from $\mathbf{u}_{i}(q)$ to a
base point $\mathbf{u}_{0}\gg 0$ _inside_ the sector $-\epsilon+I_{*}$. At
$(q,\phi)=(q_{*},0)$, the Lefschetz thimble
$\Gamma^{\pi}_{1}(q_{*})=\Gamma_{\mathbb{R}}(q_{*})$ lying over
$\mathbf{u}_{1}(q_{*})+\mathbb{R}_{\geq 0}$ does not contain the critical
points $\operatorname{cr}_{i}(q_{*})$, $2\leq i\leq k$, and therefore the
vanishing cycles at $\operatorname{cr}_{1}(q_{*})$ and
$\operatorname{cr}_{i}(q_{*})$ (with $2\leq i\leq k$) do not intersect. For
$1\leq i\leq k$, choose a path $\gamma_{i}$ starting from
$\mathbf{u}_{i}(q_{*})$ and ending at $\mathbf{u}_{0}$ which avoids other
critical points, and let $\Gamma_{i}$ denote the finite Lefschetz thimble
(with boundary in $F_{q_{*}}^{-1}(\mathbf{u}_{0})$) associated with
$\operatorname{cr}_{i}(q_{*})$ and the path $\gamma_{i}$. We choose a
sufficiently big $\eta_{0}>0$ such that $\Gamma_{i}$’s are contained in
$A_{q_{*}}(\eta_{0})$ and that $\partial A_{q_{*}}(\eta_{0})\pitchfork
F_{q_{*}}^{-1}(\mathbf{u}_{0})$. Arguing as in Parts (1), (4) in the proof of
Theorem 7.22, we see that $\Gamma_{i}$ can be continuously deformed to a
relative cycle $\Gamma_{i}(q)$ of $\big{(}A_{q}(\eta_{0}),A_{q}(\eta_{0})\cap
F_{q}^{-1}(\mathbf{u}_{0})\big{)}$ as $q$ varies in a small neighbourhood of
$q_{*}$ in $\mathcal{V}^{\rm ss}_{-}$. This shows that the vanishing cycles
$\partial\Gamma_{1}(q)$ and $\partial\Gamma_{i}(q)$ (with $2\leq i\leq k$)
have zero intersection number. The lemma is proved. ∎
###### Proof of Theorem 7.25.
Choose $q_{*}\in\mathcal{V}^{\rm sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm
sm}^{\times\circ}$. Let $W_{*}\subset\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm sm}^{\times\circ}$, $t_{*}\in(0,1)$,
$\alpha_{0}\in\big{(}0,\frac{\pi}{2J}\big{)}$ as in Lemma 7.29. By taking
smaller $\alpha_{0}$ if necessary, we may assume that the conclusion of
Proposition 7.13 holds for the same $\alpha_{0}$ at $q_{0}=q_{*}$. As in the
proof of Lemma 7.29, let
$\operatorname{cr}_{1}(q),\dots,\operatorname{cr}_{N_{-}}(q)$ denote the
convergent critical branches over a neighbourhood of $q_{*}$ in
$\mathcal{V}^{\rm ss}_{-}$ such that $\operatorname{cr}_{1}(q)$ is the
conifold point when $q\in\mathcal{M}_{\mathbb{R}}\cup\mathcal{M}^{\rm
sm}_{\mathbb{R}}$. Also, let
$\operatorname{cr}_{N_{-}+1}(q),\dots,\operatorname{cr}_{N_{+}}(q)$ denote
divergent critical branches over a neighbourhood of $q_{*}$, defined away from
$\mathcal{M}^{\rm sm}$ (they can be ramified and may not be single-valued). We
write $\mathbf{u}_{i}(q)=F_{q}(\operatorname{cr}_{i}(q))$ for the
corresponding critical value. Let $\phi_{*}\in(-\alpha_{0},\alpha_{0})$ be an
admissible phase for
$\\{\mathbf{u}_{1}(q_{*}),\dots,\mathbf{u}_{N_{-}}(q_{*})\\}$. Proposition
7.13 gives an analytic decomposition
$\widetilde{\Phi}_{\phi_{*}}^{-}\colon\
\pi^{*}\operatorname{mir}_{-}^{*}\operatorname{QDM}(\mathfrak{X}_{-})\big{|}_{B^{\prime}\times
I_{\phi_{*}}}\cong\bigoplus_{i=1}^{N_{-}}(\mathcal{A}_{B^{\prime}\times
I_{\phi_{*}}},d+d(\mathbf{u}_{i}/z)),$
where $B^{\prime}$ is an open neighbourhood of $q_{*}$ in $\mathcal{V}^{\rm
ss}_{-}$,
$I_{\phi_{*}}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\colon|\theta-\phi_{*}|<\frac{\pi}{2}+\epsilon\big{\\}}$
(for some $\epsilon>0$) and $\pi\colon\mathcal{V}^{\rm
ss}_{-}\times{\widetilde{\mathbb{C}}}\to\mathcal{V}^{\rm
ss}_{-}\times\mathbb{C}$ is the oriented real blowup, with the following
property: there exists a basis $V_{1}^{-},\dots,V_{N_{-}}^{-}$ of
$K(\mathfrak{X}_{-})$ such that $V_{1}^{-}$ is the structure sheaf of
$\mathfrak{X}_{-}$ and that
$\widetilde{\Phi}^{-}_{\phi}\big{(}e^{-\mathbf{u}_{j}(q)/z}s^{-}_{j}\big{)}=e_{j}$,
where $s^{-}_{j}$ is the flat section
$\mathfrak{s}_{V_{j}^{-}}(\operatorname{mir}_{-}(q),z)$ associated with
$V_{j}^{-}$. Choose
$\phi_{1},\phi_{2}\in\big{(}\phi_{*}-\frac{\epsilon}{2},\phi_{*}+\frac{\epsilon}{2}\big{)}$
(where $\epsilon$ is the one appearing in $I_{\phi_{*}}$) such that
$\phi_{1}<\phi_{2}$ and that all phases in $[\phi_{1},\phi_{2}]$ are
admissible for $\\{\mathbf{u}_{1}(q_{*}),\dots,\mathbf{u}_{N_{-}}(q_{*})\\}$.
By shrinking $W_{*}$ and taking smaller $t_{*}>0$ if necessary, we may assume
that
* (a)
$\bigcup\limits_{0\leq t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})\subset
B^{\prime}$;
* (b)
$\mathbf{u}_{i}(q)-\mathbf{u}_{j}(q)\notin
e^{\boldsymbol{\mathrm{i}}\theta}\mathbb{R}$ for all
$q\in\bigcup\limits_{0\leq t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$,
$\theta\in[\phi_{1},\phi_{2}]$, $i,j\in\\{1,2,\dots,N_{-}\\}$ provided that
$\mathbf{u}_{i}(q_{*})\neq\mathbf{u}_{j}(q_{*})$;
* (c)
$\bigcup\limits_{1\leq i\leq
N_{-}}\mathbf{u}_{i}(q)+\big{\\{}re^{\boldsymbol{\mathrm{i}}\theta}\colon
r\geq 0,|\theta|\leq\alpha_{0}\big{\\}}$ does not contain divergent critical
values $\mathbf{u}_{j}(q)$ with $N_{-}+1\leq j\leq N_{+}$ for
$q\in\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$.
The third point (c) is possible by Lemma 7.15(3) and the fact that
$\alpha_{0}<\frac{\pi}{2J}$.
Take
$q_{0}\in\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})\cap\mathcal{V}^{\rm
ss}_{0}$ and a phase $\phi\in(-\alpha_{0},\alpha_{0})$ which is admissible for
$\\{\mathbf{u}_{1}(q_{0}),\dots,\allowbreak\mathbf{u}_{N_{+}}(q_{0})\\}$.
First we prove the conclusion of the theorem _assuming that $\phi$ lies in
$(\phi_{1},\phi_{2})\subset(-\alpha_{0},\alpha_{0})$_. The discussion for any
admissible $\phi\in(-\alpha_{0},\alpha_{0})$ will be postponed until the last
paragraph of the proof. Since $\phi\in(-\alpha_{0},\alpha_{0})$, Lemma 7.29
(Proposition 7.8) gives an analytic decomposition
$\widetilde{\Phi}^{+}_{\phi}$
$\displaystyle\widetilde{\Phi}^{+}_{\phi}\colon\
\pi^{*}\operatorname{mir}_{+}^{*}\operatorname{QDM}(\mathfrak{X}_{+})\big{|}_{B\times
I_{\phi}}\cong\bigoplus_{i=1}^{N_{+}}(\mathcal{A}_{B\times
I_{\phi}},d+d(\mathbf{u}_{i}/z)),$
where $B$ is a neighbourhood of $q_{0}$ in $\mathcal{V}^{\rm ss}_{-}$ and
$I_{\phi}$ is a sector of the form
$\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\in{\widetilde{\mathbb{C}}}\colon|\theta-\phi|<\frac{\pi}{2}+\delta\big{\\}}$
(for some $0<\delta\leq\frac{\epsilon}{2}$) with the following property: there
exists a basis $V_{1}^{+},\dots,V_{N_{+}}^{+}$ of $K(\mathfrak{X}_{+})$ such
that $V_{1}^{+}$ is the structure sheaf of $\mathfrak{X}_{+}$ and that
$\widetilde{\Phi}^{+}_{\phi}\big{(}e^{-\mathbf{u}_{j}(q)/z}s_{j}^{+}\big{)}=e_{j}$,
where $s_{j}^{+}$ is the flat section
$\mathfrak{s}_{V_{j}^{+}}(\operatorname{mir}_{+}(q),z)$ associated with
$V_{j}^{+}$. We may assume that $B\subset B^{\prime}$ by the condition (a)
above. We have $I_{\phi}\subset I_{\phi_{*}}$ because
$\phi\in(\phi_{1},\phi_{2})\subset\big{(}\phi_{*}-\frac{\epsilon}{2},\phi_{*}+\frac{\epsilon}{2}\big{)}$.
Therefore $\widetilde{\Phi}^{-}_{\phi_{*}}$ gives the analytic lift associated
with the point $q_{0}$ and the phase $\phi$. In particular, the decomposition
(7.15) is induced by $\widetilde{\Phi}^{+}_{\phi}$ and
$\widetilde{\Phi}^{-}_{\phi_{*}}$, and the inclusion (7.16) is induced by the
map $\kappa\colon K(\mathfrak{X}_{-})\to K(\mathfrak{X}_{+})$ sending
$V_{i}^{-}$ to $V_{i}^{+}$ for $1\leq i\leq N_{-}$. It now suffices to show
that $V_{i}^{+}=\varphi^{*}V_{i}^{-}$. We already know that this is true for
$i=1$.
Recall from the proof of Propositions 7.8, 7.13 that $V_{i}^{+}$ (resp.
$V_{i}^{-}$) corresponds to the Lefschetz thimble
$\Gamma_{i}^{\pi+\phi}(q_{0})$ of $F_{q_{0}}$ (resp. the Lefschetz thimble
$\Gamma_{i}^{\pi+\phi}(q_{*})$ of $F_{q_{*}}$) under the isomorphism in
Theorem 7.5 (resp. Theorem 7.12). We claim that the map sending
$\Gamma_{i}^{\pi+\phi}(q_{*})\in\operatorname{\mathsf{Lef}}^{\rm sm}_{q_{*}}$
to $\Gamma_{i}^{\pi+\phi}(q_{0})\in\operatorname{\mathsf{Lef}}_{q_{0}}$
coincides with the map $\iota$ from Theorem 7.22. Here we regard
$\Gamma_{i}^{\pi+\phi}(q_{0})$ as a germ of
$\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}$
at $q_{*}$ by extending it to a Gauss–Manin flat section over
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$.
Fix a sufficiently large $\mathbf{u}_{0}\gg 0$. Under the isomorphism
$H_{n}\big{(}\mathcal{Y}_{q_{*}},\\{\Re(F_{q_{*}})\gg 0\\}\big{)}\cong
H_{n}\big{(}\mathcal{Y}_{q_{*}},F_{q_{*}}^{-1}(\mathbf{u}_{0})\big{)},$
the class of $\Gamma_{i}^{\pi+\phi}(q_{*})$ corresponds to the class of a
finite Lefschetz thimble fibred over a bent ray as shown in Fig. 13(ii). We
move $q_{*}$ along the sliding map. For sufficiently small $t>0$, these finite
Lefschetz thimbles can be continuously deformed to finite thimbles for
$F_{\operatorname{\mathtt{s}}_{t}(q_{*})}$ with boundary in
$F_{\operatorname{\mathtt{s}}_{t}(q_{*})}^{-1}(\mathbf{u}_{0})$, as discussed
in Parts (1) and (4) in the proof of Theorem 7.22. By straightening these
paths in the direction $e^{\boldsymbol{\mathrm{i}}\phi}$ again, we see that
these relative cycles in
$\big{(}\mathcal{Y}_{\operatorname{\mathtt{s}}_{t}(q_{*})},F_{\operatorname{\mathtt{s}}_{t}(q_{*})}^{-1}(\mathbf{u}_{0})\big{)}$
correspond to the Lefschetz thimbles
$\Gamma_{i}^{\pi+\phi}(\operatorname{\mathtt{s}}_{t}(q_{*}))$ over the
straight ray
$\mathbf{u}_{i}(\operatorname{\mathtt{s}}_{t}(q_{*}))+e^{\boldsymbol{\mathrm{i}}\phi}\mathbb{R}_{\geq
0}$. Therefore, the map $\iota$ sends $\Gamma_{i}^{\pi+\phi}(q_{*})$ to
$\Gamma_{i}^{\pi+\phi}(\operatorname{\mathtt{s}}_{t}(q_{*}))$ for sufficiently
small $t>0$. The assumptions (b), (c) above ensure that the homology class of
$\Gamma_{i}^{\pi+\phi}(q)$ stays constant as $q$ varies inside
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$; the
Picard–Lefschetz transformation can only arise from the intersection of
vanishing cycles at $\operatorname{cr}_{i}(q)$ and $\operatorname{cr}_{j}(q)$
with $i\neq j$, $\mathbf{u}_{i}(q_{*})=\mathbf{u}_{j}(q_{*})$,
$i,j\in\\{1,\dots,N_{-}\\}$, but these intersection numbers vanish since the
vanishing cycles do not intersect at $q_{*}$. This proves the claim.
Figure 13: Deforming Lefschetz thimbles: (i) semi-infinite Lefschetz thimbles
fibred over the ray $\mathbf{u}_{j}(q_{*})+\mathbb{R}_{\geq
0}e^{\boldsymbol{\mathrm{i}}\phi}$; (ii) bent rays passing through
$\mathbf{u}_{0}$; (iii) moving from $q_{*}$ to a nearby point in
$\bigcup\limits_{0<t<t_{*}}\operatorname{\mathtt{s}}_{t}(W_{*})$; (iv)
straightening the paths again. In (iii) and (iv), the paths from
$\mathbf{u}_{4}$ and $\mathbf{u}_{5}$ overlaps, but it does not matter since
the relevant vanishing cycles do not intersect.
The above discussion gives a commutative diagram
$\textstyle{\operatorname{\mathsf{Lef}}^{\rm
sm}_{q_{*}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{\iota}$$\scriptstyle{\cong}$$\textstyle{\big{(}\mathtt{i}^{-1}\mathtt{j}_{*}\operatorname{\mathtt{s}}_{>0}^{-1}\operatorname{\mathsf{Lef}}\big{)}_{q_{*}}\cong\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}_{q_{*}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{\cong}$$\textstyle{K(\mathfrak{X}_{-})\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{\kappa}$$\textstyle{K(\mathfrak{X}_{+}),}$
where the vertical arrows are induced by the isomorphisms in Theorems 7.5 and
7.12, the top horizontal arrow is the inclusion in Theorem 7.22 and the bottom
arrow $\kappa$ sends $V_{i}^{-}$ to $V_{i}^{+}$ for $1\leq i\leq N_{-}$.
Comparing this with the commutative diagram in Lemma 7.28, we conclude that
$\kappa=\varphi^{*}$ as required.
Finally, we explain that the conclusion of the theorem holds for every
admissible phase $\phi\in(-\alpha_{0},\alpha_{0})$ for
$\\{\mathbf{u}_{1}(q_{0}),\dots,\mathbf{u}_{N_{+}}(q_{0})\\}$. As we reviewed
in Section 6.2, the analytic decompositions (7.14) for $\mathfrak{X}_{\pm}$
change by mutation as the phase $\phi$ varies; see [44, Sections 2.6, 4.2 and
4.3]. In the case at hand, the analytic decompositions are given by the basis
$\\{s_{j}^{\pm}\\}$ of flat sections associated with the $K$-classes
$\\{V_{j}^{\pm}\\}$; they give rise to an asymptotic basis in the sense of
Section 6.2. Their all possible mutations are completely determined by the
configuration $\\{\mathbf{u}_{1}(q_{0}),\dots,\mathbf{u}_{N_{\pm}}(q_{0})\\}$
of the critical values and the Euler pairings $\chi(V_{i}^{\pm},V_{j}^{\pm})$.
We have $\chi(V_{i}^{+},V_{j}^{+})=\chi(V_{i}^{-},V_{j}^{-})$ for $1\leq
i,j\leq N_{-}$ since $V_{i}^{+}=\varphi^{*}V_{i}^{-}$ and $\varphi$ is
birational. The condition (c) above ensures that the basis
$\\{s_{1}^{-},\dots,s_{N_{-}}^{-}\\}$ of flat sections for $\mathfrak{X}_{-}$
and the part $\\{s_{1}^{+},\dots,s_{N_{-}}^{+}\\}$ of the basis of flat
sections for $\mathfrak{X}_{+}$ undergo the same mutation when $\phi$ varies
in $(-\alpha_{0},\alpha_{0})$. Hence the relation
$V_{i}^{+}=\varphi^{*}V_{i}^{-}$ is preserved under mutation. The theorem is
proved. ∎
###### Remark 7.30.
We hope that we can analyze general discrepant transformations
$\mathfrak{X}_{+}\leftarrow\widehat{\mathfrak{X}}\rightarrow\mathfrak{X}_{-}$
by using the functoriality under blowups (Theorem 7.25) twice. In the case of
crepant toric wall crossings, we can see how a Fourier–Mukai transformation
(as discussed in [15, 31]) arises from this result, see the slides from [63].
### 7.6 Orlov’s decomposition and analytic lift
In the previous section, we have observed that the Lefschetz thimbles
associated with ‘convergent’ critical points (at some point
$q_{0}\in\mathcal{V}^{\rm ss}_{0}\cap\mathcal{M}_{\mathbb{R}}$ and for some
phase $\phi$) correspond to $K$-classes from
$\varphi^{*}(K(\mathfrak{X}_{-}))\subset K(\mathfrak{X}_{+})$. In this
section, we see that the remaining ‘divergent’ critical points correspond to
$K$-classes supported on the exceptional divisor of
$\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$. We will see the
correspondence between Orlov’s semiorthogonal decomposition of the derived
category $D^{b}(\mathfrak{X}_{+})$ and the analytic decomposition (7.15) of
the quantum D-module of $\mathfrak{X}_{+}$.
#### 7.6.1 Decomposition of the relative homology mirror to Orlov’s
decomposition
Recall from Lemma 7.15(3) that convergent critical values over
$\operatorname{\mathtt{s}}_{t}(\mathbb{D}_{\rm sm})$ are contained in
$B_{\rho_{2}}(0)$ and divergent critical values over
$\operatorname{\mathtt{s}}_{t}(\mathbb{D}_{\rm sm})$ are contained in the $J$
‘satellite’ discs $\mathfrak{B}_{k}(t):=t^{-1/J}\cdot
B_{\rho_{1}}\big{(}3\rho_{0}e^{(-2k-1)\pi\boldsymbol{\mathrm{i}}/J}\big{)}$,
$k\in\mathbb{Z}/J\mathbb{Z}$ (see Fig. 10). We choose $t_{1}>0$ small enough
so that $\overline{B_{\rho_{2}}(0)}+\mathbb{R}_{\geq 0}$ does not intersect
any other satellite discs $\overline{\mathfrak{B}_{k}(t)}$ when $t$ is real
and $0<t\leq t_{1}$. Then, if $|\phi|$ is sufficiently small, we have that
$\mathcal{S}_{\rm conv}:=\overline{B_{\rho_{2}}(0)}+\mathbb{R}_{\geq
0}e^{\boldsymbol{\mathrm{i}}\phi}$
does not intersect with any $\overline{\mathfrak{B}_{k}(t)}$ when $0<t\leq
t_{1}$. We choose a number $h\in\\{0,1,2,\dots,J\\}$ and let
$\mathcal{S}_{k}\subset\mathbb{C}$, $k=-h,-h+1,\dots,J-h-1$ be mutually
disjoint strip regions as in Fig. 14; each $\mathcal{S}_{k}$ is a closed
region disjoint from $\mathcal{S}_{\rm conv}$, emanating from
$\overline{\mathfrak{B}_{k}(t)}$, going around the origin by the angle
$(2k-1)\pi/J+\phi$ anticlockwise, and extending straight toward the direction
$e^{\boldsymbol{\mathrm{i}}\phi}$ near the end. These regions
$\mathcal{S}_{\rm conv}$, $\mathcal{S}_{k}$ depend on $t$, $\phi$ and are
defined when $0<t\leq t_{1}$ and $|\phi|$ is sufficiently small.
Figure 14: Strip regions $\mathcal{S}_{\rm conv}$ and $\mathcal{S}_{k}$. In
this picture, $J=5$, $h=3$ and $\phi=\frac{\pi}{30}$.
For sufficiently large $M\gg 0$,
$\bigcup\limits_{k=-h}^{J-h-1}\mathcal{S}_{k}\cup\mathcal{S}_{\rm
conv}\cup\\{\Re(\mathbf{u})\geq M\\}$ is a strong deformation retract of
$\mathbb{C}$. The fibration given by $F_{q,t}$ is smoothly trivial outside
this region by Corollary 7.21, and hence we get the decomposition of the
relative homology $\operatorname{\mathsf{Lef}}_{q,t}$ (see (7.10)):
$\operatorname{\mathsf{Lef}}_{q,t}=\operatorname{\mathsf{Lef}}^{(-h)}_{q,t}\oplus\cdots\oplus\operatorname{\mathsf{Lef}}^{(-1)}_{q,t}\oplus\operatorname{\mathsf{Lef}}_{q,t}^{\rm
conv}\oplus\operatorname{\mathsf{Lef}}_{q,t}^{(0)}\oplus\cdots\oplus\operatorname{\mathsf{Lef}}_{q,t}^{(J-h-1)}$
(7.22)
for $q\in\mathbb{D}_{\rm sm}^{\times}$ and $0<t\leq t_{1}$, where we use the
notation as in Sections 7.4.2–7.4.4 and
$\displaystyle\operatorname{\mathsf{Lef}}_{q,t}^{\rm
conv}=H_{n}\big{(}F_{q,t}^{-1}(\mathcal{S}_{\rm
conv}),F_{q,t}^{-1}(\mathcal{S}_{\rm conv})\cap\\{x\colon\Re(F_{q,t}(x))\geq
M\\};\mathbb{Z}\big{)},$
$\displaystyle\operatorname{\mathsf{Lef}}_{q,t}^{(k)}=H_{n}\big{(}F_{q,t}^{-1}(\mathcal{S}_{k}),F_{q,t}^{-1}(\mathcal{S}_{k})\cap\\{x\colon\Re(F_{q,t}(x))\geq
M\\};\mathbb{Z}\big{)}.$
This decomposition is independent of $\phi$ (with $|\phi|$ sufficiently small)
and is preserved by the Gauss–Manin connection. We say that a direct sum
decomposition $A=A_{1}\oplus\cdots\oplus A_{m}$ is _semiorthogonal_ with
respect to a (not necessarily symmetric) pairing $[\cdot,\cdot)$ on $A$ if
$[a_{i},a_{j})=0$ for $a_{i}\in A_{i}$, $a_{j}\in A_{j}$ whenever $i>j$. Note
that the decomposition (7.22) is semiorthogonal with respect to the pairing
$\\#\big{(}e^{-\pi\boldsymbol{\mathrm{i}}}\Gamma_{1}\cdot\Gamma_{2}\big{)}$
discussed in Remark 7.6.
Let $E\subset\mathfrak{X}_{+}$ be the exceptional divisor of the morphism
$\varphi\colon\mathfrak{X}_{+}\to\mathfrak{X}_{-}$; this is the toric divisor
corresponding to ${\hat{b}}\in R_{+}$. Let $Z=\varphi(E)$ denote the image of
$E$; this is a toric substack corresponding to the cone $\sigma_{M_{+}}$ of
$\mathbf{\Sigma}_{-}$ (see (7.1)). We write $\varphi_{E}\colon E\to Z$ for the
restriction of $\varphi$ to $E$ and $i_{E}\colon E\to\mathfrak{X}_{+}$ for the
inclusion.
###### Theorem 7.31.
For $q\in\mathbb{D}_{\rm sm}^{\times}\cap\mathcal{M}^{\rm sm}_{\mathbb{R}}$
and $0<t\leq t_{1}$, the decomposition (7.22) of the relative homology
corresponds to the decomposition of the $K$-group
$K(\mathfrak{X}_{+})=K(Z)_{-h}\oplus\cdots\oplus
K(Z)_{-1}\oplus\varphi^{*}K(\mathfrak{X}_{-})\oplus K(Z)_{0}\oplus\cdots\oplus
K(Z)_{J-h-1}$ (7.23)
under the isomorphism $\operatorname{\mathsf{Lef}}_{q,t}\cong
K(\mathfrak{X}_{+})$ in Theorem $\ref{thm:main_intpaper}(1)$, where $K(Z)_{k}$
denotes the subgroup $\mathcal{O}(-kE)\otimes i_{E*}\varphi_{E}^{*}K(Z)\subset
K(\mathfrak{X}_{+})$.
###### Remark 7.32.
The decomposition (7.23) is semiorthogonal with respect to the Euler pairing
by Remark 7.6 and the above theorem. In view of this, we expect that
$D^{b}(\mathfrak{X}_{+})$ admits a semiorthogonal decomposition:
$D^{b}(\mathfrak{X}_{+})=\big{\langle}D^{b}(Z)_{-h},\cdots,D^{b}(Z)_{-1},\varphi^{*}D^{b}(\mathfrak{X}_{-}),D^{b}(Z)_{0},\dots,D^{b}(Z)_{J-h-1}\big{\rangle},$
where $D^{b}(Z)_{j}$ denotes the full subcategory of $D^{b}(\mathfrak{X}_{+})$
which is the image of the functor $\mathcal{O}(-jE)\otimes
i_{E*}\varphi_{E}^{*}\colon D^{b}(Z)\to D^{b}(\mathfrak{X}_{+})$. When
$\mathfrak{X}_{+}$ is the blowup of a smooth _variety_ $\mathfrak{X}_{-}$
along a smooth centre $Z$, this is the semiorthogonal decomposition proved by
Orlov [87, Theorem 4.3]; Orlov stated the result for $h=J$, but the other
cases $0\leq h\leq J-1$ follow from this case by using the fact that
$D^{b}(Z)_{-h}=\mathbb{S}\big{(}D^{b}(Z)_{J-h}\big{)}$, where $\mathbb{S}$ is
the Serre functor for $D^{b}(\mathfrak{X}_{+})$.
###### Proof of Theorem 7.31.
Observe that the subgroup $\operatorname{\mathsf{Lef}}^{\rm
conv}_{q,t}\subset\operatorname{\mathsf{Lef}}_{q,t}$ is the image of the map
$\iota\colon\operatorname{\mathsf{Lef}}^{\rm
sm}_{q}\to\big{(}\operatorname{\mathtt{s}}_{t}^{-1}\operatorname{\mathsf{Lef}}\big{)}_{q}$
in Theorem 7.22 (e.g., by considering the case $\phi=0$). Hence it corresponds
to $\varphi^{*}(K(\mathfrak{X}_{-}))\subset K(\mathfrak{X}_{+})$ by Lemma
7.28. It suffices to show that $\operatorname{\mathsf{Lef}}_{q,t}^{(k)}$
corresponds to $K(Z)_{k}$ for $-h\leq k\leq J-h-1$. Let $K^{(k)}\subset
K(\mathfrak{X}_{+})$ denote the subgroup corresponding to
$\operatorname{\mathsf{Lef}}_{q,t}^{(k)}\subset\operatorname{\mathsf{Lef}}_{q,t}$.
It suffices to show that
* (a)
$K(Z)_{k}\subset K^{(k)}$;
* (b)
the decomposition (7.23) of the $K$-group holds true.
As discussed, over $\operatorname{\mathtt{s}}_{t}(\mathbb{D}_{\rm sm})$,
convergent critical values are contained in $B_{\rho_{2}}(0)$ and divergent
critical values are contained in the $J$ satellite discs
$\mathfrak{B}_{k}(t)$, $k\in\mathbb{Z}/J\mathbb{Z}$; these statement still
hold for a non-zero complex number $t$ with $|t|\leq 1$ by naturally extending
the definition of $\operatorname{\mathtt{s}}_{t}$ and $\mathfrak{B}_{k}(t)$ to
$t\in\mathbb{C}$ (see the proof of Lemma 7.15). Consider the class
$[\Gamma_{\mathbb{R}}]\in\operatorname{\mathsf{Lef}}_{q,t}$ of the positive
real Lefschetz thimble. It corresponds to the class $[\mathcal{O}]\in
K(\mathfrak{X}_{+})$ of the structure sheaf. We study the monodromy action on
$\operatorname{\mathsf{Lef}}_{q,t}$ along the loop
$[0,2\pi]\ni\theta\mapsto\big{(}q,e^{\boldsymbol{\mathrm{i}}\theta}t\big{)}$.
The monodromy corresponds to the tensor product by $\mathcal{O}(-E)$ on
$K(\mathfrak{X}_{+})$; this follows from the same argument as in the proof of
Lemma 7.28 and the fact that this loop corresponds to the element of
$\mathbb{L}^{\star}$ given by the second projection in the decomposition
(7.21) (which equals $D_{\hat{b}}\in\mathbb{L}^{\star}$). Under this
monodromy, $[\Gamma_{\mathbb{R}}]$ undergoes the Picard–Lefschetz
transformation. Among the satellite discs, only $\mathfrak{B}_{-1}(t)$ passes
through the strip region $\mathcal{S}_{\rm conv}$ as $t$ rotates; here
$\mathfrak{B}_{-1}(t)$ becomes
$\mathfrak{B}_{-1}\big{(}e^{2\pi\boldsymbol{\mathrm{i}}}t\big{)}=\mathfrak{B}_{0}(t)$
after rotation. Thus by the Picard–Lefschetz formula, the monodromy transform
of $[\Gamma_{\mathbb{R}}]$ equals $[\Gamma_{\mathbb{R}}]-\alpha_{0}$ for some
$\alpha_{0}\in\operatorname{\mathsf{Lef}}_{q,t}^{(0)}$. Then we find that
$\alpha_{0}$ corresponds to
$[\mathcal{O}]-[\mathcal{O}(-E)]=[\mathcal{O}_{E}]\in K(\mathfrak{X}_{+})$ and
in particular that it is non-zero. Similarly, by considering the monodromy
around the inverse loop
$\theta\mapsto(q,e^{-\boldsymbol{\mathrm{i}}\theta}t)$, we find an element
$\beta_{1}\in\operatorname{\mathsf{Lef}}_{q,t}^{(-1)}$ that corresponds to
$[\mathcal{O}(E)]-[\mathcal{O}]=[\mathcal{O}_{E}(E)]\in K(\mathfrak{X}_{+})$.
By considering further monodromy actions on $\alpha_{0},\beta_{1}$, we find
elements $\alpha_{i}\in\operatorname{\mathsf{Lef}}_{q,t}^{(i)}$ with $0\leq
i\leq J-h-1$ and $\beta_{j}\in\operatorname{\mathsf{Lef}}_{q,t}^{(-j)}$ with
$1\leq j\leq h$ such that $\alpha_{i}$ corresponds to $[\mathcal{O}_{E}(-iE)]$
and that $\beta_{j}$ corresponds to $[\mathcal{O}_{E}(jE)]$. Hence we have
$[\mathcal{O}_{E}(-kE)]=\mathcal{O}(-kE)\otimes[\mathcal{O}_{E}]\in K^{(k)}$
(7.24)
for $-h\leq k\leq J-h-1$. Note that the decomposition (7.22) is invariant
under monodromy in $q\in\mathbb{D}_{\rm sm}^{\times}$. As discussed in the
proof of Lemma 7.28, the monodromy around loops in $\mathbb{D}_{\rm
sm}^{\times}$ corresponds to the tensoring $\varphi^{*}L$ with
$L\in\operatorname{Pic}(\mathfrak{X}_{-})$. Since $K(\mathfrak{X}_{-})$ is
generated by line bundles, we conclude from (7.24) that
$\mathcal{O}(-kE)\otimes\mathcal{O}_{E}\otimes\varphi^{*}V\in K^{(k)}$ for all
$V\in K(\mathfrak{X}_{-})$. Part (a) follows from the fact that $K(Z)$ is also
generated by line bundles and that the natural map
$\operatorname{Pic}(\mathfrak{X}_{-})\to\operatorname{Pic}(Z)$ is surjective.
It remains to prove Part (b). In view of part (a) and the decomposition
(7.22), it suffices to show that $K(\mathfrak{X}_{+})$ is generated by the
classes of $\mathcal{O}$ and $\mathcal{O}_{E}(-kE)$, $-h\leq k\leq J-h-1$ as a
$K(\mathfrak{X}_{-})$-module, where the module structure is given by
$\varphi^{*}\colon K(\mathfrak{X}_{-})\to K(\mathfrak{X}_{+})$. Let
$L_{b}=L_{-D_{b}}\in K(\mathfrak{X}_{+})$ denote the class of the line bundle
associated with $-D_{b}\in\mathbb{L}^{\star}$ for $b\in S$ (see Section 3.1.2
for $L_{-D_{b}}$); $1-L_{b}$ is the class of the structure sheaf of the toric
divisor associated with $b$ when $b\in R_{+}$. Similarly, let $L_{b}^{-}\in
K(\mathfrak{X}_{-})$ denote the class of the line bundle associated with
$-D_{b}\in(\mathbb{L}^{\prime})^{\star}$ for $b\in S_{-}$. We also set
$L:=L_{{\hat{b}}}=[\mathcal{O}(-E)]\in K(\mathfrak{X}_{+})$. Recall from the
proof of Lemma 7.28 that the splitting
$(\mathbb{L}^{\prime})^{\star}\to\mathbb{L}^{\star}$, $\xi\mapsto{\hat{\xi}}$
induced by the decomposition (7.21) corresponds to the pull-back of line
bundles, i.e., $\varphi^{*}L_{\xi}\cong L_{{\hat{\xi}}}$. Since the splitting
$(\mathbb{L}^{\prime})^{\star}\to\mathbb{L}^{\star}$ sends $D_{b}$ to
$D_{b}+k_{b}D_{\hat{b}}$ (with
$k_{b}=-D_{b}\cdot\delta_{\hat{b}}^{\mathbf{\Sigma}_{-}}$ as before), we have
$\varphi^{*}L_{b}^{-}=L_{b}\cdot L^{k_{b}}.$ (7.25)
On the other hand, since the intersection of the toric divisors corresponding
to rays $b\in M_{+}$ is empty in $\mathfrak{X}_{+}$, we have the following
relation in $K(\mathfrak{X}_{+})$ (see [16]):
$\prod_{b\in M_{+}}(1-L_{b})=0.$ (7.26)
Combining the two relations (7.25), (7.26), we obtain
$\prod_{b\in M_{+}}\big{(}L^{k_{b}}-\varphi^{*}L_{b}^{-}\big{)}=0.$ (7.27)
The left-hand side of the relation is a monic polynomial in $L$ of degree
$J+1=\sum\limits_{b\in M_{+}}k_{b}$ with coefficients in $K(\mathfrak{X}_{-})$
whose constant term is an invertible element in $K(\mathfrak{X}_{-})$. Note
that $\operatorname{Pic}(\mathfrak{X}_{+})$ is generated by
$\varphi^{*}\operatorname{Pic}(\mathfrak{X}_{-})$ and $L^{\pm}$; therefore any
element in $K(\mathfrak{X}_{+})$ can be written as a Laurent polynomial of $L$
with coefficients in $K(\mathfrak{X}_{-})$. Using the above relation (7.27),
we find that every element of $K(\mathfrak{X}_{+})$ can be written in the form
$\sum_{k=-h}^{J-h}a_{k}\cdot L^{k}\qquad\text{with $a_{k}\in
K(\mathfrak{X}_{-})$},$
which can also be rewritten as a $K(\mathfrak{X}_{-})$-linear combination of
$1$ and $(1-L)L^{k}=[\mathcal{O}_{E}(-kE)]$ with $-h\leq k\leq J-h-1$. Part
(b) follows. The theorem is proved. ∎
#### 7.6.2 Orlov’s decomposition as a sectorial decomposition of the quantum
D-module
Next we see that this Orlov-type decomposition actually arises from a
sectorial decomposition of the quantum D-module of $\mathfrak{X}_{+}$ – as
appears in Proposition 6.5 – associated with _some_ $\tau_{+}\in H^{*}_{\rm
CR}(\mathfrak{X}_{+})$; the point $\tau_{+}$ can be very far from the large
radius limit point and is not explicit in general (see however Example 7.34).
The analytic quantum D-module (6.1) is originally defined in a neighbourhood
of the large radius limit point. In the following theorem, we consider
analytic continuation of the quantum D-module along certain paths in
$H^{*}_{\rm CR}(\mathfrak{X}_{\pm})$; we choose a real class
$\tau_{\star,\pm}\in H^{*}_{\rm CR}(\mathfrak{X}_{\pm};\mathbb{R})$ which is
sufficiently close to the large radius limit point as a base point (see Remark
2.8).
###### Theorem 7.33.
There exist paths from $\tau_{\star,\pm}$ to $\tau_{\pm}\in H^{*}_{\rm
CR}(\mathfrak{X}_{\pm})$ and analytic continuation of the quantum D-modules
$\operatorname{QDM}^{\rm an}(\mathfrak{X}_{\pm})$ along these paths with the
following properties.
* (1)
The eigenvalues of the Euler multiplication $E\star_{\tau_{+}}$ at $\tau_{+}$
have mutually distinct imaginary parts, and we have the following sectorial
decomposition as in Proposition 6.5
$\Phi^{+}\colon\ \pi^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})\big{|}_{W\times
I}\cong\bigoplus_{i=1}^{N_{+}}(\mathcal{A}_{W\times I},d+d(\mathbf{u}_{i}/z))$
over an open neighbourhood $W$ of $\tau_{+}$ in $H_{\rm
CR}^{*}(\mathfrak{X}_{+})$, where $\pi\colon H^{*}_{\rm
CR}(\mathfrak{X}_{+})\times{\widetilde{\mathbb{C}}}\to H^{*}_{\rm
CR}(\mathfrak{X}_{+})\times\mathbb{C}$ is the oriented real blow-up,
$I=\big{\\{}\big{(}z,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\in{\widetilde{\mathbb{C}}}\colon|\theta|<\frac{\pi}{2}+\epsilon\big{\\}}$
$($for some $\epsilon>0)$ and $\mathbf{u}_{1},\dots,\mathbf{u}_{N_{+}}$ are
the eigenvalues of the Euler multiplication.
* (2)
Moreover, there exists a holomorphic submersion $f\colon W\to H^{*}_{\rm
CR}(\mathfrak{X}_{-})$ with $f(\tau_{+})=\tau_{-}$ such that we have the
similar sectorial decomposition for $\mathfrak{X}_{-}$
$\Phi^{-}\colon\ \pi^{*}f^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{W\times
I}\cong\bigoplus_{i=1}^{N_{-}}(\mathcal{A}_{W\times
I},d+d(\mathbf{u}_{i}/z)),$
where $W$ and $I$ are the same as Part $(1)$ and
$\mathbf{u}_{1},\dots,\mathbf{u}_{N_{-}}$ are the pull-backs along $f$ of the
eigenvalues of the Euler multiplication in the quantum cohomology of
$\mathfrak{X}_{-}$ which form a subset of
$\\{\mathbf{u}_{1},\dots,\mathbf{u}_{N_{+}}\\}$ in Part $(1)$.
* (3)
The eigenvalues $\\{\mathbf{u}_{1},\dots,\mathbf{u}_{N_{+}}\\}$ in Part $(1)$
are divided into $J+1$ groups
$\bigsqcup\limits_{k=-h}^{J-h-1}\big{\\{}\mathbf{u}^{(k)}_{i}\colon 1\leq
i\leq r\big{\\}}\sqcup\\{\mathbf{u}_{1},\dots,\mathbf{u}_{N_{-}}\\}$
satisfying
$\Im\big{(}\mathbf{u}^{(-h)}_{i_{1}}\big{)}>\cdots>\Im\big{(}\mathbf{u}^{(-1)}_{i_{h}}\big{)}>\Im(\mathbf{u}_{j})>\Im\big{(}\mathbf{u}^{(0)}_{i_{h+1}}\big{)}>\cdots>\Im\big{(}\mathbf{u}^{(J-h-1)}_{i_{J}}\big{)}$
for all $i_{k}\in\\{1,\dots,r\\}$ $($with $1\leq k\leq J)$ and
$j\in\\{1,\dots,N_{-}\\}$.
* (4)
There exist $K$-classes $V_{i}^{\pm}\in K(\mathfrak{X}_{\pm})$, $1\leq i\leq
N_{\pm}$ such that
$\Phi^{\pm}\big{(}e^{\mathbf{u}_{i}/z}s_{i}^{\pm}\big{)}=e_{i}$, where
$s_{i}^{\pm}$ is the flat section associated with $V_{i}^{\pm}$ via the
$\widehat{\Gamma}$-integral structure $($Definition $\ref{def:s})$ $($which is
analytically continued from $\tau_{\star,\pm}$ through the specified paths$)$
and $e_{i}$ denotes the $i$th standard basis. Moreover, we have
* $({\rm a})$
$V_{i}^{-}$, $1\leq i\leq N_{-}$ form a basis of $K(\mathfrak{X}_{-})$;
* $({\rm b})$
$\big{\\{}V_{i}^{+}\colon\text{$\mathbf{u}_{i}=\mathbf{u}^{(k)}_{j}$ for some
$j$}\big{\\}}$ gives a basis of $K(Z)_{k}\subset K(\mathfrak{X}_{+})$;
* $({\rm c})$
$V_{i}^{+}=\varphi^{*}V_{i}^{-}$ for $1\leq i\leq N_{-}$.
In particular, we have a sectorial decomposition
$\displaystyle\pi^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})\big{|}_{W\times I}\\!\cong\mathscr{R}^{\rm
an}_{-h}\oplus\cdots\oplus\mathscr{R}^{\rm
an}_{-1}\oplus\pi^{*}f^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{W\times I}\oplus\mathscr{R}^{\rm
an}_{0}\oplus\cdots\oplus\mathscr{R}^{\rm an}_{J-h-1},$
which corresponds to the decomposition (7.23) of the $K$-group via the
$\widehat{\Gamma}$-integral structure, where $\mathscr{R}^{\rm
an}_{k}=\bigoplus\limits_{i=1}^{r_{k}}\big{(}\mathcal{A}_{W\times
I},d+d\big{(}\mathbf{u}_{i}^{(k)}/z\big{)}\big{)}$.
###### Proof.
Throughout Section 7, we have assumed that $S_{-}=S\cap\Delta_{-}$ and
$S=S_{-}\cup\\{{\hat{b}}\\}$ so that $\mathcal{M}$ is the small quantum
cohomology locus of $\mathfrak{X}_{+}$. The construction of the sectorial
decompositions (7.14), however, does not require this assumption because $S$
can be arbitrarily large in the discussion of Sections 5–6. We choose a large
enough finite set ${\widehat{S}}\subset\mathbf{N}\cap\Pi$ containing $S$ such
that the corresponding mirror map $\operatorname{mir}_{+}$ is generically
submersive (this is possible by the argument in [27, Section 7.4]). Let
$\widehat{\mathcal{M}}\supset\mathcal{M}$ denote the base of the LG model
corresponding to ${\widehat{S}}$. The discussion at the beginning of Section
7.5 yields, for any $q_{0}\in\mathcal{V}^{\rm ss}_{0}$ and an admissible phase
$\phi$ for the critical values of $F_{q_{0}}$, the following decompositions
(similarly to (7.14))
$\displaystyle\pi^{*}\operatorname{mir}_{\pm}^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\pm})\big{|}_{\widehat{B}\times I_{\phi}}$
$\displaystyle\cong\bigoplus_{i=1}^{N_{\pm}}(\mathcal{A}_{\widehat{B}\times
I_{\phi}},d+d(\mathbf{u}_{i}/z))$ (7.28)
over a neighbourhood $\widehat{B}$ of $q_{0}$ in $\widehat{\mathcal{M}}$. Here
$(\mathbf{u}_{1},\dots,\mathbf{u}_{N_{+}})$ are the eigenvalues of
$E\star_{\tau}$ in the quantum cohomology of $\mathfrak{X}_{+}$ at
$\tau=\operatorname{mir}_{+}(q)$, and first $N_{-}$
$(\mathbf{u}_{1},\dots,\mathbf{u}_{N_{-}})$ of them are the eigenvalues of
$E\star_{\tau}$ in the quantum cohomology of $\mathfrak{X}_{-}$ at
$\tau=\operatorname{mir}_{-}(q)$, where $q$ varies in $\widehat{B}$. By the
choice of ${\widehat{S}}$, the eigenvalues
$\mathbf{u}_{1},\dots,\mathbf{u}_{N_{+}}$ are pairwise distinct at generic
points in $\widehat{B}$ (see Remark 6.2).
Suppose now that $q_{0}$ is a point from
$\bigcup\limits_{0<t<t_{1}}\operatorname{\mathtt{s}}_{t}\big{(}\mathcal{V}^{\rm
sm,ss}_{-,\mathbb{R}}\cap\mathbb{D}_{\rm
sm}^{\times\circ}\big{)}\cap\mathcal{V}^{\rm ss}_{0}$ and $|\phi|$ is
sufficiently small so that the conclusion of Theorem 7.25 holds; then there
exist $K$-classes $V_{i}^{\circ\pm}\in K(\mathfrak{X}_{\pm})$ such that the
associated flat sections $s_{i}^{\pm}$ (via the $\widehat{\Gamma}$-integral
structure) correspond to $e^{-\mathbf{u}_{i}/z}e_{i}$ under the decomposition
(7.28) and that $V_{i}^{\circ+}=\varphi^{*}V_{i}^{\circ-}$ for $1\leq i\leq
N_{-}$. Choose a point $q^{\circ}\in\widehat{B}$ such that the corresponding
eigenvalues $\mathbf{u}_{1}^{\circ},\dots,\mathbf{u}_{N_{+}}^{\circ}$ are
pairwise distinct, and set
$\tau^{\circ}_{\pm}=\operatorname{mir}_{\pm}(q^{\circ})$; we regard
$\tau^{\circ}_{\pm}$ as elements of $H_{\rm CR}^{*}(\mathfrak{X}_{\pm})$
(rather than their images in $[\mathcal{M}_{\rm
A}(\mathfrak{X}_{\pm})/\operatorname{Pic}^{\rm st}(\mathfrak{X}_{\pm})]$). Let
$C_{N}$ denote the configuration space of distinct $N$ points in $\mathbb{C}$:
$C_{N}:=\big{\\{}(\mathbf{u}_{1},\dots,\mathbf{u}_{N})\in\mathbb{C}^{N}\colon\text{$\mathbf{u}_{i}\neq\mathbf{u}_{j}$
if $i\neq j$}\big{\\}}/\mathfrak{S}_{N}.$
Since the eigenvalues of $E\star_{\tau}$ form a local co-ordinate system on
$H^{*}(\mathfrak{X}_{\pm})$ near a semisimple point, we can identify a
neighbourhood of
$\big{(}\mathbf{u}_{1}^{\circ},\dots,\mathbf{u}_{N_{\pm}}^{\circ}\big{)}$ in
$C_{N_{\pm}}$ with a neighbourhood of $\tau_{\pm}^{\circ}$ in $H^{*}_{{\rm
CR}}(\mathfrak{X}_{\pm})$. Let $\widetilde{C}_{N}$ denote the universal cover
of $C_{N}$. By isomonodromic deformation [40, Theorem 4.7], there exist
analytic hypersurfaces232323In the original version of the present paper, we
did not delete the hypersurfaces $H_{\pm}$ from $\widetilde{C}_{N_{\pm}}$. The
need for the deletion was pointed out by one of the referees.
$H_{\pm}\subset\widetilde{C}_{N_{\pm}}$ such that the quantum connection in a
neighbourhood of $\tau_{\pm}^{\circ}\in H^{*}_{\rm CR}(\mathfrak{X}_{\pm})$
can be extended to a meromorphic flat connection $\nabla$ on the trivial
bundle $H^{*}_{\rm
CR}(\mathfrak{X}_{\pm})\times\big{(}\widetilde{C}_{N_{\pm}}^{\circ}\times\mathbb{C}\big{)}\to\widetilde{C}_{N_{\pm}}^{\circ}\times\mathbb{C}$
of the form
$\nabla=d+\frac{1}{z}A+\left(-\frac{1}{z^{2}}U+\frac{1}{z}V\right)dz,$
where $\widetilde{C}_{N_{\pm}}^{\circ}:=\widetilde{C}_{N_{\pm}}\setminus
H_{\pm}$, $A$ is an $\operatorname{End}(H^{*}_{\rm
CR}(\mathfrak{X}_{\pm}))$-valued 1-form on $\widetilde{C}_{N_{\pm}}^{\circ}$,
$U$ and $V$ are $\operatorname{End}(H^{*}_{\rm
CR}(\mathfrak{X}_{\pm}))$-valued functions on
$\widetilde{C}_{N_{\pm}}^{\circ}$ and $A$, $U$, $V$ are independent of $z$.
Here the eigenvalues of $U$ give the co-ordinates
$(\mathbf{u}_{1},\dots,\mathbf{u}_{N_{\pm}})$ on $\widetilde{C}_{N_{\pm}}$.
Moreover, by taking bigger hypersurfaces $H_{\pm}$ if necessary, we may assume
that this defines a Frobenius manifold structure on
$\widetilde{C}^{\circ}_{N_{\pm}}$. By choosing a basis $\\{\phi_{i}\\}$ of
$H^{*}_{\rm CR}(\mathfrak{X}_{\pm})$, we can determine the flat vector fields
$\frac{\partial}{\partial\tau^{i}}$ by
$A_{\partial/\partial\tau^{i}}1=\phi_{i}$. In particular, we have a flat co-
ordinate system $\big{(}\widetilde{C}^{\circ}_{N_{\pm}}\big{)}^{~}\to
H^{*}_{\rm CR}(\mathfrak{X}_{\pm})$ on the universal cover
$\big{(}\widetilde{C}^{\circ}_{N_{\pm}}\big{)}^{~}$ which equals
$\tau^{\circ}_{\pm}$ at
$\big{(}\mathbf{u}^{\circ}_{1},\dots,\mathbf{u}^{\circ}_{N_{\pm}}\big{)}$. We
also have a submersion $g\colon\widetilde{C}_{N_{+}}\to\widetilde{C}_{N_{-}}$
sending $(\mathbf{u}_{1},\dots,\mathbf{u}_{N_{+}})$ to
$(\mathbf{u}_{1},\dots,\mathbf{u}_{N_{-}})$; this induces a submersion
$g\colon\widetilde{C}_{N_{+}}^{\circ\circ}\to\widetilde{C}_{N_{-}}^{\circ}$,
where
$\widetilde{C}_{N_{+}}^{\circ\circ}:=\widetilde{C}_{N_{+}}\setminus\big{(}H_{+}\cup
g^{-1}(H_{-})\big{)}\subset\widetilde{C}_{N_{+}}^{\circ}$.
We may assume that $q^{\circ}$ is sufficiently close to $q_{0}$ so that
$\big{\\{}\mathbf{u}_{1}^{\circ},\dots,\mathbf{u}_{N_{+}}^{\circ}\big{\\}}$
are contained in
$B_{\rho_{2}}(0)\sqcup\bigsqcup\limits_{k\in\mathbb{Z}/J\mathbb{Z}}\mathfrak{B}_{k}(t)$,
where $0<t<t_{1}$ is the number such that
$q_{0}\in\operatorname{Im}(\operatorname{\mathtt{s}}_{t})$. Moving
$\mathbf{u}_{i}^{\circ}$ along the strip regions $\mathcal{S}_{\rm
conv}\cup\mathcal{S}_{-h}\cup\cdots\cup\mathcal{S}_{J-h-1}$, we can connect
$\big{(}\mathbf{u}_{1}^{\circ},\dots,\mathbf{u}_{N_{+}}^{\circ}\big{)}$ by a
continuous path $\gamma$ inside $\widetilde{C}_{N_{+}}^{\circ\circ}$ with a
point
$\big{(}\mathbf{u}^{\Diamond}_{1},\dots,\mathbf{u}^{\Diamond}_{N_{+}}\big{)}\in\widetilde{C}_{N_{+}}^{\circ\circ}$
having mutually distinct imaginary parts: see Fig. 15. The numbers
$\mathbf{u}^{\Diamond}_{1},\dots,\mathbf{u}^{\Diamond}_{N_{+}}$ are divided
into $J+1$ groups as in Part (3) of the statement, depending on which strip
regions they belong to. Let $\tau_{+}\in H^{*}_{\rm CR}(\mathfrak{X}_{+})$ be
the analytically continued (along the path $\gamma$) flat co-ordinate at the
point
$\big{(}\mathbf{u}^{\Diamond}_{1},\dots,\mathbf{u}^{\Diamond}_{N_{+}}\big{)}\in\widetilde{C}_{N_{+}}^{\circ\circ}$
and $\tau_{-}\in H^{*}_{\rm CR}(\mathfrak{X}_{-})$ be the analytically
continued (along the path $g(\gamma)$) flat co-ordinate at the point
$g\big{(}\mathbf{u}^{\Diamond}_{1},\dots,\mathbf{u}^{\Diamond}_{N_{+}}\big{)}=\big{(}\mathbf{u}^{\Diamond}_{1},\dots,\mathbf{u}^{\Diamond}_{N_{-}}\big{)}\in\widetilde{C}_{N_{-}}^{\circ}$.
By the above construction, the quantum D-modules of $\mathfrak{X}_{\pm}$ are
analytically continued to $\tau_{\pm}$ along certain paths, and the submersion
$g$ induces, when written in flat co-ordinates, a submersion $f$ from a
neighbourhood of $\tau_{+}$ in $H^{*}_{\rm CR}(\mathfrak{X}_{+})$ to a
neighbourhood of $\tau_{-}$ in $H^{*}_{\rm CR}(\mathfrak{X}_{-})$ with
$f(\tau_{+})=\tau_{-}$.
Figure 15: A path from
$\big{(}\mathbf{u}_{1}^{\circ},\dots,\mathbf{u}_{N_{+}}^{\circ}\big{)}$ to
$\big{(}\mathbf{u}_{1}^{\Diamond},\dots,\mathbf{u}_{N_{+}}^{\Diamond}\big{)}$:
we move the left configuration $\big{(}\mathbf{u}_{i}^{\circ}\big{)}$ to the
right one $\big{(}\mathbf{u}_{i}^{\Diamond}\big{)}$ along the strip regions.
We claim that the statement of the theorem holds for $\tau_{\pm}$, $f$ and a
sufficiently small neighbourhood $W$ of $\tau_{+}$. Parts (1), (2) follow from
the construction and the Hukuhara–Turrittin decomposition (Proposition 6.5);
note that $0$ is an admissible phase for
$\big{(}\mathbf{u}_{1}^{\Diamond},\dots,\mathbf{u}_{N_{\pm}}^{\Diamond}\big{)}$.
Part (3) has been already achieved. We show Part (4). Recall that the
decomposition (7.28) corresponds to the basis
$\big{\\{}V_{i}^{\circ\pm}\big{\\}}$ of $K(\mathfrak{X}_{\pm})$ under the
$\widehat{\Gamma}$-integral structure and it gives rise to the asymptotic
basis (see Section 6.2) associated with $\tau_{\pm}^{\circ}$ and $\phi$. As we
move $(\mathbf{u}_{1},\dots,\mathbf{u}_{N_{\pm}})$ along the path $\gamma$ (or
$g(\gamma)$) and change the phase from $\phi$ to zero, this asymptotic basis
undergoes mutation as explained in Section 6.2. The basis
$\big{\\{}V_{i}^{\pm}\big{\\}}\subset K(\mathfrak{X}_{\pm})$ in Part (4)
arises from $\big{\\{}V_{i}^{\circ\pm}\big{\\}}$ by this mutation. Part (4-a)
is obvious from this construction. By the same argument as in the last
paragraph of the proof of Theorem 7.25, we see that the relation
$V_{i}^{\circ+}=\varphi^{*}V_{i}^{\circ-}$ is preserved by mutation, and we
get $V_{i}^{+}=\varphi^{*}V_{i}^{-}$ for $1\leq i\leq N_{-}$ as required in
Part (4-c). Let $\Gamma_{i}^{\pi+\phi}$ denote the Lefschetz thimbles (6.12)
of $F_{q_{0}}$ corresponding to the $i$th component of the decomposition
(7.28) (recall that components in (7.28) are naturally indexed by critical
points of $F_{q_{0}}$; see Proposition 6.18). As discussed in the proof of
Proposition 7.8, $V_{i}^{\circ+}$ equals the $K$-class
$V\big{(}\Gamma_{i}^{\pi+\phi}\big{)}$ associated with $\Gamma_{i}^{\pi+\phi}$
under the correspondence in Theorem 7.5. Note by Remark 7.6 that
$\chi\big{(}V_{i}^{\circ+},V_{j}^{\circ+}\big{)}=(-1)^{n(n-1)/2}\\#\big{(}e^{-\pi\boldsymbol{\mathrm{i}}}\Gamma_{i}^{\pi+\phi}\cdot\Gamma_{j}^{\pi+\phi}\big{)}.$
Therefore, mutation of $\big{\\{}V_{i}^{\circ+}\big{\\}}$ corresponds to
Picard–Lefschetz transformation (see [7, Chapter I]) of thimbles
$\big{\\{}\Gamma_{i}^{\pi+\phi}\big{\\}}$; here we consider Picard–Lefschetz
transformation with $q_{0}\in\mathcal{M}$ fixed. We transform
$\big{\\{}\Gamma_{i}^{\pi+\phi}\big{\\}}$ by the sequence of Picard–Lefschetz
transformations corresponding to the sequence of mutations that
$\big{\\{}V_{i}^{\circ+}\big{\\}}$ undergoes and obtain a new basis
$\\{\Gamma_{i}\\}$ of $\operatorname{\mathsf{Lef}}_{q_{0}}$. The basis
$\\{\Gamma_{i}\\}$ is the union of bases of
$\operatorname{\mathsf{Lef}}^{(k)}_{q_{0}}$ and
$\operatorname{\mathsf{Lef}}^{\rm conv}_{q_{0}}$;
$\big{\\{}\Gamma_{i}\colon\text{$\mathbf{u}_{i}=\mathbf{u}_{j}^{(k)}$ for some
$j$}\big{\\}}$ gives a basis of $\operatorname{\mathsf{Lef}}_{q_{0}}^{(k)}$.
Since we have $V_{i}^{+}=V(\Gamma_{i})$, Part (4-b) follows from Theorem 7.31.
The theorem is proved. ∎
###### Example 7.34.
We give an example where the Orlov-type decomposition occurs at an explicit
$\tau_{+}$. Set $X_{-}:=\mathbb{P}^{4}$ and let $X_{+}$ be the blowup of
$X_{-}$ along a line $Z=\mathbb{P}^{1}\subset X_{-}$. Both $X_{+}$ and $X_{-}$
are Fano, and their small quantum cohomologies are defined over polynomial
rings. Planes in $X_{-}=\mathbb{P}^{4}$ containing the line $Z$ are
parametrized by $\mathbb{P}^{2}$, and hence we have a natural projection
$X_{+}\to\mathbb{P}^{2}$. Thus $X_{+}$ is a $\mathbb{P}^{2}$-bundle over
$\mathbb{P}^{2}$:
$X_{+}\cong\mathbb{P}_{\mathbb{P}^{2}}(\mathcal{O}\oplus\mathcal{O}\oplus\mathcal{O}(-1))$.
Let $p_{1}$ be the pull-back of the ample class in
$H^{2}\big{(}\mathbb{P}^{2};\mathbb{Z}\big{)}$ and let $p_{2}=\varphi^{*}(p)$
be the pull-back of the ample class $p$ in $H^{2}(X_{-};\mathbb{Z})$. They
form a nef basis of $H^{2}(X_{+};\mathbb{Z})$. The class of the exceptional
divisor is given by $[E]=p_{1}-p_{2}$. The uncompactified LG mirror of $X_{+}$
is given by the family of Laurent polynomials
$F_{q_{1},q_{2}}=x_{1}+x_{2}+x_{3}+x_{4}+\frac{q_{1}q_{2}}{x_{1}x_{2}x_{3}x_{4}}+\frac{1}{q_{1}}x_{1}x_{2}x_{3}$
parametrized by $(q_{1},q_{2})\in(\mathbb{C}^{\times})^{2}$. The large radius
limit (LRL) point for $X_{+}$ corresponds to $q_{1}=q_{2}=0$. The mirror map
for $X_{+}$ is trivial: $\operatorname{mir}_{+}(q_{1},q_{2})=p_{1}\log
q_{1}+p_{2}\log q_{2}$. On the other hand, the uncompactified LG mirror of
$X_{-}$ is given by the family
$F_{q,t}=x_{1}+x_{2}+x_{3}+x_{4}+\frac{q}{x_{1}x_{2}x_{3}x_{4}}+tx_{1}x_{2}x_{3},$
where the LRL point for $X_{-}$ is $q=t=0$. The two families are related by
the change of co-ordinates $q=q_{1}q_{2}$, $t=q_{1}^{-1}$. The small quantum
cohomology locus for $X_{-}$ is $t=0$. It is not easy to find a closed formula
for the mirror map of $X_{-}$, but we know that it has the asymptotic form
$\operatorname{mir}_{-}(q,t)\sim p\log q+t\cdot p^{3}$ as $(q,t)\to(0,0)$ (see
Remark 4.10) and that $\operatorname{mir}_{-}(q,0)=p\log q$. The Euler vector
field gives a grading $\deg q_{1}=2$, $\deg q_{2}=3$ and $\deg t=-2$, $\deg
q=5$ (in complex unit). Define a dimensionless parameter
$\lambda:=q_{1}^{-\frac{3}{2}}q_{2}=t^{\frac{5}{2}}q$. Critical points/values
of $F_{q_{1},q_{2}}=F_{q,t}$ are given by
$x_{1}=x_{2}=x_{3}=t^{-\frac{1}{2}}x,\qquad
x_{4}=t^{-\frac{1}{2}}\big{(}x+x^{3}\big{)},\qquad
F_{q,t}(\operatorname{cr})=t^{-\frac{1}{2}}\big{(}5x+3x^{3}\big{)},$
where $x$ is a root of $x^{5}\big{(}x^{2}+1\big{)}^{2}=\lambda$. The
discriminant locus (where $x$ has multiple roots) is $\lambda=0$ or $\pm
400\sqrt{5}\boldsymbol{\mathrm{i}}/3^{9}$. Therefore the quantum cohomology is
semisimple over the positive real locus $q_{1}>0$, $q_{2}>0$. The critical
values have the asymptotics
$F_{q,t}(\operatorname{cr})=\begin{cases}t^{-\frac{1}{2}}\big{(}5\lambda^{\frac{1}{5}}+\lambda^{\frac{3}{5}}+O(\lambda)\big{)},\\\
t^{-\frac{1}{2}}\big{(}2\boldsymbol{\mathrm{i}}\pm
2\sqrt{\boldsymbol{\mathrm{i}}}\lambda^{\frac{1}{2}}+O(\lambda)\big{)},\\\
t^{-\frac{1}{2}}\big{(}{-}2\boldsymbol{\mathrm{i}}\pm
2\sqrt{-\boldsymbol{\mathrm{i}}}\lambda^{\frac{1}{2}}+O(\lambda)\big{)}\end{cases}=\begin{cases}5q^{\frac{1}{5}}+tq^{\frac{3}{5}}+O\big{(}t^{2}\big{)},\\\
2\boldsymbol{\mathrm{i}}t^{-\frac{1}{2}}\pm
2\sqrt{\boldsymbol{\mathrm{i}}}q^{\frac{1}{2}}t^{\frac{3}{4}}+O\big{(}t^{2}\big{)},\\\
-2\boldsymbol{\mathrm{i}}t^{-\frac{1}{2}}\pm
2\sqrt{-\boldsymbol{\mathrm{i}}}q^{\frac{1}{2}}t^{\frac{3}{4}}+O\big{(}t^{2}\big{)}.\end{cases}$
(7.29)
as $\lambda\to 0$ (or $t\to 0$ with $q$ fixed) and
$\displaystyle
F_{q,t}(\operatorname{cr})=t^{-\frac{1}{2}}\big{(}3\lambda^{\frac{1}{3}}+3\lambda^{\frac{1}{9}}+O(\lambda^{-\frac{1}{9}})\big{)}=3q_{2}^{\frac{1}{3}}+3q_{1}^{\frac{1}{3}}q_{2}^{\frac{1}{9}}+O\big{(}q_{1}^{\frac{2}{3}}\big{)}$
as $\lambda\to\infty$ (or $q_{1}\to 0$ with $q_{2}$ fixed). The first line of
(7.29) gives 5 ‘convergent’ critical values (depending on the choice of
$q^{\frac{1}{5}}$) and the next two lines give 4 ‘divergent’ critical values
around $t=0$. They have mutually distinct imaginary parts when $t>0$ is
sufficiently close to zero and $q>0$. We will identify the corresponding
elements in the $K$-group for the phase $\phi=0$.
Figure 16: Move of critical values: the trajectories of the critical values
are shown in the middle picture; $\mathcal{E}$ is the left mutation of
$\mathcal{O}(-H_{1})$ with respect to $\mathcal{O}(-H_{2})$; similarly
$\mathcal{F}$ is the right mutation of $\mathcal{O}(H_{1})$ with respect to
$\mathcal{O}(H_{2})$; $\mathcal{G}$ is the right mutation of
$\mathcal{O}(-2H_{2})$ with respect to $\mathcal{O}(-H_{2})$.
We consider a path where the parameter $\lambda\in\mathbb{R}$ increases from
$0$ to $\infty$. It is convenient to take
$t=t(\lambda)=\lambda^{\frac{2}{3}}+\lambda^{\frac{2}{5}}$ so that
$(q_{1},q_{2})\sim\big{(}\lambda^{-\frac{3}{2}},1\big{)}$ as
$\lambda\to\infty$ and $(q,t)\sim\big{(}1,\lambda^{\frac{2}{5}}\big{)}$ as
$\lambda\to 0$. The move of the critical values is shown in Fig. 16. When
$\lambda$ is large, say $\lambda=12.5$, we can determine the mirror partners
(in the $K$-group) of some Lefschetz thimbles by using the monodromy action on
the $(q_{1},q_{2})$-space: see the rightmost picture of Fig. 16. Here $H_{1}$,
$H_{2}$ denote the pull-backs of the hyperplanes on $\mathbb{P}^{2}$ and
$\mathbb{P}^{4}$ respectively (so that $p_{i}$ is the Poincaré dual of
$H_{i}$). A numerical calculation on computer shows that, as $\lambda$
decreases from $\lambda=12.5$ to $\lambda=0.0009$, the thimble corresponding
to $\mathcal{O}(-H_{1})$ undergoes a Picard–Lefschetz transformation with
respect to that corresponding to $\mathcal{O}(-H_{2})$. As we saw in the proof
of Theorem 7.33, this corresponds to mutation in $K$-group. After (left)
mutation, $\mathcal{O}(-H_{1})$ becomes
$\mathcal{E}=\operatorname{Cone}\big{(}\operatorname{Hom}^{\bullet}(\mathcal{O}(-H_{2}),\mathcal{O}(-H_{1}))\otimes\mathcal{O}(-H_{2})\to\mathcal{O}(-H_{1})\big{)}=\mathcal{O}_{E}(E-H_{2}).$
Considering the monodromy action near $t=0$ and performing further mutation,
we find that the exceptional collection (adapted to the decomposition (7.23)
with $J=2$, $h=1$)
$\displaystyle\mathcal{E}=\mathcal{O}_{E}(E-H_{2}),\quad\mathcal{O}_{E}(E),\quad\mathcal{O}(-H_{2}),\quad\mathcal{G}=\mathcal{O}(-2H_{2})\otimes\varphi^{*}T_{\mathbb{P}^{4}}[-1],\quad\mathcal{O},$
$\displaystyle\mathcal{H}=\mathcal{O}(2H_{2})\otimes\varphi^{*}\Omega^{1}_{\mathbb{P}^{4}},\quad\mathcal{O}(H_{2}),\quad\mathcal{O}_{E}[-1],\quad\mathcal{F}=\mathcal{O}_{E}(H_{2})[-1]$
corresponds to the Lefschetz thimbles
$\Gamma_{1}^{\pi},\dots,\Gamma_{9}^{\pi}$ (6.12) ordered in such a way that
the imaginary parts of the corresponding critical values decrease
$\Im(F(\operatorname{cr}_{1}))>\Im(F(\operatorname{cr}_{2}))>\cdots>\Im(F(\operatorname{cr}_{9}))$.
These are the classes $V_{i}^{+}$ in Theorem 7.33(4) in this case. Note that
the corresponding sectorial decomposition occurs at a point $\tau_{+}=[E]\log
t+p_{2}\log q\in H^{2}(X_{+})$, $q,t>0$ such that $t$ is sufficiently small
(in the leftmost picture of Fig. 16, $t\approx 0.0698$, $q\approx 0.698$).
###### Remark 7.35.
We can use Theorem 7.33 to prove Gamma conjecture II [44, Section 4.6] in some
cases. By applying Theorem 7.33 to the case where $Z$ is a (non-stacky) point,
we know that if the Gamma conjecture II holds for a weak-Fano compact toric
stack $\mathfrak{X}_{-}$, then it also holds for a weighted blowup
$\mathfrak{X}_{+}$ of $\mathfrak{X}_{-}$ at a non-stacky torus-fixed point (as
long as $\mathfrak{X}_{+}$ is weak-Fano).
## 8 Conjecture and discussion
### 8.1 General conjecture
In view of our main results (Theorems 5.16, 5.19, 7.25, 7.31, and 7.33), we
conjecture the following phenomena for more general discrepant birational
transformations. Suppose that we have a birational transformation
$\varphi\colon\mathfrak{X}_{+}\dasharrow\mathfrak{X}_{-}$ between smooth (not
necessarily toric) DM stacks which fits into the diagram
$\textstyle{\widehat{\mathfrak{X}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{f_{+}}$$\scriptstyle{f_{-}}$$\textstyle{\mathfrak{X}_{+}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}$$\scriptstyle{\varphi}$$\textstyle{\mathfrak{X}_{-}}$
with $\widehat{\mathfrak{X}}$ smooth and $f_{\pm}$ projective birational
morphisms, such that
$f_{+}^{*}K_{\mathfrak{X}_{+}}-f_{-}^{*}K_{\mathfrak{X}_{-}}$ is an effective
divisor. We assume that the coarse moduli spaces of $\mathfrak{X}_{\pm}$ are
projective, but some of the discussions below can be also adapted to non-
compact cases.
We choose a base point $\tau_{\star,\pm}\in H^{*}_{\rm
CR}(\mathfrak{X}_{\pm};\mathbb{R})$ which is real and sufficiently close to
the large radius limit point.
###### Conjecture 8.1 (formal decomposition).
There exist paths from $\tau_{\star,\pm}$ to $\tau_{\pm}\in H^{*}_{\rm
CR}(\mathfrak{X}_{\pm})$ and a holomorphic map $f$ from a neighbourhood $W$ of
$\tau_{+}$ in $H^{*}_{\rm CR}(\mathfrak{X}_{+})$ to $H^{*}_{\rm
CR}(\mathfrak{X}_{-})$ with $f(\tau_{+})=\tau_{-}$ such that the quantum
D-modules $\operatorname{QDM}^{\rm an}(\mathfrak{X}_{\pm})$ are analytically
continued along these paths, and that we have the decomposition of the quantum
D-modules completed in $z$ $($see (6.2)$)$:
$\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{+})|_{W}\xrightarrow{\cong}f^{*}\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{-})|_{W}\oplus\mathscr{R}.$ (8.1)
Here $\mathscr{R}$ is a locally free $\mathcal{O}_{W}[\\![z]\\!]$-module
equipped with a meromorphic flat connection $\nabla^{\mathscr{R}}$ and a
$z$-sesquilinear pairing $P^{\mathscr{R}}$, and the formal decomposition
respects both the connection and the pairing $($in particular it is orthogonal
with respect to the pairing (2.9)$)$.
Building on the above conjecture, we can also state a conjecture comparing
higher genus Gromov–Witten theories. This involves quantization of the formal
decomposition (8.1). See Section 5.5 for the notation.
###### Conjecture 8.2 (comparison in all genera).
The ancestor potentials $\mathscr{A}_{\pm,\tau}$ of $\mathfrak{X}_{\pm}$ can
be analytically continued along the paths from $\tau_{\star,\pm}$ to
$\tau_{\pm}$ in Conjecture 8.1. There exist a family
$\mathscr{A}^{\prime}_{\tau}\in\operatorname{\mathfrak{AFock}}(V_{\tau},\mathbf{D}_{\tau})$
of tame functions such that
$T_{\mathbf{s}}{\widehat{U}}_{\tau}\mathscr{A}_{+,\tau}=\mathscr{A}_{-,f(\tau)}\otimes\mathscr{A}^{\prime}_{\tau}$
for $\tau\in W$, where
$\mathbf{s}=(-z\phi_{0},\mathbf{D}_{\tau})+U_{\tau}(z\phi_{0})$,
$V_{\tau}\subset\mathscr{R}_{\tau}$ is a $\mathbb{C}$-vector subspace such
that $\mathscr{R}_{\tau}=V_{\tau}[\\![z]\\!]$ and that $P^{\mathscr{R}}$
restricts to the $\mathbb{C}$-valued pairing $V_{\tau}\times
V_{\tau}\to\mathbb{C}$, $\mathbf{D}_{\tau}\in z\mathscr{R}_{\tau}$ and
$U_{\tau}\colon H^{*}_{\rm CR}(\mathfrak{X}_{+})[\\![z]\\!]\cong H^{*}_{\rm
CR}(\mathfrak{X}_{-})[\\![z]\\!]\oplus V_{\tau}[\\![z]\\!]$ is the unitary
isomorphism obtained from (8.1) by restricting to $\tau$ and flipping the sign
of $z$.
In this conjecture we implicitly assume that the action of the operator
$T_{\mathbf{s}}$ on ${\widehat{U}}_{\tau}\mathscr{A}_{+,\tau}$ is well-
defined; this holds if $\mathscr{A}_{+,\tau}$ is rational (see Section 5.5.2).
Note also that the space
$\operatorname{\mathfrak{AFock}}(V_{\tau},\mathbf{D}_{\tau})$ itself depends
only on $\mathscr{R}_{\tau}$ and $\mathbf{D}_{\tau}$ and does not depend on
the choice of $V_{\tau}$, but that $\mathscr{A}^{\prime}_{\tau}$ depends on
the choice of $V_{\tau}$.
Next we state a conjecture relating the analytic lift of the formal
decomposition (8.1) with a semiorthogonal decomposition of the $K$-group.
Recall from (2.11) that the action of $-\nabla_{z^{2}\partial_{z}}$ on
$\operatorname{QDM}^{\rm an}(\mathfrak{X}_{\pm})|_{z=0}$ equals the Euler
multiplication $E\star_{\tau}$. In particular, the formal decomposition (8.1)
implies that $E\star_{\tau}$ on $H_{\rm CR}^{*}(\mathfrak{X}_{+})$ is
conjugate to
$E\star_{f(\tau)}\oplus\big{(}{-}\nabla^{\mathscr{R}}_{z^{2}\partial_{z}}\big{)}$
on $H^{*}_{\rm CR}(\mathfrak{X}_{-})\oplus\mathscr{R}|_{z=0}$.
###### Conjecture 8.3 (analytic lift).
We can arrange $\tau_{\pm}$ and the paths from $\tau_{\star,\pm}$ to
$\tau_{\pm}$ in Conjecture 8.1 so that $($in addition to Conjecture
$\ref{conj:formal})$ the following holds.
* (1)
We have a decomposition
$\big{(}\mathscr{R},\nabla^{\mathscr{R}},P^{\mathscr{R}}\big{)}=\big{(}\mathscr{R}_{1},\nabla^{\mathscr{R}_{1}},P^{\mathscr{R}_{1}}\big{)}\oplus\big{(}\mathscr{R}_{2},\nabla^{\mathscr{R}_{2}},P^{\mathscr{R}_{2}}\big{)}$,
where $\mathscr{R}_{i}$ is a locally free $\mathcal{O}_{W}[\\![z]\\!]$-module
equipped with a flat connection $\nabla^{\mathscr{R}_{i}}$ and a
$z$-sesquilinear pairing $P^{\mathscr{R}_{i}}$. There exist a phase
$\phi\in\mathbb{R}$ and real numbers $l_{2}<l_{1}$ such that
* (a)
all eigenvalues $\mathbf{u}$ of
$\big{(}{-}\nabla^{\mathscr{R}_{1}}_{z^{2}\partial_{z}}\big{)}$ on
$\mathscr{R}_{1}|_{z=0}$ satisfy
$\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}\big{)}>l_{1}$,
* (b)
all eigenvalues $\mathbf{u}$ of
$\big{(}{-}\nabla^{\mathscr{R}_{2}}_{z^{2}\partial_{z}}\big{)}$ on
$\mathscr{R}_{2}|_{z=0}$ satisfy
$\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}\big{)}<l_{2}$ and
* (c)
all eigenvalues $\mathbf{u}$ of $E\star_{f(\tau)}$ on $H^{*}_{\rm
CR}(\mathfrak{X}_{-})$ satisfy
$l_{2}<\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}\big{)}<l_{1}$.
* (2)
Moreover, we have a sector
$I_{\phi}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\in{\widetilde{\mathbb{C}}}\colon|\theta-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$
with some $\epsilon>0$ and an analytic decomposition
$\pi^{*}\operatorname{QDM}^{\rm an}(\mathfrak{X}_{+})\big{|}_{W\times
I_{\phi}}\cong\mathscr{R}^{\rm
an}_{1}\oplus\pi^{*}f^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})\big{|}_{W\times I_{\phi}}\oplus\mathscr{R}^{\rm
an}_{2},$ (8.2)
where $\pi\colon W\times{\widetilde{\mathbb{C}}}\to W\times\mathbb{C}$ is the
oriented real blow-up and $\mathscr{R}^{\rm an}_{i}$ is a locally free
$\mathcal{A}_{W\times I_{\phi}}$-module equipped with a flat connection, such
that $\mathscr{R}_{i}\cong\mathscr{R}^{\rm
an}_{i}\otimes_{\mathcal{A}_{W\times I_{\phi}}}\mathcal{O}_{W}[\\![z]\\!]$,
$i=1,2$ and that the formal decomposition (8.1) is induced by (8.2).
* (3)
Via the $\widehat{\Gamma}$-integral structure for $\mathfrak{X}_{+}$ and
$\mathfrak{X}_{-}$, the decomposition (8.2) is induced by a semiorthogonal
decomposition of the topological $K$-groups:
$K(\mathfrak{X}_{+})\cong K_{1}\oplus K(\mathfrak{X}_{-})\oplus K_{2}$ (8.3)
such that the associated inclusion $K(\mathfrak{X}_{-})\hookrightarrow
K(\mathfrak{X}_{+})$ respects the Euler pairing.
###### Remark 8.4.
We expect that the semiorthogonal decomposition (8.3) arises naturally from
geometry. In our setting, for example, we could hope that there is a
semiorthogonal decomposition of the bounded derived category of
$\mathfrak{X}_{+}$ of the form (see [9, Conjecture 4.3.7]):
$D^{b}(\mathfrak{X}_{+})=\big{\langle}\mathscr{C}_{1},D^{b}(\mathfrak{X}_{-}),\mathscr{C}_{2}\big{\rangle}.$
(8.4)
When $\mathfrak{X}_{\pm}$ are toric stacks arising from the variation of GIT
quotients as in Section 5, Ballard–Favero–Katzarkov [9, Theorem 5.2.1] showed
that such a semiorthogonal decomposition exists (see also [55, 71]). A
semiorthogonal summand of $D^{b}(\mathfrak{X}_{+})$ gives a $K$-motive (see
[52, Section 4]), which in turn defines a direct summand of the topological
$K$-group of $\mathfrak{X}_{+}$242424I thank Sergey Galkin for this remark and
pointing to the reference [52].. We expect that (8.3) arises from (8.4) in
this way (cf. [76] for the discussion on Hochschild homology). On the other
hand, in view of the deformation invariance of Gromov–Witten invariants, it is
more natural to state conjectures in terms of topological $K$-groups instead
of derived categories.
### 8.2 Functoriality and Riemann–Hilbert problem
We discuss how to recover the quantum cohomology of $\mathfrak{X}_{-}$ from
the quantum cohomology of $\mathfrak{X}_{+}$, assuming Conjecture 8.3. This
involves solving a Riemann–Hilbert boundary value problem.
###### Proposition 8.5.
Assume that the quantum D-modules $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{\pm})$ are of exponential type. Suppose that we are given
the analytic continuation of the quantum D-module $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})$ to a neighbourhood $W$ of $\tau_{+}\in H^{*}_{\rm
CR}(\mathfrak{X}_{+})$ and its formal decomposition
$\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{+})|_{W}=\mathscr{Q}\oplus\mathscr{R}$
corresponding to the decomposition (8.1) for which Conjecture 8.3 holds. Then
we can recover the map $f$ in Conjecture 8.3 and the quantum D-module
$f^{*}\operatorname{QDM}^{\rm an}(\mathfrak{X}_{-})$ of $\mathfrak{X}_{-}$
$($trivialized as a vector bundle over $W\times\mathbb{C})$ together with an
isomorphism $f^{*}\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{-})|_{W}\cong\mathscr{Q}$.
Before giving a proof of this proposition, we review the exponential type
assumption (see [70, Definition 2.12]). This was originally introduced by
Hertling–Sevenheck [57, Definition 8.1] under the name “require no
ramification”. We also review a mutation system of Sanda–Shamoto [101,
Definition 2.30].
The quantum D-module of $\mathfrak{X}=\mathfrak{X}_{\pm}$ is of exponential
type if for each $\tau\in H^{*}_{\rm CR}(\mathfrak{X})$, we have a formal
decomposition of the quantum D-module $\operatorname{QDM}^{\rm
an}(\mathfrak{X})_{\tau}:=\operatorname{QDM}^{\rm
an}(\mathfrak{X})|_{\\{\tau\\}\times\mathbb{C}}$ (see [57, Lemma 8.2]):
$\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X})_{\tau}\cong\bigoplus_{\mathbf{u}\in\operatorname{Spec}(E\star_{\tau})}\big{(}e^{\mathbf{u}/z}\otimes\mathcal{F}_{\mathbf{u}}\big{)}\otimes_{\mathbb{C}\\{z\\}}\mathbb{C}[\\![z]\\!],$
(8.5)
where $\operatorname{Spec}(E\star_{\tau})$ denotes the set of (mutually
distinct) eigenvalues of $E\star_{\tau}$, $e^{\mathbf{u}/z}$ denotes the rank
one connection $(\mathbb{C}\\{z\\},d+d(\mathbf{u}/z))$ and
$\mathcal{F}_{\mathbf{u}}$ is a free $\mathbb{C}\\{z\\}$-module equipped with
a regular singular meromorphic connection. The decomposition is
(automatically) orthogonal with respect to the pairing $P$, and induces a
$z$-sesquilinear pairing $P_{\mathbf{u}}$ on each $\mathcal{F}_{\mathbf{u}}$;
$\mathcal{F}_{\mathbf{u}}$ is called the _regular singular piece_ in [57,
Lemma 8.2]. Moreover, the Hukuhara–Turrittin theorem (see [57, Lemma 8.3] in
this context) implies that, for each phase $\phi$ admissible for
$\operatorname{Spec}(E\star_{\tau})$, the formal decomposition admits a unique
analytic lift over the sector
$I_{\phi}=\big{\\{}\big{(}r,e^{\boldsymbol{\mathrm{i}}\theta}\big{)}\in{\widetilde{\mathbb{C}}}\colon|\theta-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$
(for some $\epsilon>0$)
$\pi^{*}\left(\operatorname{QDM}^{\rm
an}(\mathfrak{X})_{\tau}\right)\big{|}_{I_{\phi}}\cong\bigoplus_{\mathbf{u}\in\operatorname{Spec}(E\star_{\tau})}\pi^{*}(e^{\mathbf{u}/z}\otimes\mathcal{F}_{\mathbf{u}})\big{|}_{I_{\phi}},$
(8.6)
where $\pi\colon{\widetilde{\mathbb{C}}}\to\mathbb{C}$ is the oriented real
blowup. In Section 6.1, we discussed in details the special case of these
decompositions where the quantum cohomology is semisimple.
The analytic germ at $z=0$ of the quantum D-module $\operatorname{QDM}^{\rm
an}(\mathfrak{X})_{\tau}$ can be determined by the formal decomposition (8.5)
and the Stokes data. Sanda–Shamoto [101, Definition 2.30] encoded the Stokes
data in linear-algebraic data which they called a _mutation system_. This can
be viewed as a generalization of a marked reflection system in Section 6.2.
Let $V$ denote the space of flat sections of $\operatorname{QDM}^{\rm
an}(\mathfrak{X})_{\tau}$ over the sector
$I_{\phi}^{\times}=\big{\\{}z\in\mathbb{C}^{\times}\colon|\arg
z-\phi|<\frac{\pi}{2}+\epsilon\big{\\}}$. We define a pairing $[\cdot,\cdot)$
on $V$ by (cf. Section 6.2)
$[s_{1},s_{2})=P\big{(}s_{1}\big{(}e^{-\pi\boldsymbol{\mathrm{i}}}z\big{)},s_{2}(z)\big{)},$
where $s_{1}\big{(}e^{-\pi\boldsymbol{\mathrm{i}}}z\big{)}$ denotes the
analytic continuation of $s_{1}(z)$ along the path $[0,\pi]\ni\theta\mapsto
e^{-\boldsymbol{\mathrm{i}}\theta}z$. The mutation system (see [101,
Proposition 2.5, Section 2.7]) for $\operatorname{QDM}^{\rm
an}(\mathfrak{X})_{\tau}$ associated with the admissible phase $\phi$ is given
by the data252525We omitted the data of a labelling $\tau$ in [101, Definition
2.30] since it can be recovered from the phase $\phi$.
* •
the tuple $(V,[\cdot,\cdot))$ of a vector space and a pairing;
* •
the decomposition
$V\cong\bigoplus\limits_{\mathbf{u}\in\operatorname{Spec}(E\star_{\tau})}V_{\mathbf{u}}$
induced by the analytic lift (8.6), where $V_{\mathbf{u}}$ is the space of
flat sections of $e^{\mathbf{u}/z}\otimes\mathcal{F}_{\mathbf{u}}$ over the
sector $I_{\phi}^{\times}$
satisfying the semiorthogonality:
$[v_{1},v_{2})=0\qquad\text{if $v_{1}\in V_{\mathbf{u}_{1}}$, $v_{2}\in
V_{\mathbf{u}_{2}}$ and
$\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{1}\big{)}<\Im\big{(}e^{-\boldsymbol{\mathrm{i}}\phi}\mathbf{u}_{2}\big{)}$}.$
The pairing $[\cdot,\cdot)$ restricted to $V_{\mathbf{u}}$ is induced by the
pairing $P_{\mathbf{u}}$ on $\mathcal{F}_{\mathbf{u}}$ [57, Lemma 8.4]. It was
shown [101, Proposition 2.5, Section 2.5] that a mutation system is equivalent
to Stokes data (or a Stokes filtered local system) equipped with a pairing. By
the Riemann–Hilbert correspondence (see [101, Section 2.7] in this context),
the formal structure (8.5) and the mutation system together recover the
analytic germ at $z=0$ of $\operatorname{QDM}(\mathfrak{X})_{\tau}$.
###### Proof of Proposition 8.5.
Fix $\tau\in W$. We may assume that $\phi$ in Conjecture 8.3 is admissible for
the set $\operatorname{Spec}(E\star_{\tau})$ of eigenvalues of $E\star_{\tau}$
on $H^{*}_{\rm CR}(\mathfrak{X}_{+})$, by perturbing $\phi$ if necessary.
Under the assumption that $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})_{\tau}$ is of exponential type, the summands
$\mathscr{Q},\mathscr{R}_{1},\mathscr{R}_{2}$ of
$\overline{\operatorname{QDM}^{\rm an}}(\mathfrak{X}_{+})_{\tau}$ admit
decompositions similar to (8.5). We write $\operatorname{Spec}(\mathscr{Q})$
(resp. $\operatorname{Spec}(\mathscr{R}_{i})$) for the set of the eigenvalues
of the operators $-\nabla_{z^{2}\partial_{z}}$ on $\mathscr{Q}|_{z=0}$ (resp.
on $\mathscr{R}_{i}|_{z=0}$). By Conjecture 8.3(1), the sets
$\operatorname{Spec}(\mathscr{Q})$, $\operatorname{Spec}(\mathscr{R}_{1})$,
$\operatorname{Spec}(\mathscr{R}_{2})$ are mutually distinct; therefore
$\mathscr{Q}$, $\mathscr{R}_{1}$, $\mathscr{R}_{2}$ are partial sums of the
right-hand side of the formal decomposition (8.5) for
$\mathfrak{X}=\mathfrak{X}_{+}$. Writing
$V\cong\bigoplus\limits_{\mathbf{u}\in\operatorname{Spec}(E\star_{\tau})}V_{\mathbf{u}}$
for the mutation system of $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{+})_{\tau}$, we can decompose $V$ as
$V\cong V_{\mathscr{R}_{1}}\oplus V_{\mathscr{Q}}\oplus V_{\mathscr{R}_{2}}$
(8.7)
with
$V_{\mathscr{Q}}=\bigoplus\limits_{\mathbf{u}\in\operatorname{Spec}(\mathscr{Q})}V_{\mathbf{u}}$,
$V_{\mathscr{R}_{i}}=\bigoplus\limits_{\mathbf{u}\in\operatorname{Spec}(\mathscr{R}_{i})}V_{\mathbf{u}}$.
By Conjecture 8.3(2), the decomposition
$V_{\mathscr{Q}}=\bigoplus_{\mathbf{u}\in\operatorname{Spec}(\mathscr{Q})}V_{\mathbf{u}}$
gives the mutation system for $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})_{f(\tau)}$. The $\widehat{\Gamma}$-integral structure
identifies $(V,[\cdot,\cdot))$ with
$(K(\mathfrak{X}_{+})\otimes\mathbb{C},\chi)$ and the decomposition (8.7) is
identified with that (8.3) of $K(\mathfrak{X}_{+})$ by Conjecture 8.3(3). Then
we obtain an isomorphism
$\Phi\colon V_{\mathscr{Q}}\cong K(\mathfrak{X}_{-})\otimes\mathbb{C}.$ (8.8)
Since the inclusion $K(\mathfrak{X}_{-})\to K(\mathfrak{X}_{+})$ respects the
Euler pairing, we see that the restriction of the pairing $[\cdot,\cdot)$ on
$V$ to $V_{\mathscr{Q}}$ coincides with the pairing on $V_{\mathscr{Q}}$ as a
mutation system for $\operatorname{QDM}^{\rm an}(\mathfrak{X}_{-})_{f(\tau)}$.
Therefore the mutation system for $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})_{f(\tau)}$ can be recovered as a summand of the mutation
system for $\operatorname{QDM}^{\rm an}(\mathfrak{X}_{+})_{\tau}$. Thus we
recover the analytic germ at $z=0$ of $\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})_{f(\tau)}$ by the Riemann–Hilbert correspondence. We
write $\mathscr{Q}^{\rm an}$ for the germ so reconstructed.
We extend $\mathscr{Q}^{\rm an}$ to the trivial vector bundle
$\operatorname{QDM}^{\rm an}(\mathfrak{X}_{-})_{f(\tau)}$ over
$\mathbb{C}_{z}$ and construct the fundamental solution $L(f(\tau),z)$ for
$\mathfrak{X}_{-}$ (see Section 2.4) and the map $f$. Consider the trivial
bundle
$Q^{(\infty)}:=H^{*}(\mathfrak{X}_{-})\times\big{(}\mathbb{P}^{1}\setminus\\{0\\}\big{)}\to\big{(}\mathbb{P}^{1}\setminus\\{0\\}\big{)}$
equipped with the meromorphic connection
$\nabla^{(\infty)}_{z\partial_{z}}=z\frac{\partial}{\partial
z}-\frac{c_{1}(\mathfrak{X}_{-})\cup}{z}+\mu.$
This has $z^{-\mu}z^{c_{1}(\mathfrak{X})}$ as a fundamental solution and the
facts recalled in Section 2.4 imply that the quantum connection on
$\\{f(\tau)\\}\times\mathbb{C}_{z}$ is gauge equivalent to $\nabla^{(\infty)}$
via the gauge transformation by $L(f(\tau),z)$ (which is regular and the
identity at $z=\infty$). We glue this trivial bundle $Q^{(\infty)}$ with the
germ $\mathscr{Q}^{\rm an}$ of vector bundle at $z=0$ to get a vector bundle
$\widehat{Q}$ over $\mathbb{P}^{1}$. The gluing is given by sending a flat
section $s\in V_{\mathscr{Q}}$ over the sector $I_{\phi}^{\times}$ to the flat
section for $\nabla^{(\infty)}$:
$(2\pi)^{-n/2}z^{-\mu}z^{c_{1}(\mathfrak{X}_{-})}\big{(}\widehat{\Gamma}_{\mathfrak{X}_{-}}\cdot(2\pi\boldsymbol{\mathrm{i}})^{\deg_{0}/2}\operatorname{inv}^{*}\widetilde{\operatorname{ch}}(\Phi(s))\big{)}$
with $n=\dim\mathfrak{X}_{-}$, where $\Phi$ is the isomorphism in (8.8). In
view of the definition of the $\widehat{\Gamma}$-integral structure, this
glued bundle $\widehat{Q}$ must be isomorphic to the trivial extension of
$\operatorname{QDM}^{\rm an}(\mathfrak{X}_{-})_{f(\tau)}$ to $\mathbb{P}^{1}$
(with respect to the given trivialization). In particular, $\widehat{Q}$ is
trivial, and the identification $Q^{(\infty)}|_{\infty}\cong H^{*}_{\rm
CR}(\mathfrak{X}_{-})$ at infinity induces a global trivialization
$\widehat{Q}\cong H^{*}_{\rm CR}(\mathfrak{X}_{-})\times\mathbb{P}^{1}$. The
trivial bundle $\widehat{Q}$ equipped with a meromorphic connection gives the
quantum D-module $\operatorname{QDM}^{\rm an}(\mathfrak{X}_{-})_{f(\tau)}$.
Moreover, the isomorphism $\widehat{Q}|_{\mathbb{P}^{1}\setminus\\{0\\}}\cong
Q^{(\infty)}$ written in the respective trivializations gives the fundamental
solution $L(f(\tau),z)$ as an $\operatorname{End}(H^{*}_{\rm
CR}(\mathfrak{X}_{-}))$-valued function. Varying $\tau$ in $W$, we recover the
full quantum connection for $f^{*}\operatorname{QDM}^{\rm
an}(\mathfrak{X}_{-})$ from $L(f(\tau),z)$. We also recover $f(\tau)$ from the
expansion
$L(f(\tau),z)^{-1}1=1+\frac{f(\tau)}{z}+O\big{(}z^{-2}\big{)}.$
The proposition is proved. ∎
###### Remark 8.6.
Choosing fundamental solutions for regular singular pieces, we can formulate
the above reconstruction in terms of a Riemann–Hilbert boundary value problem
for the triple $(Y,Y^{-},L)$ of fundamental solutions, where $Y$ is a
fundamental solution on the sector $I_{\phi}^{\times}$ with prescribed
asymptotics, $Y^{-}$ is a fundamental solution on the opposite sector
$I_{\phi+\pi}^{\times}$ with prescribed asymptotics and $L$ is the fundamental
solution around $z=\infty$. In the semisimple case, this was explained in
details by Dubrovin [40, Lecture 4] and the method there applies to the
situation of our main Theorem 7.33. In the semisimple case, the formal
structure (8.5) is determined only by the eigenvalues of $E\star_{\tau}$, and
therefore the asymptotic basis (or, if any, the corresponding exceptional
collection) reconstructs the quantum D-module.
###### Remark 8.7.
When a candidate formal decomposition $\overline{\operatorname{QDM}^{\rm
an}}(\mathfrak{X}_{+})_{\tau}\cong\mathscr{R}_{1}\oplus\mathscr{Q}\oplus\mathscr{R}_{2}$
and a decomposition (8.3) of the $K$-group (corresponding to the analytic lift
via the $\widehat{\Gamma}$-integral structure) are given, what is non-trivial
in the above reconstruction is the triviality of the glued bundle
$\widehat{Q}$.
###### Remark 8.8.
The fundamental solution $L(\tau,z)$ in Section 2.4 is called a _calibration_
in the theory of Frobenius manifolds. A calibration of a Frobenius manifold is
not unique in general and its ambiguity was discussed in [40, Lemma 4.1]. The
above procedure recovers, not only (the germ of) the quantum cohomology
Frobenius manifold of $\mathfrak{X}_{-}$ (if $f$ is submersive), but also its
calibration.262626I thank Vasily Golyshev for asking me a question which led
me to this observation. Since the $\widehat{\Gamma}$-integral structure was
normalized at the large radius limit point, it somehow ‘remembers’ the limit
point.
###### Remark 8.9.
Conjecture 8.3 is closely related to Dubrovin’s conjecture [39, Conjecture
4.2.2] (or Gamma conjecture [44, Section 4.6] or Dubrovin-type conjecture
[101, Definition 5.2]). It can be viewed as a relative version of these
conjectures.
## Appendix A The Brieskorn module in the weak Fano case
We discuss the coherence and the locally-freeness of the equivariant Brieskorn
module $\operatorname{Bri_{\mathbb{T}}}(F)$ mirror to the small quantum
cohomology of a weak-Fano smooth toric DM stack $\mathfrak{X}$, near the large
radius limit point $0_{\mathbf{\Sigma}}$. We stated this in Proposition 6.15.
We can describe the Brieskorn module as a certain variant of the GKZ system
(see [27, Section 5.2]). The coherence of the relevant GKZ system near the
large radius limit point has been discussed by the author [62, Proposition
4.4] (on a neighbourhood of $0_{\mathbf{\Sigma}}$ with the logarithmic locus
deleted), Reichelt–Sevenheck [91, Theorem 3.7] (on a neighbourhood of
$0_{\mathbf{\Sigma}}$ for toric manifolds) and Mann–Reichelt [81, Theorem
4.10] (similarly for toric orbifolds). We adapt the argument of [81] to our
Brieskorn module with minor modifications. Note that we impose only minimal
assumptions on $\mathfrak{X}$ and $S$; we do not assume compactness of
$\mathfrak{X}$ nor a generation condition for $S$. We also deal with the
equivariant case. In this sense our result is slightly more general than [81].
Let $\mathfrak{X}=\mathfrak{X}_{\mathbf{\Sigma}}$ be a semiprojective smooth
toric DM stack from Section 3.1.1 which is weak Fano, i.e.,
$-K_{\mathfrak{X}}$ is nef. Let $\Delta\subset\mathbf{N}_{\mathbb{R}}$ denote
the fan polytope, that is, the union of simplices spanned by
$\\{0\\}\cup\\{b\in R(\mathbf{\Sigma})\colon\overline{b}\in\sigma\\}$ over all
maximal cones $\sigma$ of $\mathbf{\Sigma}$. The weak Fano assumption implies
that $\Delta$ is a convex polytope. We assume that the set $S$ (which is used
to construct the LG mirror) is contained in the fan polytope:
$S\subset\mathbf{N}\cap\Delta.$ (A.1)
This means that the base space $\mathcal{M}$ of the LG model corresponds to
the _small quantum cohomology locus_ of $\mathfrak{X}$ in Section 6.3. The
definition of the Brieskorn module on the affine chart
$\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$
does not rely on Assumption 3.1 and we do not need this assumption in the
following discussion.
The equivariant Brieskorn module $\operatorname{Bri_{\mathbb{T}}}(F)$ on the
affine chart
$\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$ is
given by the module
$\mathsf{G}:=\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}][z].$
Recall from Section 4.1 that, by choosing a splitting
$\mathbb{L}_{\mathbb{C}}^{\star}\to\big{(}\mathbb{C}^{S}\big{)}^{\star}$,
$\xi\mapsto{\hat{\xi}}$ of (3.4), $\mathsf{G}$ has the structure of a module
over the ring of differential operators:
$\mathsf{D}:=R_{\mathbb{T}}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}][z]\left\langle
z\xi q\frac{\partial}{\partial
q}\colon\xi\in\mathbb{L}^{\star}_{\mathbb{C}}\right\rangle,$
where $\chi_{i}\in R_{\mathbb{T}}$ acts by $zx_{i}\frac{\partial}{\partial
x_{i}}+x_{i}\frac{\partial F}{\partial x_{i}}$ and $z\xi
q\frac{\partial}{\partial q}$ acts by $z{\hat{\xi}}u\frac{\partial}{\partial
u}+{\hat{\xi}}u\frac{\partial F}{\partial u}$. For convenience, we choose co-
ordinates
$q_{1},\dots,q_{m}\in\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})]$
corresponding to a $\mathbb{Z}$-basis of
$\boldsymbol{\Lambda}(\mathbf{\Sigma})$ and write
$\theta_{i}=q_{i}\frac{\partial}{\partial q_{i}}$; then we have
$\mathsf{D}=R_{\mathbb{T}}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}][z]\langle
z\theta_{1},\dots,z\theta_{m}\rangle.$
Let $\mathscr{G}$ and $\mathscr{D}$ denote the sheaves on
$B:=\operatorname{Spec}(R_{\mathbb{T}}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}][z])=\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}])\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$
corresponding to $\mathsf{G}$ and $\mathsf{D}$ respectively. The main result
in the appendix is the following.
###### Proposition A.1.
Suppose, as above, that $\mathfrak{X}$ is a weak Fano semiprojective toric
stack and that $S$ satisfies (A.1). There exists a Zariski open subset $U$ of
$\operatorname{Spec}(\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}])$
containing the large radius limit point $0_{\mathbf{\Sigma}}$ such that
$\mathscr{G}|_{U\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}}$ is a
locally free coherent
$\mathcal{O}_{U\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}}$-module
of rank $\dim H^{*}_{\rm CR}(\mathfrak{X})$.
### A.1 Generators and relations
By Remark 3.17, the equivariant Brieskorn module $\mathsf{G}$ is generated by
$w_{v}:=u^{(\Psi^{\mathbf{\Sigma}}(\overline{v}),v)}$ with
$v\in\mathbf{N}\cap\Pi$ as a
$\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}][z]$-module. Relations
among these generators as a $\mathsf{D}$-module are given as follows.
###### Lemma A.2.
For $b\in S$, we write $e_{b}^{\star}=\widehat{D}_{b}+\chi(b)$ with
$\chi(b)\in\mathbf{M}$ $($recall that
$D_{b}=D(e_{b}^{\star})\in\mathbb{L}^{\star})$. We have the following relation
in $\mathsf{G}$:
$\displaystyle\left(\prod_{b\in
S}\prod_{c=0}^{\nu_{b}-1}\left(zD_{b}q\frac{\partial}{\partial
q}+\chi(b)-\big{(}\Psi^{\mathbf{\Sigma}}_{b}(v)+c\big{)}z\right)\right)w_{v}$
$\displaystyle\qquad{}=\left(\prod_{b\in
S}u_{b}^{\nu_{b}}\right)w_{v}=q^{\Psi(v)+\sum_{b\in
S}\nu_{b}e_{b}-\Psi(v+\sum_{b\in S}\nu_{b}b)}w_{v+\sum_{b\in S}\nu_{b}b}$
for every $(\nu_{b})_{b\in S}\in(\mathbb{Z}_{\geq 0})^{S}$ and
$v\in\mathbf{N}\cap\Pi$.
###### Proof.
By definition, $zD_{b}q\frac{\partial}{\partial q}+\chi(b)$ acts on
$\mathsf{G}$ by $zu_{b}\frac{\partial}{\partial u_{b}}+u_{b}$. The first
equality follows from this and $u_{b}\frac{\partial}{\partial
u_{b}}w_{v}=\Psi_{b}(v)w_{v}$. The second equality is just by definition, see
Section 3.5. ∎
When $b\in R(\mathbf{\Sigma})$ and $v\in\mathbf{N}\cap\Pi$ lie in the same
cone of $\Sigma$, we have a relation
$w_{v+b}=\left(zD_{b}q\frac{\partial}{\partial
q}+\chi(b)-z\Psi_{b}^{\mathbf{\Sigma}}(v)\right)w_{v}$
in $\mathsf{G}$ by Lemma A.2. From this we can see that $\mathsf{G}$ is
generated by finitely many $w_{v}$ as a $\mathsf{D}$-module. For example, the
set $\\{w_{v}\colon v\in\operatorname{Box}(\mathbf{\Sigma})\\}$ generates
$\mathsf{G}$. By Lemma A.2, $w_{v}$ is annihilated by
$P_{v,\lambda}\in\mathsf{D}$
$\displaystyle P_{v,\lambda}:=\prod_{b\in
S\colon\lambda_{b}>0}\prod_{c=0}^{\lambda_{b}-1}\left(zD_{b}q\frac{\partial}{\partial
q}+\chi(b)-\big{(}\Psi^{\mathbf{\Sigma}}_{b}(v)+c\big{)}z\right)$
$\displaystyle\hphantom{P_{v,\lambda}:=}{}-q^{\lambda}\prod_{b\in
S\colon\lambda_{b}<0}\prod_{c=0}^{-\lambda_{b}-1}\left(zD_{b}q\frac{\partial}{\partial
q}+\chi(b)-\big{(}\Psi^{\mathbf{\Sigma}}_{b}(v)+c\big{)}z\right)$ (A.2)
for any
$\lambda\in\mathbb{L}\cap\operatorname{\widehat{NE}}(\mathfrak{X}_{\mathbf{\Sigma}})\subset\mathbb{Z}^{S}$,
cf. [27, Section 5.1].
### A.2 Characteristic variety and coherence
Define an increasing filtration $\mathcal{F}_{l}(\mathscr{D})$ of
$\mathscr{D}$ by the rank of differential operators, i.e.,
$\mathcal{F}_{l}(\mathscr{D})$ consists of differential operators of the form
$\sum_{k_{1}+\cdots+k_{m}\leq
l}a_{k}(q,\chi,z)(z\theta_{1})^{k_{1}}\cdots(z\theta_{m})^{k_{m}}.$
Choose generators $w_{v_{1}},\dots,w_{v_{k}}$ of $\mathsf{G}$ as a
$\mathsf{D}$-module and introduce a filtration on $\mathscr{G}$ by
$\mathcal{F}_{l}(\mathscr{G}):=\sum_{i=1}^{k}\mathcal{F}_{l}(\mathscr{D})w_{v_{i}}.$
An easy argument shows that if
$\operatorname{gr}_{\mathcal{F}}(\mathscr{G})|_{V}$ is finitely generated as
an $\mathcal{O}_{V}$-module for an open set $V\subset B$, then
$\mathscr{G}|_{V}$ is also finitely generated as an $\mathcal{O}_{V}$-module.
We shall show that $\operatorname{gr}_{\mathcal{F}}(\mathscr{G})$ is finitely
generated on a neighbourhood of
$\\{0_{\mathbf{\Sigma}}\\}\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$.
The associated graded module $\operatorname{gr}_{\mathcal{F}}(\mathscr{G})$ is
a $\operatorname{gr}_{\mathcal{F}}(\mathscr{D})$-module generated by
$w_{v_{1}},\dots,w_{v_{k}}$. We have
$\operatorname{gr}_{\mathcal{F}}(\mathscr{D})=\mathcal{O}_{B}[\xi_{1},\dots,\xi_{m}]$,
where $\xi_{i}$ denotes the image of
$z\theta_{i}\in\mathcal{F}_{1}(\mathscr{D})$. The _characteristic variety_
$\operatorname{Ch}(\mathscr{G})$ of $\mathscr{G}$ is defined to be the support
of $\operatorname{gr}_{\mathcal{F}}(\mathscr{G})$ as an
$\mathcal{O}_{B}[\xi_{1},\dots,\xi_{m}]$-module. It is a closed subset of
$B\times\mathbb{C}^{m}$ invariant under the dilation
$(\xi_{1},\dots,\xi_{m})\mapsto(\lambda\xi_{1},\dots,\lambda\xi_{m})$ with
$\lambda\in\mathbb{C}^{\times}$. Then
$\operatorname{gr}_{\mathcal{F}}(\mathscr{G})|_{V}$ is a finitely generated
$\mathcal{O}_{V}$-module over the following set $V$:
$V=\\{x\in
B\colon(x,\xi)\in\operatorname{Ch}(\mathscr{G})\Longrightarrow\xi=0\\}.$ (A.3)
Note that $\operatorname{Ch}(\mathscr{G})$ induces a closed subset $C\subset
B\times\mathbb{P}^{m-1}$ and $V$ is the complement of $\pi(C)$, where
$\pi\colon B\times\mathbb{P}^{m-1}\to B$ is the projection; thus $V$ is
Zariski-open.
For a differential operator
$a\in\mathcal{F}_{l}(\mathscr{D})\setminus\mathcal{F}_{l-1}(\mathscr{D})$, its
_principal symbol_ $\sigma(a)$ is the image of $a$ in
$\operatorname{gr}_{\mathcal{F}}(\mathscr{D})$; explicitly
$\displaystyle\sigma(a):=\sum_{k_{1}+\cdots+k_{m}=l}a_{k}(q,\chi,z)\xi_{1}^{k_{1}}\cdots\xi_{m}^{k_{m}}\qquad\text{if
$a=\sum\limits_{k_{1}+\dots+k_{m}\leq
l}a_{k}(q,\chi,z)(z\theta_{1})^{k_{1}}\cdots(z\theta_{m})^{k_{m}}$.}$
The principal symbol of the relation $P_{v,\lambda}$ in (A.2) is given by
$\sigma(P_{v,\lambda})=\begin{cases}\displaystyle\prod_{b\in
S\colon\lambda_{b}>0}D_{b}(\xi)^{\lambda_{b}}-q^{\lambda}\prod_{b\in
S\colon\lambda_{b}<0}D_{b}(\xi)^{-\lambda_{b}}&\displaystyle\text{if}\
\sum\limits_{b\in S}\lambda_{b}=0,\\\ \displaystyle\prod_{b\in
S\colon\lambda_{b}>0}D_{b}(\xi)^{\lambda_{b}}&\displaystyle\text{if}\
\sum\limits_{b\in S}\lambda_{b}>0,\\\ \displaystyle-q^{\lambda}\prod_{b\in
S\colon\lambda_{b}<0}D_{b}(\xi)^{-\lambda_{b}}&\displaystyle\text{if}\
\sum\limits_{b\in S}\lambda_{b}<0,\end{cases}$
where $D_{b}(\xi):=\sigma\big{(}zD_{b}q\frac{\partial}{\partial q}\big{)}$ is
a linear form in $\xi_{1},\dots,\xi_{m}$. Because $\sigma(P_{v,\lambda})$ is
independent of $v$, it is an annihilator of
$\operatorname{gr}_{\mathcal{F}}(\mathscr{G})$. Therefore
$\operatorname{Ch}(\mathscr{G})$ is contained in the closed subset of
$B\times\mathbb{C}^{m}$ defined by $\sigma(P_{v,\lambda})=0$ for all
$\lambda\in\mathbb{L}\cap\operatorname{\widehat{NE}}(\mathfrak{X})$.
###### Lemma A.3.
There exists a Zariski-open subset $U$ of
$\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$
containing $0_{\mathbf{\Sigma}}$ such that
$U\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$ is contained in the
locus $V$ in (A.3).
###### Proof.
Note that $\sigma(P_{v,\lambda})$ does not depend on
$(\chi,z)\in\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$. Therefore it
suffices to show that $\xi=0$ if $\xi\in\mathbb{C}^{m}$ satisfies
$\sigma(P_{v,\lambda})\big{|}_{q=0_{\mathbf{\Sigma}}}=0\qquad\text{for all
$\lambda\in\mathbb{L}\cap\operatorname{\widehat{NE}}(\mathfrak{X})$.}$ (A.4)
Suppose that $\xi\in\mathbb{C}^{m}$ satisfies (A.4). We first show that there
exists a cone $\sigma\in\Sigma$ such that $\\{b\in S\colon D_{b}(\xi)\neq
0\\}=R(\mathbf{\Sigma})\cap\sigma$. Let $\\{b_{1},\dots,b_{s}\\}$ be the set
of $b\in S$ such that $D_{b}(\xi)\neq 0$. The relative interior of the convex
hull of $\\{b_{1},\dots,b_{s}\\}$ intersects with the relative interior of
some cone $\sigma$ of $\Sigma$. Hence we get a relation of the form
$\sum_{i=1}^{s}c_{i}\overline{b}_{i}-\sum_{b\in
R(\mathbf{\Sigma})\cap\sigma}f_{b}\overline{b}=0$
for some $c_{i}>0$ satisfying $\sum\limits_{i=1}^{s}c_{i}=1$ and some
$f_{b}>0$. The convexity of $\Delta$ together with (A.1) implies that
$\sum\limits_{b\in R(\mathbf{\Sigma})\cap\sigma}f_{b}\leq 1$. We may further
assume that $c_{i}$ and $f_{b}$ are rational numbers. Then for some positive
integer $l$,
$\lambda:=\sum_{i=1}^{s}lc_{i}e_{b_{i}}-\sum_{b\in
R(\mathbf{\Sigma})\cap\sigma}lf_{b}e_{b}\in\mathbb{Z}^{S}$
belong to $\mathbb{L}\cap\operatorname{\widehat{NE}}(\mathfrak{X})$ (recall
the definition of $\operatorname{\widehat{NE}}(\mathfrak{X})$ around (3.14)).
Note that
$\sum\limits_{b\in
S}\lambda_{b}=l\left(\sum\limits_{i=1}^{s}c_{i}-\sum\limits_{b\in
R(\mathbf{\Sigma})\cap\sigma}f_{b}\right)\geq 0.$
Therefore, if $\lambda\neq 0$, we have the relation
$0=\sigma(P_{v,\lambda})\big{|}_{q=0_{\mathbf{\Sigma}}}=\prod_{i=1}^{s}D_{b_{i}}(\xi)^{lc_{i}}.$
This contradicts the fact that $D_{b_{1}}(\xi)\neq 0,\dots,D_{b_{s}}(\xi)\neq
0$. Hence $\lambda=0$ and we conclude that
$\\{b_{1},\dots,b_{s}\\}=R(\mathbf{\Sigma})\cap\sigma$.
Now we have $D_{b}(\xi)=0$ for all $b\notin R(\mathbf{\Sigma})\cap\sigma$.
Since $\\{D_{b}\in\mathbb{L}_{\mathbb{C}}^{\star}\colon b\notin
R(\Sigma)\cap\sigma\\}$ spans $\mathbb{L}^{\star}_{\mathbb{C}}$, we have
$\xi=0$. The lemma is proved. ∎
###### Corollary A.4.
There exists a Zariski-open neighbourhood $U$ of $0_{\mathbf{\Sigma}}$ in
$\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$
such that
$\mathscr{G}|_{U\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}}$ is a
coherent
$\mathcal{O}_{U\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}}$-module.
### A.3 Locally freeness and rank
We complete the proof of Proposition A.1. Recall from Theorem 4.8 that the
completed equivariant Brieskorn module is isomorphic to the quantum D-module
of $\mathfrak{X}$. Thus we have
$\mathsf{G}/\mathfrak{m}_{\mathbf{\Sigma}}\mathsf{G}\cong\widehat{\mathsf{G}}/\mathfrak{m}_{\mathbf{\Sigma}}\widehat{\mathsf{G}}\cong
H^{*}_{{\rm CR},\mathbb{T}}(\mathfrak{X})[z],$
where
$\mathfrak{m}_{\mathbf{\Sigma}}\subset\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$
denotes the maximal ideal corresponding to $0_{\mathbf{\Sigma}}$ and
$\widehat{\mathsf{G}}$ denotes the $\mathfrak{m}_{\mathbf{\Sigma}}$-adic
completion as discussed in Section 4.2. This implies that the restriction
$\mathscr{G}|_{\\{0_{\mathbf{\Sigma}}\\}\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}}$
is free of rank $\dim H^{*}_{\rm CR}(\mathfrak{X})$. Hence by coherence,
$\mathscr{G}$ is generated by $\dim H^{*}_{\rm CR}(\mathfrak{X})$ many
sections in a neighbourhood of
$\\{0_{\mathbf{\Sigma}}\\}\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$.
On the other hand, the localization map “$\operatorname{Loc}$” appearing in
[27, Definition 4.17] gives $\dim H^{*}_{\rm CR}(\mathfrak{X})$ many linearly
independent solutions of $\mathscr{G}$ for a generic
$(\chi,z)\in\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$; the weak Fano
condition ensures the convergence of the power series solution
$\operatorname{Loc}$. This implies that $\mathscr{G}$ is locally free of rank
$\dim H_{\rm CR}^{*}(\mathfrak{X})$ in a neighbourhood of
$\\{0_{\mathbf{\Sigma}}\\}\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$.
To see that $\mathscr{G}$ is locally free on an open set of the form
$U\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$ (for some open set
$U\subset\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$
containing $0_{\mathbf{\Sigma}}$), we use the grading operator (4.1). The
grading operator makes $\mathscr{G}$ a $\mathbb{C}^{\times}$-equivariant
sheaf; the induced $\mathbb{C}^{\times}$-action on the base is given by the
same grading operator on
$\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}][z]$ and the weight one
$\mathbb{C}^{\times}$-action on $\operatorname{Lie}\mathbb{T}$.
###### Lemma A.5 (cf. [62, Section 3.1.4]).
When $\mathfrak{X}$ is weak Fano,
$\mathbb{C}[\mathbb{O}(\mathbf{\Sigma})_{+}]$ is non-negatively graded with
respect to the grading operator (4.1).
###### Proof.
It suffices to show that $\sum\limits_{b\in S}\lambda_{b}\geq 0$ for any
$(\lambda,v)\in\mathbb{O}(\mathbf{\Sigma})_{+}$. By the definition (3.15) of
$\mathbb{O}(\mathbf{\Sigma})_{+}$, it suffices to show that $\sum\limits_{b\in
S}\lambda_{b}\geq 0$ for all maximal cones $\sigma\in\Sigma$ and
$\lambda\in\widetilde{C}_{\mathbf{\Sigma},\sigma}$ (see (3.14)). Define a
linear function $h\colon\mathbf{N}_{\mathbb{R}}\to\mathbb{R}$ by
$h(\overline{b})=1$ for all $b\in R(\mathbf{\Sigma})\cap\sigma$. Then the weak
Fano condition (i.e., the convexity of $\Delta$) together with (A.1) implies
that $h(\overline{b})\leq 1$ for all $b\in S$. Hence, for
$\lambda\in\widetilde{C}_{\mathbf{\Sigma},\sigma}$, we have
$0\leq h(\beta(\lambda))=\sum_{b\in
R(\mathbf{\Sigma})\cap\sigma}\lambda_{b}+\sum_{b\notin
R(\mathbf{\Sigma})\cap\sigma}\lambda_{b}h(\overline{b})\leq\sum_{b\in
S}\lambda_{b}.$
This proves the lemma. ∎
In particular, $\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$ is non-
negatively graded. Because the locus where $\mathscr{G}$ is locally free is
preserved by the $\mathbb{C}^{\times}$-action and contains a neighbourhood of
$(0_{\mathbf{\Sigma}},0,0)\in B$, it follows that $\mathscr{G}$ is locally
free on an open set of the form
$U\times\operatorname{Lie}\mathbb{T}\times\mathbb{C}_{z}$. The proof of
Proposition A.1 is now complete.
###### Remark A.6.
The generic rank of the GKZ system has been studied by many people, notably by
Gelfand–Kapranov–Zelevinsky [46], Adolphson [6], Matusevich–Miller–Walther
[83] and has been identified with the volume272727The volume is normalized so
that the standard simplex has volume 1. When we allow $\mathbf{N}$ to have
torsions, the generic rank is $|\mathbf{N}_{\rm
tor}|\times\operatorname{vol}(\Delta)$. of $\Delta$ (when $\chi$ is not
special). Over the open torus $(\mathbb{C}^{\times})^{m}$ contained in
$\operatorname{Spec}\mathbb{C}[\boldsymbol{\Lambda}(\mathbf{\Sigma})_{+}]$,
the Brieskorn module in this paper corresponds to the better-behaved GKZ
system of Borisov–Horja [17]; they showed that the generic rank of the better-
behaved GKZ system equals $\operatorname{vol}(\Delta)$ (independently of
$\chi$).
## Appendix B Proof of Lemma 7.24
We only prove Part (1) of the lemma; the argument for Part (2) is the same. It
is easy to see that $F_{q,0}^{-1}(\mathbf{u})$ and $\partial A_{q,0}(\eta)$
intersect transversally at $x\in F_{q,0}^{-1}(\mathbf{u})\cap\partial
A_{q,0}(\eta)$ if and only if $\operatorname{grad}F_{q,0}(x)$ and
$\operatorname{grad}H(x)$ are linearly independent over $\mathbb{C}$, where we
set
$\operatorname{grad}f(x)=\left(\overline{x_{i}\frac{\partial f}{\partial
x_{i}}}\right)_{i=1}^{n}.$
Suppose that the lemma is not true. Then we can find sequences
$(q(k),\mathbf{u}(k))\in K$ and $x(k)\in\mathcal{Y}^{\rm sm}_{q(k)}$ such that
the following holds:
* •
$\eta_{k}=H(x(k))\to\infty$ as $k\to\infty$;
* •
$F_{q(k),0}(x(k))=\mathbf{u}(k)$;
* •
$\operatorname{grad}F_{q(k),0}(x(k))$ and $\operatorname{grad}H(x(k))$ are
linearly dependent over $\mathbb{C}$, i.e., there exists
$\alpha_{k}\in\mathbb{C}$ such that
$\operatorname{grad}F_{q(k),0}(x(k))=\alpha_{k}\operatorname{grad}H(x(k))$.
Define an $\mathbb{R}^{n}$-valued function $\mathbf{v}(x)$ by
$\mathbf{v}(x)=\sum_{b\in S_{-}}|x^{b}|^{2}\overline{b}.$
Then we have
$\operatorname{grad}H(x)=\frac{\mathbf{v}(x)}{2H(x)}.$
Writing
$\mathbf{v}\cdot\mathbf{w}=\sum\limits_{i=1}^{n}\mathbf{v}_{i}\mathbf{w}_{i}$
for the $\mathbb{C}$-bilinear scalar product, the third condition above can be
written as
$\operatorname{grad}F_{q(k),0}(x(k))=\frac{\operatorname{grad}F_{q(k),0}(x(k))\cdot\mathbf{v}(x(k))}{\|\mathbf{v}(x(k))\|^{2}}\mathbf{v}(x(k)).$
By the curve selection lemma in [85, Lemma 2], we can find a real analytic
curve $(0,\epsilon)\ni s\mapsto(q(s),\mathbf{u}(s),x(s))$ admitting a Laurent
expansion at $s=0$ such that for $0<s<\epsilon$, $(q(s),\mathbf{u}(s))\in K$,
$F_{q(s),0}(x(s))=\mathbf{u}(s)$,
$\operatorname{grad}F_{q(s),0}(x(s))=\frac{\operatorname{grad}F_{q(s),0}(x(s))\cdot\mathbf{v}(x(s))}{\|\mathbf{v}(x(s)\|^{2}}\mathbf{v}(x(s)),$
(B.1)
and $\lim\limits_{s\to+0}H(x(s))=\infty$. Since $K$ is compact,
$(q(0),\mathbf{u}(0)):=\lim\limits_{s\to+0}(q(s),\mathbf{u}(s))$ exists in
$K$. We write $x_{i}(s)=s^{\xi_{i}}a_{i}(1+O(s))$ with $a_{i}\neq 0$ and
$\xi_{i}\in\mathbb{Z}$. Then the leading term for $H(x(s))^{2}$ is
$H(x(s))^{2}=\left(\sum_{b\in\sigma}|a|^{2b}\right)s^{-2m}+\text{higher order
terms},$ (B.2)
where we set $\sigma:=\\{b\in S_{-}\colon\xi\cdot\overline{b}=-m\\}$ with
$\xi=(\xi_{1},\dots,\xi_{n})$ and $-m:=\min\\{\xi\cdot\overline{b}\colon b\in
S_{-}\\}$, and $|a|^{2b}=\prod\limits_{i=1}^{n}|a_{i}|^{2b_{i}}$. Note that
elements of $\sigma$ spans a face of the polytope $\Delta_{-}$. Since
$\lim\limits_{s\to+0}H(x(s))=\infty$, we have $m>0$. We calculate:
$\displaystyle\mathbf{v}(s)=\left(\sum_{b\in\sigma}|a|^{2b}\overline{b}\right)s^{-2m}+\text{higher
order terms},$ $\displaystyle\mathbf{v}(s)\cdot\frac{d\log
x(s)}{ds}=-m\left(\sum_{b\in\sigma}|a|^{2b}\right)s^{-2m-1}+\text{higher order
terms},$
$\displaystyle\overline{\operatorname{grad}F_{q(s),0}(x(s))}=\sum_{b\in
S_{-}}q(s)^{\ell_{b}}x(s)^{b}\overline{b}=\left(\sum_{b\in\sigma}a^{b}q(0)^{\ell_{b}}\overline{b}\right)s^{-m}+\text{higher
order terms}.$
By differentiating the equality $\mathbf{u}(s)=F_{q(s),0}(x(s))$ in $s$, we
get
$\displaystyle\frac{du(s)}{ds}-\sum_{i=1}^{n}\frac{\partial
F_{q(s),0}(x(s))}{\partial
q^{i}}\frac{dq^{i}(s)}{ds}=\overline{\operatorname{grad}F_{q(s),0}(x(s))}\cdot\frac{d\log
x(s)}{ds}$
$\displaystyle\qquad{}=\left(\overline{\operatorname{grad}F_{q(s),0}(x(s))}\cdot\frac{\mathbf{v}(x(s))}{\|\mathbf{v}(x(s)\|^{2}}\right)\cdot\left(\mathbf{v}(x(s))\cdot\frac{d\log
x(s)}{ds}\right),$ (B.3)
where $\\{q^{i}\\}$ denotes a local co-ordinate system on $\mathcal{M}^{\rm
sm,\times}$ and we used (B.1) in the second line. We compare the leading order
terms as $s\to+0$. By the above calculation, the right-hand side of (B.3) has
the leading term
$c\left(\sum_{b\in\sigma}a^{b}q(0)^{\ell_{b}}\overline{b}\right)\cdot\left(\sum_{b\in\sigma}|a|^{2b}\overline{b}\right)s^{-m-1}$
(B.4)
with $c=-m\sum\limits_{b\in\sigma}|a|^{2b}\neq 0$. On the other hand, because
$q(s)$, $\mathbf{u}(s)$ are regular at $s=0$ and
$\left|\frac{\partial F_{q,0}(x(s))}{\partial q^{i}}\right|=\left|\sum_{b\in
S}\frac{\partial q(s)^{\ell_{b}}}{\partial q^{i}}x^{b}\right|\leq C\cdot
H(x(s))\qquad\text{for some $C>0$},$
the left-hand side of (B.3) has poles of order at most $m$ by (B.2). Hence the
quantity (B.4) must vanish. This together with (B.1) implies:
$\displaystyle\overline{\operatorname{grad}F_{q(s),0}(x(s))}=\frac{\overline{\operatorname{grad}F_{q(s),0}(x(s))}\cdot\mathbf{v}(x(s))}{\|\mathbf{v}(x(s)\|^{2}}\mathbf{v}(x(s))=O\big{(}s^{-m+1}\big{)}.$
On the other hand, Proposition 7.19 and (B.2) give an estimate of the form
$\|\operatorname{grad}F_{q(s),0}(x(s))\|\geq\epsilon_{1}H(x(s))\geq\epsilon_{2}s^{-m}$
for sufficiently small $s>0$ (for some $\epsilon_{1},\epsilon_{2}>0$). These
two estimates contradict each other. Lemma 7.24 is proved.
### Acknowledgements
I would like to thank Pedro Acosta, Arend Bayer, Andrea Brini, Tom Coates,
Alessio Corti, Sergey Galkin, Vasily Golyshev, Eduardo González, Claus
Hertling, Yuki Hirano, Paul Horja, Yunfeng Jiang, Yuan-Pin Lee, Chiu-Chu
Melissa Liu, Wanmin Liu, Thomas Reichelt, Yongbin Ruan, Kyoji Saito, Fumihiko
Sanda, Christian Sevenheck, Yota Shamoto, Mark Shoemaker, Takuro Mochizuki,
Mauricio Romo, Hsian-Hua Tseng, Chris Woodward for many insightful discussions
and explanations. I also thank the anonymous referees for their careful
reading and helpful comments. This work is supported by EPSRC grant
EP/E022162/1, and JSPS Kakenhi Grants Number 22740042, 23224002, 24224001,
25400069, 26610008, 16K05127, 16H06335, 16H06337 and 17H06127. Part of this
work was done while I was in residence at the Mathematical Sciences Research
Institute in Berkeley, California, during the Spring semester of 2018 and the
stay was supported by the National Science Foundation under Grant No.
DMS-1440140. I thank the organizers and participants of the programme for many
stimulating discussions.
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| 28,018 |
https://github.com/kazu/fbshelper/blob/master/query/base/util.go | Github Open Source | Open Source | MIT | 2,021 | fbshelper | kazu | Go | Code | 993 | 2,964 | package base
import "github.com/kazu/loncha"
const (
SizeOfbool = 1
SizeOfint8 = 1
SizeOfint16 = 2
SizeOfuint16 = 2
SizeOfint32 = 4
SizeOfuint32 = 4
SizeOfint64 = 8
SizeOfuint64 = 8
SizeOffloat32 = 4
SizeOffloat64 = 8
SizeOfuint8 = 1
SizeOfbyte = 1
)
const (
TypeBool = iota
TypeByte
TypeInt8
TypeInt16
TypeInt32
TypeInt64
TypeUint8
TypeUint16
TypeUint32
TypeUint64
TypeFloat32
TypeFloat64
)
const (
FieldTypeNone = 1 << iota
FieldTypeStruct
FieldTypeTable
FieldTypeUnion
FieldTypeSlice
FieldTypeBasic1
FieldTypeBasic2
FieldTypeBasic4
FieldTypeBasic8
)
type Bool bool
type Byte byte
type Int8 int8
type Int16 int16
type Int32 int32
type Int64 int64
type Uint8 uint8
type Uint16 uint16
type Uint32 uint32
type Uint64 uint64
type Float32 float32
type Float64 float64
var NameToType map[string]int = map[string]int{
"bool": TypeBool,
"byte": TypeByte,
"int8": TypeInt8,
"int16": TypeInt16,
"int32": TypeInt32,
"int64": TypeInt64,
"unt8": TypeUint8,
"uint16": TypeUint16,
"uint32": TypeUint32,
"uint64": TypeUint64,
"float32": TypeFloat32,
"float64": TypeFloat64,
"Bool": TypeBool,
"Byte": TypeByte,
"Int8": TypeInt8,
"Int16": TypeInt16,
"Int32": TypeInt32,
"Int64": TypeInt64,
"Unt8": TypeUint8,
"Uint16": TypeUint16,
"Uint32": TypeUint32,
"Uint64": TypeUint64,
"Float32": TypeFloat32,
"Float64": TypeFloat64,
}
var TypeToGroup map[int]int = map[int]int{
TypeBool: FieldTypeBasic1,
TypeByte: FieldTypeBasic1,
TypeInt8: FieldTypeBasic1,
TypeInt16: FieldTypeBasic2,
TypeInt32: FieldTypeBasic4,
TypeInt64: FieldTypeBasic8,
TypeUint8: FieldTypeBasic1,
TypeUint16: FieldTypeBasic2,
TypeUint32: FieldTypeBasic4,
TypeUint64: FieldTypeBasic8,
TypeFloat32: FieldTypeBasic4,
TypeFloat64: FieldTypeBasic8,
}
var TypeToSize map[int]int = map[int]int{
TypeBool: 1,
TypeByte: 1,
TypeInt8: 1,
TypeInt16: 2,
TypeInt32: 4,
TypeInt64: 8,
TypeUint8: 1,
TypeUint16: 2,
TypeUint32: 4,
TypeUint64: 8,
TypeFloat32: 4,
TypeFloat64: 8,
}
var IsStructName map[string]bool = map[string]bool{}
func SetNameIsStrunct(name string, enable bool) bool {
if enable {
IsStructName[name] = true
return true
}
return false
}
func NameToTypeEnum(s string) int {
if v, ok := NameToType[s]; ok {
return v
}
return -1
}
func HasNameType(s string) bool {
_, ok := NameToType[s]
return ok
}
func AtoiNoErr(i int, e error) int {
if e != nil {
Log(LOG_WARN, func() LogArgs {
return F("AtoiNoErr(%d, e=%v) has error\n", i, e)
})
return 0
}
return i
}
const FieldTypeBasic = FieldTypeBasic1 | FieldTypeBasic2 | FieldTypeBasic4 | FieldTypeBasic8
func IsFieldStruct(i int) bool {
return IsMatchBit(i, FieldTypeStruct)
}
func IsFieldUnion(i int) bool {
return IsMatchBit(i, FieldTypeUnion)
}
func IsFieldBytes(i int) bool {
return IsMatchBit(i, FieldTypeSlice) && IsMatchBit(i, FieldTypeBasic1)
}
func IsFieldSlice(i int) bool {
return IsMatchBit(i, FieldTypeSlice)
}
func IsFieldTable(i int) bool {
return IsMatchBit(i, FieldTypeTable)
}
func IsFieldBasicType(i int) bool {
return IsMatchBit(i, FieldTypeBasic)
}
var UnionAlias map[string][]string = map[string][]string{}
func SetAlias(union, alias string) bool {
if UnionAlias[union] == nil {
UnionAlias[union] = []string{}
}
UnionAlias[union] = append(UnionAlias[union], alias)
return true
}
func IsUnionName(s string) bool {
_, ok := UnionAlias[s]
return ok
}
func ToBool(s string) bool {
return s == "true" || s == "True"
}
var All_IdxToType map[string](map[int]int) = map[string](map[int]int){}
var All_IdxToTypeGroup map[string](map[int]int) = map[string](map[int]int){}
var All_IdxToName map[string](map[int]string) = map[string](map[int]string){}
var All_NameToIdx map[string](map[string]int) = map[string](map[string]int){}
var IdxNames []string = []string{}
var Name2Idx map[string]int = map[string]int{}
func AddName(s string) {
if _, ok := Name2Idx[s]; ok {
return
}
IdxNames = append(IdxNames, s)
idx, err := loncha.IndexOf(IdxNames, func(i int) bool { return IdxNames[i] == s })
if err != nil {
Log(LOG_WARN, func() LogArgs {
return F("IdxNames: fail to add %s ", s)
})
return
}
Name2Idx[s] = idx
return
}
func Symbol(s string) int {
v, ok := Name2Idx[s]
if !ok {
return -1
}
return v
}
func SymbolToString(i int) string {
if i >= len(IdxNames) {
return ""
}
return IdxNames[i]
}
func NodeFieldSynmbol(node, field string) (uint32, error) {
nidx := uint32(Symbol(node))
fidx := uint32(Symbol(field))
if nidx < 0 || fidx < 0 {
return 0, ERR_INVALID_INDEX
}
nidx = nidx << 16
nidx += fidx
return nidx, nil
}
func SymbolToNames(idx uint32) (node, field string, e error) {
nidx := idx >> 16
fidx := idx - ((idx >> 16) << 16)
node = SymbolToString(int(nidx))
if node == "" {
e = ERR_INVALID_INDEX
return
}
field = SymbolToString(int(fidx))
if field == "" {
e = ERR_INVALID_INDEX
return
}
return
}
func IsSameTable(i, j uint32) bool {
return (i >> 16) == (j >> 16)
}
func IsSameField(i, j uint32) bool {
return (i - ((i >> 16) << 16)) == (j - ((j >> 16) << 16))
}
func SetNameToIdx(name string, v map[string]int) {
All_NameToIdx[name] = v
}
func SetIdxToName(name string, v map[int]string) {
All_IdxToName[name] = v
}
func SetIdxToType(name string, v map[int]int) {
All_IdxToType[name] = v
}
func SetdxToTypeGroup(name string, v map[int]int) {
All_IdxToTypeGroup[name] = v
}
func GetTypeGroup(s string) (result int) {
result = 0
if enum, ok := NameToType[s]; ok {
return TypeToGroup[enum]
}
if _, ok := UnionAlias[s]; ok {
return FieldTypeUnion
}
if len(s) >= 6 && s[0:6] == "[]byte" {
return FieldTypeSlice | FieldTypeBasic1
}
if len(s) >= 2 && s[0:2] == "[]" {
result |= FieldTypeSlice
}
if enum, ok := NameToType[s[2:]]; ok {
result |= TypeToGroup[enum]
return
}
if IsStructName[s] {
result |= FieldTypeStruct
} else {
result |= FieldTypeTable
}
return
}
type ReqestNameField struct {
Names []string
fNum int
}
var requestNameFields []ReqestNameField = []ReqestNameField{}
func RequestSettingNameFields(nName, fName, fType string, fNum int) bool {
requestNameFields = append(requestNameFields,
ReqestNameField{
Names: []string{nName, fName, fType},
fNum: fNum,
})
return true
}
func ApplyRequestNameFields() {
if len(requestNameFields) == 0 {
return
}
loncha.Delete(&requestNameFields, func(i int) bool {
req := requestNameFields[i]
grp := GetTypeGroup(req.Names[2])
idxs := All_IdxToTypeGroup[req.Names[0]]
idxs[req.fNum] = grp
return true
})
return
}
// RootName undocumented
var RootName string = ""
// SetRootName undocumented
func SetRootName(s string) {
if len(RootName) == 0 {
RootName = s
}
}
// MaxInt ... return maxinum value from values
func MaxInt(vals ...int) (r int) {
r = vals[0]
for _, v := range vals {
if v > r {
r = v
}
}
return
}
// MinInt ... return minimum value from values
func MinInt(vals ...int) (r int) {
r = vals[0]
for _, v := range vals {
if v < r {
r = v
}
}
return
}
// SumInts ... sum of []int
func SumInts(ints []int) int {
sum := 0
for _, v := range ints {
sum += v
}
return sum
}
| 14,682 |
sn82016413_1908-09-10_1_6_1 | US-PD-Newspapers | Open Culture | Public Domain | null | None | None | English | Spoken | 3,225 | 6,241 | y?mfH ' ' BVWyWO HDtfBTH nJHOOLU, T..1T., THURSDAY. SKPT. 10. 1008 TiprTS" I V it" W Oceanic Steamship Company TIME TABLE The steamers of this line will arrive act leave this port as hereunder: FROM SAN FRANCISCO : FOR SAN FRANCISCO : 'ALAMEDA SKl'T. 11 ALAMHDA SEPT. 16 ALAMKUA OCT. 2 ALAMHDA OCT. 7 ALAMHDA OCT. 23 ALAMEDA OCT. 28 ALAMEDA NOV. 13 ALAMEDA NOV. IS NOTICE. On and after June 84th, 1008, the SALOON RATES will be as follows: Single Fare, $65; Round Trip, $110. Family rooms extra. In connection with the sallng of the above steamers, the agents are prepared, to Issue the Intending passengers, coupon through tickets, by any railroad from San Francisco to all points In the United States, and from New YerK by any steamship line to all European ports. FOR FURTHF.R PARTICULARS APPLY TO Vm. G. Irwin & Co, Ltd OCEANIC 3., S. CO. GENERAL AQENT3. Pacific Mai) Steamship Co Cccidental and Oriental Steamship Co., and Toyo Kisen Kaisha Steamers of the above companies will at Honolulu and leave this port on or about the dates below mentioned: FOR JAPAN AND CHINA: ASIA MONGOLIA .. TIJNYO MARU .SEPT. in .sept. 21 ..OCT. 2 FOR GENERAL INFOK . ...CN' APPLY TO Ht Hackfeld & CoM Ltd, ' AMERICAN-HAWAHAN STEAMSHIP COMPANY. Weekly Sailings la Tehauntepec. FROM NEW YORK TO HONOLULU. Freight received nt nil times at the Company's .Wharf, 41st Street, South Droo klyn. ritOJI HONOLULU TO SAN FRAN- FROM SEATTLE AND TACOMA TO CISCO. HONOLULU DIRECT. ALASKAN. TO SAII SEPT 11 VIROINIAN, TO SAI L SEPT. 20 VIRGINIAN, TO SAIL OCT. D FROM SAN TRANCISCO TO HONO- LULU DIRECT. ARIZONAN, TO SAIL ...SEPT. 9 COLUMBIAN, TO SAIL... SEPT. 23 Freight received nt Company's wharf, Greenwich Street. Canadian-AustraSian Royal Mall Steamahlp Company. Steamers of the above line, running In connection with the CANAD IAN PACIFIC RAILWAY CO. between Vancouver, B. C, and Sydney, N. S. W., and calling at Victoria, B. C, Honolulu and 8uva, FIJI, and Bris bane, are DUE AT HONOLULU on or about the dates below stated, viz.: FOR FIJI AND AUSTRALIA: FOR VANCOUVER: MANUKA SEPT. 19 MARAMA SEPT. 16 MARAMA '.OCT. 10 AORANGI OCT. 14 LVR V. Ill call nt Fanning Inland. Through Tickets Issued from Honolulu to Canada, United States and Europe. For Freight and Passage and all general Information, apply to Theo. U. Daies & Co., Lid. Genera! Ageita. Matson Navigation Company The S. S. "HILONIAN" and "LURLINE" of this line, carrying paa . Sanger and freight, will run in a direct service between this port and San Francisco, sailing and arriving on or about the following dates: ARRIVE HONO. LEAVE HONO. S. S. "LURLINE" AUO. 19tU SEPT. 1st R. 8. "HILONIAN" SEPT. 2nd SEPT. 8th S. S. "LURLINE" SEPT. 26th OCT. 5th S. S. -HILONIAN" SEPT. 30th OCT. Gth s. s. "LURLINE" N0V. cth .NOV. 17th Passenger Rates to S. F.: First Cabin, $60: Round Trip First Class $110.00 For further particulars apply to CASTLE & COOKE, LTD., Agents. Union -Pacific Transfer Co., Ltd. Furniture and Piano Moving. Hustace-Peck Co., Ltd. Phone 298. DRAYMBN 63 Queen Street. P. 0. Box 212. Estimates Given on all kinds of teaming. Dealers in FIREWOOD, STOVE, STEAM AND BLACKSMITH COAL. CRUSHED ROCK, BLACK AND WHITE SAND, GARDEN SOIL. HAY, GRAIN, Weekly Bulletin, $1 Year ' i Don't Worry We will buy your Diamonds, Old Watches, and Jewelry for Spot Cash. J. f ARLO, 1018 NUUANU AVE. and BRANCH, FORT ST. near HOTEL. Bulletin Business Office Phone 256. Bulletin Editorial Room Phone 185. FOR SAN FRANCISCO: KOREA SEPT. 19 am.::.! v nr OCT. 2 St " t OCT. 10 For further Information apply to II. HACKFELD & CO..LTD., Agents Honolulu. C. P. MORSE. General Freight Agent. MOANA .. MANUKA. .NOV. 11 .DEC. 8 E Baggage Shipping Storage Wood Picking Coal 58 CEMENT, ETC. Past Schooner CONCORD Sailing for KAPUNA, HONOIPU, KAILUA and HOOKENA From Sorenson's Wharf. Apply, on Board or to HAWAIIAN BALLASTING CO., Agt Telephone 396, Maunnkca St., below King. P. 0. Box 8E0. BULLETIN ADS PAY hii ESTAEU8HCU IN US. Bishop & Co. ANKER. Commercial and Travelers' Letters of Credit issiu! on the Bank of California ind riieLondonJoirst Stock Hank, Ltd., London. Correspondents foi the mencan Express Conn any .ii J Vhos Cook & 5on. meres' allowto on term n i 5iivii; tijtiU DeiniS.ts. Claus Spreckcli. Wm. G. Irwin. Claus Spreckels & Co. BANKERS. HONOLULU, : : : T. H. San Francisco Agents The Ne vada National Bank of San Francisco. Draw exchange on the Nevada Na tional Rank of San rranclsco. London Tho Union of London anil Smith's Bonk, Ltd. New York American Exchange Natlonnl Bank. Chicago Corn Exchange National Bank. Paris Credit Lyonnals. Hongkong and Yokohama Hon kone-Shsngbal Banking Corporation. New Zealand and Australia Bank of Now Zealand and Bank of Austra lasia. Victoria and Vancouver Bank of British North Amorlca. Deposits received. Loans made on approved security. Commercial and Travelers' Credits Issued. Bills of Exchange bought and sold. Collections Promptly Accounted For. The First AMERICAN SAVINGS AND TRUST GO. OF HAWAII, LTD. SUBSCRIBED CAPITAL. .$800,000.00 PAID UP CAPITAL $100400.00 President Cecil Brown Vice President M. P. Reblntan Cashier L. T. Peck Offlco: Corner Fort and King Sts. 3AVINQS DEPOSITS received and Interest allowed for yearly deposits at tjio rate of 4ft per cent, pen annum. Rules and regulations furnished upon application. Tho Yokohama Specie Bank, Limited Established I880 Capital (Paid up) . .Yen 24,000,009 Reserved Fund Yen 16,050,000 Special Reserved Fund. Yen 2,000,000 HEAD OFFICE, YOKOHAMA. Branches and Agencies: Toklo, Kobe, Osaka, Nagasaki, London, Lyons, New York, Ban Fran cisco. Bombay. Hongkong. Shaaghal, Hankow, 'Chcfoo, Tientsin, Peking, Newchang, Dalny, Port Arthur, An-tung-Hslen, Llaoyang, Mukden, Tien ling, Changchun. The bank buys and receives for collection bills of exchange, Issues Drafts and Letters of Credit and transact a general banking business. Honolulu Branch, 67 8. King Street Oahu Railway Time Table. OUTWARD. For Walanao, Waialua, Kahuku and Way Stations : 15 a. m., 3:20 p. m. For Pearl City, Ewa Mill and Way Stations 17:80 a. m., 9;15 a. m., 11:05 n. ra., 2:U p. m 320 p. m., 6:15 p. m., J0;30 p. m., tU:00 p. m. For Wohlaiva 'Orie a. m. and 5:15 p. m. INWARD. Arrive Honolulu from Kahuku, Waialua and Watanoe 8:3G n. m., ..E:3l p. in. Arrive In Honolulu from Ewa Mill and Pearl City J7: 48 a. m., 8:30 u m., 10:38 a. m, 1:40 p. in., 4:SX p m., 5:31 p. m., 7:30 p. m. Arrive Honolulu from Wahlawa 8:3G a. m. and 5:S1 p. m. Dally. t Ex. Sunday. i Sunday Only. Tho Halelna Limited, a two hour train (only flrstomsB tickets hon ored), leaves Honolulu every Sunday at 8: 22 a, ra.; returning, arrives lu Honolulu at U:10 p. m. The Limited stops only at Pearl City and Walanue. Q. P. DENISON, F. C. SMITH, Alexander & Baldwin LIMITED. J. P. COOKE Manager OFFICERS AND DIRECTORS: H. P. Baldwin President J. B. Castle Vice President W, M. Alexander. .Seoond Vice Pres. J. P. Cooke Third Vice Pres. J. WaterhoUse Treasurer E. E. Paxton Secretary w. 0. Smith Director O. R. Carter Director w. R. Castle i. Director SUGAR FACTORS, COMMISSION MERCHANTS and INSURANCE A6ENTS Agents for Hawaiian Commercial & Sugar Co. Haiku Sugar Company, Paia Plantation. Maui Agricultural Company. Kihei Plantation Company. Hawaiian Sugar Company. Kahuku Plantation Company. Kahului Railroad Company. Haleakala Ranch Company. Honolua Ranch. Castle & Cooke, Ltd Honolulu, T. H. SHIPPING AND COMMISSION MER CHANTS, SUGAR FACTORS ftyid 0EN1RAL INSURANCE AGENTS representing Ewa Plantation Go. Waialua Agricultural Co., Ltd. jLonaia sugar uo. Waimet, lunar Mill Co. Apohaa Sugar Co., Ltd. Fulton Iron Works of St. Louis Blake Btesun Pumps Weston's Centrifugals Jiabcocx Wilcox Boilers Green's Fuel Economizers Marsh Steam Pumps Matson Navigation Co. Planters' Line Shipping Co. Wm. 6. Irwin & Go, LIMITED. SUGAR FACTORS and COMMISSION AGENTS. Wm. G. IRWIN President JNO. D. SPRECKELS... 1st V. Prts. W. M. GIFFARD 2d V. Pres. H. M. WHITNEY Treasure RICHARD IVERS Secretary D. 0. MAY Auditor ( Agents for Oceanic Steamship Co., San Francis co, Cal.v Baldwin Locomotive Works, rhila delpnia','r Pa. Hakalau Plantation Co., Hilo Sugar Co., Honolulu Plantation Co., Hutchinson Sugar Plantation , Co., Kilauea Sugar Plantation Co., Olowalu Company, Paauhau Sugar Plantation Co., Walma nalo Sugar Co. C. Brewer & Co., Ltd. QUEEN STREET, HONOLULU, T. H. AGENT8 FOR: Hawaiian Agricultural Co., Ookala Sugar Plant. Co., Oncmea Sugar Co., Honomu Sugar Co., Walluku Sugar Co., Pepeekeo Sugar Co., The Planters Line of 8an Franelseo Packets, LIST OF OFFICERS: C. M. Cooke, President; George Robertson, Vice President and Mana ger; E. F. Bishop, Treasurer and Sec retary; F. W. Macfarlane, Auditor; P. C. Jones, C. M. Cooke and J, R, Gait, Directors. FIRE INSURANCE THE 6. F. DILLINGBAIH CO. L1IITEI, General Agent for Hawaii: Atlas Assurance Company of London. New York Underwriters' Agency. Providence Washington Inourance Co. 4th FLOOR, STANCCINWALD BLPQ. LIFE INSURANCE Is not a Luxury; It Is a Necessity. But you Must have the BEST snd that Is provided by the famous and most equitable Laws of Massa chusetts, In the New England Mutual Life Insurance Co., OF BOSTON, MA83ACHU8ETTS. If you would be fully Informed about these laws, address Castle & Cooke, GENERAL AGENTS, , HONOLULU, T. H. WM. C IRW1N& C0..LTO. AGENTS FOR THE Royal Insur. Co. of Liverpool, Eng. Commorcial Union Assurance Co., Ltd., of London, England. Scottish Union & National Ins. Co. of Edinburgh, Scotland. The Upper Rhino Ins. Co., Ltd Proper Treatment for Floors, Woodwork and Furniture This is the title of a hand somely illustrated booklet is sued by S. C. Johnson & Son. It is a practical and useful guide for lovers of up-to-date homes. FREE ON REQUEST AT Lewers & Cooke LIMITED 177 S. King Si. Phone 775. IronBeds LARGE STOCK. LOWEST PRISES. Coyne Furniture Co. Our Baby Rings Baby Pins, Baby Cups Baby Napkin Rings, or Baby Spoons will surely make baby happier. J.A.R.Vieira&Co. 113 HOTEL ST. , LOOK at the automobiles, buggies and car nages we have recently overnauiea nnd painted THEN BEE US. W. W. Wright Go, King Street near South Tel. 202 LUNCHES and DRINKS The most popular place in town. The Fashion Saloon, Hotel St. near Port, Jaek Scully. Jack Roberts. The Encore Saloon Thy a drink at the new place and have "MATT" HEFFERN serve you. COR. HOTEL and NUUANU. S. SAIKI, Bamboo' Furniture Made to Order. Picture Framiag a Specialty. 068 S. BERETANIA ST. TELEPHONE 497. Suits Pressed At Short Notice and Quick Delivery. EAGLE DYEING AND CLEANINO WORKS. Fort Street. Phone 57S. For Expert Repairs on Bicycle, Mo torcycle, Automobiles, etc., call on J. E. Santos, Phone 422. . Union St. FINEST FIT and eloth of A-l quality can be pur chased from SAINO CHAIN, MeOANDLEfiS BLDG., P. 0. Box 961. Telephone 831, WahYingChone;Co. King Street, Ewa of Fishmarket. DRY GOODS AND FURNISHING GOODS of EVERY DE SCRIPTION. BAMBOO FURNITURE Of All Kinds And Descriptions At Reasonable Prices. SEE OUR DISPLAY. S. TATAINI Emma St. near Beretania. A Skin of Beauty is a Joy Forever PR. T. FELIX tiOURAUB'S ORIENTAL CREAM OR MAGICAL BEAUtlFIER TltmofM Tun, MmptaL I-reck.lt. Mnlh fatchfi, Rub, and Mln tMnfwn, nn vrrrj sirrniM rtnbeautjr.atirlit. ! rlftMtVm, h hM tootl lilt tMt of yn, n4 la o htrmleM wi tkottUKtrtnurflt ts rrostrlr mui, Acrfpinocountft ftlt of HmU.u Mm. Dr. 1 A. Parrt ild to My nt tb hmt. loo (ft f)rUlfM! MA you Udlet will uw thro '(Uftrmtd rrrgm m h 1ui btimful of fi tht kin jtrtptrfti loM." t r Hit trr all 4 nutgmi Fwur Ooodi iffftleri la tht Uillid Butt Cnd -ai Iwcr. iEIID.T.HeHIIS,Pfcp, 37 Gitst fats Ilnst.'s'itTnl rcui)fta , POLITICAL NOTICES. ANNOUNCEMENT. I hereby atinounio my candidacy for rcnomlnntlon for HKPRLSENTATIVB, FOURTH DISTRICT subject to the action of tho Repub lican Convention. A. D. CASTIIO. ANNOUNCEMENT. 1 hereby announce myself as can- dldnto for SUPERVISOR mihject to the action of tho Republi can County Convention.. 4101-tf J. C. QUINN. ANNOUNCEMENT. I hereby aunounce my candidacy for tho Republican .nomination (or REPRESENTATIVE OP THE FOURTH DISTRICT. 4092-tt QEO. MAKALENA. ANNOUNCEMENT. I hereby announce myself aa can didate for REPRESENTATIVE, FIFTH DISTRICT, subject to tho action of the Repub lican Convention. BERNARD II. KELEKOLIO. ANNOUNCEMENT. I hereby announce my candidacy for the RopuMIcnn nomination for COUNTY CLERK for the County of Oahu. DAVID KA1.AUOKALANI, JR. 4090-tt ANNOUNCEMENT. I hcrrhy announce myself as a can dldatp for REI'UKSKNTATIVE, FIFTH DIS TRICT subject In the action of the Repub lican convention. WILLIAM H. CRAWFORD. 4090-tt ANNOUNCEMENT. I heretiy announce my candidacy for tho Republican nomination for MAYOR OF HONOLULU. CHARLES HUSTACE, JR, 4090-tf ANNOUNCEMENT. I hereby nnnounco my candidacy for the Republican renomlnatlon for COUNTY AUDITOR, for the County of Oahu. 40Dl-tt JAS. UICKNELL. Grand Reduction Sale 20 per cent, off K. Isoshima, 30 KINO ST. Japanese Bazaar, 1137 FORT ST. , ' TOM SHARP, THE PAINTER ELITE , BUILDING i Phone 397 CHARP CIGNC Ask Your Grocer FOR Pau-Ka-Hana Soap HONOLULU SOAP WORKS CO., Ltd. FashionableDressmakihg Reasonable Prices, MADAME LAMBERT. BERETANIA NEAR FORT a2s jaP&St- r REAL ESTATE TRANSACTIONS Recorded Aug. 1, 1908. Ynmadtv Hatsunosky to Ku Moon;' L; pc land, Puna Rd, Puna, Hawaii; 20 yrs at $22 SO. 11 298, p 410. Dat ed Juno 1, 1908. M Ilrnnco to M R Capclo; Rel; Ld Patents 3938 nnd 4189, Hcnchcncula, etc. Hamnkua, Hawaii; SlfiOO. I) 301, I 436. Dated July 25, 1908. Manocl H Capcllo nnd wf to John T Gomez; D; lot 7, Land Patent 4189, Kalneho homesteads, Hnmaktm, Ha waii; $800. H 305, p 232. Dated Jiy 14, 1908. John T Gomez and wf to Manoel Branco; M; Int In lots 7 and 12, 30 acres Innd, Knlnehc, Hainakua, Ha waii ; $000. B 301, p 43G. Dated July 14, 1908. M R Cncl!o and wf to Anthony Lid Kate; M; Land Patent 3938, Hcnchono ula, Humakua, Hawaii; $1000. U 301, p 438. Dated July 24, 1908. Recorded August 3, 1908. Chong Yeo Chow to Wong; Sing On; CM; leaseholds, bananas, etc, McCul ly Tract, Honolulu; $G00. D 301, p 441. Dated Aug 3, 1908. Usabura Ooo to Sung Tung Sang; CM; leasehold, bldgs, etc, cor Pllkol and Klnnu sts, Honolulu; $000. D 301, 442. Dated Aug 1, 1908. W C Achl Tr nnd wf to Eddlo Wong ham; D; lot 34, R P E667, Kill G93, Ap 2, Kcklo Tract, Honolulu, Oahu; $500., D 305. p 245. Dated Mar 10, 1903. Wllllnm R Castlo Tr to W C Achl Tr; Par Rel; lot 34, Keklo Tract, Ho nolulu! $125. D 301, p'447. Dated Aug 3, 1908. Wing Hlng Co; Co P I); general indsc, cic, 46 Hotel St, Honolulu; Cap $2400. II 301, p 301. Dated Aug 1, 1908. Rlto Nlcwa (w) to Manocl V. Ad rian; D; lot 5 Gr 4999, rents, etc, Wnl punalel Hbmcstcad Tract, N Hllo, Ha waii; $1000. D 305, p 235. Dated July 28, 1908. Manocl F. Adrian nnd wf to Manocl Ilrnnco; M; lot 15, Gr 4493 and lot 5, Gr 4999, Wnlpnnalcl Homestead Tract, N Hllo, Hawaii; $100. D 309, p 109. Dated July 29, 1908. Kano Plkn to Ahlglrhl; L; por Kill 10861, bldgs, etc, Nlillltuka, Knlmla, Hawaii; 12 yrs at $30 per yr. B 29S, p 417. Dated July 1, 1908. Ktiokoa (w) to Pacific Sugar Mill; L; Int In R P (Gr) 1882. IIanap.il, Ha malum, Hawaii; $10 yrs at $3 per a per jr. U 298, p 118. Dated July 1C, 1908. David K Kaackuahlwl to Pacific Sugar Mill; L; Int In R P (Gr) 930, Haukol, Haniakua, Hawaii; 15 yrs at $4 per a lMjr yr. II 298, p 420. Dated July 6, 1908. Knlanlluiii (w) tn Hnelcku Sugar Co Ltd; D; por R P (Gr) 2621. bldgr $50. 13 305, p 239. Dated July 31, 1908. Kahuo llllll nnd wf to Maul Railroad & S S Co; D; 1 Bharo In huo land, Po nhl, Hninukualoa, Maul; $140. 11 305, p 240. Dated July 27, 1908. Kahuo to Maui Railroad & S S Co; D; 1 shore tn huo land, I'cnhl, llama kunlon, Maui; $140. U 305, p 242. Dated July 27, 1908. John Plunkctt and wf to Maul Rail road & S S Co; D; 1 ttliaro in hul land, I'cnhl, Hamakualoa, Maul; $140. 11 305. p 243. Dated July 25, 1908. Kamakau (k) ct al by Alft of mtgco to P E R Strauch; Fore Affdt; R P (Gr) 1508. Maluuka, Homnula, Maul. 1) 301, p 444. Dated Aug 3, 1908. Kamakau (k) el ul by nitgeo to r B R Strauch: D; R P (Gr) 1508, Na- luaka, Homauln, Maul: $125. D 305, p 244. Dated Aug 3, 1908. Lahapa W Moka (widow) to moko Kukaulua Jr; I); Kill 240G, Aps 1 nnd 2 and 2 shares In hul lands, Moloan, etc, Koolau, Kauai; $60. 11 305, p 236. Dated July 23, 1908. A Moko Kuhaulua and wf to KU Opto (k):D; Aps 1 nnd 2, Kill 240G, Moloan, Koolau, Kauai; $1. II 305, p 237. Dated July 25, 1908. Joseph K Kupuna to Koloa Sugar Co; D; Gr 1419 Kakca Wellyoll, Koloa. Kauai; $100. B 305, p 247. Dated Aug 3, 908. Recorded August 4, 1908. Wm n Olcson ct al to Trs of Oahu Collego; Addn Chge; lots 8 and 9. hlk 8, Collego Hills, Honolulu: $1000. D 301, p 448. Dated Aug 4, 1908. Hank of Hawaii Ltd to W M Min ion; Par Rel; lot 10, hlk 64, Wttlulao Tract, Honolulu: $1, D 301, p 449. tinted Aug 3, 1908. ' Win R Castlo Tr to Lam On: Rel: por Kill 741. Ap 1 nnd 2 pes land Vine yard St, Honolulu; $1100. U 301, p 450. Dated Aug 4, 1908. Dank of Hawaii Ltd to Chang Yat Ping et al; D; lot 10, King St, Hono lulu; $1. D 305, p 248. Dated Aug 4, 1908. David A Dowsott and wf to Clifton II Tracy; D; por lotB 21 and 22, blk A, Gr 177, Young St", Honolulu; por lot 21, Blk 3, Mngoon Tract, Honolulu; $1, 1) 305, p 249. Dated Aug 3, 1908. Clifton II Trncy to Adellno K Dow sett; D; .por lots 21 and 22, blk A Gr. 177 Young St: por lot 21, blk A, Mn goon Tract, Honolulu; $1. R 305, p 251. Dated Aug 3, 1908. D K Namalioo et ul to Ahaiiu; L; po land and R W Walakea, Hllo. Ha waii; 10 yrs at $140 per yr. 11 298, p 422. Dated July 7, 1908. ' How Lung to Chy Chow Kol; L; pc land nnd R W, Walakea, Hllo. Ha watt; 16 yrs at $15 per yr. II 298, p 424. Dated Oct 7, 1902. W H Fenton-Smtth et al Trs to Prot estant Episcopal Church tn tho Hawn Islands: D; por R P 4399, Kul 1783. bldgs, rents, ets, Watanuenue and Pleasant Sts, Hllo, Hawaii; $1. B 305, p 252. Dated July 20, 1908. W H Fenton-Smtth ct al Trs to Tr of Church of Holy Apostles; D; por R P 4399. Kul 1783, bldgs, rents, otc, Walanucnuo St, Hilo, Hawaii; $1. B 305, p 254. Dated July 20, 1908. W'ells I'Yirgo's business for the fis cal year nets a prom of C0.98 por cent. on. tho $8,000,000 of "cnpltnl slock. 1 iiLj?UJi.. | 39,413 |
MLT-COM-IV-2013-037-FRE.txt_1 | Marianne-Europe | Open Government | Various open data | null | None | None | English | Spoken | 7,944 | 11,118 | ANNEXE : POINT DE VUE DU GOUVERNEMENT
L'annexe qui suit ne fait pas partie de l'analyse et des propositions
de l'ECRI concernant la situation à Malte.
Conformément à la procédure pays-par-pays, l’ECRI a ouvert un dialogue
confidentiel avec les autorités de Malte sur une première version du rapport.
Au cours de ce dialogue, l’ECRI n’a reçu aucune indication des autorités
concernant d’éventuelles erreurs factuelles.
Les autorités ont demandé à ce que le point de vue suivant soit reproduit en
annexe du rapport de l’ECRI.
Response
of the Maltese authorities
to ECRI’s Draft Report on Malta
(fourth monitoring cycle)
20 March 2013
INTRODUCTION
The following pages contain the detailed response of the Maltese authorities to ECRI’s fourth report. We regret
that ECRI’s report, like its predecessors, relies heavily on anonymous sources. We have identified more than 20
instances of such phrases as “ECRI has been informed”, “ECRI has received information”, “ECRI’s sources have
confirmed”, “representatives of civil society have informed ECRI”, “ECRI’s interlocutors” and “civil society has
stated” (see e.g. paragraphs 6, 16, 17, 24, 37, 44, 47, 52, 57 etc). Maltese NGOs are well known, operate freely
in public and have access to public funds. ECRI’s efforts to hide the identity of its sources are, therefore,
regretted and out of place.
It is also regretted that non-facts and factual errors have found their way in ECRI’s report (e.g. in paragraphs 66,
84, 104, 106, 107, 108, 122, 126, 129, 137, 144 and 147) and that the report reveals inadequate knowledge of
Maltese law and its interpretation (see e.g. paragraphs 14, 23, 24, 29, 45, 48, 84, 89, 90, 91, 108, 110, 116 and
131).
ECRI’s report makes many recommendations (e.g. in paragraphs 18, 21, 35, 45, 99, 104, 126, 131, 137, 140,
142, 145 and 159), but does not proceed to cost them, let alone to provide the necessary funds for their
implementation. The report also fails to make any economic, social or environmental impact assessment of the
challenges of irregular migration in Malta.
ECRI has once more lost an opportunity to highlight Malta’s need for support in the areas of irregular migration
and asylum, including in particular the need for relocation opportunities for persons granted international
protection in Malta. This is above all to the detriment of the beneficiaries of international protection themselves.
Surely, the ECRI delegation could see that Malta cannot possibly integrate, in the long term, all the persons
whom it recognises as in need of international protection. This is due to the limits imposed by Malta’s geophysical realities, including a small labour market prone to saturation.
Instead, ECRI’s report underestimates Malta’s considerable contribution in the asylum sphere, particularly given
the disproportionately large number of asylum applications being received year after year, as well as the
country’s high asylum recognition rate. Moreover, in the years since the influx began in 2002 the personnel of the
Armed Forces of Malta have saved the lives of thousands of irregular immigrants - a fact not given due
recognition by the ECRI report. The efforts of Detention Service officials and AWAS personnel have also been
underestimated or left unmentioned. These officials have striven to provide appropriate reception conditions and
services to irregular migrants and asylum seekers, even in circumstances of exceptional pressure.
We understand that ECRI does not agree with all the policies followed by Malta in the area of irregular
immigration. However, ECRI could have acknowledged that Malta is fully committed to the principle of asylum
and has fully abided by the principle of non-refoulement. ECRI could also have recognised that Malta has
safeguarded the rights of all immigrants despite very difficult circumstances.
ECRI RECOMMENDATIONS AND COMMENTS
International legal instruments
4. ECRI reiterates its recommendation that Malta sign
and/or ratify the following international instruments:
Protocol No. 12 to the European Convention on
Human Rights ; the European Convention on
Nationality; the Convention on the Participation of
Foreigners in Public Life at Local Level; the
International Convention on the Protection of the
Rights of All Migrant Workers and Members of their
Families; and the Convention on Cybercrime and its
Additional Protocol concerning the criminalisation of
acts of a racist and xenophobic nature committed
through computer systems.
RESPONSE OF THE MALTESE AUTHORITIES
As of the time of writing, none of the EU’s 27 Member States had signed or ratified the International Convention on the
Protection of the Rights of Migrant Workers and their Families. The Maltese authorities have already informed ECRI that
they have no intention of signing or ratifying the said Convention. Malta has signed the European Convention on
Nationality, the Convention on Cybercrime and its additional Protocol concerning the criminalisation of acts of a racist and
xenophobic nature committed through computer systems.
Only 17 of the Council of Europe's 47 Member States have signed and ratified Protocol No 12 to the ECHR, while 20
other Member States have signed, but stopped short of ratifying, it.
Citizenship legislation
6. …. In addition, civil society has stated that even ECRI gives no indication whatsoever of the source of the statement, or who it means by “civil society”.
when the above-mentioned requirements are
satisfied, in practice, it may take up 15 to 20 years to
obtain naturalisation.
9. ECRI recommends that the Maltese authorities The Maltese authorities have taken note of ECRI’s recommendation.
amend the Citizenship Act so as to: introduce clear,
objective and measurable requirements in connection
with the acquisition of citizenship through
naturalisation; ensure that decisions relating to the
acquisition, retention, loss, recovery or certification of
nationality are open to review ; and, as far as cases
of loss of citizenship are concerned, remove any less
favourable treatment afforded to persons who have
acquired their citizenship through naturalisation or
registration – particularly where fundamental rights
are concerned.
Criminal law provisions
ECRI RECOMMENDATIONS AND COMMENTS
14. ECRI recommends that the Maltese authorities
complement the existing criminal law provisions
against racism by expressly prohibiting: the creation
or leadership of a group which promotes racism; and
racial discrimination in the exercise of one’s public
office as per ECRI’s GPR No. 7 paragraph 18 (g) and
(h). Furthermore, ECRI strongly recommends that the
Maltese authorities maintain national origin and
citizenship as grounds under which racist conduct
and racial discrimination are prohibited.
16. …many of ECRI’s interlocutors have highlighted
that most racist comments made online, particularly
comments to news articles, go unpunished.
RESPONSE OF THE MALTESE AUTHORITIES
The Maltese Criminal Code provides for an increase in the punishment if the intention behind the particular offence is
racially motivated. To this effect, article 83B of the Maltese Criminal Code (Cap 9 of the Laws of Malta) provides for an
aggravation of punishment by one to two degrees in respect of all offences which are racially motivated.
With regard to racial discrimination in the exercise of one’s public office, such conduct would definitely fall under the
articles of the Criminal Code carrying also the aggravation of punishment. Moreover, other disciplinary and administrative
measures may also be applied under the Public Administration Act (Cap 497 of the Laws of Malta) as well as under the
Public Service Management Code.
ECRI is citing anonymous “interlocutors” who complain that online comments to news articles go “unpunished”. The news
articles are public and published and so are the allegedly “racist comments”. This notwithstanding, the ECRI report does
not give a single example of “most racist comments made online” that should be punished. In any case the Maltese
Constitution protects freedom of speech, as does the European Convention on Human Rights.
The record of the Maltese Police Force in solving crimes compares well with that of any police force in any European
Moreover, ECRI expresses its concern that the country. In carrying out its investigations the Maltese Police Force abides by the rule of law.
investigations opened in 2005 and 2006, in
connection with the arson attacks committed against
anti-racist organisations and persons who had
spoken out against racism (see paragraph 114 of
ECRI’s third report), have not identified any culprits.
The authorities have explained that the investigations
were hampered by the refusal of the telephone
company concerned by the investigation to provide
location data for certain mobile phones. Notably,
according to the telephone company, because the
data requested did not concern a specific subject,
granting access to such data would breach the
privacy of an undetermined number of persons.
ECRI RECOMMENDATIONS AND COMMENTS
RESPONSE OF THE MALTESE AUTHORITIES
17. ECRI has been informed by legal practitioners As is the case throughout the report, ECRI does not identify its anonymous informants. The 2009 EU-MIDIS survey is
that neither lawyers nor judges are provided with based on very dubious methodology.
specific training on criminal law provisions in force
against racism.
However, ECRI was informed by representatives of
vulnerable groups and NGOs that police frequently
do not follow up on complaints lodged by migrants on
grounds of racism or racial discrimination (see the
subsection of this report on access to public places
and services) and that, for this reason, few report
them.
Such state of underreporting and the underlying
reasons are confirmed by the 2009 EU-MIDIS
Minorities and Discrimination Survey….
18. ECRI reiterates its recommendation to the
Maltese authorities to provide regular training to all
those involved in the criminal justice system on
criminal law provisions in force against racism and
racial discrimination and sensitise the same on the
importance of: countering manifestations of racist
expression and racially motivated conduct; as well of
acknowledging racist bias, if and when it is present.
The Judicial Studies Committee, catering for training for members of the Judiciary, had organized a seminar on ‘Asylum
Seekers in Malta: Key Legal Issues’.
Issues relating to racism were discussed during these sessions. Speakers included an official from the Ministry for
Home Affairs, two legal officers from the UNHCR Office in Geneva, a representative of the local UNHCR office, a
Magistrate and a speaker from the Agency for Welfare Asylum Seekers (AWAS).
Moreover, two members of the Judiciary participated in a conference on Anti-Discrimination in Trier. The topics covered
in this seminar treated a wide area of discrimination such as sexual orientation, age, disability, as well as the treatment of
minority groups.
With regard to the Police, ongoing lectures take place at the Police Academy for all new recruits as well as in-service
professional development courses for all serving members of the Police Force, including lectures on criminal law vis-à-vis
racism and racial discrimination.
ECRI RECOMMENDATIONS AND COMMENTS
21. ECRI recommends that the Maltese authorities
collect data on the application of criminal law
provisions against racism in a systematic way so that
their effectiveness can be assessed, notably by
breaking down the information, per reference year, by
the: number of opened investigations, number of
cases referred to court, number of discontinued pretrial investigations and the outcome of the trials.
Administration of justice
23. ECRI strongly recommends that the Maltese
authorities abrogate the provisions of the law which
provide that the only victims of crime who may apply
for compensation before a criminal court are Maltese,
EU nationals or habitual residents of Malta.
24. In addition, ECRI has received information
indicating that the rules of release on bail are not
applied equally to Maltese nationals and nonnationals and that, for the latter, bail is set extremely
high. In this connection, ECRI refers to its
considerations on the importance of training all those
involved in the criminal justice system
Civil and administrative law provisions
29. ECRI recommends that the Maltese authorities
include citizenship, language and religion as
prohibited grounds of discrimination under the antidiscrimination legal framework in place.
31. ECRI recommends that the authorities collect
systematically and make available to the public
information on the application of anti-discrimination
legislation, including the number and nature of the
civil and administrative complaints/actions filed per
reference year, the decisions rendered and the
redress or compensation awarded, so that the
effectiveness of these provisions can be assessed.
RESPONSE OF THE MALTESE AUTHORITIES
Human and financial resources put a limit on the amount of data and statistics that can and should be collected. The
Maltese authorities collect data on serious criminal offences, including racism. The collection of additional data depends
on the competing demands on limited resources.
In the view of the Maltese authorities, current legislation does not amount to differential treatment.
The Maltese authorities cannot take cognizance of this anonymous and gratuitous information.
This is already regulated by the Maltese Constitution which provides that no law shall make any provision that is
discriminatory on the basis of race, place of origin, political opinions, colour, creed or sex, either of itself or in its effect.
The National Commission for the Promotion of Equality already collects and publishes statistics in relation to the
complaints it receives and this is done on a yearly basis in NCPE’s annual report.
ECRI RECOMMENDATIONS AND COMMENTS
35. ECRI recommends that the Maltese authorities
continue to raise awareness on the provisions in
force against racial discrimination and the existing
remedies to seek redress among the general public
and, in particular, among potential victims of racial
discrimination. The information sessions organised
by the National Commission for the Promotion of
Equality should be replicated and extended to all
groups of concern to ECRI.
Anti-discrimination bodies and other institutions
37. As already observed in the subsection on civil
and administrative law provisions of this report, some
discrimination complaints on grounds of racial and
ethnic origin have been lodged before the NCPE
since 2008. The limited number of complaints
received has been ascribed by civil society to the
limited powers attributed to this body.
A study carried out by the NCPE on racial
discrimination in Malta also shows that 70% of the
interviewees belonging to a minority ethnic group had
no knowledge of the NCPE’s existence and role.
ECRI therefore recommends that greater resources
be spent in raising vulnerable groups’ awareness of
the NCPE and other authorities competent to receive
discrimination complaints.
RESPONSE OF THE MALTESE AUTHORITIES
NCPE confirms that such information sessions have already taken place and since the writing of the report, further
sessions have been held for the African Community on how to advocate for their rights, through a project entitled ‘I’m not
racist, but…’
The ECRI report refers to an anonymous “civil society” and then ascribes to it arguments that it supports.
The way resources are spent is decided by the House of Representatives.
ECRI RECOMMENDATIONS AND COMMENTS
39. ECRI recommends that the Maltese authorities
ensure that the national specialised body for
combating racism and racial discrimination is entirely
independent and is responsible, inter alia, for:
hearing and considering complaints in all fields of life
(both private and public) on grounds of “race”, colour,
language, religion, citizenship or national/ethnic
origin; providing assistance to victims; initiating and
participating in court proceedings; monitoring
legislation and providing advice to legislative and
executive authorities; raising awareness on issues of
racism and racial discrimination among society and
promoting policies and practices to ensure equal
treatment, as per ECRI’s GPR No. 2.
42. ECRI recommends that the Maltese authorities
use the National Action Plan against Racism and
Xenophobia designed by the National Commission
for the Promotion of Equality in order to devise an
anti-discrimination policy.
Employment
44. Moreover, ECRI has been informed by
representatives of migrants and of civil society that, in
practice, the allowance is not always granted even
though the applicant satisfies the requirements.
RESPONSE OF THE MALTESE AUTHORITIES
The Maltese authorities take note of ECRI’s recommendation. The NCPE already functions independently.
The Maltese authorities take note of ECRI’s recommendation.
Again, the ECRI report cites anonymous sources.
ECRI RECOMMENDATIONS AND COMMENTS
45. ECRI recommends that the Maltese authorities
provide, by law, that persons who have been granted
subsidiary protection be entitled to receive social
assistance, when specific requirements are met.
RESPONSE OF THE MALTESE AUTHORITIES
The rights pertaining to beneficiaries of subsidiary protection are already set out in Subsidiary Legislation 420.07, on
Procedural Standards in Examining Applications for Refugee Status Regulations. The legislation in question provides that
a beneficiary of subsidiary protection shall be entitled:
(i) to remain in Malta with freedom of movement and to be granted
personal documents, including a residence permit for a period of one year, which shall be renewable,
(ii) to be provided with documents which enable him to travel especially when serious humanitarian reasons arise that
require his presence in another State, unless compelling reasons of national security or public order otherwise require;
and,
(iii) to have access to employment, subject to labour market considerations, core social welfare benefits, appropriate
accommodation, integration programmes, State education and training, and to receive core State medical care, especially
in the case of vulnerable groups of persons.
47. ECRI’s attention has been drawn in particular to
cases of persons residing in the open reception
centres (mostly Africans with varying types of
statuses) who loiter in the streets and in the
roundabouts, waiting to be offered work. In one case
for example, representatives of civil society informed
ECRI that after a day of hard labour, several of these
workers were paid 25 cents, instead of 25 Euros as
they had been promised.
48. ECRI reiterates its recommendation to the
Maltese authorities to take steps to counter the
labour exploitation of refugees, persons granted
humanitarian protection and immigrants by
addressing their over-representation in undeclared
employment. It urges the authorities to monitor and
ensure the application of Legal Notice 432 of 2011.
It is therefore considered that this recommendation is already being implemented.
Again, the ECRI report cites anonymous sources.
The Immigration Police carry out checks in places of employment in order to verify that all Third Country nationals found
working, are properly documented and are in possession of all the required permits.
Moreover, places of employment are being monitored in accordance with Legal Notice 432 of 2011 on Minimum
Standards on Sanctions and Measures against Employers of Illegally Staying Third-Country Nationals Regulations, 2011.
In case of an infringement, proper action is taken in line with Legal Notice 432 of 2011.
ECRI RECOMMENDATIONS AND COMMENTS
RESPONSE OF THE MALTESE AUTHORITIES
Access to public places and services
52. Despite the fact that the Equal Treatment of The 2009 EU-MIDI survey is based on a dubious methodology.
Persons Order prohibits discrimination on grounds of
racial or ethnic origin in the provision of goods and
services, 35% of Africans who participated in the
2009 EU-MIDIS survey claimed they had faced
discrimination in cafés, restaurants, nightclubs or
shops in the 12 months prior to the research.
Again, the ECRI report cites anonymous sources.
ECRI’s sources have confirmed, in fact, that it is not
uncommon for drivers of public transportation to
refuse persons considered to be migrants to board
the bus or to refrain from stopping at bus stops
located in areas in which refugees, asylum seekers
and migrants live.
54. ECRI strongly recommends that the Maltese The initiatives launched by NCPE in the field of housing are constantly being extended by NCPE. NCPE has just closed
authorities extend the initiatives launched by the a project entitled ‘I’m not racist, but’. This project looked into discriminatory issues with regard to the housing sector.
National Commission for the Promotion of Equality in
the field of housing (notably the commissioning of
studies and the awareness raising campaigns on
racial discrimination), to access to public places and
services in general and, more specifically, to the
entertainment and public transportation sectors.
Health
ECRI RECOMMENDATIONS AND COMMENTS
55. ECRI is pleased to note that in August 2008, a
Migrant Health Unit was set up within the Department
of Primary Health in order to address and respond to
the specific needs of migrants (lack of knowledge
about the health care system of the host country;
language barriers etc.), in light in particular of the
heavy influx of migrants registered in recent years.
The objectives of this unit are to: provide community
based health education to migrants in their mother
tongue (addressing issues such as access to the
Maltese health care system, nutrition, food and
kitchen safety, H1N1 - Swine flu, sexual &
reproductive health); help migrants access health
care services; provide translated material; train health
care professionals and students on culture and
diversity issues in health care; and train cultural
mediators. The services provided are free of charge.
Racist Violence
57. According to the 2009 EU-MIDIS survey, 29% of
the respondents of the survey (immigrants from
Africa) claimed that they had been victims of racially
motivated assault, threat or serious harassment. The
report further shows that over 50% of the racially
motivated assaults had not been reported to the
police, on the most part, for lack of confidence in the
authorities. ECRI has received some reports of
violent attacks on migrants, particularly of African
origin, which were allegedly ignored by the police.
Furthermore, it has been informed of violent offences
having been committed against migrants near the Hal
Far and Marsa open reception centres for asylum
seekers and refugees, such as, for instance, the
throwing of bags of urine and pepper spraying.
Climate of opinion and racism in public discourse
RESPONSE OF THE MALTESE AUTHORITIES
Whilst the Maltese authorities provide these services free of charge to the clients, their cost is very significant. Services
provided include treatment for disease that had previously been eradicated from Malta.
In addition the NGO Health Consumer Powerhouse has written. See:
http://www.healthpowerhouse.com/files/EHIVI%202009%20Press%20release%20Malta.pdf
“The care and conditions for people living with HIV/AIDS in Malta are very good … The total number of HIV/AIDS cases
is still small compared to other countries, but growing fast… in recent years the number of people on the island infected
with HIV has quadrupled; half of the cases being treated in Malta involve African immigrants.” In another extract it adds:
“Most of the increase in HIV diagnoses among heterosexuals is among persons originating from infected high-prevalence
countries outside Europe, primarily in sub-Saharan Africa. Data from several countries suggest that the majority of these
persons have been infected in their country of origin, although transmission within the host EU country does occur.”
Again, the ECRI report cites the 2009 EU-MIDI survey, which relies on dubious methodology, and on anonymous
sources.
ECRI RECOMMENDATIONS AND COMMENTS
61. ECRI reiterates its recommendation to the
Maltese authorities to promote a public debate and
raise awareness on the issues of immigration and
asylum that reflects the human rights dimension of
these phenomena, providing more information on the
circumstances from which immigrants and asylum
seekers are fleeing and clearly explaining the
difference between persons with a protection status
and irregular migrants.
63. …ECRI regrets that no specific debate has been
held by Parliament… on immigration and asylum that
reflect the human rights dimension of these
phenomena….
64. ECRI furthermore urges the authorities to
introduce legal provisions allowing for the
suppression of public financing for those political
parties whose members are responsible for racist
acts, as well as provisions within the Parliament’s
Code of Ethics which sanction racist speech or
conduct.
The media
66. At the same time, ECRI has been informed that
certain media, most notably the Times of Malta, have
started to reverse this trend and are increasingly
careful in using the correct terminology.
RESPONSE OF THE MALTESE AUTHORITIES
In their interventions relating to migration and asylum, Government officials already raise awareness in relation to the
human rights dimension. Moreover, information is provided on the circumstances leading to the arrival of asylum seekers
in Malta and other countries.
The House of Representatives determines its programme and procedure without interference from outside bodes.
The House of Representatives determines its programme and procedure without interference from outside bodies.
Again, the ECRI report cites anonymous sources.
At the same time, there have also been examples of
more balanced reporting and cases in which migrants Pending the publication of the report by the enquiring magistrate, the facts of this case have not been authoritatively
have been cast in a positive light. For example, an established.
Eritrean refugee who lost his life while trying to
rescue a tourist who was drowning was portrayed by
the media as a national hero.
ECRI RECOMMENDATIONS AND COMMENTS
67. ECRI recommends that the authorities, through
the National Commission for the Promotion of
Equality or the Broadcasting Authority, launch
initiatives aimed at offering journalists training in
issues concerning the fight against racism and racial
discrimination and on ways in which the latter can
contribute to promoting acceptance of different
vulnerable groups.
69. As concerns the prosecution of cases of
incitement to hatred, including when committed
through the Internet…. Furthermore, ECRI notes that
in the present day there is no authority which
monitors comments on newspaper websites made in
reaction to their articles. In this connection, as
confirmed by representatives of civil society, it is not
infrequent that comments to articles reporting on
migrants, asylum seekers and refugees express
racist views or use racist discourse.
70. ECRI recommends that the Maltese authorities
set up a law-enforcement unit tasked with monitoring
continuously the Internet for instances of racism or
racial discrimination and empowered to act ex officio
in case of breach of the anti-discrimination legislation
or the provisions against incitement to hatred.
72. In addition, representatives of civil society have
informed ECRI that this Commission is not well
known by migrants, refugees and asylum seekers.
73. ECRI recommends that the Maltese authorities
ensure that an independent body be mandated to
receive complaints (or to raise cases ex officio) for
breach of the Press Act and that it be empowered to
inflict sanctions. This body’s mandate should then be
publicised as widely as possible.
Migrants
RESPONSE OF THE MALTESE AUTHORITIES
Training in relation to racism and racial discrimination has already taken place.
Again, the ECRI report cites anonymous sources.
The Maltese authorities are not in agreement with this recommendation insofar as it involves the setting up of a unit
tasked specifically with monitoring the Internet for instances of racism or racial discrimination. Whilst monitoring of the
internet is carried out by the Police authorities as required, be it in the case of racism or other crimes, the setting up of a
monitoring unit specifically for cases of racism or racial discrimination is not necessary. The Police authorities may
already act ex officio in cases of breach of anti-discrimination legislation or incitement to hatred.
Again, the ECRI report cites anonymous sources.
The Maltese authorities consider that current arrangements relating to the enforcement of the Press Act are adequate.
They do not intend to introduce press censorship.
ECRI RECOMMENDATIONS AND COMMENTS
RESPONSE OF THE MALTESE AUTHORITIES
84. ECRI recommends that the Maltese authorities The procedure for detention is prescribed by Article 5 of the Immigration Act (Cap. 217, Laws of Malta). Once a removal order
amend their legislation in order to ensure that all is served, the person is detained pending his/her removal. A person who has been detained is given a pamphlet informing
persons held in the detention centres are provided with him/her of his/her rights. The person is also informed that he/she has a right to appeal from the removal order and from
a speedy and effective judicial remedy to challenge the his/her detention and that he/she is entitled to apply for international protection.
lawfulness of their detention.
Article 25A (9) of the Immigration Act (Cap. 217 of the Laws of Malta) stipulates that: “The [Immigration Appeals] Board shall
also have jurisdiction to hear and determine applications made by persons in custody in virtue only of a deportation or
removal order to be released from custody pending the determination of any application under the Refugees Act or otherwise
pending their deportation….”
The Immigration Appeals Board is a judicial body. The Board members enjoy security of tenure. They are appointed for a
period of 3 years and are eligible for reappointment. They may only be removed from office by the President acting on the
advice of the Prime Minister, on grounds of gross negligence, conflict of interest, incompetence, or acts or omissions
unbecoming a member of the Board.
Furthermore, the same disqualifications and reasons for removal from office that are applicable to the Judiciary also apply to
the members of the Immigration Appeals Board. In practice, sittings before the Board are conducted in a similar manner to
those before the Courts. Individuals may be assisted by a legal representative, evidence is heard by the Board and
submissions are made by the parties.
Article 11(10) of the Common Standards and Procedures for Returning Illegally-Staying Third-Country Nationals Regulations
stipulates that:
“The third-country national subject to the provisions of subregulation (8) [detained for the purpose of removal] shall be entitled
to institute proceedings before the [Immigration Appeals] Board to contest the lawfulness of detention and such proceedings
shall be subject to a speedy judicial review.”
The provisions of Article 11 of the aforementioned Regulations do not apply to third country nationals who are subject to a
refusal of entry in accordance with Article 13 of the Schengen Borders Code or who are apprehended or intercepted by the
competent authorities in connection with the irregular crossing by sea or air of the external border of Malta and who have not
subsequently obtained an authorisation or a right to stay in Malta.
In view of the above considerations the Maltese authorities consider that Malta is already in compliance with ECRI’s
recommendation.
ECRI RECOMMENDATIONS AND COMMENTS
RESPONSE OF THE MALTESE AUTHORITIES
89. ECRI strongly recommends that the Maltese Detention as practised in Malta is fully compliant with Council of Europe recommendations (Recommendation 2003(5))
authorities provide non-custodial alternatives to on the detention of asylum seekers. In fact, the Recommendation outlines that detention is justified:
detention and refrain from resorting to the detention of
migrants and asylum seekers unless it is strictly - when their identity, including nationality, has in case of doubt to be verified, in particular when asylum seekers have
necessary in the particular circumstances of an destroyed their travel or identity documents or used fraudulent documents in order to mislead the authorities of the host
individual case.
state;
- when elements on which the asylum claim is based have to be determined which, in the absence of detention, could
not be obtained;
- when a decision needs to be taken on their right to enter the territory of the state concerned; or
-when protection of national security and public order so requires.
Malta’s detention policy is also in line with the first limb of Article 5 (1)(f) of the European Convention on Human Rights
(ECHR), that is, detention for the purposes of preventing unauthorised entry into the country, as well as the second
limb, that is detention for the purposes of removal.
In Malta the detention requirement is not applied indiscriminately. In fact, vulnerable persons are not subject to the
detention requirement. Hence, not all migrants and asylum seekers are detained.
Also, detention as prescribed in the context of the Common Standards and Procedures for Returning Illegally-Staying
Third-Country Nationals Regulations is to be applied “unless other sufficient and less coercive measures are
applicable”.
90. ECRI also recommends that third-country nationals The authorities pursue efforts to make the necessary arrangements to remove irregular migrants throughout the entire
who are detained with a view to deportation should be period of detention; provided that return is not pursued whilst asylum applications are pending.
freed when it is clear that it is no longer possible to
Contacts are maintained with countries of origin to acquire any necessary documentation in order to effect removal.
effect the deportation.
Moreover, the persons concerned are given the opportunity to return to their respective countries voluntarily.
In addition, Article 11(8) of the Common Standards and Procedures for Returning Illegally-Staying Third-Country
Nationals Regulations provides, in the case of detention for the purpose of removal, that detention shall be for a short
period and shall subsist as long as the removal procedure is in progress and is executed with due diligence. It is
therefore considered that this recommendation is already being implemented.
ECRI RECOMMENDATIONS AND COMMENTS
RESPONSE OF THE MALTESE AUTHORITIES
91. It further recommends that the Maltese authorities Such limit has been transposed in Article 11(14) of the Common Standards and Procedures for Returning Illegallyprovide under Maltese law a limit to the duration of the Staying Third-Country Nationals Regulations.
detention of migrants in an irregular situation, in line
with Directive 2008/115/EC on common standards and
procedures in member States for returning illegally
staying third-country nationals.
93. ECRI acknowledges the fact that the European The report of the CPT’s visit to Malta of 26-30th September 2011 is unpublished and it is therefore not clear how ECRI,
Committee for the Prevention of Torture (the CPT) is in footnote 53 of its report (reproduced in this document as footnote 1), states what the CPT did during that visit.
the monitoring body of the Council of Europe which is
best placed for assessing the material conditions of
places of detention, including the detention centres for
migrants, as well as the treatment of persons detained
therein1. ECRI, nevertheless, takes note of the
information it has received by the authorities that on 31
March 2012, two out of the three detention centres
were in use (Safi Barracks and Lyster Barracks) and
held 543 migrants and asylum seekers. The authorities
have also informed ECRI that they have successfully
replaced many army and police staff with civilian
personnel in the detention centres. Whereas in 2005
there were, respectively, 122 and 54 army and police
personnel, in 2012 the staff included 40 army, one
police and 140 civilian officers. ECRI commends the
authorities’ efforts and encourages them to complete
the transition to staffing composed solely of civilian
personnel.
94. Nonetheless, many representatives of civil society Again, the ECRI report cites anonymous sources.
have pointed out that there is an extremely limited
array of meaningful activities available to detained
migrants and that in many cases their mental health
deteriorates.
1
In its visit to Malta of 26 to 30 September 2011, the CPT reviewed the conditions in the detention centres for immigrants at Lyster and Safi Barracks.
ECRI RECOMMENDATIONS AND COMMENTS
RESPONSE OF THE MALTESE AUTHORITIES
98. ECRI recommends that the Maltese authorities Efforts are being made by the authorities concerned to finalise such investigations as soon as possible.
conclude as soon as possible all the inquiries and the
criminal investigations opened further to the deaths of
a Nigerian and a Malian national in 2011 and 2012,
while in the custody of detention personnel and give
the public full access to the results.
99. ECRI strongly recommends the Maltese authorities Since 2008 the Detention Service embarked on a tailor-made yearly training programme for detention officers and other
to provide detention personnel with training on human personnel involved in giving a service in the Closed Centres. The training is organized by UNHCR and is supported by
rights,
including
provisions
against
racial Detention Service and other organizations. The programme sees the participation of NGOs as partners as well as
discrimination. ECRI further recommends that the persons directly involved in providing services to irregular immigrants. The programme is aimed at providing job specific
authorities raise the detention personnel’s awareness training for all Detention Service personnel.
of the fact that abuse of power and the use of
excessive force will be severely punished.
The recommendation is therefore being implemented.
104. ECRI strongly recommends that the Maltese The detention requirement does not apply across the board, as vulnerable persons, including unaccompanied minors,
authorities ensure that all unaccompanied minors and women with children, families and disabled persons are not subject to detention. Vulnerable persons are not kept in
persons suffering from serious physical or mental detention and transferred to apposite centres to cater for their specific needs.
conditions are promptly identified and transferred to an
appropriate, non custodial setting, suitable for their In the case of the more dubious cases the freedom of such persons is restricted only until such time as the necessary
vulnerable condition.
medical clearances are obtained.
These situations may be rendered more difficult because of the unavailability of documents certifying a person’s age
and dubious and sometimes shifting statements regarding age.
ECRI RECOMMENDATIONS AND COMMENTS
106. ECRI acknowledges Malta’s merit in carrying out rescue
operations in its search and rescue zone (SAR zone).
Nonetheless, there have been reports according to which some
migrants at sea were not rescued, even though they had been
spotted by a Maltese military patrol or had been located in
Malta’s SAR zone. According to the Council of Europe
Commissioner of Human Rights, in one incident in 2009, a boat
from Libya was adrift in the Mediterranean sea for twenty days.
The persons aboard were reportedly not rescued by the Maltese
military patrol which had approached the boat and had offered
food, water and fuel. As a result, only 5 out of more than 70
people (mainly Eritreans) survived. The UNHCR has also
expressed concern about a rescue operation in June 2010. It
noted that Malta had relied on Libyan vessels to conduct the
rescue operation inside Malta’s SAR zone. The migrants
(including three women and an eight year old child), almost all
Eritreans, were taken to Libya. According to the Council of
Europe Commissioner of Human Rights, a similar incident
happened in July 2010, whereby 55 Somali nationals travelling
from Libya were intercepted at sea by a Maltese military vessel
in its SAR zone. 28 were allowed on board and were taken to
Malta; the remaining 27 boarded another ship and were
returned to Libya, where they were reportedly beaten and
tortured. Although the authorities have stated that the 27
migrants returned to Libya voluntarily, this has been contested.
In this connection, ECRI reminds the Maltese authorities that
the prohibition of torture and inhuman or degrading treatment is
a human right which admits no derogation and that Parties to
the ECHR must ensure that their actions do not expose people
to such treatment. Furthermore, Libya is not a party to the 1951
Convention on the Status of Refugees and does not have
asylum legislation or procedures in place to allow asylum
seekers to lodge asylum requests. Therefore, relinquishing
responsibility for rescue operations to Libya implies accepting
the possibility that persons will be subject to ill-treatment or
torture, or will be sent back to a country where they are at risk of
persecution on account of their race, religion, nationality,
membership of a particular social group or political opinion.
RESPONSE OF THE MALTESE AUTHORITIES
In the last 10 years, the Armed Forces of Malta (AFM) have saved thousands of lives, often risking the lives of Maltese
personnel. The AFM never failed to respond to a potential distress situation within the Malta SRR and have often
intervened in cases within the SRR of a third country. In addition Malta cooperates closely with Italy to ensure that lives
are not lost at sea.
As regards an incident referred to, the migrant craft in question had only five persons on board when approached by
Maltese units; they all refused assistance and insisted on proceeding to Lampedusa. The Maltese unit remained in the
vicinity of the migrant craft to provide assistance, should it be required. The information or allegation that originally there
had been up to 70 persons on board was transmitted by the migrants following disembarkation in Lampedusa.
ECRI also refers to a rescue operation in June 2010, in which Malta had relied on Libyan vessels to conduct the rescue
operation inside Malta’s SRR. The AFM has no knowledge of any such case. However, there was a particular case
where four migrants (including three women and an eight year old child), almost all Eritreans, were taken to Libya.
A similar incident happened in July 2010, when 55 Somali nationals travelling from Libya were intercepted at sea by a
Maltese military vessel in its SRR. 28 were allowed on board and were taken to Malta; the remaining 27 boarded
another ship and were returned to Libya, where they were reportedly beaten and tortured. In this particular case, a
Maltese unit was already engaged in conducting the rescue at which point a Libyan unit appeared on scene and began
to undertake rescue operations simultaneously. No coercion of any sort was exercised by the Maltese Unit. In addition,
Malta could not forbid the Libyan unit from providing assistance, in accordance with its international obligations.
ECRI RECOMMENDATIONS AND COMMENTS
RESPONSE OF THE MALTESE AUTHORITIES
107. ECRI has also been informed that there are The different interpretation of the law by Italy and Malta has never resulted in the failure to rescue persons or to any
regular disputes between Italy and Malta concerning loss of life. Both the Maltese and Italian authorities have always conducted rescues first and only then addressed the
search and rescue operations, particularly in cases of issues regarding disembarkation.
boats located in Malta’s SAR region which are
physically closer to the Italian island of Lampedusa.
Malta, on the one hand, claims that disembarkation
should occur at the nearest port of call regardless of
the SAR zone in which the boat is located. Italy, on the
other hand, claims that responsibility over the SAR
zone takes precedence. ECRI considers that it is
unacceptable that legal disputes of this nature result in
failure to rescue persons in distress, or worse in loss of
lives.
108. ECRI recommends that the Maltese authorities Malta already fully respects its obligations under international legal instruments. This was confirmed by IMO auditors in
fully respect the principles laid down by international 2011. The disembarkation regime applicable within the Malta SRR is that of disembarkation in the nearest place of
law with respect to rescue at sea.
safety in accordance with the principles of international law.
109. ECRI’s attention has also been drawn to the Again, the ECRI report cites anonymous sources.
refusal of the Public Registry to allow migrants who
have not qualified for refugee status or subsidiary
protection to get married.
110. ECRI recommends that the Maltese authorities The grounds for a marriage to be registered at the Public Registry in Malta are :
ensure that the right to marry is enjoyed by all persons
present in Malta.
if the said marriage is celebrated in Malta in terms of the Marriage Act (Cap 255 of the Laws of Malta); and
if a citizen of Malta marries abroad and at the request of any person interested, the act of marriage of the said
citizen of Malta drawn up or registered in a foreign country by a competent authority in that country, is
registered in Malta in terms of Article 244 of the Civil Code ( Cap 16 of the Laws of Malta).
Third Country Nationals would not qualify for the latter as they are not Maltese citizens but do qualify for the former if
the celebration of the marriage is preceded by a request for the publication of banns of matrimony according to the
abovementioned law.
Refugees and asylum seekers
ECRI RECOMMENDATIONS AND COMMENTS
112. ECRI has been informed that in the past, these
had not been clearly defined by the law and that, in
practice, persons with subsidiary protection did not
receive them. However, in 2011, the authorities
issued a policy clarification specifying that
beneficiaries of subsidiary protection can receive
certain forms of social assistance from the
Department of Social Security, if for instance they
cannot work.
115. ECRI was informed by civil society that persons
benefiting from THPN sign an informal agreement
with the Refugee Commissioner that they will make
efforts to integrate into society.
116. ECRI recommends that the Maltese authorities
ensure that the rights attached to temporary
humanitarian protection and temporary humanitarian
protection for former applicants for international
protection, are laid down by statute.
117. ECRI recommends that the Maltese authorities
provide persons who have been granted temporary
humanitarian protection for former applicants for
international protection and have lived in the country
for a number of years, a permit to stay which offers a
longer-term perspective, particularly when their level
of integration in Maltese society has already been
positively assessed.
RESPONSE OF THE MALTESE AUTHORITIES
Again, the ECRI report cites anonymous sources.
Again, the ECRI report cites anonymous sources.
The Maltese authorities consider that the policy currently in place, which has been adopted on Malta’s own initiative,
provides sufficient guarantees to the persons concerned.
The current provisions are considered adequate, particularly as the permit to stay may be renewed.
ECRI RECOMMENDATIONS AND COMMENTS
122. ECRI encourages the Maltese authorities in their
efforts to ensure that all persons entitled to refugee
status actually secure this status.
RESPONSE OF THE MALTESE AUTHORITIES
The Office of the Refugee Commissioner notes that all asylum claims are considered on their individual merit. All the
asylum-seekers are given an opportunity for a personal interview during which they are given ample time to explain in
detail the reasons for seeking asylum. The evidence presented by the asylum-seeker, including verbal as well as other
documentary evidence is examined thoroughly.
When assessing an asylum claim, the Office of the Refugee Commissioner starts by examining whether the applicant
satisfies the criteria to be recognised as a refugee in terms of Article 1A of the 1951 Geneva Convention. Failing this, the
Office proceeds to examine whether the asylum seeker risks facing serious harm as defined in Article 15 of the Council
Directive 2005/85/EC, if s/he had to be returned to his/her home country.
The Office of the Refugee Commissioner has introduced a number of measures to ensure efficiency and to retain a high
level of quality in the decisions issued. In fact, it is to be noted that the recognition rate in Malta at the end of December
2012 stood at 86 per cent. The European average is 25 per cent. To this effect, Malta has the highest recognition rate in
Europe.
ECRI RECOMMENDATIONS AND COMMENTS
126. ECRI recommends that the Maltese authorities
provide at the earliest stages of the asylum
procedure, during the information sessions and in the
information booklet, a definition and an explanation of
the concept of refugee; the persecution grounds
should figure therein.
RESPONSE OF THE MALTESE AUTHORITIES
The Office of the Refugee Commissioner continued with its commitment to improve the services offered to asylumseekers. In fact in 2009, through an ERF co-funded Project, the Office started providing information with respect to rights
and obligations, to asylum seekers, applying for asylum in Malta.
Through this ERF Project 2009-2011 ‘Post Application client preparation and asylum determination interviewing centre for
asylum seekers which aims to adequately prepare TCNs for their asylum determination process’, this Office has invested
in a new system for the delivery of information sessions to asylum seekers.
Within one or two working days of the arrival of irregular migrants to Malta, staff from the Office of the Refugee
Commissioner visit the closed centres (in the case of people arriving irregularly by boat/air and then detained) and deliver
information about the asylum procedure in Malta. This Office makes sure that it caters for all levels of educational and
cultural backgrounds of asylum applicants. The same procedure of information sessions is also adopted in case of
persons who apply for asylum directly at this Office.
Information is delivered using different means (a) by personnel of this Office explaining the purpose of the session with
the help of an interpreter; (b) an audio visual presentation available in the most common (eleven) languages for our
asylum population; and a booklet that contains a transcript of the audio-visual presentation also available in eleven
different languages. The Office of the Refugee Commissioner further notes that those third country nationals that apply
for protection are assigned an interpreter who helps them fill in a registration form known as a preliminary questionnaire.
This good practice, to provide information to potential asylum-seekers, adopted by the Office of the Refugee
Commissioner is in line with European as well as International legislation.
| 19,232 |
cihm_38822_77 | English-PD | Open Culture | Public Domain | 1,795 | A new system of modern geography, or, A geographical, historical and commercial grammar and present state of the several kingdoms of the world [microform] : containing, I. the figures, motions and distances ... : to which are added, I. a geographical index ... II. a table of the coins ... III. a chronological table ... | None | English | Spoken | 7,039 | 13,649 | l.ulf it<.ore U» EGYPT. liuH'a niilf broiul. In ihe environs are many country lioufcs Ijolonglng to ChriC- tiiiii iiariliants, with line gardens, procUicinf; the cliuiteft fruits of the Laft. '|1 ic Miiliniiieilaii iiili;ibilaiits are liere alfo particularly civil ami polite. Cairo, now Mafr, tlie prefeiit capital of Kgypt, is a larj^e and populous, but a (lirai:reeable reliilence, on account of its pcftilential air, and narrow Iheets. It is liivided into two towns, ilie Old and ilie New, and defended by an old callle, the uoiks of wiiich are laid In be three miles in circundercnee. 'I hii calile is faid to liave be<n built bv Saladine: at the well end are the remains of very noble apait- nients, foiric of wdieli are covered witli domes, and adorned with pictures in Mufaie Wurk ; but thefe tipartnieiiis are now only ufcd for weaving cnd)ioidcry, and pre- l)aring the hangings and coverings annually fent to Mecca. The well, calk\l Jofepli's Wi II, is a ciulous piete of methanifin, about 300 t'eet deep. 'I'lie ineniory <il' tliat paiiiardi is (lill revered in I'-g} pt, where they Ihcw granaries, and niaiu- I'thcr wdiks of pid)lic ui'lil)-, that go under Iiis nanK\ 'J'liey are certaiidy of \alt nnii»)uity ; but it is very i|ueliionable whetlier they were erected by him. One oi' liis granaries is lliewn in Old Cairo, but captain Norden fufpects it is a Saraciu work, nor does lie give us any higli idea of the buildings of the city ilfeil". On tlie bank of the Nile, facin;; Cairo, lies the village of Gize, whicli is ihoi.glit |.) be ilii' anciint Memphis. Two miles well, is liulae, called the |)ort of Cairo, 'l\\^i Cluiliians of Cairo pradife a lioly cheat, during the Kaller holidays, by pretending tliat tlie lind)s and bodies of tlic dead arife tVom their graves, to wliich they return jieaceably. The llreels of Cairo are peik-red with the jugglers and fortune-tellers already mentioned, (^ne of their favourite exhibitions is their dancing caniels, whicli, v\hen }oung, they place upon a large heated lloor: the intenfe heat niakei the poo'- creatures c;n)er, anil being plied all the time with the found of a drum, the noifc of that inilrument fets them a dancing all their lives after. The other town.s of note in ligypt arc Damielt;., fuppofed to be the ancient Pe- hillmn ; Seyd, on tlie will banks uf the Nile, 200 miles foutli of Cairo, faid to be the am lent I''.g\plian '1 lubes ; and Colliar, on the weft coaft of the Red Sea. 'Ihege- neial practice of fti.ingers, who vilit thofe places, is to iiire a Janizary, whole au- thority commonly protects them from the iiifults of the other natives. Suez, for- merly a place of giCat trade, is nnw a fmall city, and gives name to the IlUimus, th;it loins Atrica with -\lia. 'I he chiklreii i.l Ifiael are fuppofed to liave niarclud near ibis city, wlieii ihey left l-gypt, in their way towards the Red Sea. 'I'his fea appears to have certainly derived its name tVom Kdom, long and early its powerful mailer, tiiat word (igiiifying lied in Hebrew. It tormerly went by the name of the f<.;\ of l.'".(Iom, or idumea. Almoft every ubjecl and village in this country prefeius foriic amazing piece of antiijuity. Mauiu,k qj'aR^ "•-*■] " It I'.as been a wonder Tays Mr. Bruce in his journcv ;icr(jfs tlie delert of the '1 liebaid from K-enne to Coli'eir! with ail travellers, and with myfelf aniong the reft, where the ancients procured that prodigious quantity of fine marble, with wliic h all their buildings abound. That wonder, however, aniung many others, n'lw ceafes alter liaviiig palfeti, in four days, more granite, [)orph\r\, marlde, and jafuer, than woold build Rome, Athens, Corinth, Syracufe, .\leiiiplii>, Ai< xaiidiia, am! half a dozi n fuch cities. It feemed to be very vilible that thole n(»eningt« in the hills, whicli 1 call defiles, were not natural, but ariiticial, and that wboK- momitaii.i. had been lut out at tlirle |)laces. " The p.iiph\r\ il.ews ittl.if by a fine purple land, witliout any glofs, or glitter tm it, and i.. c\cee(.ii.igly agreeable to the e)e. It i.> mixed with tiie native uliiie faiid, and (ixid gra\el of the plains. C.reen uiivariegated marble is generailv feeu in tUe fame mounluin with the porpliyry. Where the two veins meet, tuo marble E Sst marble is for fomc iiiiln.s brittle, but the porphyry of tlic fame liardnefs as in hiIrt places. " 'I he granito is covered with faiicis, and it)i)ks lil;c rtoiic of a dirty, brown colour. l)Ut this is iml) the chaDLre and impieiiioii the fun and weather have made upon it ; fiir upon breaking it, you fee it is grey granite, with black fpots, with a reddilli catt, 1)1- bliilh owr it. 'Ihin red feenis to lade, (>r fuller from the outward air, but, upon worlviiig or i)o!illiiiig the furface, this colour again appears, it is in greater cpian- tity tlian thi- porpliyry, and nearer the Red Siea. I'ompey's pillar feems to have l)een from tlii-> "piairy. " Ne.\t to the granite, but never, as I obferved, joined with it in the fame monn- tiiin, is the red marl)le. It is covered with fand of the fame colour, ar.d looks as if the whole mountain were fpread over wiili brick dull'. 'J here is alfo a red mar- ble with white veins, whicli I have often i\-.-n at Rome, l)Ut r\ot in prine!|>al ful)- yih. I have alf) feen it in llritain. 'Ihe common green (called fer|)enliiU' looks ;;s if covered over with Brazil fniilV. Joined with this gieen, 1 faw two famples of that beautiful marble, they call Ifubella ; one of them wiili a yellowilh c;\ll, v. hich v't' call t,Juaker-c('lour, the other with a blueilh, which is commonlv termed thjve- enlnur. In this green, likewife, it was, we faw the vein of Jafper ; i)ut whether il was abfohii "ly the fame with this, wliich is the bloody jalper, or blood-lkme, is what we had not time to fettle. " 1 ihould fnlt have made mention of the verde antico, the dark green with white irregular fpots, becaufe it is of the greatell value, and nearelt the Nile. '1 his is produced in the mountains of the plain green, or ferpentine, as is the jalper, and is not difcoverable by the duft, or any particular colour upcui it. Kirli, there is ;i blue lleaky Hone. After lifting this, we come to the beds of tfte verde antico ; and here the cpiarrying is very obvious, for it has been uncovered in patclies, not al)o\ u twenty-feet lipiare. Then, in another part, the green Hone has been removed, and- another pit ot it wrought. " 1 faw, in feveral places in the plain, fmall pieces of African marble fcattcred about, but no rocks or mountains of it. This prodigious (tore ui marble is placed u|i(in a lidge, whenci- there is a defcent to the call, or welt, either to the ISile or Kid Sea. 'I he level groui;d, and hard-fixed gravel are proper for the heaviell car- riaL;os, n.d will eafil\ and fninothly (.'onvey any weiglu whatever to its place ot em- barkation on the Nile ; fo that another wonder cealid, how the ancients iranlportcd. tlii'fe vatl bUnks of mar!)!e to Tlubes, Memphis, and Alexandiia *." Masl"' \cifRKS AND CO M M 1'. Rc K. i 1 lie I'lgvptiaus export prodigious quan- tities of unnianufatturcd as well as prepared tlax, thread, cotton, and leather of all forts, callicoes, vellow, wax, fal anmioniiiv , I'alfron, fug;ir, fena, and caliia. They ti;i(le with the Arals tor coliee, drugs, I'pices, callicoe:., and o'her mere'.r.mdl fes, which are lan;led at Suez, fro:n w'.ience they fend them to harope. Several liii ruiiean Itatis have confuls reliileiu in I'gypt, but the culioms ot the Turkilh go- vernment are managed by Jiws. A number ot I'.nglilh velfels arrive yearly at Alexandria ; fome ot whi(.h are laden nn account ot tlie owneis, but moil of il, • a iire hired and employed ;■.!> carrier.i lo the Jews, Armenians, and Maliometlan traders. Constitution and covi.RXMf.NT.j A viceroy is tent tu i:.gypt t'rom ll.o I'lirte under the title of the pallia or '., 'uivv of Cairo, and is one of the ;;reate'l iitiiters of the Ottoman e:n|)ire. But u.iCe the revolution of Ali Bey, the power (it the Turks in l'g}!>t is inoie precarious than in any other province. the g.jve'-ii- boih nn>iiartl\ical and rei)ublican. ilie monarehical is exec, .led iiiunt of I'^gypt IS Driici'i Travi'i?, .(to. vu ['. 1=6, !»;, i£3. by ill EG Y ^ T. by \]\c pallia. The ropiihliciin, or rathr the nnllncTiUical part of tli<- ;^^overnmcnt, (.onliils (if a divan, compoioii ot" iwoiity; mr fap^iiH-ks, brjs or loids. Tlie hciul ot tlicm is called tlie llioik belief, \vlio is choffii liy tin- divan, and tonHrmcd hy tlie pallia, livery one of tlie faiigiatks is arbitrary in bis own territory, and exerts fovoreii^n power'; the inajnr ])ait uf iluui lefide a» Cairo. If the ^rand iif^nior's pallia acts in oppolition to the iVnfe of the divan, or atlcnipts to violate their \n]. vile^es, they will not fuller him to conliiuie in his poll, and the I'orte is ohlif^cd lo fend another. 'I hey havi.' an aiilheiUic grant of privik'gcs. .ialed in the year 131-. in whieh year .Sultan Selim coniiuered Kgypt fioni the \iainaliikeb. RuvKNi'KS.] Thefe are very incnnfiderablr, when compared with the natural riches of the country, and the defpotifm of its i;ovi rnmeiit. Some fay they amount to a million llorling, and that two thirds of i'^;' whole is fpent in the country. Mii.i i.\uv srRKN<;TH.] '^Ili^ conlinsin the Mnmalukes, fome hodiesol whon, are caiiti>ned in the villages to exat4i»'l'bute, and fuj)port authority. 'I'he greaur pait are ali'eml;led at Cairo. They amoiinl to about eight ihoiifand men, attnclud li> the diirerent hey-^, wiiom they enable t ' contend with each other, and to lit tin. 'J'mks at defiance. I lis 1 OR v.] It is generally agreed that tiu* princes of the line of the Pharoalis fat on the throne of Kg\ pt, in an iininterrui)tcd fucceliion, till Camby Ics, the ficond king of IVrlia, con<|iured the I'.gypti.ins 320 years before tin birth of Clirill ; and thai in the reign of thole princes, the pyramids were railed ; flruttures, wiiicji cannot now be slewed wi'liout allonilhment. I'-g) pt continued a part of 1 lie Pcr- lian empire, till Alexander the (jreat vancpiilhed Darius, when it fell under the dominion of that ])rince, who foou after built the celebrated city of Alexandria. The cominells of Alexander, wlio died in the prime of lite, being fei/ed upon hy his general.s, the ])rovince ol I'.gyiit fell to tin- Ihaie ot Ptolein\', by fome fiiiinofcil to ha\e bi-en a hall-brotl.er of Alexander, when it again became an independeiU kingdom, about joo \ears betore Clirill. His fuccellors, who foinetimes exieiul- C'd their dominions over great part cf Syria, ever after retained the nameofl'io- lemies, and in that line I'-gypt continued between two and three luindred vcars till the tamoi'.s Cleoi)atra, the wife and tiller of i'tuleiny Dionylius, ilu- lalt kiiiij' affciided tlie throne. After tlie death of C!leopatra, who h.id been luiUrefs fuccel- llvely to Julius C.efar and Mark y\nthony, l'-gy|'t became a Koinan province, and thus remained till the reign of Omar, the (econd Calif of the fuccellors of Mahomed, who ixpelled tlie Komans, after it had been in their hands too vears. '■ ■ • famous library of Alexandria, faid to coiilili of 700,000 volumes, was to!- lectxl 1)\ I'loK my I'hiladelphus, fon of the tiill Ptolemy; ;ii',d the fame prince caufed the Old Teftamenl 10 hi; tranllated into Greek, but whether by feventv-two interjui tirs, and in the manner commonly related, is julUy (|uellioned : this trans- lation is known by lie name of the Septuagint. Om;ir fiibjeded Kgypt to the .Ma- homed. in ))oner, about the year 640, ;m(l the CaliN ot Habslou were foserei^iis of the coiMitry till 870, wlu u the l^gyptiaiis fet up a gosoriior of tlieir own called the C.'ilif of Cairo. About the time of the crufades, l^etweeii tV.e year t i ;o;ind 1 ii;o, i'.gvpt wasci- verned 1)\' .Nornhlin, the Siuacen falt;in of Dauiatcus, wliiii\- llm, the lainoiis .Sala- tiine, provid In tnnnidalde to thofc ('hriliian .■uUenttui r^, ;iiul reu ok from tln'iii Ji- rufalcm. lie inllituted the miliiar)- corps o( M.im ilukcs, like the J;inizarn.s o\ Conliaiilinople, vim, about th;- yriir 1242, ad.aiued one of ihelr own ollieirs to tlie throne, and ever after ( hofe their [irince out of their own body. i'",gypt, lor fome li.ne, mad<' a lisnirt' uiulL-r iliofe illufirloiis ufiirj)ers, and uiiide a noble lhin<l ;i|,Miii(l the prevailin;^ pjwcr of the Turks, till under ik-luii, wlio, about llie \i.-.i! '51;. %" JIT E G Y V T. ffjj Ht7, after giving tlie Matnalukcs fcvcral bloody defeats, reduced E;{ypt to its prc- fjiii it;>i>-' "f fiilijicrioii. U'hile Si-lini wns tVitling the govcnuiu'nt of I'.gypt, great miniln'r.s of the an- cient inbaliiiants witlidrcvv into tiic dtferts and plains, utuUr /iiigancus, froni wlionce tlu'v attacked tlie citie-, and vilhigcs of tlie Nil'-, and iilinuLied wliaievcr It'll in tlieir way. Si!i .1 and lii; nlliccrs pcicuvin^ tliat it would lie u matter of f^reat ditficuity to cxliii)ate iholc marauders, left tluin at lilaily to i[iiit tlie linmiry, which iiiey did in gu.ii numbers, and their pollcriiy were known over Europe and Alia, by the name of (iiplirs. An attempt was made a few years fnice to deprive tlie Ottoman I'oite of ils ai!- lliority over Kgypt by Ali Hey, wliofe father wai a prirll of the (neik cluiieh. Ali turned Maliomedan, and being a man of abilities and addrefs, rendered hiiufelf cx- treinelv popular in I'.gypt. A falfe accufalioii having been madi: ai^ainll liiin to llie ifrand li'jtiior, liis head was ordered to be lent to Conllantino[)le, but lieiiig ap- iiii/ed of the delif^n, he feized and put to deatli the melTenger who broiii^lit the or- ,K r, put liimfelf at tlie he^id nf an army and taking advantage of the diiirefsful and (|an"^erous lituation to which t!>e 'I'urkilh empire was reduced, in confeciuence of llu' war with Kullla, lioldly mounted tiie llirone. But not content with the kinc;- iloin of I'-K^pU ''*■' "'f" ''''^ clami to Syria, I'aleftine, and that part of Arabia which liiid beloni;ed to tlie ancient Sultans. He marcheil at the liead of his troopx to fiiiiport tliefe pr* teiilions, and attually fuhdued fi'ine of the neighbourinj^ provinces lioih of Arabia and S)ria. At tne fame time tluit lie was engiiged in thele f;reat t'literprizes, he was not lefs attentive to the ellablilliing of a regular government jn a country that had been long the feat of anarchy and cont'ufioii. His views were ciiually extended as to commerce ; for which purpofe he gave great encourage- ,miit to the Chrillian traders, and took olV foine Ihameful lelbaints and indii;iiiiies, to which they were fubjected in that barbaious country. He alfo wrote a letter to the republic of Venice, wiili the greatcit alfurances of his triendihip, and that their iiKiThants Ibouid meet with every degree of protetlion and fafety. His jjreal delign was laid to be, to make liimfelf p.aller of the Red Sia ; to open the [)ort of Sue/, to all nations, but particularly to the Kuropeans, ar,d to render I'.jrypt once more the Rreat centre ot commerce. Ihe condutt and views of Ali IJey Ihewed an extent of thought and ability that indicated nothing of the barbarian, and befpoke a mind equal to the founding of an empire. He alhiined the titles and Hate of the ineieiit Sultans o( Hgypi. and was ably fupported bv Sheik Daher, and fonie other Arabian princes, who warmly efpoufid his interells. Mmk iJaher accepted the Fortes full amnelly, and trutiing to tlieir alfurances, em- braced the captain pallia's inviiation to din.' on board his ihip, when the captain. nriiduceil hi^ orders, and the brave Daher, Ali Bey's ally, had his head cut olV in the 8i;th vear of ids age. I'Vom that time Kgypt has \<cn tin 11 by a civil war, betweeii the adherents of Ali and o-.ier In vs <.r iiriiuv',-., who rofe on his ruins. Of thefe the princip.il arc Moriul and 'I bra'him, wlto having driven their eneniics into banilhiiKiit, l.e-an lo 824 TiiL SrATi-.'* or II A R II A R Y. <|iiari>,l aiiKin.c; ilKiiikhis. Allcriiincly expelled trom Cairo, tlicy fiiiully agnvd to a rdiiiproiiiiCr, Mnicli, !7f>v 'I 111- I'oiti- fllll retains a pallia in l•'^^l>l ; l>ut this pallia, coiilinod and watclu-d in the lalilc of Cairo, is. railicr the priloiii.r of the MaiiwiukL'.s, iliait the rcprcfcii- tativc- ot' the bultun. u TiiK States ok HARBARY*. NDl'.R this head arc included the eountries ot, i, Morocco and Fez; 2. Al- J fliers; ^. Tunis; 4. Tripoli and Harca. The empire of Morocco, inriudinj^ Fez, is bounded on the North by the Me- diterranean fea ; on the South, by Tahlet , and on the I'.alt, by Sefjelinella and llip kini^ddin of Algiers, being 500 miles in length, and 480 in breadlli. Fez, which is now united to Morocco, is about 125 miles in lenjfth, and muili the fame in breadth. It lies belwe-n the kingdom of Algiers to the Eall, and Mo- roceo on the South, and is ("urniiinded in other jiarts by the fea. Algiers, formerly a kingdom, is boinuliMl on the l'',ail by the kingdom of Tunis on the North by the Mediterranean, on the South by Mount Atlas, and on the Welt by the kingdoms of Morrocco and 'I'afilet. According to Dr. Shaw, who relidcd 12 years at Algiers in (piality of cliaj)lain to the Britilh factory, and has corn-itcd many errors ot ancient and modern geographers refjiecting the Hates of Barbarv this country extends in length 4S0 miles along the coallof the Mediterranean, aiid is betwicn 40 and 100 miles in breatlth. Tunis is bounded by the Mediterranean on tlic North and Eaft; by the king. <loni of Algiers on the Well ; and by Tripoli, with part of Hiledulgerid, on the South ; being 2;'o niiic^ in lengtli trom .North to South, and 170 in breadth from J'.all to W eft. IVipoli, including Harca, is bounded on the North by the Mediterranean fia • on the South by the lountry of the Heribcries ; on the Well by the kin"doni uf 'I'unis. liikdidgeriii, and the teriitory of the (jadainis; ar.d on liie Kait i)y Kgvnt; iMcndiiig ab(jut iioo iniks along the lea-coalt ; and the breailth is from 100 td •iflo miles. i"',aeh caj'ital bears the name ot the date or kingdom to whieh it belon"-;;, bat the ca])ital of I'ileduigerid itlie ancient Numidia! is Dara. 'I he Baibaiy liates lorin a great politieal lonfedcracy, however independent lai h may be a-, to the exen ife ol its internal jxiiiey ; nor is there a greau r diliereiicc than liaj)i)ens in diti'erenl inoxiuces ol the fame kingdom, in the cuftonis and man- ners of the inhabitants. Am Asn SEASONS.] Tlie air of .Morocco is mild, as is that <>f Algiers, and in- deed of all the other Ibites, exci pt in tlu' nurntlis of July and Auguli. Son, \ r.(;i; rAiii. !•: and ammat. ) 'I his country, under the Roman empire, PRoneci IONS, jiv ska and i.and. 3 was jnlily denominated the garden of tin- vorld ; and to hawa n-lideiue there, waseonliden d \\s tlie higiieli Hate of lu.\un '1 he produce of tlie foil formed tliofe magazines, which furnithed all Italy, aiid great jiart of the Roman eivjiire, with corn, wine, and oil. Though the lands are nosv uneultivaled, through the opprellioii and barbarity of their coiiltiiutie;!, • Tills territory w-'i crillfd D.iImiI.i liy tin- fi;',riif\ iiigy/f/Vr,/, which vvastlit orijniialo(Cii|i;i':(jri tiitiJi.' i.iiJ Kouiai.-, Iruiii ti'-'ihtr, m tac ()iij,;aal ol the iiiliabit;iiit5, liru«cS Trjvti^^, vcl. i, |i. 304. The Statei of BARDARY. 8»5 vet ihfy nre flill fertile, not only in the above mentioned commodities, but in (latcs, fij;s, railiiis, almonds, apples, pears, cherries, plums, litrons, lemons, oranges, pomegranates, wilii plenty ot routs and herbs in their kitchen gardens. Kxccllent liLiup and flax fjrow ov tinir plains; and, by the report <>t" Kuropeans who have lived there tor Imnc lime, the country abounds with all that can add to the plea- fiires of life ; for the great people find means to evade the fobriety prefcribed by the Mahomedan law, and make free with excellent wines and fpirits, of their own j/rovvth and manufatture. Algiers produces falt-petre, and great miantilics of ex- tillent fait; and lead and iron have been found in feveral places ot liarbary. Neither the eli:phant nor the rhinoceros are to be found in the dates of Bi.r- bary ; but tiicir dcferts abound with lions, tigers, leopards, liy;cna», and monftrous Icipents. 'I'he IJarbary horfes were formerly very valuable, and tliought equal to the Arabian, 'Ihougli their bleed is now faid to be decayed, yet fomo very fine (iiKv, are occafionally imported into Kngland. Dromedaries, ades, mules, and kumraiis, a moll ferviceablc crca'ure, begot by an afs upon u cow, are their beads ot burden. IJut from the fervices of the camel they derive their grcatcft advantages. This iifcuil quadruped enables the African to pertorm his long and toilfoine journies acrofs that continent. The camel is, therefore, (fays NIr. Hruce) emphatically tailed tlu- jAip of the defett. He feems to have been created for this very trade, en- dued with parts and qualities adapted to the office he is employed to difchargc. The dried tliiftle, and the bared thorn, is all the food this ufeful animal requires ; and fventliefe, to fave time, he eats while advancing on his journey. As it is his lot tocrofs immcnfo deferts, where no water is found, and countries not even moiftened bv tiie dew of heaven, he is endued with the power, at one watering-place to lay ill a dore with which he fuj)plies himfelf for thirty days to come. To contain this enormous quantity of Huid, nature has formed large ciderns within him, from whieli, once tilled, he draws at pleafure the quantity he wants, and pours it into his lioiiiach with the fame cffett as if he tlien drew from a fpring ; and with this he travels, patiently and vigorouily, all day long, carrying a prodigious load iq)on liiin, tlirough countries infected with poifonous winds, and glowing with parch* iii;r and never-co4)ling finids. liieir cows are but fmall, and barren of milk ; their Iheep yield but indilTerent flcaes, b;it are very largo, as arc their goats. Bears, porcupines, foxi s, apes, liares, rabbits, ferrets, wealels, mole-;, camelions, and all kinds ot reptiles are found hire, iielides vermin, fays Ur. Shaw ^fpeaking of his travels through Barbarv), till' apprehenlions we were under, in fome parts at lead of this country, of beinij Iniicii or dung bv the fcorpion, the viper, or the venomous fpider, rarely failed to iiiti.rni|it our repofi' ; a refrelhment fo very ijiatot'iil and fo higlily neeelliuy to a wiarv traveller. Partridges ai\d (luaiis, eagles, iiawks, and all kinds of wild-fowl, ar found on this cnad ; and of the fmaljer birds, llie eapl"a-f])anow is remarkable fni its iieautv, and the fweetncfsot its note, wiileh is thought to exceed thai of any oihcr bird ; but it cannot live out of its own climate. 'I'he fcas and bays of Har- larv abound with a variety ot the lineii tith which were preferred by the ancients Ij iliwle o\ luirope. I'oi'L'LATioN, iNHAniTANis, MAN-'j Moroceo was formerly far more po- M.RS, CUSTOMS, AM' nivi-.RsioNs. jpuliuis than it is now, it, as travellers f.!v, its capital contained loo.oco lumfes, wliereas at prefent it is thouglit not to loiii.iin abo\e 23,000 inhahitant-- : nor can we iliink that the oilier parts of the omiitr) are more populou-., ii il is true that tlieii kini^or emperor has 80,000 horfo aiiil toot, 1)1' toreign negroes, in his armies. Til' cit\' ol -Algit-rfc ii faid to c<.>iilain 100.000 Muho:ncd:ins, 15,000 Jew.s. and / N icjo Chriuian tif> Tirr. SrATF.j of B A U n A R Y. cooo riirlftian (lavi's -, but no i-ftiinnti- lan In- ('ormcd iis to tlio jir.piiioiiflnfs of if« territory. Some travoIK-rH report, llmt it is iiih.ibiti'ii Uy a tiiviully liol'iiitiiUlo pcopli', who arc very diU'crciit in their maiiiiLrs and charaittr from thufc of' tlu' nuiroiiollH. 'I'liiiis is tho moft polilhod republic of nil the Ibrhary ftates. 'I he capital, wjij, |, alfo bars the naim- ot'Tiuiis, is a large and tlourilliitif; city. Tlje peoph-are more livili/fd ihiui ill .\lt;iers, and the j^overiinieut milder, but the ( limate is vi-rv far from lu'iii!' lb i^ood. Tunis is low, hot, and damp ; and dellitiite of good water, with which (accordiiif; to Mr. Uruce) Algiers is t'lippiiid from a ihonland fprine ' It contains 10,000 t'amilies, and above 3000 tradeluun's (hops, and its fuburiis eon- fill of looo houfes. 'I'lie 'I'uiiiliiies are indeed exceptions to the olhcr liates of Haiharv ; for iven the moll civijifetl ol the i'.uropean gnvcrnmcnis niii;lit iniijrove (idin their manners. Their dillin^tions are well kept up, and propi r r> I'pett is m\i to the mililary, mercantile, and learned |irol'ellloMS. 'i hey cultivate frioiulilnn willi tlie luiropean ilales ; arts and manuf.ictures iravc been lately inlroduuil ainoii'jr tluvn ; and the inhabitants are faiil at i>refent to be well ae(]uaintc,| wjil) the \;nio;is labours of the loom. 'I'he 'i'uniline women are exci.edint;lv l)aiidli)iin; in tlieir perfons ; and though the men are I'un-burni, the complexion of ilie ladiii is very delicate, nor are tliey lei's neat and elegant in thiir ilrefs ; but thev injprovt; the beauty of their eyes by art, particularly the powder of lead-ore, the fame u'n'. ment, accniding to tlie opinion of the learned Dr. Shaw, that Jozebil niadt' ^^(^■',\' when (lie is laid {1 Kings, ihap. ix. verfe 30.) to have painted her face; the words C(f the original being, that Ihe let olT her eyes with the powder of lead-ore. 'J'he gentlemen, in general, are fiber, orderly, and clean in their perfons, their hchavi. our genteel and complaifant, and a wonderful regularity reigns through all the llreeis and city. Tripoli was once the richeft, molt jwpulous, and opulent of ail the thtes on tlio coall ; but is now mucli reduced ; and the inhabitants, who are laid to amount to I/. 'tween 4 and 500.000, have all the vices oi" tin. ,\lgerines lluir maimers arc much of a piece with thole of the Kgvptians already dcfcrili- cil. I lie ltd)jetts of the Uarbary itatcs. in general fublilimg bv piracy, are allow- ed to be bold intrepid ni.uiiKis, anil will fight defperately when tliey'meet wiili ,1 pri/e at fea. They arc nntwitlilhinding i.ir interior to the luiglilh, and other Kun^- j)ea') Ihilcs, both in the onliruction and management of their vellels. Thev an 11 we except the Tunifines, void of all arts and lileraturo. '1 he niifciy and povi riv of the inhabitants of Moi>'CH), who are not immediately in the cm|)eror's frrvuc are bevond dcK ription ; but tliofe who inh.ibit the inland parts of the country ,"rc Jm holpi'able inoli'enlive pimple; and indi-ed it is a geiuial obler\ation, tliat liif t> ore uiihmt tlie inhabilants of thofe liates are Iroiu tiie teals of their goveriuiieiil their ituinners arc the more pure. N'oiwithllanding their poven\, thev have a livi-' lii.cf' about them, cfpecially thote who arc of the Arabic defceni, that gives tlicm an ar of ■ ooientment ; and having nothing to lofe, thev are peaeeahjc aiin'ii" tiieiiiielves. 'I he .Moors are bijipoted to hf the original inhabiumls, hut are now bleiiUed Willi the Arii's, and both are cruelly opprell'ed by a handful of inl'olent doiniicering iurks, the refufe of the llreets of Conllaiitiiiople. ORI'.bS j I'he drefs ot thefe people is a linen thirt, over which thev lie a i'k or eloih veltment v, i'.ti a talh, and over that a lool'e coat. Their draweri are m-Mw «'f liir. n Ihe arms and leg:, ot thew.'aier are bare, but tlie\ have liipuirs ca tiiei.' teet ; and perfor.s ot condition lumetinies wear bulknis. Ihev ne^er nunc iheir turban, bit pull olf their llippers when they attend religious duties, or li.i.' jHil'on of their fuvcrt ign. They aie foiul nf llriped and t'aneied iiiks. ihe iluu ff the women is not very dilfcj\iit tioui that ol the men, but their drawer. ;,!c "i luiiijir, Ts of it* "c ot' tl\J \l,\v\u<l> ;iri' n\oi\r t >(.Ty I'.ir mI wator, (I l'i>r'inp >Ull>S I'd.l- r Uatcs ot it 'mi\>ri)vc oil is I laid triciuilluii intiDiluuA iint^',1 sviili ■ liaiiJIoii'.i' it' llic I'.alii i K'V iiujirosc 10 lame pii:- luailo iifo ' \ ; \\\C \V(ir»'.^ ,d-i)rp. 'llio Lboir behavi- )Ugh all <lio Uatis on the to amount lo roady dcfcrili- ;•, , .iro allow y moot \v\lh a ul other Kviri'- jls. They arc, rv and poverty leror's Icvvite, [lie eoimtrv are ation. tiiat llio ill jrovcn\ineut, [u'V liavr alivv-- ihat J^ive^ tluin tteuble aini'iiv |s, but ari- now [.ll'ul ot inl'olcnt li tbev tie a 1 'k lasver-. are iiv.ka- liavc llil»pi '■>'■> liev ne^er iihaj L 'duties, or li.c Ilk*. 1 he dub .ir drawer^ ■''■<: loiiji'-t, Tim Statki op H A U B A U Y. Ij7 longer, and ihev wear n fort of cnwis on their headi iiillead of ;i tuil)an. 'I In? (liief furniture of their hi)ufes conlidn of carpets and niadrelli's, on which Ihey, l,t and lie. In lalinj;, their llovenlinefs is Ihotkin^. 'I hey are prohibitiil fr^ld :iiid liUer vellels ; untl their meat, which they fwallow by liaitdt'ids, is iioiied or iiialied to raf-s. Uiuir.io.s.l AM t'oreijijiiers are liere allowed the open protellion of their ri*- li.'lon, hut the inhahilantsi of thefc tlatcs are Muliomeilans ; and many fubjeeU ol'' Movocio follow the tenets of I lamed, a modern feetary, and an enemy to tlie inieient tloelrine of ihi" Cahts. All of them have mmh relpect for idiots ; wliofe iiiiiteclion in fmie lafes fercens oll'enders from pnnilhment. 'I lio Moors of liar- \[.r\, fo tailed from Mauritania, the ancient name of their coimtry, liave adnpiid the very worll parts of the Mahoniechm religion, and feeni to have rctalneil only as much of it as countenances their vices. Adultery in the women is punilhed wit It (Kaili ; but thouj^h the men are iiidiil'^rd with it plurality ol wives and ioncubiiie-., tlnv commit the moll tnmatural crimes with impunity. l,\NorA0B.J As the Ihites of Ihirbary poli'els thofe countries that tormerly went by the nunio of Mauritania and Numidia, the ancient African lanj^ua'^e is liill fpii'ken in lomo of the inland cuuntries, and even by fome inhabitants of the iltv of iNhirocco. In the fea-port towns, and niaiilime countries, a corrupt kind (if Arabic is fpoken : and fea-farini; ix-ople are no dran^ is to thai medley of living iiiul dead lani>;iia);e<, Italian, Krench, Latin, ii^c. that is lo well known in all the iKirls of llic Meciiurranean, by the name of Li>i\^ua hiiurii. ANriqj'iriKs and curiosi riK.s, ) This article is well wortlt the tUidy of .m NAi iKAi. AND ARTiiitiAL. J aiitiqu.iry, but the fubjedsof it are dithcult (ifacci'fs. bein^ fcaltered over a wide extent ot country, inhabited by ignorant and iiiliolpilable barbarians. The reader can learccly doubt that the countries which contained Carthage, and the pride of the Plui-nician, (ircek, and Roman works, are replete with the moll curious remains ot antiijuity. Some memorials <)>" (he M;iiniiaiiiiiii and Numidian g-'eatnels are llill ty be met with, and many ruins of lilies wliiili bear evidences ot their ancient grandeur and populoufiiefs. Julia Celarea of the Romans was little intirior in magnitieeiice to Carthage ittelf. A few of the acpieducts of Carthage are laid to be Uill remaining, but no velligo of in walls*. The fame is the tale of Ltica, tainous tor the retreat and death of Caio, and manv other renowned cities ot antiipiity ; and fo (wer-run is the country will) liarbarifm. that their very lites are not known, even by their ruins, amplii- llieaires, and other public buildings, which remain Itiil in tolerable prelVrvatioii. Bclides thofe of cl.illical iuiliquity, many Saracen monuments, of the motl llupen- i! HIS ma',niticence, are likewile tound in this vail trad; thelo were crctled unc.r ilv C'alil^ ol liagdad, an<l the ancient kings of the country, before it was fubdiied In ihe lurks, or reduced to its prefenl t'orm ot government. Their walls (orm the i)rincii>al fortifications in tlie country, liotli inland and maiilime. \\ c know of fi \v or no natural curiolilies bel )ek>ngmg to this coimtry, except its falt- iis, which in Ionic ])laccs take ui) an area ol li.\. miles. Dr. .Shaw mentions Ipiin^s found heie that are fo hot as to boil a large piece of mutton very tender ill a tiiiaiter of an hour. • Mr. ht.Tiilcv, h.Av'mj; Ind frequent opportimi- I'i-ipl jioiii}; iivt.T till' rciiLiiiis, ib I I ( inniim llut \\\\ .clibr.itcil 1 ity vv.is iil)oiit littrtn ii'ilf. in tir- iumt(rii:i.f. Ttiirc aic three inuniims wMlIi arrlo n-ai \ 1 fap ot Hue niarlilr pounded ti>KiiluT, a-.l were in all piob:il.ilit.v, the litt •^ nl tt mplis, and ctUf liiftinguilliid buildinp. He oliKives, lli.it the prefint biiildint;«nrc not tlwr remains nftlu' in- c'liit (.ity dcllniytd liy i ic Roniaiii, who intinly r.iilcd it, und plmiphcd up the very foiiiidnti(.i:'. 'I'licv Me tlir ruins ot the iit\ which «as luiilt on the luc ot tlie (orilier, .Tnd wliiih was dtltroycd l y tilt- .Siiraiiiu iu I'le bti;in;aiig ot the Uveiith tiii- tin\. ; iS 2 Ci i I us tiS The Statu or B A R B A R Y. CiTiF.t AMD PTiMC BviLDiKoi ] Mention hni already been matte of Moroc. CO, thecH|iilal dftliat kinf;tli>m, Imt trnw iiliiKid in ruint, itic court having rcinovcJ to Mc«juiiu'z, n lity of IV/, ;^o mil* h dilliini, nnd viry popiil-iiii. Iiicn-diblc thinej arc rctorili*! oJ' llu- niii({iiitit».iit palacci in bolli '•'•••- ' > - • ■ ill n (lirtv IIdvi'dI il viry popi citifi ; but tliu common people livj in n dirty lloviMily niiiriiur. 'Ilic city «)f Al>;iiT» is not nbnvc n mili- nnd n lialf in circuit, tliough it ig co^i. j)iit«tl t) i'onfain mat lao.ooo iiili;ibiliiiits, i ^,ooo houCt-i, and 107 m()f(|ius, '\']\^.\f puhlii bntb', iui' liirgv niul liamlfoiiu-ly |.avi'<| witli marble. 'I'ho profpctl of tlio country mid lea from AlK'crH is vorv Itiaulit'ui, being built nn ilu- dulivitv ol" n inoimtiiin ; but tin- city, lluMij.'ii tor Icviral ages it lias braved fome otijie grealijl luiweis ill Cfirilti lulom, eould nuike bit ii taint detencc acaiiilt a regular (icjr,. llif >|i,iiiiar(U bovvi viT all K keil it in tlii; year '775.l)y laiuland by lea, but wen- repulli.cl with gieat lnl%, ilioiit;li tliev hail near io,ooo foot and aooo liorfe, nml 47 kui'^'s llii|)K <if dill.niii rates, niul ^46 tranfporls. In the year 178} and K4, tiie\ iiiRvveil till ir attacks by lea to ilellroy the city and gallies, but alter fp.ndinw a quantity ut' ainnuinition, l)onil>s, {JiC. were forced to retire without cither iu eni). turc or extiiu'tion. 'I'he nmle ot i1k- iiailimir is 500 paces in length, extending from tile continent lo a finall illan<l where tliere is a calile and large battery. 'I'lie kingdom of' Tunis, whidi is naturally the lined of" all thele llates, contains the remains of' inanv noble cities, loine of' them Kill in good condition. The cini- tal, about 30 miles louth ol" old Carthage, has fortifications, and is about three mile» in circumterence. The ftreets (lays Mr. .Stanley) are narrow, as in moll hot coim. tries i and, not beinjj paved, they are dirty in winter, and dully in fuininer. 'liio lioul'es arc not magiutieent, but neat and commodious ; moll of them have a porch or gateway, with benches on each lide, covered with mats, where the mailer of tlii; houfe iranfatts his bulincfs, and receives his f'rieiuls ; no perfons, except on fome extraordinary occalioiis, having any further admillion. Heyond this is an open court paved with marble Ibnie, or gl.i/ed tiles, according to tbe ability of the owner co- veicd over, and Iheltered from the fun and weather, by a cloth which by means of pullies may be folded or uiifoKled at |)leafure. When entertainments are given the company meets in the court, which is always kept very dean, The public ex' tiiange for iner.liants and their goods is commodious. Moll of the water ufed in this city is rain-wafer, preferved in ciftorns, info which it is ccmveyed l>v pipes I'roni the rooU of the hoiifes, which are all flat. Thefe cif- terns are fo large, that thej hold enough to ferve the f'amilies live or fix months Alniofl every ciliern has the bafe of a narble column hollowed out to cover the mouth ; th'iiifands of them beinr; put to this ufe all over the country. Mtifa, two ihort miles I'lom ( arthage, and eievi'ii from Tunis, is a very pUafant litualinn. Here tlie b(>\ has two country-houfi's, one of which has been a colHyr work, built by llallan Hey, t'lirnamed llic (iood. From thele houfes are oraiiui." gardens, reaching alniolt to the fea-lhore ; on the edge of which is a famous w,. '11 of fweet water, elleemed the !'eft and lighted in the kingdom ; and tlofe to this a C'liree-hoiife. Numbers o| people from the neighbouring places, rt.fort here to drink coffee, and a glafs of this nati'ral luxury, fo preuliarlv enjoyed in the ciliiri to. mines ; (cw perfons, cxeejU ihol'e who have lived in hot climates, kiiowin" \\[v bicirmg of a good fpring. In the midiile of tlie i (unt is a large niulbcrry-tree, under the Ihade of v. hii h i!ic\ III and fmoke, and pla_\ al eliel's, iiiiuiling the comforlabie lea-breeze, liiat reliellk's this V harming fpot. .Noihing can be move picturefque, than to fee tiic .\Iuors "al- lantiy mounted, with their atiendanls, c<i,n|)liiiu'uting each other. 'I'he water is drawn up by a camel, with llie IVilia.i wheel, and diftributeii lu llie neighbuuriiiij countries. 7 'fi..; Tut Statei or nARRARY. 9<9 o whii h Iffl' cil- nxmihs. .-over the lilcaf;iiit nis Willi "t to litis a ll luiV t'l If ratiiTl •.lliill tlli'V ,t ri'liillKs TtiP city of Tripoli CDiidrts nf nn <i!tl and new Idwn, the Inttcr hcin(j ibo nmft flourilhing ; bul ncvrr can luako niiy tonrirlirubii' f'li^un*, on luioiint of the inton- veiiicntii'ii lUtcndinj; its lituation, pjirticulurry the want of fwict water. The city of (Jian, l>iiij( upon tins ecinft, i» ahout a inili- in (.irciimfircnti . and is fortified l)oth l)v nrf ai\d iintiiri'. It wax a plait- of lonliilirahie tradt , mid the olijotl of man/ bloody dirpiili'i Ik twion the Spaniard', and the Moors. CoiUluntina was the ancient C'irta, and one of the llrongell cities in Nnniidia, luin^; inacccliibic on ail lide:i, cx< topt the foiilh well. nclide< tlie ahove towns and cilie*, many otlurs, formerly of great renown, liu fiallered up and down this inn\ienfe trail ot' coiintiy. I he city of I'e/, at pul'ent the capital of tlie kingdom fit called, i> faid to contain near joo,ooo iiihahiiants, beddes nurchants and foreigners. Its niofcpies amotml to ^ooj tine of them mag- nificent beyond defcriplion, and about a mile ami a half in circumference. M«. (jiiinez is elUenud the great emporium of all I'arliary. Saiiee was formerly tamoui t ir the piracy of its inhabitant-.. Tangier, fitualed about two miles within the lliaits of (Gibraltar, was given by the crown of Portugal as part ot the dowrv of i|iii"en Catharine, confort of (liarles II. of Kngland. Hut the niifimderllanding* between that king and bis parliament occalioned the deniolition of its tortificati.iiH iiiul harbour ; fotliat tVom being one of the lined cities in .Africa, it i'. now little bet- ter than a tilhiitg town. Ceuta, upon the fume llrait, almoll opp ilite to Gibraltar, i. Hill in the hands of the Spaniards, but olien, il not aluays. In heged or blocked up by the Moors. Tetiian, which lies withii\ twenty miles of Ceuta, is now but iiii ordinary town, containinjj about 800 lunifcs 1 but the iiduibitants arc faid to be rich, .and tiderably civilized m their numners, Ihe provinces of Suz, Tatilei, and (iefiila, t'orm no part of the Hates of Barbary, llioiigh the king of Morocco pretends to be their fovcrcign : nor do they contain any thing that is particularly curious. /aara is a defcrt country, thinly peopled, and nearly doflitute of both water and pro\i(ions. Manufactures AND COM MF.RCE.] 'Hie lower fubjefls of thefe dates know very few imaginary wants, and depend partly upon their piracies to be fnpiilied with necei- fiiry utiiilils and manufadures ; lo that tlieii export-, coiillll cbietly of Uather, fim; mats, embroidered handkerchiet's, fword-knols, and carpets, whiib are clu aper, and flitter than thofv in Turkey, though not fo good in other refpects. As they leave almod all their commercial aflair-, to tlie Jews and Cluillians fettled among them, the latter have cllablilhed lilk and linen works, which I'lipply the higher ranks of tluir own fubjei'-ls. They have no ihijis that, properly fpeaking, are emjiloNed in Kimmerce; fo thai the I'reiieh and h'li^lilh carry on ihr ;.;reatell jiart o;' their tra<le. 'llu-ir exiiorts, belides thofe already nuationed, conlil't of elephant's teeth, otbieb • featlur>, copp.-r, tin, wool, hides, honey, wax, dates, railiiis, olives, ahnoiuN, gum- amine, and laiubac. I'he inhabitants ot Morocio are likeuife laid to carrv on a eoiilideiable trade b) caravaiu to Mecc., M' diiia.and foiiie inland ji.irls of .\fiiea, from whence they bring back \,itl niiinbeis ot nej^roes, who ferve in their armies, iiial arc ll.ive?. in tlu ir honfe-, and liekU. In return for their exports, the Kuropeans furnifli them with timber, artil!er\ o*-' Jill kind., gmipowder, ami whatever they want, either in their juiblie or piivate lapaeitie . ; the pariienlars of which are too many to Ipecity. '1 he dutie-. paid by the l'ai"lilh in the ports ot Morocco, are but half thole paid by ntlier hairopeaiis. | 34,601 |
https://pt.wikipedia.org/wiki/Conde%20de%20Castelo%20Melhor | Wikipedia | Open Web | CC-By-SA | 2,023 | Conde de Castelo Melhor | https://pt.wikipedia.org/w/index.php?title=Conde de Castelo Melhor&action=history | Portuguese | Spoken | 174 | 343 | Conde de Castelo Melhor, título criado pelo Rei Filipe II de Portugal, por carta de 21 de Março de 1611, a favor de Rui Mendes de Vasconcelos, senhor das vilas de Almendre e Valhelhas e alcaide-mor de Penamacor.
Em 10 de Outubro de 1766, D. José I, criou o tíulo de Marquês de Castelo Melhor a favor de D. José de Vasconcelos e Sousa Caminha Câmara Faro e Veiga, 4.º Conde de Castelo Melhor. A partir daí, o título de conde de Castelo Melhor tem sido atribuído a alguns dos herdeiros presuntivos do Marquesado.
Condes de Castelo Melhor
Rui Mendes de Vasconcelos
João Rodrigues de Vasconcelos e Sousa (1593-1650), em 1649 nomeado Governador Geral do Brasil
Luís de Vasconcelos e Sousa (1636 — 1720)
José de Vasconcelos e Sousa Caminha Faro e Veiga (1706-1769), depois 1.º Marquês de Castelo Melhor
Bernardo Manuel de Vasconcelos e Sousa, primogénito da 7.ª Marquesa de Castelo Melhor
Após a implementação da República e o fim do sistema nobiliárquico, tornou-se pretendente ao título D. Bernardo de Vasconcelos e Sousa. | 3,235 |
US-6573806-A_2 | USPTO | Open Government | Public Domain | 2,006 | None | None | English | Spoken | 6,170 | 8,255 | A supplementary observation will be given with reference to FIG. 6( h). When heating is performed in an oxygen atmosphere, carbon atoms constituting fullerenes will bind to oxygen chemically. Accordingly, even if the fullerenes are heated in vacuum or in an inert gas, recovery of their conductivity will not be realized because the oxygen will be resistive to dissociation.
(Dependence of the Conductivity of Fullerenes on the Concentration of Impurities Therein)
FIG. 7 shows the data representing the correlation of the conductivity of C₆₀ with the concentration of impurities therein. As seen from FIG. 7, the conductivity a correlates negatively with the concentration of oxygen or water contained in fullerenes. However, the conductivity does not depend solely on the concentration of oxygen or water independently of each other. For example, when the concentration of water is high, the conductivity does not become high no matter how much the concentration of oxygen is reduced.
The concentration of oxygen and the concentration of water have a cumulative effect on the conductivity. Taking this relationship into consideration and collecting many relevant data, the graph shown in FIG. 8 was prepared. The coordinate system in FIG. 8, where the ordinate represents the concentration of oxygen in a logarithmic scale, and the abscissa the concentration of water in a logarithmic scale, shows zones where fullerenes act as an insulator (σ<10⁻⁶ (Ω·cm)⁻¹), semiconductor (σ>10⁻⁶ (Ω·cm)⁻¹) and high conductive semiconductor (σ>10⁻¹ (Ωcm)⁻¹).
It can be seen from FIG. 8 that when fullerenes have a concentration of oxygen not higher than 10¹⁶ molecules/cm³ and a concentration of water not higher than 10¹⁸ molecules/cm³, they will have a conductivity falling in the semiconductor zone; and when fullerenes have a concentration of oxygen not higher than 10¹⁴ molecules/cm³ and a concentration of water not higher than 10¹⁶ molecules/cm³, they will have a conductivity falling in the highly conductive semiconductor zone.
To achieve the increased conductivity of fullerenes, it is preferred to keep the concentration of oxygen therein not higher than 10¹⁶ molecules/cm³ and concentration of water not higher than 10¹⁸ molecules/cm³, more preferably keep the concentration of oxygen not higher than 10¹⁴ molecules/cm³ and concentration of water not higher than 10¹⁶ molecules/cm³, and most preferably keep the concentration of oxygen not higher than 10¹² molecules/cm³ and concentration of water not higher than 10¹⁴ molecules/cm³.
(Highly Conductive Fullerenes)
The terms “highly conductive semiconductor zone” and “highly conductive fullerenes” are used herein, although they are not generally used in the prior art, to specifically designate the highly conductive fullerenes having a conductivity of σ>10⁻¹ (Ωcm)⁻¹) which are only produced by the inventive method, because they as organic semiconductors exhibit a far superior conductivity as compared with common semiconductors.
(Passivation)
FIG. 9 shows the change in conductivity of fullerenes when the fullerenes receive the coating of a protective membrane (passivation membrane) on its surface. Immediately after a fullerene film having a thickness of 0.4 μm was formed by vapor deposition, nitrogen was passed by purging through a vessel without removing the film from the vessel, and a protective membrane of polyimide was deposited to a thickness of about 2 μm by spin coating on the top of the fullerene film. After the protective membrane was deposited, oxygen was allowed to enter into the vessel, and stay there for 10 minutes. As shown in the figure, no reduction in conductivity is observed. From this it is shown that to prevent the adsorption of oxygen and water to fullerenes, it is effective to recover or improve the conductivity of fullerenes by heating them in an inert gas, and then to form a protective membrane on the surface of the fullerene film. The preventive effect of the passivation membrane against the adsorption of impurities to fullerenes is not only observable in void fullerenes but also in fullerenes at large as will be mentioned later.
The suitable material for the protective membrane includes, in addition to polyimide, SiO₂, Si₃N₄, polyimide, polymethylmethacrylate, polyvinylidenefluoride, polycarbonate, polyvinylalcohol, acryl resin or glass. Formation of the protective membrane may be achieved, in addition to spin coating, by CVD, PVD, spray coating, or dip coating.
(Condition Suitable for the Production of Highly Conductive Fullerenes)
A system was prepared by applying ultra-clean technology as much as possible to the fabrication of a chamber where vapor deposition and measurement will be performed similar to the one shown in FIG. 1 with an aim to minimize the dissociation of oxygen and water from the vacuum vessel itself. A vessel corresponding to vessel 1 of FIG. 1 has its surface coated for protection with a passivation membrane made of chromium oxide; a gas inflow tube corresponding to gas inflow tube 3 is made of a stainless steel and has its internal surface coated with a passivation membrane made of chromium oxide; all-metal valves are so constructed as to minimize redundant species which may cause the stagnation of gas flow; a mass flow control is used; and an adsorption unit equipped with a liquid-nitrogen trap and molecular sieve is installed to remove oxygen and water very marginally present in an inert gas such as nitrogen or argon entering through the gas inflow tube, to thereby produce a ultra-clean inert gas.
It was found by studying fullerenes produced by the above-described method suitable for the production of highly conductive fullerenes that it is possible to deposit a fullerene film having a high conductivity without requiring the heating in an inert gas simply by precipitating fullerenes by vapor deposition. To produce a fullerene film having a high conductivity, it is preferred to employ the following conditions as described below.
(1) The fullerene material should be so pure as to contain carbon at 99.6 wt % or higher.
(2) The vessel for vapor deposition should be made of a stainless steel material, and its internal wall have its surface coated for protection with a passivation membrane made of chromium oxide, aluminum oxide or metal fluoride. Alternatively, the vessel should have an internal wall, which is made of a material that allows the discharge of gas therefrom to be 1×10⁻¹⁵ (Torr*1/sec*cm²) or less.
(3) The degree of vacuum during vapor deposition should be kept at 10⁻⁹ Torr or lower, more preferably 10⁻¹⁰ Torr or lower, most preferably 10⁻¹¹ Torr or lower.
As described above, the system suitable for recovering or improving the conductivity of a material comprising fullerenes or nanotubes by heating the material in an atmosphere of an inert gas should preferably include one that comprises a vessel equipped with a gas inflow tube and gas outflow tube, a heating means, a heating controlling means, and a gas flow controlling means. In addition, the system is preferably so constructed as to allow the heating condition and gas flow condition to be controlled in association, so that the temperature rise during heating, heating temperature, and gas flow can be finely controlled in synchrony.
(Fullerenes)
The production method according to the invention can be applied not only to void fullerenes, but also to any materials that will have a reduced conductivity when they are subject to the adsorption of oxygen and water, and the method is effective for recovering or improving the conductivity of those materials. The method is particularly effective when it is applied to “fullerenes.” The term “fullerenes” used herein includes common fullerenes, endohedral fullerenes, heterofullerenes, chemically modified fullerenes, fullerene oligomers, fullerene polymers, etc. The term “endohedral fullerene” means a spherical carbon molecule entrapping an atom or molecule other than carbon within the hollow of its cage-like shell.
The inventive production method can be applied not only to C₆₀ but also to C₆₀, C₇₀, C₇₆, C₇₈, C₈₂, and C₈₄ that have the same electric properties as does C₆₀, and a mixture thereof, obviously with the same results.
Furthermore, the inventive production method can be applied not only to a fullerene-based film but also to a fullerene containing solid, powder, coating membrane, single crystal, poly-crystal, film, fiber, dopant material, vapor-deposited material, and co-deposited material. When the inventive method is applied for the preparation of such a material, the material will have its conductivity recovered or improved.
Still further, the inventive production method can be applied for the preparation of a nanotube such as a carbon nanotube and a nanotube prepared by the inventive method will have its conductivity recovered or improved.
(Application to Gas Sensor)
Gas adsorption to a fullerene, endohedral fullerenes, or fullerenes, or to a nanotube affects reversibly and sensitively the electric properties of that conjugated carbon system. Based on this phenomenon, it is possible to utilize a fullerene, endohedral fullerenes, or fullerenes, or a nanotube as a highly sensitive gas sensor with a wide dynamic range.
It is possible by using such a sensor to detect the concentration of oxygen and water highly sensitively in a range of 1 ppb to 1000 ppm, with its dynamic range being kept very wide.
The gas to be detected by such a sensor can not include, as far as based on current knowledge, rare gas elements such as He, Ar, etc., and inert gases such as nitrogen, etc., because the adsorption of such a gas to the sensor will not affect the electric properties of the sensor. However, with regard to many other gases, it is possible by using a sensor based on fullerenes or a nanotube to sensitively detect the presence of, in addition to oxygen and water, alcohols, halogen gases, oxidizing gases, reducing gases such as hydrogen, carbon monoxide, nitrogen oxides, etc., and gases that when adsorbed to fullerenes, tend to entrap electrons or holes.
An endohedral fullerene is particularly suitable, among those fullerenes, for the construction of a gas sensor, and it is thus possible by using an endohedral fullerene as a material to produce a highly sensitive gas sensor. In particular, use of a fullerene doped with an alkali metal element, alkali earth metal element, rare earth element, halogen element or V group element will lead to the improved performance of the sensor.
Next, description will be given about the relationship between the concentration of a test gas adsorbed to a sensor body and the concentration of the test gas in an atmosphere in contact with the sensor body. The electric resistance of a test sample varies depending on the concentration of a gas adsorbed to the test sample. When the concentration of the test gas in the atmosphere is higher than the concentration of the test gas adsorbed to the sensor body, the test gas molecules will migrate from the atmosphere to the sensor body (adsorption), and the concentration of the test gas adsorbed will reach a saturation level corresponding to the concentration of the test gas in the atmosphere after a certain time interval. On the contrary, when the concentration of the test gas in the atmosphere is lower than the concentration of the test gas adsorbed to the sensor body, the test gas molecules will migrate from the sensor body to the atmosphere (dissociation), and the concentration of the test gas adsorbed will reach a saturation level corresponding to the concentration of the test gas in the atmosphere after a certain time interval similarly to the above. However, there is a great difference between the speed at which adsorption of a gas occurs and the dissociation speed of the gas: adsorption of a gas reaches a saturation level in a comparatively short period (0.1 to several seconds) while dissociation of the gas is very slow in reaching its saturation level.
It is possible to make a real-time measurement of the concentration of a gas using a sensor body comprising fullerenes, or a nanotube. It is also possible to prepare a highly responsive gas sensor (0.1 to several seconds) by allowing it to have a structure as described below. Namely, the gas sensor includes plural sensor bodies, which will be heated in an inert gas, flowed by purging independently of each other. Prior to use, all the sensor bodies are heated in an inert gas flowed by purging to remove the gas previously adsorbed to the sensor bodies. A first sensor body is used for measuring the concentration of a test gas. Then, at a second timing, a second sensor body is used for measuring the concentration of the test gas. This time, the first sensor body is subjected to the inert gas heating to remove the gas adsorbed to the sensor body. At a third timing, the first sensor body and a third sensor body are used for measuring the concentration of the test gas. This, the second sensor body is subjected to the inert gas heating to remove the gas adsorbed to the sensor body. How many sensor bodies should be prepared may be determined as appropriate depending on the speed of gas dissociation, speed of response, and specified requirement of the task.
When it is required to prepare a highly responsive gas sensor, it is possible to utilize the initial rising phase of electric resistance instead of its saturation phase for the detection of a test gas. When a test gas is adsorbed to a sensor, the electric resistance of the sensor will be increased, and it will reach a saturation level after a certain time interval. The rate at which the electric resistance of the sensor increases before it reaches a saturation level varies depending on the concentration of a test gas adsorbed to the sensor. Namely, when the amount of a test gas adsorbed to the sensor is large, the rate at which the electric resistance of the sensor increases will also be large, while when the amount of a test gas adsorbed to the sensor is small, the rate at which the electric resistance of the sensor increases will also be small. It is possible by utilizing this feature to prepare a gas sensor capable of measuring the highly variable change in concentration of a test gas lasting only for 1 msec to 0.1 second.
The ultra-sensitive real time analysis of gas components performed with atmospheric pressure ionization mass spectroscopy (API/MS) has been attracting attention as a technique indispensable for the plants engaged in the fabrication of state-of-the-art semiconductors. The API/MS is a highly sensitive gas analysis technique that allows the analysis of gas components with a sensitivity 1000 times as high as a conventional gas chromatography-mass spectroscopic machine. However, disadvantageously the mass spectroscopy machine is very bulky and expensive. In contrast, it is possible to analyze gas components in a sample by combining an ionic molecule reaction unit with a sensor body comprising fullerenes including a fullerene, endohedral fullerene, or fullerenes, or a nanotube into a gas sensor, allowing ions derived by ionization from the gas components to be adsorbed to the sensor body, and detecting the change in electric resistance of the sensor body in association with the adsorption of ions. This gas sensor will detect the presence of gas components in a sample and their respective concentrations more sensitively than a conventional gas sensor, which analyzes gas components in a sample by bringing its sensor portion into direct contact with the sample. The ionic molecule reaction unit suitable for the purpose may include a number of commercially available units such as those based on electro-spraying, or on atmospheric pressure chemical ionization. By combining such an ionic molecule reaction unit with a sensor body comprising fullerenes including a fullerene, endohedral fullerene, or fullerenes, or a nanotube, it will be possible to obtain a more compact, low-cost, and portable gas sensor than a conventional gas sensor.
Such a compact, low-cost gas sensor will command wide applications, which will go beyond semiconductor fabrication industries. Specifically, in chemical product plants and nuclear power plants, it will be used as a gas sensor for checking the leak of gas from plumbing systems; in general plants and automobile factories, it will be used for measuring the gas components of exhaust gas from a boiler or an automobile; in air-ports and public facilities, it will be used for checking the possible presence of an explosive, a toxic substance, unlawful chemicals such as narcotics; in general factories it will be used as an aid in the development research of a fuel cell (in the measurement of hydrogen concentration); and in medicine it will be used as an analyzer of the components of gas expired by the patient.
FIG. 11( a) shows a first illustrative example of a gas sensor prepared according to the present invention. This represents a sectional view of the gas sensor with a refresh function capable of determining the concentration of gas on a real time basis. In the particular gas sensor shown in FIG. 11( a), two sensor bodies are depicted in their profiles. However, the sensor may include three or more sensor bodies. The gas sensor comprises gas inflow tubes 22, 23 for introducing a test gas 21 which are separated with a partition wall from each other. Each of sensor bodies 26, 27 is obtained by depositing a film comprising endohedral fullerenes on a substrate, and attaching an electrode for resistance measurement to each side of the film. The gas introduced through gas inflow tubes 22, 23 is brought into contact with sensor bodies 26, 27 so that the gas can be detected with sensor bodies 26, 27 independently of each other. When the gas is adsorbed to the sensor body, the electric resistance of the sensor body is changed. This change of electric resistance is measured by a metering device 30 where the measurement data is processed to be converted into a gas concentration data. It is possible to quickly eliminate the portion of the gas adsorbed to the sensor body by introducing nitrogen via nitrogen inflow tubes 24, 25, and activating heaters 28, 29 at the same time. In the manner as described above, it is possible to measure the concentration of a gas on a real time basis by using a gas sensor comprising plural sensor bodies.
FIG. 11( b) shows a second illustrative example of a gas sensor prepared according to the present invention. This represents a gas sensor equipped with a unit for ionizing a test gas by atmospheric pressure ionization. A test gas 31 is introduced into the ionization unit through a gas inflow tube 32. Heating of a flow 34 of the test gas occurs when the flow passes through the hollow of a tubular heater 33, and the gas flow is converted into gas ions 36 under the influence of an electric field formed between the wall of the heater and a grid electrode 37 by a power supply 35. A portion of the gas ions is adsorbed to a sensor body 38, which produces a change in the electric resistance of the sensor body to be detected by a resistance measurement meter 39 where the measurement data is processed to be converted into a gas concentration data.
EXAMPLES
The present invention will be described below with reference to examples. However, the present invention should not be limited in any way to those examples.
Example 1 Vapor Deposition in an Ultra-Clean Environment
An environment suitable for manufacturing a fullerene film according to the above-described condition appropriate for the production of highly conductive fullerenes was prepared using a system as shown in FIG. 1 where the degree of vacuum within vessel 1 was made 5×10⁻¹⁰ Torr (6.65×10⁻⁸ Pa). According to an API-MS machine connected to the vessel 1, it was found that the concentration of water at a site where a fullerene film would be formed was 3 ppt. A 50 mg of fullerenes C₆₀ (Tokyo Chemical Industry) was placed in a molybdenum-made boat for vapor deposition, and the boat was heated at 500° C. for 1 hour so that a fullerene film having a thickness of about 0.4 μm was deposited on a substrate 8. Under an As-Depo state where the substrate temperature was 82° C., the measurement was made by applying a voltage of 2V between two terminals which resulted in the passage of current of 1.1 mA, and the conductivity was found to be 0.34 (Ωcm)⁻¹. Then, the vessel was slowly cooled to room temperature or 27° C. where the conductivity was found to be 0.11 (Ωcm)⁻¹.
Example 2 Vapor Deposition in an Ultra-Clean Environment
An environment suitable for manufacturing a fullerene film according to the above-described condition appropriate for the production of highly conductive fullerenes was prepared using a system as shown in FIG. 1. The vessel or chamber was baked at 150° C. for one week. As a result, the degree of vacuum within vessel 1 was found to be 10⁻¹¹ Torr. According to an API-MS machine connected to the vessel 1, it was found that the concentration of water at a site where a fullerene film would be formed was 1 ppt or less. A 50 mg of fullerenes C₆₀ (Tokyo Chemical Industry) was placed in a molybdenum-made boat for vapor deposition, and the boat was heated at 470° C. for 30 minutes so that a fullerene film having a thickness of about 0.1 μm was deposited on a substrate 8. Under an As-Depo state where the substrate temperature was 74° C., the measurement was made by applying a voltage of 0.2V between two terminals which resulted in the passage of current of 2.6 mA, and the conductivity was found to be 32.5 (Ω·cm)⁻¹. Then, the vessel was slowly cooled to room temperature or 27° C. where the conductivity was found to be 10.2 (Ωcm)⁻¹.
Example 3 Recovery of Conductivity Via Co-Deposition and Inert Gas Heating in an Ultra-Clean Environment
An environment suitable for manufacturing a co-deposited film comprising fullerenes according to the above-described condition appropriate for the production of highly conductive fullerenes was prepared using a system as shown in FIG. 1. The vessel or chamber was baked at 150° C. for one week. As a result, the degree of vacuum within vessel 1 was found to be 10⁻¹¹ Torr. According to an API-MS machine connected to the vessel 1, it was found that the concentration of water at a site where a fullerene film would be formed was 1 ppt or less. A 50 mg of fullerenes C₆₀ (Tokyo Chemical Industry) and 50 mg of copper phthalocyanine were placed in a molybdenum-made boat for vapor deposition, and the boat was heated at 470° C. for 30 minutes so that a fullerene/copper phthalocyanine film having a thickness of about 0.1 μm was deposited on a substrate 8. Under an As-Depo state where the substrate temperature was 74° C., the measurement was made by applying a voltage of 0.4V between two terminals which resulted in the passage of current of 10.4 mA, and the conductivity was found to be 63.1 (Ωcm)⁻¹. Then, the vessel was slowly cooled to room temperature or 27° C. where the conductivity was found to be 20.4 (Ωcm)⁻¹.
Later, nitrogen gas was allowed to enter via an adsorption unit equipped with a molecular sieve into the chamber to regain a normal atmospheric pressure. The sample was transferred via a passage with a road-lock to a separate chamber. Oxygen gas was allowed to pass continuously for 10 minutes through the chamber where the sample was settled. Then, the sample was returned to the original chamber. Next, while nitrogen gas was allowed to flow through the chamber, the conductivity of the sample was measured and found to be 4×10⁻⁸ (Ωcm)⁻¹. While nitrogen gas was flowed as before, voltage was applied to a ceramic heater upon which the sample was fixed to heat it. When the heater was activated for 15 minutes, the sample was heated to 160° C. where the measurement was made and the conductivity of the sample was found to be 15.2 (Ωcm)⁻¹ a value close to the one prior to the oxygen exposure.
The combination of fullerenes with another element in the formation of a film can occur in two manners: one is the formation of a co-deposited film, and the other is the formation of a laminated film comprising a fullerene layer and a layer of another element. The evaluation result given above is only concerned with a co-deposited film. However, it was found that the production method of the invention could successfully recover the lowered conductivity for a lamination film as well.
Example 4 Recovery of the Conductivity of a Fullerene Film Left in Oxygen Atmosphere
An environment suitable for manufacturing a fullerene film according to the above-described condition appropriate for the production of highly conductive fullerenes was prepared using a system as shown in FIG. 1. The degree of vacuum within vessel 1 was found to be 5×10⁻¹⁰ Torr. According to an API-MS machine connected to the vessel 1, it was found that the concentration of water within vessel 1 was 3 ppt.
A 50 mg of fullerenes C₆₀ (Tokyo Chemical Industry) was placed in a molybdenum-made boat for vapor deposition, and the boat was heated at 500° C. for 1 hour so that a fullerene film having a thickness of about 0.4 μm was formed on a substrate 8 fixed onto a ceramic heater. Under an As-Depo state where the substrate temperature was 82° C., the measurement was made by applying a voltage of 2V between two terminals which resulted in the passage of current of 1.1 mA, and the conductivity was found to be 0.34 (Ωcm)⁻¹. Then, the vessel was slowly cooled to room temperature or 27° C. where the conductivity was found to be 0.11 (Ωcm)⁻¹.
Later, nitrogen gas was allowed to enter via an adsorption unit equipped with a molecular sieve into the chamber to regain a normal atmospheric pressure. The sample was transferred via a passage with a road-lock to a separate chamber. Oxygen gas was allowed to pass continuously for 10 minutes through the chamber where the sample was settled. Then, the sample was returned to the original chamber. Next, while nitrogen gas was allowed to flow through the chamber, the conductivity of the sample was measured and found to be 2×10⁻⁹ (Ωcm)⁻¹. While nitrogen gas was flowed as before, voltage was applied to the ceramic heater upon which the sample was fixed to heat it. When the heater was activated for 15 minutes, the sample was heated to 160° C. where the measurement was made and the conductivity of the sample was found to be 0.1 (Ωcm)⁻¹ a value close to the one prior to the oxygen exposure.
Example 5 Recovery of the Conductivity of a Fullerene Film Left in Normal Atmosphere
An environment suitable for manufacturing a fullerene film according to the above-described condition appropriate for the production of highly conductive fullerenes was prepared, and the degree of vacuum was found to be 0.75×10⁻⁷ Torr.
A 50 mg of fullerenes C₆₀ (Tokyo Chemical Industry) was placed in a molybdenum-made boat for vapor deposition, and the boat was heated at 500° C. for 1 hour so that a fullerene film having a thickness of about 0.4 μm was formed on a substrate 8 fixed onto a ceramic heater. Under an As-Depo state where the substrate temperature was 80° C., the measurement was made and the conductivity was found to be 0.06 (Ωcm)⁻¹. Then, the vessel was slowly cooled to room temperature or 27° C. where the conductivity was found to be 0.02 (Ωcm)⁻¹.
Later, argon gas was allowed to enter via an adsorption unit equipped with a molecular sieve into the chamber to regain a normal atmospheric pressure. The sample was transferred via a passage with a road-lock to a separate chamber. Oxygen gas was allowed to pass continuously for 10 minutes through the chamber where the sample was settled. Then, the sample was returned to the original chamber. Next, while nitrogen gas was allowed to flow through the chamber, the conductivity of the sample was measured and found to be 4.2×10⁻¹¹ (Ωcm)⁻¹. While argon gas was flowed as before, voltage was applied to the ceramic heater upon which the sample was fixed to heat it. When the heater was activated for 15 minutes, the sample was heated to 160° C. where the measurement was made and the conductivity of the sample was found to be 0.0096 (Ωcm)⁻¹. Heating was further continued at 180° C. for 1 hour where the conductivity was found to be 0.05 (Ωcm)⁻¹.
Example 6 Improvement of Conductivity of a Fullerene Film by Inert Gas Heating
An environment suitable for manufacturing a fullerene film according to the above-described condition appropriate for the production of highly conductive fullerenes was prepared, and the degree of vacuum was found to be 3.1×10⁻⁷ Torr.
A 50 mg of fullerenes C₆₀ (Tokyo Chemical Industry) was placed in a molybdenum-made boat for vapor deposition, and the boat was heated at 500° C. for 1 hour so that a fullerene film having a thickness of about 0.4 μm was formed on a substrate 8 fixed onto a ceramic heater. Under an As-Depo state where the substrate temperature was 80° C., the measurement was made and the conductivity was found to be 0.03 (Ωcm)⁻¹. Then, the vessel was slowly cooled to room temperature or 27° C. where the conductivity was found to be 0.01 (Ωcm)⁻¹.
Later, the chamber was baked at 150° C. for 4 days. On day 4 of baking, the measurement was made and it was found that the conductivity of the test film lowered to 0.0008 (Ωcm)⁻¹. On completion of baking, the chamber was cooled to 30° C. over 1 day. The degree of vacuum was then 2×10⁻¹¹ Torr. Nitrogen gas was allowed to enter via an adsorption unit equipped with a molecular sieve into the chamber to regain a normal atmospheric pressure. While nitrogen gas was allowed to flow as before, voltage was applied to a ceramic heater upon which the sample was fixed to heat it.
When the heater was activated for 25 minutes, the sample was heated to 303° C. where the measurement was made and the conductivity of the sample was found to be 0.76 (Ωcm)⁻¹. Then, the vessel was slowly cooled to room temperature or 28° C. where the conductivity was found to be 0.12 (Ωcm)⁻¹ which was higher than the value obtained at the As-Depo state.
Example 7
In this example, the experimental set-up was the same as in Example 1 except that the degree of vacuum of vessel was made 10⁻¹¹ Torr. In this example, the test sample exhibited a higher conductivity than in Example 1.
INDUSTRIAL APPLICABILITY
As described above, fullerenes and a nanotube prepared according to the invention and the inventive method for the production thereof will greatly enhance the conductivity of organic materials, and contribute to the improved performance of organic semiconductor devices, and thus be particularly useful in the field of electronics.
1. Fullerenes, which contain oxygen at 10¹⁴ molecules/cm³ or less, and water at 10¹⁶ molecules/cm³ or less.
2. Fullerenes, which contain water at 10¹⁶ molecules/cm³ or less.
3. Fullerenes, which have an electric conductivity of 10⁻¹ (Ωcm)⁻¹ or higher, and 10 (Ωcm)⁻¹ or lower when measured at 27° C.
4. Fullerenes, which have an electric conductivity of 10⁻¹ (Ωcm)⁻¹ or higher, and 10³ (Ωcm)⁻¹ or lower when measured at 27° C.
5. The fullerenes as claimed in claim 1, which are C₆₀, C₇₀, C₇₆, C₇₈, C₈₂, or C₈₄, or a mixture thereof.
6. A nanotube, which contains oxygen at 10¹⁴ molecules/cm³ or less, and water at 10¹⁶ molecules/cm³ or less.
7. A nanotube, which contains water at 10¹⁶ molecules/cm³ or less.
8. A solid body, powder, coating membrane, single crystal, poly-crystal, film, fiber, dopant material, vapor-deposited material, or co-deposited material which contains fullerenes as claimed in claim
1. 9. A transistor, solar battery, fuel cell, organic EL, sensor, or resistance, which incorporates fullerenes as claimed in claim
1. 10. A method of producing fullerenes or a nanotube which comprises heating fullerenes as claimed in claim 1 at a temperature not lower than 200° C. and not higher than 700° C. in an inert gas for a period not shorter than 10 seconds and not longer than 10 hours.
11. A method of producing fullerenes or a nanotube which comprises heating fullerenes as claimed in claim 1 at a temperature not lower than 100° C. and not higher than 700° C. for a period not shorter than 10 seconds and not longer than 10 hours in an inert gas within a vessel while the inert gas is being purged from the vessel.
12. A method of producing fullerenes or a nanotube which comprises heating fullerenes or a nanotube at a temperature not lower than 100° C. and not higher than 700° C. for a period not shorter than 10 seconds and not longer than 10 hours in an inert gas within a vessel having a volume of V liter while the inert gas is being continuously flowed at a rate not lower than 3V liter/min and not higher than 10V liter/min.
13. A method of producing fullerenes or a nanotube which comprises heating fullerenes or a nanotube at a temperature not lower than 100° C. and not higher than 700° C. for a period not shorter than 10 seconds and not longer than 10 hours while the heating is allowed to proceed at a rate not higher than 20° C./min.
14. A method of producing fullerenes or a nanotube as claimed in claim 10, wherein the fullerenes are C₆₀, C₇₀, C₇₆, C₇₈, C₈₂, or C₈₄, or a mixture thereof.
15. A method of producing fullerenes or a nanotube as claimed in claim 10, wherein the inert gas comprises a gas selected from the group comprising pure nitrogen, Ar, He, Kr, Ne, and Xe, and a mixture thereof.
16. A method of producing fullerenes or a nanotube as claimed in claim 10, wherein the inert gas environment in contact with the fullerenes or the nanotube contains oxygen at 10 ppb or lower, and water at 10 ppb or lower.
17. A method of producing fullerenes or a nanotube as claimed in claim 10, wherein the vessel or the tube through which an inert gas is introduced into the vessel has an internal wall made of a stainless steel material which receives, on its surface, the protective coating of a passivity membrane made of chromium oxide, aluminum oxide or metal fluoride.
18. A method of producing fullerenes or a nanotube as claimed in claim 10, wherein the vessel or the tube through which an inert gas is introduced into the vessel is made of a material which releases gas from its surface at a rate not higher than 1×10⁻¹⁵ (Torr*1/sec*cm²).
19. A method of producing an organic device which comprises preparing a film made of fulleres or a nanotube produced by a method as claimed in claim 10, and forming a protective film made of SiO₂, Si₃N₄, polyimide, polymethylmethacrylate, polyvinylidenefluoride, polycarbonate, polyvinylalcohol, acryl resin or glass by CVD, PVD, spin coating, spray coating, or dip coating.
20. A deposited film made of fullerenes or a nanotube which is deposited, using fullerenes having a carbon content not lower than 99.6 wt %, in a vacuum having a degree of vacuum not higher than 10⁻⁹ Torr within a vacuum vessel which has an internal wall made of a stainless steel material receiving, on its surface, the protective coating of a passivity membrane made of chromium oxide, aluminum oxide or metal fluoride.
21. A deposited film made of fullerenes or a nanotube which is deposited, using fullerenes having a carbon content not lower than 99.6 wt %, in a vacuum having a degree of vacuum not higher than 10⁻¹¹ Torr within a vacuum vessel with an internal wall which releases gas from its surface at a rate not higher than 1×10⁻¹⁵ (Torr*1/sec*cm²).
22. A method of producing a deposited film made of fullerenes or a nanotube which comprises using fullerenes having a carbon content not lower than 99.6 wt %, and depositing the film in a vacuum having a degree of vacuum not higher than 10⁻⁹ Torr within a vacuum vessel with an internal wall made of a stainless steel material which receives, on its surface, the protective coating of a passivity membrane made of chromium oxide, aluminum oxide or metal fluoride.
23. A method of producing a deposited film made of fullerenes or a nanotube which comprises using fullerenes having a carbon content not lower than 99.6 wt %, and depositing the film in a vacuum having a degree of vacuum not higher than 10⁻¹¹ Torr within a vacuum vessel having an internal wall which releases gas from its surface at a rate not higher than 1×10⁻¹⁵ (Torr*1/sec*cm²).
24. A system for producing fullerenes or a nanotube which comprises a vessel equipped with a gas inflow port and a gas outflow port, a heating means, a heating control means, and a gas flow control means, and which can control both the heating condition and the gas flow condition in association.
25. A gas sensor using, as a sensor body, fullerenes as claimed in claim
1. 26. A gas detection method for checking the presence of a gas or determining its concentration by monitoring the change in resistance of fullerenes as claimed in claim
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