Confluentes Mathematici最新文献

{"title":"Polish groups and Baire category methods","authors":"Julien Melleray","doi":"10.5802/CML.28","DOIUrl":"https://doi.org/10.5802/CML.28","url":null,"abstract":"This memoir presents my work since the end of my doctoral work. The unifying theme is the use of Baire category methods in various domains where Polish groups appear naturally.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"25 1","pages":"89-164"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78370580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cône nilpotent sur un corps fini et q-séries hypergéométriques@@@Nilpotent cone over a finite field and hypergeometric q-series","authors":"P. Caldero","doi":"10.5802/CML.30","DOIUrl":"https://doi.org/10.5802/CML.30","url":null,"abstract":"L’accès aux articles de la revue « Confluentes Mathematici » (http://cml.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://cml.cedram.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation á fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"14 1","pages":"3-22"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90781163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Forcing the truth of a weak form of Schanuel’s conjecture","authors":"M. Viale","doi":"10.5802/CML.33","DOIUrl":"https://doi.org/10.5802/CML.33","url":null,"abstract":"Schanuel’s conjecture states that the transcendence degree over Q of the 2n-tuple (λ1, . . . , λn, eλ1 , . . . , eλn ) is at least n for all λ1, . . . , λn ∈ C which are linearly independent over Q; if true it would settle a great number of elementary open problems in number theory, among which the transcendence of e over π. Wilkie [11], and Kirby [4, Theorem 1.2] have proved that there exists a smallest countable algebraically and exponentially closed subfield K of C such that Schanuel’s conjecture holds relative to K (i.e. modulo the trivial counterexamples, Q can be replaced by K in the statement of Schanuel’s conjecture). We prove a slightly weaker result (i.e. that there exists such a countable field K without specifying that there is a smallest such) using the forcing method and Shoenfield’s absoluteness theorem. This result suggests that forcing can be a useful tool to prove theorems (rather than independence results) and to tackle problems in domains which are apparently quite far apart from set theory. A brief introduction We want to give an example of how we might use forcing to study a variety of expansions of the complex (or real) numbers enriched by arbitrary Borel predicates, still maintaining certain “tameness” properties of the theory of these expansions. We clarify what we intend by “tameness” as follows: in contrast with what happens for example with o-minimality in the case of real closed fields, we do not have to bother much with the complexity of the predicate P we wish to add to the real numbers (we can allow P to be an arbitrary Borel predicate), but we pay a price reducing significantly the variety of elementary superstructures (M,PM ) for which we are able to lift P to PM so that (R, P ) ≺ (M,PM ) and for which we are able to use the forcing method to say something significant on the first order theory of (M,PM ). Nonetheless the family of superstructures M for which this is possible is still a large class, as we can combine (Woodin and) Shoenfield’s absoluteness for the theory of projective sets of reals with a duality theorem relating certain spaces of functions to forcing constructions, to obtain the following1: Theorem 1 (V. and Vaccaro [10]). — Let X be an extremally disconnected (i.e. such that the closure of open sets is open) compact Hausdorff space. Let C+(X) be the space of continuous functions f : X → S2 = C ∪ {∞} such that the preimage of ∞ is nowhere dense (S2 is the one point compactification of C). For any p ∈ X, let C+(X)/p be the ring of germs in p of functions in C+(X). Given any Borel predicate R on C, define a predicate RX/p ⊆ (C+(X)/p)n by the Math. classification: 03E57, 03C60, 11U99.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"60 1","pages":"59-83"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89857195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Limiting absorption principle for a new class of Schrödinger Hamiltonians","authors":"Alexandre Martin","doi":"10.5802/CML.46","DOIUrl":"https://doi.org/10.5802/CML.46","url":null,"abstract":"We prove the limiting absorption principle and discuss the continuity properties of the boundary values of the resolvent for a class of form bounded perturbations of the Euclidean Laplacian $Delta$ that covers both short and long range potentials with an essentially optimal behaviour at infinity.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83066605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Contramodules","authors":"L. Positselski","doi":"10.5802/cml.78","DOIUrl":"https://doi.org/10.5802/cml.78","url":null,"abstract":"Contramodules are module-like algebraic structures endowed with infinite summation (or, occasionally, integration) operations satisfying natural axioms. Introduced originally by Eilenberg and Moore in 1965 in the case of coalgebras over commutative rings, contramodules experience a small renaissance now after being all but forgotten for three decades between 1970-2000. Here we present a review of various definitions and results related to contramodules (drawing mostly from our monographs and preprints arXiv:0708.3398, arXiv:0905.2621, arXiv:1202.2697, arXiv:1209.2995, arXiv:1512.08119, arXiv:1710.02230, arXiv:1705.04960, arXiv:1808.00937) - including contramodules over corings, topological associative rings, topological Lie algebras and topological groups, semicontramodules over semialgebras, and a\"contra version\"of the Bernstein-Gelfand-Gelfand category O. Several underived manifestations of the comodule-contramodule correspondence phenomenon are discussed.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81619643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Models of Two-Phase Fluid Dynamics à la Allen-Cahn, Cahn-Hilliard, and ... Korteweg!","authors":"H. Freistühler, M. Kotschote","doi":"10.5802/CML.24","DOIUrl":"https://doi.org/10.5802/CML.24","url":null,"abstract":"","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"18 1","pages":"57-66"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74135072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sur un problème non linéaire pour la divergence et le déterminant","authors":"B. Dacorogna","doi":"10.5802/CML.23","DOIUrl":"https://doi.org/10.5802/CML.23","url":null,"abstract":"On etudie dans cet article, dedie a Denis Serre pour ses soixante ans, les problemes { div u = f (x, u,∇u) dans Ω u = u0 sur ∂Ω et { det∇φ = f (x, φ,∇φ) x ∈ Ω φ (x) = x x ∈ ∂Ω. On montre que sous des hypotheses appropriees les deux problemes sont resolubles sans conditions integrales.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"10 46","pages":"49-55"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72387340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global well-posedness of a system from quantum hydrodynamics for small data","authors":"C. Audiard","doi":"10.5802/cml.21","DOIUrl":"https://doi.org/10.5802/cml.21","url":null,"abstract":"This article describes a joint work of the author with B.Haspot on the existence and uniqueness of global solutions for the Euler-Korteweg equations in the special case of quantum hydrodynamics. Our aim here is to sketch how one can construct global small solutions of the Gross-Pitaevskii equation and use the so-called Madelung transform to convert these into solutions without vacuum of the quantum hydrodynamics. A key point is to bound the the solution of the Gross-Pitaevskii equation away from 0, this condition is fullfilled thanks to recent scattering results.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"49 1","pages":"7-16"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77851313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximation of the two-dimensional Dirichlet problem by continuous and discrete problems on one-dimensional networks","authors":"Maryse Bourlard-Jospin, S. Nicaise, Juliette Venel","doi":"10.5802/CML.16","DOIUrl":"https://doi.org/10.5802/CML.16","url":null,"abstract":"L’accès aux articles de la revue « Confluentes Mathematici » (http://cml.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://cml.cedram.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation á fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"25 1","pages":"13-33"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73435725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Coulomb Branch Formula for Quiver Moduli Spaces","authors":"J. Manschot, B. Pioline, A. Sen","doi":"10.5802/cml.41","DOIUrl":"https://doi.org/10.5802/cml.41","url":null,"abstract":"In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable representations of quivers with generic superpotential in terms of a set of invariants associated to ‘single-centered’ or ‘pure-Higgs’ states. The distinguishing feature of these invariants is that they are independent of the choice of stability condition. Furthermore they are uniquely determined by the χy-genus of the moduli space. Here, we provide a self-contained summary of the Coulomb branch formula, spelling out mathematical details but leaving out proofs and physical motivations.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"1 1","pages":"49-69"},"PeriodicalIF":0.0,"publicationDate":"2014-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90044456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}