{"title":"Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds","authors":"Hiroshi Goda, Takayuki Morifuji","doi":"10.5802/ambp.416","DOIUrl":"https://doi.org/10.5802/ambp.416","url":null,"abstract":"","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134909155","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}
A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.
{"title":"Matching Cells","authors":"Gaël Meigniez","doi":"10.5802/ambp.417","DOIUrl":"https://doi.org/10.5802/ambp.417","url":null,"abstract":"A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134909166","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}
We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke category at the field of fractions. Knowing explicit formulas for the localization is a key technical tool in software for computations with Soergel bimodules.
{"title":"Localized calculus for the Hecke category","authors":"Ben Elias, Geordie Williamson","doi":"10.5802/ambp.415","DOIUrl":"https://doi.org/10.5802/ambp.415","url":null,"abstract":"We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke category at the field of fractions. Knowing explicit formulas for the localization is a key technical tool in software for computations with Soergel bimodules.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136381328","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}
We prove a sharp uniform generalized Gaussian bound for the Green’s function of the Lax–Wendroff and Beam–Warming schemes. Our bound highlights the spatial region that leads to the well-known (rather weak) instability of these schemes in the maximum norm. We also recover uniform bounds in the maximum norm when these schemes are applied to initial data of bounded variation.
{"title":"The Green’s function of the Lax–Wendroff and Beam–Warming schemes","authors":"J.-F. Coulombel","doi":"10.5802/ambp.413","DOIUrl":"https://doi.org/10.5802/ambp.413","url":null,"abstract":"We prove a sharp uniform generalized Gaussian bound for the Green’s function of the Lax–Wendroff and Beam–Warming schemes. Our bound highlights the spatial region that leads to the well-known (rather weak) instability of these schemes in the maximum norm. We also recover uniform bounds in the maximum norm when these schemes are applied to initial data of bounded variation.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48242193","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":"Calogero–Moser cells of dihedral groups at equal parameters","authors":"C. Bonnafé, J. Germoni","doi":"10.5802/ambp.410","DOIUrl":"https://doi.org/10.5802/ambp.410","url":null,"abstract":"We prove that Calogero–Moser cells coincide with Kazhdan–Lusztig cells for dihedral groups in the equal parameter case.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41792806","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}
We define an extension operator and study (L , L) boundedness of Hardy–Littlewood–Sobolev inequality and weighted Hardy–Littlewood–Sobolev inequality on upper Half space for the Dunkl transform.
{"title":"Hardy–Littlewood–Sobolev Inequality for Upper Half Space","authors":"V. P. Anoop, S. Parui","doi":"10.5802/ambp.401","DOIUrl":"https://doi.org/10.5802/ambp.401","url":null,"abstract":"We define an extension operator and study (L , L) boundedness of Hardy–Littlewood–Sobolev inequality and weighted Hardy–Littlewood–Sobolev inequality on upper Half space for the Dunkl transform.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45769652","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 asymptotic Fermat over the ℤ 2 -extension of ℚ","authors":"Nuno Freitas, Alain Kraus, S. Siksek","doi":"10.5802/ambp.397","DOIUrl":"https://doi.org/10.5802/ambp.397","url":null,"abstract":"","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42697210","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}
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. This unifying feature is quite appealing and motivated our analysis. We show its potentiality with some selected examples including initial-value, Cauchy problems for ODEs; non-linear, monotone PDEs; linear and non-linear hyperbolic problems; and steady Navier–Stokes systems. Though the paper has the structure of a survey, we would like to explore in the future how this perspective could help in advancing for some new situations in PDEs.
{"title":"On a general variational framework for existence and uniqueness in Differential Equations","authors":"P. Pedregal","doi":"10.5802/ambp.405","DOIUrl":"https://doi.org/10.5802/ambp.405","url":null,"abstract":"Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. This unifying feature is quite appealing and motivated our analysis. We show its potentiality with some selected examples including initial-value, Cauchy problems for ODEs; non-linear, monotone PDEs; linear and non-linear hyperbolic problems; and steady Navier–Stokes systems. Though the paper has the structure of a survey, we would like to explore in the future how this perspective could help in advancing for some new situations in PDEs.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48032033","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}
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