Annales de la Faculté des sciences de Toulouse : Mathématiques最新文献_第3页

On the top-dimensional ℓ 2 -Betti numbers 在顶维的l2 -Betti数上

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2022-03-11 DOI: 10.5802/afst.1695

Damien Gaboriau, Camille Noûs

引用次数: 3

Homogenization of Maxwell’s equations and related scalar problems with sign-changing coefficients 麦克斯韦方程组的均匀化及相关变符号系数标量问题

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2022-03-11 DOI: 10.5802/afst.1694

R. Bunoiu, L. Chesnel, K. Ramdani, Mahran Rihani

{"title":"Homogenization of Maxwell’s equations and related scalar problems with sign-changing coefficients","authors":"R. Bunoiu, L. Chesnel, K. Ramdani, Mahran Rihani","doi":"10.5802/afst.1694","DOIUrl":"https://doi.org/10.5802/afst.1694","url":null,"abstract":"In this work, we are interested in the homogenization of time-harmonic Maxwell's equations in a composite medium with periodically distributed small inclusions of a negative material. Here a negative material is a material modelled by negative permittivity and permeability. Due to the sign-changing coefficients in the equations, it is not straightforward to obtain uniform energy estimates to apply the usual homogenization techniques. The goal of this article is to explain how to proceed in this context. The analysis of Maxwell's equations is based on a precise study of two associated scalar problems: one involving the sign-changing permittivity with Dirichlet boundary conditions, another involving the sign-changing permeability with Neumann boundary conditions. For both problems, we obtain a criterion on the physical parameters ensuring uniform invertibility of the corresponding operators as the size of the inclusions tends to zero. In the process, we explain the link existing with the so-called Neumann-Poincare operator, complementing the existing literature on this topic. Then we use the results obtained for the scalar problems to derive uniform energy estimates for Maxwell's system. At this stage, an additional difficulty comes from the fact that Maxwell's equations are also sign-indefinite due to the term involving the frequency. To cope with it, we establish some sort of uniform compactness result.","PeriodicalId":169800,"journal":{"name":"Annales de la Faculté des sciences de Toulouse : Mathématiques","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133769085","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}

引用次数: 4

Magnetic Ginzburg–Landau energy with a periodic rapidly oscillating and diluted pinning term 具有周期快速振荡和稀释钉住项的磁金兹堡-朗道能

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-12-06 DOI: 10.5802/afst.1688

Mickaël Dos Santos

引用次数: 0

On equivalence of singularities of second order linear differential equations by point transformations 二阶线性微分方程奇异性的点变换等价

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-10-26 DOI: 10.5802/afst.1684

Martin Klimeš

{"title":"On equivalence of singularities of second order linear differential equations by point transformations","authors":"Martin Klimeš","doi":"10.5802/afst.1684","DOIUrl":"https://doi.org/10.5802/afst.1684","url":null,"abstract":"— The article provides a local classification of singularities of meromorphic second order linear ordinary differential equations with respect to analytic/meromorphic linear point transformations, that is, transformations of both the unknown function and of the independent variable. In particular, it is shown that under a non-degeneracy condition two linear differential equations are analytically equivalent if and only if the associated companion systems are analytically equivalent as systems. Also the Lie algebras of analytic linear infinitesimal symmetries of the singularities are determined. RÉSUMÉ. — L’article propose une classification locale des singularités des équations différentielles linéaires du second ordre aux coefficients méromorphes par rapport aux transformations ponctuelles analytiques/méromorphes, c’est-à-dire, les transformations de la fonction inconnue aussi que de la variable indépendante. En particulier, il est montré que sous une condition de non-dégénérescence deux équations différentielles linéaires sont analytiquement équivalentes si et seulement si les systèmes compagnons associés sont analytiquement équivalents comme systèmes. Aussi les algèbres de Lie des symétries linéaires analytiques infinitésimales des singularités sont déterminées.","PeriodicalId":169800,"journal":{"name":"Annales de la Faculté des sciences de Toulouse : Mathématiques","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129439869","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}

引用次数: 0

A right inverse of Cauchy–Riemann operator ∂ ¯ k +a in the weighted Hilbert space L 2 (ℂ,e -|z| 2 ) 柯西-黎曼算子∂¯k + A在加权希尔伯特空间l2 (，e -|z| 2)中的右逆

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-10-26 DOI: 10.5802/afst.1686

Shaoyu Dai, Yifei Pan

引用次数: 4

Dirichlet twists of GL n -automorphic L-functions and hyper-Kloosterman Dirichlet series GL n -自同构l函数的狄利克雷扭转与超kloosterman狄利克雷级数

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-10-26 DOI: 10.5802/afst.1687

Jeanine Van Order

{"title":"Dirichlet twists of GL n -automorphic L-functions and hyper-Kloosterman Dirichlet series","authors":"Jeanine Van Order","doi":"10.5802/afst.1687","DOIUrl":"https://doi.org/10.5802/afst.1687","url":null,"abstract":"— We calculate mean values of GLn-automorphic L-functions twisted by primitive even Dirichlet characters of prime-power conductor, at arbitrary points within the critical strip, by derivation of special Voronoi summation formulae. Our calculation is novel in that the twisted sum can be expressed in terms of the average itself, and also that it sees the derivation of various new summation formulae in the setting of prime-power modulus. One consequence, as we explain, is to show the analytic continuation and additive summation formulae for hyper-Kloosterman Dirichlet series associated to GLn-automorphic L-functions. RÉSUMÉ. — Nous calculons les valuers moyennes des fonctions L automorphes sur GLn tordues par des caractères de Dirichlet primitifs et pairs, du conducteur une puissance d’un nombre premier, à des points arbitraires dans la bande critique, en dérivant des formules de sommation spéciales du type Voronoi. Notre calcul est nouveau car la somme est exprimé en termes de la moyenne elle-même, et aussi qu’il voit la dérivation de diverses nouvelles formules de sommation dans le regime des puissances d’un nombre premier. Une conséquence, comme nous l’expliquons, est de montrer les prolongations analytiques et des formules de sommation additive pour les séries de Dirichlet hyper-Kloosterman associées aux fonctions L automorphes sur GLn.","PeriodicalId":169800,"journal":{"name":"Annales de la Faculté des sciences de Toulouse : Mathématiques","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124018793","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}

引用次数: 1

Volume spécial à l’occasion du semestre thématique “Calculus of Variations and Probability” 专题学期“变数与概率微积分”特刊

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-07-09 DOI: 10.5802/AFST.1672

M. Fathi, Yuxin Ge, M. Mariş, Xavier Lamy

引用次数: 0

Regularity of optimal transport maps on locally nearly spherical manifolds 局部近球面流形上最优输运映射的正则性

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-07-09 DOI: 10.5802/AFST.1678

Yuxin Ge, Jian Ye

{"title":"Regularity of optimal transport maps on locally nearly spherical manifolds","authors":"Yuxin Ge, Jian Ye","doi":"10.5802/AFST.1678","DOIUrl":"https://doi.org/10.5802/AFST.1678","url":null,"abstract":"— Given a compact connected n-dimensional Riemannian manifold, we investigate the smoothness of the optimal transport map between the smooth densities with respect to the squared Riemannian distance cost. The optimal map is characterized by exp(grad u), where the potential function u satisfies a Monge– Ampère type equation. Delanoë [7] showed the smoothness of u on the Riemannian surfaces when the scalar curvature is close to 1 in C2 norm. In this work, we study the regularity issue on Riemannian manifolds with curvature sufficiently close to curvature of round sphere in C2 norm in all dimensions and prove that the C-curvature on such Riemannian manifolds satisfies an improved Ma-Trudinger-Wang condition and the Jacobian of the exponential map is positive. As a consequence, we imply the smoothness of the optimal transport map by the continuity method. RÉSUMÉ. — Etant donné une variété riemannienne compacte connexe de dimension n, nous étudions la régularité de l’application du transport optimal entre les densités lisses par rapport au coût de la distance riemannienne au carré. L’application du transport optimal est caractérisée par exp(grad u), où la fonction potentielle u satisfait une équation de type Monge–Ampère. Delanoë [7] a montré la régularité de u sur les surfaces riemanniennes lorsque la courbure scalaire est proche de 1 dans la norme C2. Dans ce travail, nous étudions le problème de régularité sur les variétés riemanniennes avec courbure suffisamment proche de la courbure de la sphère usuelle dans la norme C2 en toutes les dimensions et prouvons que la C-courbure sur de telles variétés riemanniennes satisfait une condition Ma-Trudinger-Wang améliorée et le jacobien de l’application exponentielle est strictement positive. Par conséquent, nous impliquons la régularité de l’application du transport optimal par la méthode de continuité.","PeriodicalId":169800,"journal":{"name":"Annales de la Faculté des sciences de Toulouse : Mathématiques","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125801556","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}

引用次数: 0

Topological singularities for vector-valued Sobolev maps and applications 向量值Sobolev映射的拓扑奇异性及其应用

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-07-09 DOI: 10.5802/AFST.1677

Giacomo Canevari, G. Orlandi

{"title":"Topological singularities for vector-valued Sobolev maps and applications","authors":"Giacomo Canevari, G. Orlandi","doi":"10.5802/AFST.1677","DOIUrl":"https://doi.org/10.5802/AFST.1677","url":null,"abstract":"— We review the analysis of topological singularities of Sobolev maps into manifolds and their applications to variational problems of Ginzburg–Landau type and to the lifting problem for BV maps into manifolds. We describe in particular recent results obtained in the vector-valued case related to variational models of material science, more precisely the Landau–de Gennes model. RÉSUMÉ. — Nous passons en revue certains résultats d’analyse des singularités topologiques des fonctions de Sobolev à valeurs dans des variétés, ainsi que leurs applications aux problèmes variationnels de type Ginzburg–Landau et au problème du relèvement dans l’espace BV. En particulier, nous présentons des résultats récents, portant sur les fonctions à valeurs vectorielles, qui trouvent leur application dans l’étude des modèles variationnels pour la science des matériaux, tels que le modèle de Landau–de Gennes. 1. Topological singularities of Sobolev maps into spheres 1.1. Motivating example: the Ginzburg–Landau energy Consider the Ginzburg–Landau functional u ∈W 1,2(Ω, C) 7→ EGL ε (u) := ∫ Ω { 1 2 |∇u| 2 + 1 4ε2 (1− |u| 2)2 }","PeriodicalId":169800,"journal":{"name":"Annales de la Faculté des sciences de Toulouse : Mathématiques","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129702830","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}

引用次数: 0

Topologie et dénombrement des courbes algébriques réelles 实代数曲线的拓扑与计数

Annales de la Faculté des sciences de Toulouse : Mathématiques Pub Date : 2021-06-29 DOI: 10.5802/afst.1698

Christophe Simon

引用次数: 1