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A non-trivial family of bundles fixed by the square of Frobenius 一个由Frobenius平方固定的非平凡束族
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02109-7
Yves Laszlo
{"title":"A non-trivial family of bundles fixed by the square of Frobenius","authors":"Yves Laszlo","doi":"10.1016/S0764-4442(01)02109-7","DOIUrl":"10.1016/S0764-4442(01)02109-7","url":null,"abstract":"<div><p>One shows the existence of a smooth projective curve over <span><math><mtext>F</mtext><msub><mi></mi><mn>2</mn></msub></math></span> and of representations of the arithmetic fundamental group of <em>X</em>⊗<em>k</em> with values in <span><math><mtext>SL</mtext><msub><mi></mi><mn>2</mn></msub><mtext>(k[[t]])</mtext></math></span>, with <em>k</em> suitable finite field of characteristic 2, such that the image of the geometric fundamental group is infinite. This gives a negative answer to a question of A.J. de Jong.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 651-656"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02109-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73996082","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: 12
Un algorithme discret de décomposition de domaines pour l'équation des ondes en dimension 1 一种二维波方程的离散域分解算法
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02083-3
Martin J. Gander , Laurence Halpern
{"title":"Un algorithme discret de décomposition de domaines pour l'équation des ondes en dimension 1","authors":"Martin J. Gander ,&nbsp;Laurence Halpern","doi":"10.1016/S0764-4442(01)02083-3","DOIUrl":"10.1016/S0764-4442(01)02083-3","url":null,"abstract":"<div><p>We have introduced in a previous Note a variant of the Schwarz algorithm without overlap for wave propagation. We present here a nonconforming finite volume discretization of the algorithm and analyze the convergence of the discrete algorithm.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 699-702"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02083-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83428598","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: 3
On Chern's proof of Baum–Bott's theorem 论陈对鲍姆-博特定理的证明
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02140-1
Marcio G. Soares
{"title":"On Chern's proof of Baum–Bott's theorem","authors":"Marcio G. Soares","doi":"10.1016/S0764-4442(01)02140-1","DOIUrl":"10.1016/S0764-4442(01)02140-1","url":null,"abstract":"<div><p>In [2] Chern proved, through methods of differential geometry, the Baum–Bott theorem in the non-degenerate case, that is, for one-dimensional holomorphic foliations whose singular set consists of isolated points and such that, in a neighborhood of such a point, any vector field defining the foliation has linear part with non-zero eigenvalues at the point in question. In this Note we show that, by slightly modifying Chern's proof, we can prove Baum–Bott's result as stated in [1], hence without the “non-degenerate” assumption.</p><p>Dans [2] Chern a démontré, en n'utilisant que des méthodes de géometrie différentielle, le théorème de Baum–Bott dans le cas non dégénérée, c'est-à-dire, pour les feuilletages holomorphes de dimension un avec points singuliers isolées et tells que, au voisinage d'un tel point, un champ définissant le feuilletage admet une partie linéaire avec toutes ses valeurs propres non nulles au point en question. Le but de cette Note est de montrer que la preuve donnée par Chern peut être un peu modifiée, de façon a obtenir le résultat de Baum–Bott dans [1], où l'hypothèse «non dégénérée » n'intervient pas.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 757-761"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02140-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87304468","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
Stabilizing and commuting cochains 稳定和交换共链
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02118-8
Max Karoubi
{"title":"Stabilizing and commuting cochains","authors":"Max Karoubi","doi":"10.1016/S0764-4442(01)02118-8","DOIUrl":"10.1016/S0764-4442(01)02118-8","url":null,"abstract":"<div><p>As it is well known in <em>K</em>-theory, stabilization of matrices enables them to commute “up to homotopy”. The purpose of this short paper is to describe an analogous philosophy for cochains on a space. It is in fact a direct application of a paper of Henri Cartan [1], together with a new idea of stabilization for cochains, similar to matrices. The application below may be also deduced from a paper of J. Halperin and J. Stasheff [2] by a quite different method. This paper is part of a joint project with P. Baum about the cohomology of homogeneous spaces. Since it has some independent interest, it might be useful to present it on its own right.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 769-771"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02118-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80533463","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
Differentiability of convex envelopes 凸包络的可微性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02117-6
Bernd Kirchheim , Jan Kristensen
{"title":"Differentiability of convex envelopes","authors":"Bernd Kirchheim ,&nbsp;Jan Kristensen","doi":"10.1016/S0764-4442(01)02117-6","DOIUrl":"10.1016/S0764-4442(01)02117-6","url":null,"abstract":"<div><p>We prove that the convex envelope of a differentiable, or C<sup>1,<em>α</em></sup>-function <em>f</em> is C<sup>1</sup>, or C<sup>1,<em>α</em></sup> respectively, provided only that the function satisfies the very mild growth condition that <em>f</em>(<em>x</em>) tends to +∞ if |<em>x</em>| does so.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 725-728"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02117-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91079037","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: 49
Composition conditions and center problem 构成条件与中心问题
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02124-3
Seok Hur
{"title":"Composition conditions and center problem","authors":"Seok Hur","doi":"10.1016/S0764-4442(01)02124-3","DOIUrl":"10.1016/S0764-4442(01)02124-3","url":null,"abstract":"<div><p>This Note presents a composition condition which yields vanishing of all the obstructions to a center displayed in Françoise's algorithm for the computation of higher order Melnikov functions [6,9]. We discuss some examples and the relation with the composition condition of Alwash and Lloyd [1,2].</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 779-784"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02124-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"107200677","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: 5
Une justification d'un modèle d'assemblages de coques cylindriques collées 粘接圆柱壳组件模型的论证
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)01964-4
Véronique Lods
{"title":"Une justification d'un modèle d'assemblages de coques cylindriques collées","authors":"Véronique Lods","doi":"10.1016/S0764-4442(01)01964-4","DOIUrl":"10.1016/S0764-4442(01)01964-4","url":null,"abstract":"<div><p>We consider two thin linearly elastic cylindrical shells, bonded to each other. The thickness of each shell is 2<em>ε</em>, <em>ε</em> being small. The adhesive material is assumed to be a linearized Saint-Venant Kirchhoff material, with Lamé constants of order <em>ε</em><sup><em>q</em></sup> with <em>q</em>&gt;0 as in [1,2]. This material then constitutes a cylindrical shell with a thickness <em>ε</em><sup><em>r</em></sup> with <em>r</em>&gt;1. The upper shell is loaded with a volumic density of order <em>ε</em><sup>2</sup>. We consider the case <em>q</em>=3+<em>r</em>. We then establish the convergence, in appropriate spaces, of the scaled displacements and scaled stress tensors when <em>ε</em> goes to zero. The limit displacement satisfies a flexural model which involve the shear and the normal stress of the adhesive part. These stresses depend on the jump of the tangential and normal displacements of the bonded shells.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 813-816"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)01964-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83856450","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
Étude du système de Schrödinger–Bloch modélisant la propagation d'un laser dans un gaz schrodinger - Bloch系统模拟激光在气体中的传播的研究
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02105-X
Rémi Abgrall, Thierry Colin, Boniface Nkonga
{"title":"Étude du système de Schrödinger–Bloch modélisant la propagation d'un laser dans un gaz","authors":"Rémi Abgrall,&nbsp;Thierry Colin,&nbsp;Boniface Nkonga","doi":"10.1016/S0764-4442(01)02105-X","DOIUrl":"10.1016/S0764-4442(01)02105-X","url":null,"abstract":"<div><p>In this Note, we study a two-level Schrödinger–Bloch system: first we introduce a nondimensional form of the system in which a small parameter appears. Then we prove an existence theorem and an asymptotic result. Finally, we propose an efficient numerical scheme that is uniform with respect to the small parameter.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 689-692"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02105-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80697474","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
Compatibilité des structures pseudo-riemanniennes et des structures de Poisson 伪黎曼结构与泊松结构的相容性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02132-2
Mohamed Boucetta
{"title":"Compatibilité des structures pseudo-riemanniennes et des structures de Poisson","authors":"Mohamed Boucetta","doi":"10.1016/S0764-4442(01)02132-2","DOIUrl":"10.1016/S0764-4442(01)02132-2","url":null,"abstract":"<div><p>We will introduce two notions of compatibility between pseudo-Riemannian metric and Poisson structure using the notion of contravariant connection introduced in [1], we will study some properties of manifold endowed with such compatible structures and we will give some examples.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 763-768"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02132-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83405820","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: 49
Le peigne à Dirac et la brosse à Bezout 狄拉克的梳子和贝佐特的刷子
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02134-6
André Unterberger
{"title":"Le peigne à Dirac et la brosse à Bezout","authors":"André Unterberger","doi":"10.1016/S0764-4442(01)02134-6","DOIUrl":"10.1016/S0764-4442(01)02134-6","url":null,"abstract":"<div><p>We construct a distribution on <span><math><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup></math></span>, invariant under the linear action on <span><math><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup></math></span> of the group <span><math><mtext>Γ=</mtext><mtext>SL</mtext><mtext>(2,</mtext><mtext>Z</mtext><mtext>)</mtext></math></span>, whose decomposition into homogeneous terms depends on all non-holomorphic modular forms for the group <em>Γ</em>, and which plays a major role in the automorphic Weyl calculus.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 629-634"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02134-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90959640","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
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