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Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable 具有可变渗透率的达西方程的自适应体积或有限元图
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02071-7
Yves Achdou , Christine Bernardi
{"title":"Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable","authors":"Yves Achdou ,&nbsp;Christine Bernardi","doi":"10.1016/S0764-4442(01)02071-7","DOIUrl":"10.1016/S0764-4442(01)02071-7","url":null,"abstract":"<div><p>We consider Darcy's equations with variable permeability coefficient in a two- or three-dimensional domain. We propose a finite volume scheme, which turns out to be equivalent to a finite element problem, and we derive optimal a priori error estimates. We describe error indicators and prove that they provide an appropriate tool for mesh adaptivity, since estimates allow to compare them with the error.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 693-698"},"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)02071-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84426973","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: 15
Idéaux p-adiques de p-rang d et le théorème des zéros p-adiques p阶d的p- adic理想和p- adic零定理
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02110-3
Ahmed Srhir
{"title":"Idéaux p-adiques de p-rang d et le théorème des zéros p-adiques","authors":"Ahmed Srhir","doi":"10.1016/S0764-4442(01)02110-3","DOIUrl":"10.1016/S0764-4442(01)02110-3","url":null,"abstract":"<div><p>We introduce here the notion of <em>p</em>-adic ideal of <em>p</em>-rank <em>d</em> and the one of <em>p</em>-adic radical of <em>p</em>-rank <em>d</em> of an ideal by analogy with the real case. We use it to give another proof of the <em>p</em>-adic Nullstellensatz.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 605-610"},"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)02110-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81233594","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
Morrey regularity of strong solutions to parabolic equations with VMO coefficients 带VMO系数抛物方程强解的Morrey正则性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02107-3
Lubomira G Softova
{"title":"Morrey regularity of strong solutions to parabolic equations with VMO coefficients","authors":"Lubomira G Softova","doi":"10.1016/S0764-4442(01)02107-3","DOIUrl":"10.1016/S0764-4442(01)02107-3","url":null,"abstract":"<div><p>We consider a regular oblique derivative problem for a linear parabolic operator <span><math><mtext>P</mtext></math></span> with VMO principal coefficients. Its unique strong solvability is proved in [15], when <span><math><mtext>P</mtext><mtext>u∈</mtext><mtext>L</mtext><msup><mi></mi><mn>p</mn></msup><mtext>(Q</mtext><msub><mi></mi><mn>T</mn></msub><mtext>)</mtext></math></span>. Our goal here is to show that the solution belongs to the parabolic Morrey space W<sub><em>p</em>,<em>λ</em></sub><sup>2,1</sup>(<em>Q</em><sub><em>T</em></sub>), when <span><math><mtext>P</mtext><mtext>u∈</mtext><mtext>L</mtext><msup><mi></mi><mn>p,λ</mn></msup><mtext>(Q</mtext><msub><mi></mi><mn>T</mn></msub><mtext>)</mtext></math></span>, <em>p</em>∈(1,∞), <em>λ</em>∈(0,<em>n</em>+2), and <em>Q</em><sub><em>T</em></sub> is a cylinder in <span><math><mtext>R</mtext><msub><mi></mi><mn>+</mn></msub><msup><mi></mi><mn>n+1</mn></msup></math></span>. The a priori estimates of the solution are derived through L<sup><em>p</em>,<em>λ</em></sup> estimates for singular and nonsingular integral operators.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 635-640"},"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)02107-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72602545","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: 2
On pointwise dimensions and spectra of measures 测度的点维和谱
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02043-2
Jean-René Chazottes , Benoît Saussol
{"title":"On pointwise dimensions and spectra of measures","authors":"Jean-René Chazottes ,&nbsp;Benoît Saussol","doi":"10.1016/S0764-4442(01)02043-2","DOIUrl":"10.1016/S0764-4442(01)02043-2","url":null,"abstract":"<div><p>We give a new definition of the lower pointwise dimension associated with a Borel probability measure with respect to a general Carathéodory–Pesin structure. Then we show that the spectrum of the measure coincides with the essential supremum of the lower pointwise dimension. We provide an example coming from dynamical systems.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 719-723"},"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)02043-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79724055","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: 8
On a result of Eliashberg and Gromov 根据Eliashberg和Gromov的结果
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)01939-5
Marc Chaperon
{"title":"On a result of Eliashberg and Gromov","authors":"Marc Chaperon","doi":"10.1016/S0764-4442(01)01939-5","DOIUrl":"10.1016/S0764-4442(01)01939-5","url":null,"abstract":"<div><p>We give a very simple proof of a theorem of Eliashberg and Gromov implying that intersection between the conormal bundles <em>νM</em> and <em>νN</em> of two proper submanifolds <em>M</em>, <em>N</em> of <span><math><mtext>R</mtext><msup><mi></mi><mn>n</mn></msup></math></span> is persistent under compactly supported Hamiltonian deformations of <em>νM</em> and <em>νN</em>.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 657-661"},"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)01939-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81613840","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
Random distributions, random affine systems, sampling of renewal processes 随机分布，随机仿射系统，更新过程的抽样
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02120-6
Christian Mazza, Didier Piau
{"title":"Random distributions, random affine systems, sampling of renewal processes","authors":"Christian Mazza,&nbsp;Didier Piau","doi":"10.1016/S0764-4442(01)02120-6","DOIUrl":"10.1016/S0764-4442(01)02120-6","url":null,"abstract":"<div><p>Let <em>F</em> be a neutral to the right, random distribution function on [0,+∞[, with a stationary subordinator. We introduce new linear functionals of the increments of <em>F</em>. Each of them is distributed like the unique fixed point of a random affine system. For gamma subordinators, we prove, building on earlier work, that their densities involve linear combinations of hypergeometric functions. We apply these ideas to the random sampling of alternating renewal processes.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 669-672"},"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)02120-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85167869","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
Sur la géométrie du groupe de Thompson 关于汤普森群的几何
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02143-7
Xavier Martin
{"title":"Sur la géométrie du groupe de Thompson","authors":"Xavier Martin","doi":"10.1016/S0764-4442(01)02143-7","DOIUrl":"10.1016/S0764-4442(01)02143-7","url":null,"abstract":"<div><p>Using lambda coordinates from Teichmüller theory, we study the action of the Thompson group <em>T</em> on a relative Teichmüller space, which is defined in terms of piecewise projective homeomorphisms. As an application, we give a geometric interpretation of the homology equivalence between <em>BT</em> and the free loop space <span><math><mtext>L</mtext><mtext>S</mtext><msup><mi></mi><mn>3</mn></msup></math></span>.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 773-778"},"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)02143-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87235296","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: 8
Algorithme de dualité pour un problème d'optimisation non convexe : application à un problème de Stokes non linéaire∗ 非凸优化问题的二元算法:对非线性斯托克斯问题的应用
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02130-9
Nadia Raïssi, Mustapha Serhani
{"title":"Algorithme de dualité pour un problème d'optimisation non convexe : application à un problème de Stokes non linéaire∗","authors":"Nadia Raïssi,&nbsp;Mustapha Serhani","doi":"10.1016/S0764-4442(01)02130-9","DOIUrl":"10.1016/S0764-4442(01)02130-9","url":null,"abstract":"<div><p>We apply a duality method for solving a nonconvex optimization problem. We construct an algorithm converging to a <em>∂</em>-critical point and we establish the relationship with critical point of the primal problem. The application of this method to a nonlinear Stokes problem leads to a weak solution.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 801-806"},"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)02130-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81713506","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
Une condition nécessaire et suffisante d'existence de la série discrète d'un groupe localement compact 局部紧群离散级数存在的充分必要条件
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02027-4
Mohamed Akkouchi , Allai Bakali , Samir Kabbaj
{"title":"Une condition nécessaire et suffisante d'existence de la série discrète d'un groupe localement compact","authors":"Mohamed Akkouchi ,&nbsp;Allai Bakali ,&nbsp;Samir Kabbaj","doi":"10.1016/S0764-4442(01)02027-4","DOIUrl":"10.1016/S0764-4442(01)02027-4","url":null,"abstract":"<div><p>Let <em>G</em> be a topological locally compact group. The aim of this Note is a contribution to the study of the existence problem for square integrable continuous and unitary representations for <em>G</em>. One of our main results (Theorem 6.2) will give a necessary and sufficient condition for the existence of the discrete series for <em>G</em>. Our approach is based on the notions of units and bounded elements in L<sup>2</sup>(<em>G</em>) introduced by R. Godement in [6]. We perform a study of these notions. A particular attention is paid to the case of pure units. We associate to each pure unit a transform called Plancherel transform. We characterize the pure units with the use of their Plancherel transforms. We develop new methods giving a new proof to the well known theorem of Bargmann (see [3]) in the case of Lorentz groups, the Harish-Chandra theorem (see [5]) in the case of semi-simple Lie groups and a well known theorem of Duflo and Moore (see [4]) in the case of general nonunimodular locally compact groups. Our methods allow us to give an explicit expression of the formal operator introduced in [4] by Duflo and Moore.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 611-616"},"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)02027-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88220703","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
Invariants topologiques d'applications polynomiales 多项式应用的拓扑不变量
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02093-6
Enrique Artal Bartolo , Pierrette Cassou-Noguès , Hélène Maugendre
{"title":"Invariants topologiques d'applications polynomiales","authors":"Enrique Artal Bartolo ,&nbsp;Pierrette Cassou-Noguès ,&nbsp;Hélène Maugendre","doi":"10.1016/S0764-4442(01)02093-6","DOIUrl":"10.1016/S0764-4442(01)02093-6","url":null,"abstract":"<div><p>Let <span><math><mtext>φ:=(f,g):</mtext><mtext>C</mtext><msup><mi></mi><mn>2</mn></msup><mtext>→</mtext><mtext>C</mtext><msup><mi></mi><mn>2</mn></msup></math></span> with <em>f</em> and <em>g</em> polynomial mappings. We establish the connection that exists between the Newton polygon of the curve which is the union of the discriminant and of the non-proper locus of <em>φ</em> and the topology of the links at infinity of the curves <em>f</em><sup>−1</sup>(0) and <em>g</em><sup>−1</sup>(0).</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 751-754"},"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)02093-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86540439","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
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