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Comptes Rendus de l'Académie des Sciences - Series I - Mathematics最新文献

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Fragments de l'arithmétique et fonctions de couplage 算术碎片和耦合函数
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02151-6
Yerzhan Baisalov
{"title":"Fragments de l'arithmétique et fonctions de couplage","authors":"Yerzhan Baisalov","doi":"10.1016/S0764-4442(01)02151-6","DOIUrl":"10.1016/S0764-4442(01)02151-6","url":null,"abstract":"<div><p>We prove a conjecture of I. Korec [4] on decidability of some fragments of arithmetic equipped with a pairing function; as consequence, we give an axiomatization of the fragment of arithmetic equipped with Cantor pairing function, precising a result of [5].</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 817-820"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02151-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89919913","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
Algorithmes de Hastings–Metropolis en interaction
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02147-4
Didier Chauveau, Pierre Vandekerkhove
{"title":"Algorithmes de Hastings–Metropolis en interaction","authors":"Didier Chauveau,&nbsp;Pierre Vandekerkhove","doi":"10.1016/S0764-4442(01)02147-4","DOIUrl":"https://doi.org/10.1016/S0764-4442(01)02147-4","url":null,"abstract":"<div><p>We propose an adaptive MCMC method consisting of a set of parallel but non-Markovian and non i.i.d. discrete time processes, where each marginal uses the Hastings–Metropolis dynamic based on proposal densities depending on the other processes and learning from their past. We prove the geometric convergence of each marginal with a rate a.s. better than any arbitrary independent Hastings–Metropolis algorithm.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 881-884"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02147-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90002401","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
Sur une conjecture de Zahariuta et un problème de Kolmogorov 关于Zahariuta猜想和Kolmogorov问题
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02042-0
Stéphanie Nivoche
{"title":"Sur une conjecture de Zahariuta et un problème de Kolmogorov","authors":"Stéphanie Nivoche","doi":"10.1016/S0764-4442(01)02042-0","DOIUrl":"10.1016/S0764-4442(01)02042-0","url":null,"abstract":"<div><p>We prove the Zahariuta's conjecture, which itself solves a Kolmogorov's problem on the <em>ε</em>-entropy of classes of analytic functions. For a given holomorphically convex compact subset <em>K</em> in a bounded pseudoconvex domain <em>D</em> in <span><math><mtext>C</mtext><msup><mi></mi><mn>n</mn></msup></math></span>, the Zahariuta's conjecture consists in approximating uniformly on any compact subset of <em>D</em>⧹<em>K</em>, the relative extremal function <em>u</em><sub><em>K</em>,<em>D</em></sub> by a sequence of pluricomplex Green functions on <em>D</em> with logarithmic poles in the compact set <em>K</em>.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 839-843"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02042-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78740754","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
Points cubiques sur la quartique de Klein 克莱因四分位上的三次点
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02141-3
Oumar Sall
{"title":"Points cubiques sur la quartique de Klein","authors":"Oumar Sall","doi":"10.1016/S0764-4442(01)02141-3","DOIUrl":"10.1016/S0764-4442(01)02141-3","url":null,"abstract":"<div><p>In this Note, we determine the set of algebraic points of degree at most 3 on the Klein quartic curve. This result extends a previous result given by Hurwitz, who described the set of rational points.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 931-934"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02141-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76591431","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
Stabilisation et contrôle intermittent de l'équation des ondes 波动方程的间歇稳定与控制
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02128-0
Patrick Martinez, Judith Vancostenoble
{"title":"Stabilisation et contrôle intermittent de l'équation des ondes","authors":"Patrick Martinez,&nbsp;Judith Vancostenoble","doi":"10.1016/S0764-4442(01)02128-0","DOIUrl":"10.1016/S0764-4442(01)02128-0","url":null,"abstract":"<div><p>We study the stabilization of the one-dimensional wave equation with a boundary or locally distributed feedback that is positive-negative or on-off. We also give results of controllability in “arbitrarily short time” for the one-dimensional wave equation with a locally distributed control.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 851-854"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02128-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78690031","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
U-statistiques conditionnelles universellement consistantes pour des modèles de Markov cachés 隐藏马尔可夫模型的普遍一致条件u统计量
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02148-6
Michel Harel , Madan L Puri
{"title":"U-statistiques conditionnelles universellement consistantes pour des modèles de Markov cachés","authors":"Michel Harel ,&nbsp;Madan L Puri","doi":"10.1016/S0764-4442(01)02148-6","DOIUrl":"10.1016/S0764-4442(01)02148-6","url":null,"abstract":"<div><p>A general class of conditional <em>U</em>-statistics was introduced by W. Stute [3] as a generalization of the Nadaraya–Watson estimates of a regression function. It was shown that such statistics are universally consistent (Stute [3]). Also, universal consistency of the window and <em>k</em><sub><em>n</em></sub>-nearest neighbor estimators (as two special cases of the conditional <em>U</em>-statistics) were proved by Stute [3]. In this paper, we extend these results from the independent case to dependent case.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 953-956"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02148-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80199841","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 negative eigenvalues of regular graphs 正则图的负特征值
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02155-3
Wen-Ching Winnie Li
{"title":"On negative eigenvalues of regular graphs","authors":"Wen-Ching Winnie Li","doi":"10.1016/S0764-4442(01)02155-3","DOIUrl":"10.1016/S0764-4442(01)02155-3","url":null,"abstract":"<div><p>In this Note we prove that if {<em>G</em><sub><em>n</em></sub>} is a sequence of connected <em>k</em>-regular graphs in which the length of odd cycles approaches infinity as <em>n</em>→∞, then the <span><math><mtext>lim</mtext><mspace></mspace><mtext>sup</mtext></math></span> of the smallest eigenvalue of <em>G</em><sub><em>n</em></sub> greater than −<em>k</em> is at most <span><math><mtext>−2</mtext><mtext>k−1</mtext></math></span> as <em>n</em> tends to infinity.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 907-912"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02155-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86755709","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: 11
Tourbillons dansants 涡跳舞
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02162-0
Tadashi Tokieda
{"title":"Tourbillons dansants","authors":"Tadashi Tokieda","doi":"10.1016/S0764-4442(01)02162-0","DOIUrl":"https://doi.org/10.1016/S0764-4442(01)02162-0","url":null,"abstract":"<div><p>The motion of point vortices in a 2-dimensional ideal fluid is treated as a Hamiltonian system. We describe an infinite family of periodic solutions for an even number of vortices on the sphere, the ellipsoid, the torus, and other surfaces, as well as some of their relative variants.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 943-946"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02162-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137309782","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
Structures intelligentes pour le contrôle des bruits dans une tuyauterie 用于控制管道噪音的智能结构
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02154-1
Philippe Destuynder
{"title":"Structures intelligentes pour le contrôle des bruits dans une tuyauterie","authors":"Philippe Destuynder","doi":"10.1016/S0764-4442(01)02154-1","DOIUrl":"10.1016/S0764-4442(01)02154-1","url":null,"abstract":"<div><p>From a uni-dimensional model for acoustic waves in a flow duct, an analysis of the exact controllability of initial perturbations is suggested using the so-called HUM method of J.-L. Lions. Several restrictive hypothesis are required and the minimum delay necessary for an exact control is a function of the three following velocities: the one of the steady flow, and the two waves celerities in the flexible structure and in the flow. Then we discuss the possibility to use actuators in order to control the noise perturbations. The goal of the study is to evaluate a new technology for a noise insulator in an air conduct.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 961-966"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02154-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85565744","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
Un modèle semi-paramétrique pour variables aléatoires hilbertiennes 希尔伯特随机变量的半参数模型
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02163-2
Jacques Dauxois , Louis Ferré , Anne-Françoise Yao
{"title":"Un modèle semi-paramétrique pour variables aléatoires hilbertiennes","authors":"Jacques Dauxois ,&nbsp;Louis Ferré ,&nbsp;Anne-Françoise Yao","doi":"10.1016/S0764-4442(01)02163-2","DOIUrl":"10.1016/S0764-4442(01)02163-2","url":null,"abstract":"<div><p>This Note deals with a semi-parametric model for Hilbertian random variables. The model is said semi-parametric by analogy with the finite dimensional case since the model involves a composition of any measurable mapping with a linear mapping which represents the “parametric” part. Under mild conditions, we derive a way for estimating this linear component in a particular case. We show that this method is actually a generalization of Li's Sliced Inverse Regression. However, in the Hilbertian context, SIR requires some adaptations of the estimation procedure and results concerning the consistency of the proposed estimates are given.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 947-952"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02163-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86677029","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: 34
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