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

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Brownian bridge on Riemannian symmetric spaces 黎曼对称空间上的布朗桥
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02145-0
Philippe Bougerol, Thierry Jeulin
{"title":"Brownian bridge on Riemannian symmetric spaces","authors":"Philippe Bougerol,&nbsp;Thierry Jeulin","doi":"10.1016/S0764-4442(01)02145-0","DOIUrl":"10.1016/S0764-4442(01)02145-0","url":null,"abstract":"<div><p>We consider the Brownian bridge of length <em>T</em> on a symmetric space of the noncompact type. We prove that this process, properly rescaled, converges when <em>T</em>→+∞ to a process whose generalized radial part is the bridge of the Euclidean Brownian motion in the Weyl chamber killed at the boundary.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 785-790"},"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)02145-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75625796","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
Principe local d'invariance pour des variables aléatoires i.i.d. 随机变量的局部不变性原理
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02112-7
Jean-Christophe Breton, Youri Davydov
{"title":"Principe local d'invariance pour des variables aléatoires i.i.d.","authors":"Jean-Christophe Breton,&nbsp;Youri Davydov","doi":"10.1016/S0764-4442(01)02112-7","DOIUrl":"10.1016/S0764-4442(01)02112-7","url":null,"abstract":"<div><p>For a sequence of independent identically distributed random variables, the normalized step-processes associated are weakly convergent to the Wiener process. We strengthen for the functional distributions the convergence for the variation distance for a class of functionals.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 673-676"},"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)02112-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81525785","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
Calcul de Weyl automorphe
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02135-8
André Unterberger
{"title":"Calcul de Weyl automorphe","authors":"André Unterberger","doi":"10.1016/S0764-4442(01)02135-8","DOIUrl":"10.1016/S0764-4442(01)02135-8","url":null,"abstract":"<div><p>We introduce the operators the Weyl symbols of which are automorphic distributions on <span><math><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup></math></span> and we study their symbolic calculus.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 729-734"},"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)02135-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84091851","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
Non-oscillating Paley–Wiener functions 非振荡佩利-维纳函数
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02131-0
Iossif Ostrovskii , Alexander Ulanovskii
{"title":"Non-oscillating Paley–Wiener functions","authors":"Iossif Ostrovskii ,&nbsp;Alexander Ulanovskii","doi":"10.1016/S0764-4442(01)02131-0","DOIUrl":"10.1016/S0764-4442(01)02131-0","url":null,"abstract":"<div><p>A non-oscillating Paley–Wiener function is a real entire function <em>f</em> of exponential type belonging to <span><math><mtext>L</mtext><msub><mi></mi><mn>2</mn></msub><mtext>(</mtext><mtext>R</mtext><mtext>)</mtext></math></span> and such that each derivative <em>f</em><sup>(<em>n</em>)</sup>, <span><math><mtext>n=0,1,2,…</mtext><mspace></mspace></math></span>, has only a finite number of real zeros. We show that the class of such functions is non-empty and contains functions of arbitrarily fast decay on <span><math><mtext>R</mtext></math></span> allowed by the convergence of the logarithmic integral. We also give a close to the best possible asymptotic (as <em>n</em>→∞) estimate of the size of the smallest interval containing all real zeros of <em>n</em>-th derivative of a function <em>f</em> of the class.</p><p>Une fonction entière réelle du type exponentiel appartenant à <span><math><mtext>L</mtext><msup><mi></mi><mn>2</mn></msup><mtext>(</mtext><mtext>R</mtext><mtext>)</mtext></math></span> est une fonction non oscillante de Paley–Wiener si chacune de ses dérivées <em>f</em><sup>(<em>n</em>)</sup>, <span><math><mtext>n=0,1,2,…</mtext><mspace></mspace></math></span>, possède un nombre fini de zéros. Nous montrons que la classe de ces fonctions n'est pas vide. De plus, elle contient des fonctions qui décroissent arbitrairement vite, à condition que la vitesse de décroissance n'interdise pas la convergence de l'intégrale logarithmique. Nous établissons aussi une estimation de la longueur de l'intervalle minimal contenant tous les zéros réels de la <em>n</em>-ième dérivée d'une fonction de cette classe. D'un certain point de vue, cette estimation est optimale.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 735-740"},"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)02131-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87314262","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
Loi du logarithme itéré de l'estimateur à noyau du mode 模态核估计量的迭代对数定律
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02119-X
Joséphine Leclerc
{"title":"Loi du logarithme itéré de l'estimateur à noyau du mode","authors":"Joséphine Leclerc","doi":"10.1016/S0764-4442(01)02119-X","DOIUrl":"10.1016/S0764-4442(01)02119-X","url":null,"abstract":"<div><p>We characterize the strong limiting behavior of the kernel density estimates of the mode using law of the iterated logarithm type results.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 681-684"},"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)02119-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89682104","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
Groupes engendrés par des réflexions, designs sphériques et réseau de Leech∗ 由反射、球形设计和水蛭∗网络生成的组
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02142-5
Pierre de la Harpe , Boris Venkov
{"title":"Groupes engendrés par des réflexions, designs sphériques et réseau de Leech∗","authors":"Pierre de la Harpe ,&nbsp;Boris Venkov","doi":"10.1016/S0764-4442(01)02142-5","DOIUrl":"10.1016/S0764-4442(01)02142-5","url":null,"abstract":"<div><p>For a finite subset <span><math><mtext>X⊂</mtext><mtext>R</mtext><msup><mi></mi><mn>n</mn></msup></math></span> of unit vectors, <em>G</em><sub><em>X</em></sub> denotes the group generated by reflections <em>r</em><sub><em>x</em></sub> fixing hyperplanes orthogonal to <em>x</em>∈<em>X</em>. When <em>X</em> is a spherical <em>t</em>-design and <em>π</em><sup>(<em>k</em>)</sup><sub>har</sub> the representation of <em>G</em><sub><em>X</em></sub> in the harmonic polynomials in <em>n</em> variables of degree <em>k</em>, the spectrum of the Markov operator <span><math><mtext>1</mtext><mtext>|X|</mtext><mtext>∑</mtext><msub><mi></mi><mn>x∈X</mn></msub><mtext>π</mtext><msup><mi></mi><mn>(k)</mn></msup><msub><mi></mi><mn><mtext>har</mtext></mn></msub><mtext>(r</mtext><msub><mi></mi><mn>x</mn></msub><mtext>)</mtext></math></span> is analyzed. If <em>k</em> is small enough, this operator is a scalar multiple of the identity. When <em>X</em> is the spherical 11-design of short vectors in a Leech lattice, it is shown that the infinite group <em>G</em><sub><em>X</em></sub> contains the finite Conway group Co and is a quotient of a remarkable Coxeter group.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 745-750"},"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)02142-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83520601","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
Extinction for discretizations of some semilinear parabolic equations 一类半线性抛物型方程离散化的消光
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02078-X
Théodore K. Boni
{"title":"Extinction for discretizations of some semilinear parabolic equations","authors":"Théodore K. Boni","doi":"10.1016/S0764-4442(01)02078-X","DOIUrl":"10.1016/S0764-4442(01)02078-X","url":null,"abstract":"<div><p>We obtain some conditions under which solutions for semidiscretizations of semilinear parabolic equations extinct in a finite time and estimate their extinction time. A similar study is also undertaken for full discretizations.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 795-800"},"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)02078-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78513966","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: 50
Testing the shape of a regression curve 检验回归曲线的形状
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02114-0
Cheikh A.T. Diack
{"title":"Testing the shape of a regression curve","authors":"Cheikh A.T. Diack","doi":"10.1016/S0764-4442(01)02114-0","DOIUrl":"10.1016/S0764-4442(01)02114-0","url":null,"abstract":"<div><p>This paper proposes a hypothesis testing procedure for nonparametric regression models based on regression splines. We assume that the sample is a part of stationary sequence which satisfy a mild mixing property. The approach yields tests of monotonicity and convexity.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 677-680"},"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)02114-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80208262","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: 6
Convergence d'un schéma à profils stationnaires pour les équations quasi linéaires du premier ordre avec termes sources 具有源项的一阶拟线性方程的稳态轮廓图的收敛性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)01975-9
Alain Yves Le Roux, Marie Noëlle Le Roux
{"title":"Convergence d'un schéma à profils stationnaires pour les équations quasi linéaires du premier ordre avec termes sources","authors":"Alain Yves Le Roux,&nbsp;Marie Noëlle Le Roux","doi":"10.1016/S0764-4442(01)01975-9","DOIUrl":"10.1016/S0764-4442(01)01975-9","url":null,"abstract":"<div><p>When a source term is present, the constants are no longer solutions to quasilinear equations. Some numerical techniques based on this property need to be generalized. A stationary profile scheme uses an approximate solution made of stationary solutions in each cell. We propose such a scheme, for which we prove some results of stability and convergence towards the entropy solution. The numerical tests show that this scheme is well adapted to the simulation of well balanced states, and often far better than the usual splitting methods.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 703-706"},"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)01975-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92500534","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: 7
Observabilité frontière indirecte de systèmes faiblement couplés 弱耦合系统的间接边界可观测性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI: 10.1016/S0764-4442(01)02076-6
Fatiha Alabau
{"title":"Observabilité frontière indirecte de systèmes faiblement couplés","authors":"Fatiha Alabau","doi":"10.1016/S0764-4442(01)02076-6","DOIUrl":"10.1016/S0764-4442(01)02076-6","url":null,"abstract":"<div><p>This work is concerned with the indirect boundary observability of a coupled system of two wave equations. We show that for a sufficiently large time, the observation of the trace of the normal derivative of the first component of the solution on a part of the boundary allows us to get back a weakened energy of the initial data, this if the coupling parameter is sufficiently small, but non vanishing. This result leads to a new uniqueness theorem and also to an indirect exact controllability result.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 645-650"},"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)02076-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85713789","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: 26
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