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

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Principe de grandes déviations autonormalisées pour des chaı̂nes de Markov 茶的大偏差autonormalisées原则为ı̂nes的马可夫
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)01953-X
Mathieu Faure
{"title":"Principe de grandes déviations autonormalisées pour des chaı̂nes de Markov","authors":"Mathieu Faure","doi":"10.1016/S0764-4442(01)01953-X","DOIUrl":"https://doi.org/10.1016/S0764-4442(01)01953-X","url":null,"abstract":"<div><p>We prove a self-normalized large deviation principle for sums of Banach space valued functions of a Markov chain. Self-normalization applies to situations for which a domination hypothesis would be necessary in order to obtain a full large deviation principle. We follow the lead of Dembo and Shao [2] who state partial large deviations principles for independent and identically distributed random sequences.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 885-890"},"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)01953-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91591363","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
Diffeomorphisms, isotopies, and braid monodromy factorizations of plane cuspidal curves∗ 平面尖角曲线的异同态、同位素和编织单因子分解
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02115-2
Viatcheslav Kharlamov , Viktor Kulikov
{"title":"Diffeomorphisms, isotopies, and braid monodromy factorizations of plane cuspidal curves∗","authors":"Viatcheslav Kharlamov ,&nbsp;Viktor Kulikov","doi":"10.1016/S0764-4442(01)02115-2","DOIUrl":"10.1016/S0764-4442(01)02115-2","url":null,"abstract":"<div><p>In this paper we prove that there is an infinite sequence of pairs of plane cuspidal curves, <em>C</em><sub><em>m</em>,1</sub> and <em>C</em><sub><em>m</em>,2</sub>, of degree deg(<em>C</em><sub><em>m</em>,1</sub>)=deg(<em>C</em><sub><em>m</em>,2</sub>)→∞, such that the pairs <span><math><mtext>(</mtext><mtext>CP</mtext><msup><mi></mi><mn>2</mn></msup><mtext>,C</mtext><msub><mi></mi><mn>m,1</mn></msub><mtext>)</mtext></math></span> and <span><math><mtext>(</mtext><mtext>CP</mtext><msup><mi></mi><mn>2</mn></msup><mtext>,C</mtext><msub><mi></mi><mn>m,2</mn></msub><mtext>)</mtext></math></span> are diffeomorphic, but <em>C</em><sub><em>m</em>,1</sub> and <em>C</em><sub><em>m</em>,2</sub> have non-equivalent braid monodromy factorizations. These curves give rise to the negative solutions of “Dif ⇒ Def” and “Dif ⇒ Iso” problems for plane irreducible cuspidal curves. In our examples, <em>C</em><sub><em>m</em>,1</sub> and <em>C</em><sub><em>m</em>,2</sub> are complex conjugate.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 855-859"},"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)02115-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89336713","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: 18
Symmetric varieties over arbitrary fields 任意域上的对称变量
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02152-8
Tohru Uzawa
{"title":"Symmetric varieties over arbitrary fields","authors":"Tohru Uzawa","doi":"10.1016/S0764-4442(01)02152-8","DOIUrl":"10.1016/S0764-4442(01)02152-8","url":null,"abstract":"<div><p>We give basic results, such as restricted root systems and a model of <em>G</em>/<em>H</em> over the ring of integers, for the theory of symmetric varieties valid over fields of all characteristics.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 833-838"},"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)02152-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74421525","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
Relations d'équivalence analytiques complètes 完全解析等价关系
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02160-7
Alain Louveau, Christian Rosendal
{"title":"Relations d'équivalence analytiques complètes","authors":"Alain Louveau,&nbsp;Christian Rosendal","doi":"10.1016/S0764-4442(01)02160-7","DOIUrl":"10.1016/S0764-4442(01)02160-7","url":null,"abstract":"<div><p>We prove that various concrete analytic equivalence relations arising in model theory or analysis are complete, i.e., maximum in the Borel reducibility ordering. The proofs use some general results concerning the wider class of analytic quasi-orders.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 903-906"},"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)02160-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82009779","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
Generalized scattering phase for long range perturbations of elliptic operators 椭圆算子长程扰动的广义散射相位
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02144-9
Jean-Marc Bouclet
{"title":"Generalized scattering phase for long range perturbations of elliptic operators","authors":"Jean-Marc Bouclet","doi":"10.1016/S0764-4442(01)02144-9","DOIUrl":"10.1016/S0764-4442(01)02144-9","url":null,"abstract":"<div><p>We show that limits on the real axis of arguments of regularized relative determinants for differential operators on <span><math><mtext>R</mtext><msup><mi></mi><mn>d</mn></msup></math></span>, exist in the weak sense. We call these limits generalized scattering phases. They extend, in the case of long range perturbations, the usual definition of scattering phase given by Birman–Krein theory. In Euclidean scattering, we give high energy expansions under a non-trapping assumption.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 845-850"},"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)02144-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90496661","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
The Navier–Stokes limit for the Boltzmann equation 玻尔兹曼方程的纳维-斯托克斯极限
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02136-X
François Golse , Laure Saint-Raymond
{"title":"The Navier–Stokes limit for the Boltzmann equation","authors":"François Golse ,&nbsp;Laure Saint-Raymond","doi":"10.1016/S0764-4442(01)02136-X","DOIUrl":"https://doi.org/10.1016/S0764-4442(01)02136-X","url":null,"abstract":"<div><p>Appropriately scaled families of DiPerna–Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L<sup>1</sup> topology) are governed by a Leray solution of the limiting Navier–Stokes equations. This completes the arguments in Bardos–Golse–Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667–753] for the steady case, extended by Lions–Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173–193] to the time-dependent case.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 897-902"},"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)02136-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91621330","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: 16
Convergence presque sûre de l'estimateur linéaire local de la fonction de répartition conditionnelle 条件分布函数的局部线性估计量几乎肯定收敛
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02113-9
Gilles R. Ducharme, Mariem Mint El Mouvid
{"title":"Convergence presque sûre de l'estimateur linéaire local de la fonction de répartition conditionnelle","authors":"Gilles R. Ducharme,&nbsp;Mariem Mint El Mouvid","doi":"10.1016/S0764-4442(01)02113-9","DOIUrl":"10.1016/S0764-4442(01)02113-9","url":null,"abstract":"<div><p>The local linear estimator of the conditional cumulative distribution function is shown to be the ratio of two <em>U</em>-statistics. Using results from the theory of <em>U</em>-statistics, we show the almost sure convergence of this estimator both locally and globally. This is used to establish the almost sure convergence of conditional quantiles computed from the linear estimator.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 873-876"},"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)02113-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79258204","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
Invariants algébriques de graphes et reconstruction 图的代数不变量与重构
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02137-1
Maurice Pouzet, Nicolas M. Thiéry
{"title":"Invariants algébriques de graphes et reconstruction","authors":"Maurice Pouzet,&nbsp;Nicolas M. Thiéry","doi":"10.1016/S0764-4442(01)02137-1","DOIUrl":"10.1016/S0764-4442(01)02137-1","url":null,"abstract":"<div><p>We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 821-826"},"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)02137-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73248257","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: 18
Existence de solutions pour un modèle de drapé d'un tissu 织物悬垂模型的解决方案的存在
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02156-5
Nadjombé Faré, Emmanuel Maitre
{"title":"Existence de solutions pour un modèle de drapé d'un tissu","authors":"Nadjombé Faré,&nbsp;Emmanuel Maitre","doi":"10.1016/S0764-4442(01)02156-5","DOIUrl":"10.1016/S0764-4442(01)02156-5","url":null,"abstract":"<div><p>In this Note we establish the existence of minimizer of a nonconvex energy functional. This functional is an energy of deformation of a woven fabric subject only to his own weight and fixed on a part of its boundary. A typical example is the case of a tablecloth on a table. We make the hypothesis that the fabric is inextensible in the direction of the fibers but can undergo membrane shear and flexion deformations. We use technics introduced in [3], in the no membrane shear case. The studied energy involves tensors analog to those of [7] and [5] to which we added a regularizing term accounting for shear angle variation.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 967-972"},"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)02156-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90336061","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
L'homologie de Novikov des entrelacs de Waldhausen 诺维科夫对瓦尔德豪森交错的同源性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02159-0
David Cimasoni
{"title":"L'homologie de Novikov des entrelacs de Waldhausen","authors":"David Cimasoni","doi":"10.1016/S0764-4442(01)02159-0","DOIUrl":"10.1016/S0764-4442(01)02159-0","url":null,"abstract":"<div><p>A graph multilink is a link with multiplicities in a homology 3-sphere whose exterior is a graph manifold. In this Note, we compute the Novikov homology of graph multilinks. As a corollary, we give a sharp majoration for the number of Novikov modules on a given graph link.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 939-942"},"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)02159-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88344889","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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