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

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De l'existence de solutions d'équations différentielles assujetties à rester dans un ensemble fermé 微分方程解的存在性服从于闭集
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02165-6
Grzegorz Gabor , Marc Quincampoix
{"title":"De l'existence de solutions d'équations différentielles assujetties à rester dans un ensemble fermé","authors":"Grzegorz Gabor ,&nbsp;Marc Quincampoix","doi":"10.1016/S0764-4442(01)02165-6","DOIUrl":"10.1016/S0764-4442(01)02165-6","url":null,"abstract":"<div><p>In this Note, we prove existence of trajectories to – possibly multivalued – differential equations remaining in a given closed set of constraints. It is a consequence of behaviour of solutions on the boundary of the set of constraints.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 913-918"},"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)02165-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90940256","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
Well-posedness of the full Ericksen–Leslie model of nematic liquid crystals 向列液晶的Ericksen-Leslie模型的完备性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02161-9
Daniel Coutand, Steve Shkoller
{"title":"Well-posedness of the full Ericksen–Leslie model of nematic liquid crystals","authors":"Daniel Coutand,&nbsp;Steve Shkoller","doi":"10.1016/S0764-4442(01)02161-9","DOIUrl":"10.1016/S0764-4442(01)02161-9","url":null,"abstract":"<div><p>The Ericksen–Leslie model of nematic liquid crystals is a coupled system between the Navier–Stokes and the Ginzburg–Landau equations. We show here the local well-posedness for this problem for any initial data regular enough, by a fixed point approach relying on some weak continuity properties in a suitable functional setting. By showing the existence of an appropriate local Lyapunov functional, we also give sufficient conditions for the global existence of the solution, and some stability conditions.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 919-924"},"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)02161-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89311466","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
Arithmétique des groupes algébriques linéaires sur certains corps géométriques de dimension deux 某些二维几何域上线性代数群的算术
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02123-1
Jean-Louis Colliot-Thélène , Philippe Gille , Raman Parimala
{"title":"Arithmétique des groupes algébriques linéaires sur certains corps géométriques de dimension deux","authors":"Jean-Louis Colliot-Thélène ,&nbsp;Philippe Gille ,&nbsp;Raman Parimala","doi":"10.1016/S0764-4442(01)02123-1","DOIUrl":"10.1016/S0764-4442(01)02123-1","url":null,"abstract":"<div><p>Let <em>k</em> be an algebraically closed field of characteristic zero. Let <em>K</em> be either a function field in two variables over <em>k</em> or the fraction field of a 2-dimensional, excellent, strictly henselian local domain with residue field <em>k</em>. We show that linear algebraic groups over such a field <em>K</em> satisfy most properties familiar in the context of number fields: finiteness of <em>R</em>-equivalence, Hasse principle for complete homogeneous spaces.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 827-832"},"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)02123-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84906732","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
Le cône kählérien d'une variété hyperkählérienne hyperkahler品种的kahler锥体
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02158-9
Sébastien Boucksom
{"title":"Le cône kählérien d'une variété hyperkählérienne","authors":"Sébastien Boucksom","doi":"10.1016/S0764-4442(01)02158-9","DOIUrl":"10.1016/S0764-4442(01)02158-9","url":null,"abstract":"<div><p>We answer a question of D. Huybrechts about the Kähler cone of a compact hyperkähler manifold. More precisely, we show how the methods he uses to describe the closure of this cone do in fact extend to get the following description: the Kähler cone of a hyperkähler manifold is the set of elements of the positive cone attached to the canonical quadratic form which are positive on the rational curves.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 935-938"},"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)02158-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87899543","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: 31
Généralisations du théorème de Bartle–Graves 巴特尔-格雷夫斯定理的推广
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02149-8
Belmesnaoui Aqzzouz
{"title":"Généralisations du théorème de Bartle–Graves","authors":"Belmesnaoui Aqzzouz","doi":"10.1016/S0764-4442(01)02149-8","DOIUrl":"10.1016/S0764-4442(01)02149-8","url":null,"abstract":"<div><p>In this paper we give generalizations of Bartle–Graves theorem [2]. We define some functional spaces which take their values in quotient spaces.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 925-930"},"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)02149-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77654055","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: 9
Une technique nouvelle d'antidiffusion dynamique 动态防扩散新技术
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02138-3
Ghislaine Godinaud , Alain Yves Leroux , Raphaël Loubère , Jean Ovadia
{"title":"Une technique nouvelle d'antidiffusion dynamique","authors":"Ghislaine Godinaud ,&nbsp;Alain Yves Leroux ,&nbsp;Raphaël Loubère ,&nbsp;Jean Ovadia","doi":"10.1016/S0764-4442(01)02138-3","DOIUrl":"10.1016/S0764-4442(01)02138-3","url":null,"abstract":"<div><p>We propose a new technique for enhancing the results coming from computational simulations with a hyperbolic system. The process works only on the extracted data obtained after an interruption of the program, and is not depending neither on the mathematical model nor on the numerical scheme, as long as the model is a hyperbolic one and the scheme is diffusive enough. The numerical tests show a good sharpening of the discontinuities, on less than two cells, and also a good precision on the rarefaction waves and the conservation of some quantities, such as the mass.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 957-960"},"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)02138-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82196947","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
Asymptotics of coupled solutions of the Kadomtsev–Petviashvili equation Kadomtsev-Petviashvili方程耦合解的渐近性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02070-5
Igor Anders
{"title":"Asymptotics of coupled solutions of the Kadomtsev–Petviashvili equation","authors":"Igor Anders","doi":"10.1016/S0764-4442(01)02070-5","DOIUrl":"https://doi.org/10.1016/S0764-4442(01)02070-5","url":null,"abstract":"<div><p>We determine a subset in <span><math><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup></math></span> and a measure on this set which allow to construct coupled non-localized solutions of the KP-I equation, which are connected by the change of variables (<em>x</em>,<em>t</em>)↦(−<em>x</em>,−<em>t</em>), and split into asymptotic solitons as <em>t</em>→∞ in the neighbourhood of the leading edge of the solutions. The solitons corresponding to each of the solutions have different amplitudes and lines of constant phase.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 891-896"},"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)02070-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90002402","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
Matched pairs of Leibniz algebroids, Nambu–Jacobi structures and modular class Leibniz代数群的匹配对，Nambu-Jacobi结构和模类
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02150-4
Raúl Ibañez , Belén Lopez , Juan C Marrero , Edith Padron
{"title":"Matched pairs of Leibniz algebroids, Nambu–Jacobi structures and modular class","authors":"Raúl Ibañez ,&nbsp;Belén Lopez ,&nbsp;Juan C Marrero ,&nbsp;Edith Padron","doi":"10.1016/S0764-4442(01)02150-4","DOIUrl":"10.1016/S0764-4442(01)02150-4","url":null,"abstract":"<div><p>The notion of a matched pair of Leibniz algebroids is introduced and it is shown that a Nambu–Jacobi structure of order <em>n</em>, <em>n</em>&gt;2, over a manifold <em>M</em> defines a matched pair of Leibniz algebroids. As a consequence, one deduces that the vector bundle <span><math><mtext>⋀</mtext><msup><mi></mi><mn>n−1</mn></msup><mtext>(</mtext><mtext>T</mtext><msup><mi></mi><mn>∗</mn></msup><mtext>M)⊕⋀</mtext><msup><mi></mi><mn>n−2</mn></msup><mtext>(</mtext><mtext>T</mtext><msup><mi></mi><mn>∗</mn></msup><mtext>M)→M</mtext></math></span> is a Leibniz algebroid. Finally, if <em>M</em> is orientable, the modular class of <em>M</em> is defined as a cohomology class of order 1 with respect to this Leibniz algebroid.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 861-866"},"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)02150-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88527065","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
Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs 由吸引子的均匀分岔和零密度产生的非均匀双曲马蹄铁
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02139-5
Jacob Palis , Jean-Christophe Yoccoz
{"title":"Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs","authors":"Jacob Palis ,&nbsp;Jean-Christophe Yoccoz","doi":"10.1016/S0764-4442(01)02139-5","DOIUrl":"10.1016/S0764-4442(01)02139-5","url":null,"abstract":"<div><p>Let <em>f</em><sub>0</sub> be a surface diffeomorphism such that the maximal invariant set in an open set <em>V</em> is the union of a horseshoe and a quadratic tangency between the stable and unstable foliations of this horseshoe. We assume that the dimension of the horseshoe is larger than but close to one. We announce that, for most diffeomorphisms <em>f</em> close to <em>f</em><sub>0</sub>, the maximal <em>f</em>-invariant set in <em>V</em> is a non-uniformly hyperbolic horseshoe, with dynamics of the same type as met in Hénon attractors.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 867-871"},"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)02139-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87891567","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
Vers un test d'additivité en régression non paramétrique sous des conditions de mélange 混合条件下的非参数回归可加性检验
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-11-01 DOI: 10.1016/S0764-4442(01)02146-2
Christine Camlong-Viot
{"title":"Vers un test d'additivité en régression non paramétrique sous des conditions de mélange","authors":"Christine Camlong-Viot","doi":"10.1016/S0764-4442(01)02146-2","DOIUrl":"10.1016/S0764-4442(01)02146-2","url":null,"abstract":"<div><p>In the setting of additive models, this paper studies kernel marginal integration estimates. These estimates are used for the construction of a test of additivity. We propose to show the asymptotic normality of a test statistic under conditions of absolute regularity.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 877-880"},"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)02146-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79091917","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
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