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Théorie des résidus de Leray et formes de Barlet sur une intersection complète singulière 奇异完全交点上的Leray残差理论和Barlet形式
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02166-8
Aleksandr G. Aleksandrov, Avgust K. Tsikh
{"title":"Théorie des résidus de Leray et formes de Barlet sur une intersection complète singulière","authors":"Aleksandr G. Aleksandrov,&nbsp;Avgust K. Tsikh","doi":"10.1016/S0764-4442(01)02166-8","DOIUrl":"10.1016/S0764-4442(01)02166-8","url":null,"abstract":"<div><p>Let <em>S</em> be a complex analytic manifold and <em>C</em>⊂<em>S</em> a reduced complete intersection. We construct a complex <span><math><mtext>Ω</mtext><msub><mi></mi><mn>S</mn></msub><msup><mi></mi><mn>•</mn></msup><mtext>(</mtext><mtext>log</mtext><mtext>C)</mtext></math></span> of sheaves of the so-called multi-logarithmic differential forms on <em>S</em> with respect to <em>C</em> and define a residue map <span><math><mtext>res</mtext><mtext>:Ω</mtext><msub><mi></mi><mn>S</mn></msub><msup><mi></mi><mn>•</mn></msup><mtext>(</mtext><mtext>log</mtext><mtext>C)→ω</mtext><msub><mi></mi><mn>C</mn></msub><msup><mi></mi><mn>•</mn></msup></math></span> from this complex onto the Barlet complex <em>ω</em><sub><em>C</em></sub><sup>•</sup> of regular meromorphic differential forms on <em>C</em>. The residue map is proved to be a natural morphism between the two complexes; it follows then that sections of the complex <em>ω</em><sub><em>C</em></sub><sup>•</sup> may be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the map res can be given explicitly in terms of a certain integration current.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 973-978"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02166-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81159144","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: 24
Fibrations en tores et n-formes de Liouville en dimension 2n
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02170-X
Francisco-Javier Turiel
{"title":"Fibrations en tores et n-formes de Liouville en dimension 2n","authors":"Francisco-Javier Turiel","doi":"10.1016/S0764-4442(01)02170-X","DOIUrl":"10.1016/S0764-4442(01)02170-X","url":null,"abstract":"<div><p>In this work we prove a kind of Arnold–Liouville theorem for <em>n</em>-forms <em>ω</em> in dimension 2<em>n</em>, whose local model is <span><math><mtext>ω=∑</mtext><msub><mi></mi><mn>j=1</mn></msub><msup><mi></mi><mn>n</mn></msup><mtext>d</mtext><mtext>y</mtext><msub><mi></mi><mn>j</mn></msub><mtext>∧</mtext><mtext>d</mtext><mtext>x</mtext><msub><mi></mi><mn>1</mn></msub><mtext>∧⋯∧</mtext><mtext>d</mtext><mtext>̂</mtext><mtext>x</mtext><msub><mi></mi><mn>j</mn></msub><mtext>∧⋯∧</mtext><mtext>d</mtext><mtext>x</mtext><msub><mi></mi><mn>n</mn></msub></math></span>. Some global aspects of these forms are studied as well.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 995-998"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02170-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81672245","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
Deformations of stable maps of curves 稳定曲线映射的变形
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02167-X
Catriona Maclean
{"title":"Deformations of stable maps of curves","authors":"Catriona Maclean","doi":"10.1016/S0764-4442(01)02167-X","DOIUrl":"10.1016/S0764-4442(01)02167-X","url":null,"abstract":"<div><p>Given a smooth variety, <em>X</em> and a map <em>g</em>:<em>X</em>→<em>Δ</em> such that <em>g</em><sup>−1</sup>(0) is a normal crossing variety <em>X</em><sub>0</sub>=<em>X</em><sub>1</sub>∪<sub><em>Z</em></sub><em>X</em><sub>2</sub>, we consider stable maps <em>F</em><sub>0</sub>:<em>C</em><sub>0</sub>→<em>X</em><sub>0</sub> which appear as the central fibre of a family of maps <span><span><img></span></span> Splitting such a stable map up into <em>F</em><sub>1</sub>:<em>C</em><sub>1</sub>→<em>X</em><sub>1</sub> and <em>F</em><sub>2</sub>:<em>C</em><sub>2</sub>→<em>X</em><sub>2</sub>, we derive conditions on the 0-cycle <em>C</em><sub><em>i</em></sub>∩<em>Z</em><sub><em>i</em></sub> in the Chow group <em>A</em><sup>0</sup>(<em>F</em><sup>−1</sup><sub><em>i</em></sub>(<em>Z</em>)). These conditions provide an elementary geometric justification for the work of Li and Ruan in [4] and of Gathmann in [2].</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 985-990"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02167-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73649166","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
Existence of solution of an elastohydrodynamic Reynolds–Koiter model 弹性流体动力学Reynolds-Koiter模型解的存在性
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02181-4
Iñigo Arregui, J.Jesús Cendán, Carlos Vázquez
{"title":"Existence of solution of an elastohydrodynamic Reynolds–Koiter model","authors":"Iñigo Arregui,&nbsp;J.Jesús Cendán,&nbsp;Carlos Vázquez","doi":"10.1016/S0764-4442(01)02181-4","DOIUrl":"10.1016/S0764-4442(01)02181-4","url":null,"abstract":"<div><p>In this paper the existence of solution for a new elastohydrodynamic model for journal bearing devices is proved. The lubricant pressure and the concentration are governed by Reynolds equation combined with Elrod–Adams model for cavitation, while the bearing displacement follows a Koiter model for shells. A regularization procedure is proposed to overcome the Heaviside concentration–pressure relation. A fixed point theorem leads to the solution of the regularized problem. The introduction of prolongation and restriction operators copes with the additional difficulty of elastic and hydrodynamic subproblems posed on different domains. The estimates for the regularized problem allow to pass to the limit and state the existence result.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 1047-1052"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02181-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80472722","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
Exact asymptotic errors of the hazard rate kernel estimator under truncated and censored data 截断和截尾数据下危险率核估计的精确渐近误差
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02172-3
Mohamed Lemdani , Elias Ould-Said
{"title":"Exact asymptotic errors of the hazard rate kernel estimator under truncated and censored data","authors":"Mohamed Lemdani ,&nbsp;Elias Ould-Said","doi":"10.1016/S0764-4442(01)02172-3","DOIUrl":"10.1016/S0764-4442(01)02172-3","url":null,"abstract":"<div><p>In this Note, we give the exact asymptotic mean integrated squared error and the mean squared error for the kernel estimator of the hazard rate from truncated and censored data. Martingale techniques and combinatory calculus are used to obtain these results. A probability bound and the optimal bandwidth choice are also given.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 1035-1040"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02172-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87470842","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 l'indépendance d'un temps d'arrêt T et de la position BT d'un mouvement brownien (Bu,u⩾0) 停止时间T和布朗运动位置BT的独立性(Bu,u小于或等于0)
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02168-1
Bernard De Meyer , Bernard Roynette , Pierre Vallois , Marc Yor
{"title":"Sur l'indépendance d'un temps d'arrêt T et de la position BT d'un mouvement brownien (Bu,u⩾0)","authors":"Bernard De Meyer ,&nbsp;Bernard Roynette ,&nbsp;Pierre Vallois ,&nbsp;Marc Yor","doi":"10.1016/S0764-4442(01)02168-1","DOIUrl":"10.1016/S0764-4442(01)02168-1","url":null,"abstract":"<div><p>In this Note, we describe many examples of two-dimensional random variables {<em>B</em><sub><em>T</em></sub>,<em>T</em>} obtained from the position of a Brownian motion <span><math><mtext>(B</mtext><msub><mi></mi><mn>t</mn></msub><mtext>;</mtext><mspace></mspace><mtext>t⩾0)</mtext></math></span> at a stopping time <em>T</em> such that <em>T</em> and <em>B</em><sub><em>T</em></sub> are independent. For such pairs, the law of <em>T</em> determines that of <em>B</em><sub><em>T</em></sub> and vice versa; we study the constraints on these laws induced by the independence assumption.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 1017-1022"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02168-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"96378987","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
Gibbs states on loop lattices: existence and a priori estimates 环格上的吉布斯态:存在性与先验估计
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02175-9
Sergio Albeverio , Yuri Kondratiev , Tatiana Pasurek , Michael Röckner
{"title":"Gibbs states on loop lattices: existence and a priori estimates","authors":"Sergio Albeverio ,&nbsp;Yuri Kondratiev ,&nbsp;Tatiana Pasurek ,&nbsp;Michael Röckner","doi":"10.1016/S0764-4442(01)02175-9","DOIUrl":"10.1016/S0764-4442(01)02175-9","url":null,"abstract":"<div><p>We prove existence and uniform a priori estimates for Euclidean Gibbs states of quantum lattice systems with unbounded spins. These results substantially extend all previous existence results. Detailed proofs are contained in [3].</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 1005-1009"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02175-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"98343118","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
Reduced dynamics for momentum maps with cocycles 带有环的动量图的简化动力学
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02171-1
Ulrike Scheerer , Claudia Wulff
{"title":"Reduced dynamics for momentum maps with cocycles","authors":"Ulrike Scheerer ,&nbsp;Claudia Wulff","doi":"10.1016/S0764-4442(01)02171-1","DOIUrl":"10.1016/S0764-4442(01)02171-1","url":null,"abstract":"<div><p>We generalize the results on the explicit form of Hamilton's equations in local coordinates near a group orbit of Roberts, Wulff and Lamb to local momentum maps with cocycles. We use these equations to study the dynamics near relative equilibria.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 999-1004"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02171-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91196696","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
Divisions selon les puissances fractionnaires d'un idéal engendré par une suite régulière dans l'anneau des germes à l'origine de fonctions holomorphes sur C2 根据C2上全纯函数起源的芽环中规则序列所产生的理想的分数次幂进行划分
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02086-9
Jamil Sawaya
{"title":"Divisions selon les puissances fractionnaires d'un idéal engendré par une suite régulière dans l'anneau des germes à l'origine de fonctions holomorphes sur C2","authors":"Jamil Sawaya","doi":"10.1016/S0764-4442(01)02086-9","DOIUrl":"10.1016/S0764-4442(01)02086-9","url":null,"abstract":"<div><p>Consider the ring of germs of analytic functions at the origin of <span><math><mtext>C</mtext><msup><mi></mi><mn>2</mn></msup></math></span>. Let <em>I</em> be an ideal of this ring, and let us denote by <span><math><mtext>I</mtext></math></span>, the integral closure of this ideal. J. Lipman and B. Teissier proved that the following formula: <span><math><mtext>I</mtext><msup><mi></mi><mn>n+1</mn></msup><mtext>=</mtext><mtext>I</mtext><mtext>·I</mtext><msup><mi></mi><mn>n</mn></msup></math></span>, holds for every integer <em>n</em>. In this paper, we discuss, under certain condition over <em>I</em>, of a similar formula for the fractional powers of <em>I</em>.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 991-994"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02086-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79979925","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
Équation de la chaleur pour les applications p-harmoniques entre variétés riemanniennes compactes 紧黎曼流形之间p调和映射的热方程
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI: 10.1016/S0764-4442(01)02176-0
Ali Fardoun, Rachid Regbaoui
{"title":"Équation de la chaleur pour les applications p-harmoniques entre variétés riemanniennes compactes","authors":"Ali Fardoun,&nbsp;Rachid Regbaoui","doi":"10.1016/S0764-4442(01)02176-0","DOIUrl":"https://doi.org/10.1016/S0764-4442(01)02176-0","url":null,"abstract":"<div><p>Let (<em>M</em><sup><em>m</em></sup>,<em>g</em>) and (<em>N</em><sup><em>n</em></sup>,<em>h</em>) (<em>m</em>⩾2) be two compact Riemannian manifolds without boundary. When Riem<sub><em>N</em></sub>⩽0, we show the global existence of a weak solution of the heat equation for <em>p</em>-harmonic maps (<em>p</em>&gt;1) and the convergence of this solution at infinity to a regular weakly <em>p</em>-harmonic map; so generalizing the result of Eells–Sampson for harmonic maps to the case that <em>p</em>&gt;1.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 979-984"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02176-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137276250","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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