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ON THE NONBENDABILITY OF CLOSED SURFACES OF TRIGONOMETRIC TYPE 关于三角型封闭曲面的不可弯曲性
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V071N02ABEH001408
Yu. A. Aminov
{"title":"ON THE NONBENDABILITY OF CLOSED SURFACES OF TRIGONOMETRIC TYPE","authors":"Yu. A. Aminov","doi":"10.1070/SM1992V071N02ABEH001408","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001408","url":null,"abstract":"In connection with a well-known problem on the existence of closed bendable surfaces in E3 the author considers the class of surfaces for which each component of the radius vector is a trigonometric polynomial in two variables. Two theorems on the nonbendability of surfaces in this class are proved, and an expression for the volume of the domain bounded by such a surface is established. Theorem 1 (the main theorem) asserts the nonbendability of a surface under the condition that some Diophantine equation does not have negative solutions. In this case the coefficients of the second fundamental form can be expressed in a finite-valued way in terms of the coefficients of the first fundamental form as algebraic expressions.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121693108","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
SOME CLASSICAL PROBLEMS IN THE THEORY OF ANALYTIC FUNCTIONS IN DOMAINS OF PARREAU-WIDOM TYPE 泛智型域解析函数理论中的几个经典问题
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V073N01ABEH002545
M. Samokhin
{"title":"SOME CLASSICAL PROBLEMS IN THE THEORY OF ANALYTIC FUNCTIONS IN DOMAINS OF PARREAU-WIDOM TYPE","authors":"M. Samokhin","doi":"10.1070/SM1992V073N01ABEH002545","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002545","url":null,"abstract":"Domains and Riemann surfaces of Parreau-Widom type are considered, along with the extension to these domains of classical results on the Hardy spaces and on representing measures and orthogonal measures (the theorems of the Riesz brothers), and so on.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132825524","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
SOLVABILITY OF SOME ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT OF NONLINEARITY 一类非线性临界指数椭圆型问题的可解性
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V068N02ABEH002108
I. Kuzin
{"title":"SOLVABILITY OF SOME ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT OF NONLINEARITY","authors":"I. Kuzin","doi":"10.1070/SM1991V068N02ABEH002108","DOIUrl":"https://doi.org/10.1070/SM1991V068N02ABEH002108","url":null,"abstract":"The problem is investigated, where is an open domain in , , is the critical exponent, and has a growth exponent less than the critical one.Theorems on the existence of a nontrivial solution of this problem is the space and spaces of more regular functions are proved under appropriate assumptions.Bibliography: 17 titles.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115726904","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
AFFINE MODULAR LIE ALGEBRAS 仿射模李代数
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V070N02ABEH001387
Y. Billig
{"title":"AFFINE MODULAR LIE ALGEBRAS","authors":"Y. Billig","doi":"10.1070/SM1991V070N02ABEH001387","DOIUrl":"https://doi.org/10.1070/SM1991V070N02ABEH001387","url":null,"abstract":"The paper is devoted to the construction of affine Kac-Moody algebras via defining relations arising from an integral affine Cartan matrix, in the case where the ground field has positive characteristic p > 7. Explicit constructions are given for algebras obtained in this way; in distinction with the zero characteristic case they have infinite-dimensional center. A theorem on the universality of this central extension is proved, and a series of finite-dimensional factors of affine modular algebras over the ideals having trivial intersection with Cartan's subalgebra is constructed. Moreover, a construction for the PI-envelopes of affine Kac-Moody algebras is given.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116919673","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
RIESZ TRANSFORMS AND PARTIAL DERIVATIVES Riesz变换和偏导数
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V069N02ABEH002115
V. Yudin
{"title":"RIESZ TRANSFORMS AND PARTIAL DERIVATIVES","authors":"V. Yudin","doi":"10.1070/SM1991V069N02ABEH002115","DOIUrl":"https://doi.org/10.1070/SM1991V069N02ABEH002115","url":null,"abstract":"New estimates are given in the two-dimensional case for special operators that are linear combinations of Riesz transforms. They are used to investigate the distances between partial derivatives , , on the class","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121281724","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
THE PONTRYAGIN PERSISTENCE PHENOMENON AND STABLE DUCK CYCLES OF MULTIDIMENSIONAL RELAXATION SYSTEMS WITH ONE SLOW VARIABLE 具有一个慢变量的多维松弛系统的庞特里亚金持续现象和稳定的鸭子循环
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V070N01ABEH002117
A. Kolesov, E. Mishchenko
{"title":"THE PONTRYAGIN PERSISTENCE PHENOMENON AND STABLE DUCK CYCLES OF MULTIDIMENSIONAL RELAXATION SYSTEMS WITH ONE SLOW VARIABLE","authors":"A. Kolesov, E. Mishchenko","doi":"10.1070/SM1991V070N01ABEH002117","DOIUrl":"https://doi.org/10.1070/SM1991V070N01ABEH002117","url":null,"abstract":"It is assumed that the equilibrium state of the relaxation system where and , passes generically through a point of discontinuity as varies. Under this condition stable duck cycles and cycles arising in a neighborhood of the equilibrium state are constructed.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124900377","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
THE ONE-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR THE WAVE EQUATION 波动方程的一维逆散射问题
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V070N02ABEH001386
N. Grinberg
{"title":"THE ONE-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR THE WAVE EQUATION","authors":"N. Grinberg","doi":"10.1070/SM1991V070N02ABEH001386","DOIUrl":"https://doi.org/10.1070/SM1991V070N02ABEH001386","url":null,"abstract":"A constructive method is given for solving the inverse scattering problem for the wave equation on the line and half-line. The slowness function is assumed to have a derivative everywhere except at a finite number of points, and both it and its derivative are assumed to be functions of bounded variation. In addition, the slowness n(x) is required to tend to 1 sufficiently rapidly as x→∞. In this case the slowness function can be reconstructed from the reflection coefficient.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"37 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126154807","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: 14
APPLICATION OF DIVISOR THEORY TO THE NUMERICAL INTEGRATION OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES 除数理论在多变量周期函数数值积分中的应用
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V069N02ABEH001250
N. Temirgaliev
{"title":"APPLICATION OF DIVISOR THEORY TO THE NUMERICAL INTEGRATION OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES","authors":"N. Temirgaliev","doi":"10.1070/SM1991V069N02ABEH001250","DOIUrl":"https://doi.org/10.1070/SM1991V069N02ABEH001250","url":null,"abstract":"The author exhibits an application of ideal theory to the exact integration of trigonometric polynomials with arbitrarily prescribed coefficient spectrum and to the approximate integration of functions of certain multidimensional classes E, W, and H.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125267809","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
PROFINITE GROUPS THAT ACT ON TREES AND DO NOT HAVE FREE NONABELIAN PRO-p-SUBGROUPS 作用于树上的无限群，没有自由的非abel的亲-对-子群
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V069N01ABEH001204
P. Zalesskii
{"title":"PROFINITE GROUPS THAT ACT ON TREES AND DO NOT HAVE FREE NONABELIAN PRO-p-SUBGROUPS","authors":"P. Zalesskii","doi":"10.1070/SM1991V069N01ABEH001204","DOIUrl":"https://doi.org/10.1070/SM1991V069N01ABEH001204","url":null,"abstract":"","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"275 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114441036","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: 12
ORIENTABILITY OF BUNDLES: OBSTRUCTION THEORY AND APPLICATIONS TO K-THEORY 束的可定向性:阻碍理论及其在k理论中的应用
Mathematics of The Ussr-sbornik Pub Date : 1991-02-28 DOI: 10.1070/SM1991V068N02ABEH001934
Yuli B. Rudyak
{"title":"ORIENTABILITY OF BUNDLES: OBSTRUCTION THEORY AND APPLICATIONS TO K-THEORY","authors":"Yuli B. Rudyak","doi":"10.1070/SM1991V068N02ABEH001934","DOIUrl":"https://doi.org/10.1070/SM1991V068N02ABEH001934","url":null,"abstract":"An obstruction theory is constructed for orientability of vector, piecewise-linear, and topological Rn-bundles and homotopy sphere bundles (spherical fibrations) in generalized cohomology theories. The results are applied to study the orientability of bundles in complex K-theory. In particular, it turns out that the problem of K-orientability for each of the four classes of bundles mentioned above is to be solved differently. Bibliography: 20 titles.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129871328","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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