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GROUP SYMMETRY OF THE LYAPUNOV-SCHMIDT BRANCHING EQUATION AND ITERATIVE METHODS IN THE PROBLEM OF A BIFURCATION POINT 李雅普诺夫-施密特分支方程的群对称性及分岔点问题的迭代方法
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V073N01ABEH002535
B. Loginov, N. Sidorov
{"title":"GROUP SYMMETRY OF THE LYAPUNOV-SCHMIDT BRANCHING EQUATION AND ITERATIVE METHODS IN THE PROBLEM OF A BIFURCATION POINT","authors":"B. Loginov, N. Sidorov","doi":"10.1070/SM1992V073N01ABEH002535","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002535","url":null,"abstract":"Using group-theoretic methods (MR 80d: 58072, 83m: 58082), the authors construct the general form of the branching equation, symmetric with respect to fundamental representations of the rotation group, and on the basis of this form they propose an iterative method for calculating families of small branching solutions in a neighborhood of a bifurcation point, depending on free parameters.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"144 3 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":"129540161","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
Order Estimates of Smallest Norms, with Respect to the Choice of N Harmonics, of Derivatives of the Dirichlet and Favard Kernels Dirichlet和Favard核导数关于N次谐波选择的最小范数的阶估计
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V072N02ABEH002150
É. M. Galeev
{"title":"Order Estimates of Smallest Norms, with Respect to the Choice of N Harmonics, of Derivatives of the Dirichlet and Favard Kernels","authors":"É. M. Galeev","doi":"10.1070/SM1992V072N02ABEH002150","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH002150","url":null,"abstract":"The Dirichlet kernel is defined for periodic functions of several variables; it consists of harmonics and has minimal order of the norm with respect to the choice of harmonics of the mixed Weyl derivative in the space . A similar problem on the minimal order of the norm is solved for the Favard kernel. Both problems generalize to the case of several derivatives.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"241 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":"133781488","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
SYSTEMS WITH A HOMOCLINIC CURVE OF MULTIDIMENSIONAL SADDLE-FOCUS TYPE, AND SPIRAL CHAOS 具有多维鞍-焦点型同斜曲线的螺旋混沌系统
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V073N02ABEH002553
I. Ovsyannikov, L. Shilnikov
{"title":"SYSTEMS WITH A HOMOCLINIC CURVE OF MULTIDIMENSIONAL SADDLE-FOCUS TYPE, AND SPIRAL CHAOS","authors":"I. Ovsyannikov, L. Shilnikov","doi":"10.1070/SM1992V073N02ABEH002553","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002553","url":null,"abstract":"Consider the space of dynamical systems having an isolated equilibrium point of saddle-focus type with a one- or two-dimensional unstable manifold and a trajectory homoclinic at .The following results are proved:Systems with structurally unstable periodic motions are dense in . Systems with a countable set of stable periodic motions are dense in the open subset of comprised of systems whose second saddle parameter is negative. Neither the subset of consisting of systems satisfying 0$ SRC=http://ej.iop.org/images/0025-5734/73/2/A07/tex_sm_2553_img7.gif/> nor any sufficiently small neighborhood of in the space of all dynamical systems contains a system with stable periodic motions in a sufficiently small neighborhood of the contour .","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"3 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":"125099608","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: 57
SUBGROUPS SATISFYING AN IDENTITY IN A CLASS OF ABSTRACT GROUPS 一类抽象群中满足恒等的子群
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V071N02ABEH002132
Yu V Tishin
{"title":"SUBGROUPS SATISFYING AN IDENTITY IN A CLASS OF ABSTRACT GROUPS","authors":"Yu V Tishin","doi":"10.1070/SM1992V071N02ABEH002132","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH002132","url":null,"abstract":"A description is obtained of the subgroups of groups acting on a tree that do not contain nonabelian free subgroups; it is a new interpretation of a result of Bass. The author considers the class consisting of all groups constructive from cyclic groups using amalgamated free products and HNN-extensions, with certain restrictions. A description is obtained of all the subgroups of groups in that satisfy identities, and it is shown that the groups in satisfy the Tits alternative. The proof uses the techniques of group actions on trees.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"48 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":"121785995","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
ON A WAY OF OBTAINING LOWER ESTIMATES FOR THE ERRORS OF QUADRATURE FORMULAS 求求正交公式误差较低估计的一种方法
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V071N01ABEH001396
V. Temlyakov
{"title":"ON A WAY OF OBTAINING LOWER ESTIMATES FOR THE ERRORS OF QUADRATURE FORMULAS","authors":"V. Temlyakov","doi":"10.1070/SM1992V071N01ABEH001396","DOIUrl":"https://doi.org/10.1070/SM1992V071N01ABEH001396","url":null,"abstract":"The purpose of this article is to obtain best possible lower estimates of the errors of quadrature formulas with a fixed number of nodes for classes of functions with bounded mixed derivative. The results obtained here lead to a strengthening of known lower estimates for the deviation of grids.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"72 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":"121797699","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: 51
LOCALLY CONFORMALLY KHLERIAN MANIFOLDS OF CONSTANT HOLOMORPHIC SECTIONAL CURVATURE 常全纯截面曲率的局部共形克勒流形
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V072N02ABEH002142
V. F. Kirichenko
{"title":"LOCALLY CONFORMALLY KHLERIAN MANIFOLDS OF CONSTANT HOLOMORPHIC SECTIONAL CURVATURE","authors":"V. F. Kirichenko","doi":"10.1070/SM1992V072N02ABEH002142","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH002142","url":null,"abstract":"The author studies the structure of the curvature tensor of -manifolds, i.e., almost Hermitian manifolds whose metric is, at least locally, conformally related to a Kahlerian metric (with the same structure operator).","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"60 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":"121336106","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
ON PRIMITIVE ELEMENTS IN FINITE FIELDS AND ON ELLIPTIC CURVES 有限域和椭圆曲线上的原始元
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V071N01ABEH001389
I. E. Shparlinskii
{"title":"ON PRIMITIVE ELEMENTS IN FINITE FIELDS AND ON ELLIPTIC CURVES","authors":"I. E. Shparlinskii","doi":"10.1070/SM1992V071N01ABEH001389","DOIUrl":"https://doi.org/10.1070/SM1992V071N01ABEH001389","url":null,"abstract":"An asymptotic formula for the number of primitive polynomials of the form f (x) + a, a = 1, ..., h, where f (x)Fp[x], is obtained, \"on the average\" over all polynomials f of fixed degree, and an estimate for the number of \"sparse\" factorable polynomials is also obtained.","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":"115553371","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: 27
ON UNIQUE RECOVERABILITY OF CONVEX AND VISIBLE COMPACTA FROM THEIR PROJECTIONS 凸紧与可见紧的唯一可恢复性
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V073N01ABEH002531
V. Golubyatnikov
{"title":"ON UNIQUE RECOVERABILITY OF CONVEX AND VISIBLE COMPACTA FROM THEIR PROJECTIONS","authors":"V. Golubyatnikov","doi":"10.1070/SM1992V073N01ABEH002531","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002531","url":null,"abstract":"The question is: Under what conditions does the congruence of the projections of two compacta on every two-dimensional plane imply the congruence of the compacta themselves? The results are extended to the cases of (n – 2)-visible and (n – 2)-convex compacta, and even to the case when it is known the projections of the compacta are merely similar.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"5 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":"130584212","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
On Verbal Factors of almost Free Groups in Varieties 论品种中几乎自由群体的言语因素
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V073N02ABEH002559
S. Rychkov
{"title":"On Verbal Factors of almost Free Groups in Varieties","authors":"S. Rychkov","doi":"10.1070/SM1992V073N02ABEH002559","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002559","url":null,"abstract":"Under the assumption of the axiom of constructibility of set theory it is shown that for varieties of groups of exponent zero and for uncountable, regular, not weakly compact cardinals k there can be constructed k-separable groups having no nontrivial decomposition into a verbal product.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"39 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":"124029814","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
NONTRIVIAL EXPANSIONS OF ZERO IN ABSOLUTELY REPRESENTING SYSTEMS. APPLICATIONS TO CONVOLUTION OPERATORS 零在绝对表示系统中的非平凡展开式。卷积算子的应用
Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI: 10.1070/SM1992V073N01ABEH002534
Y. Korobeinik
{"title":"NONTRIVIAL EXPANSIONS OF ZERO IN ABSOLUTELY REPRESENTING SYSTEMS. APPLICATIONS TO CONVOLUTION OPERATORS","authors":"Y. Korobeinik","doi":"10.1070/SM1992V073N01ABEH002534","DOIUrl":"https://doi.org/10.1070/SM1992V073N01ABEH002534","url":null,"abstract":"By using a general representation of nontrivial expansions of zero in absolutely representing systems of the form , where , is the Mittag-Leffler function, and are complex numbers, the author obtains a number of results in the theory of -convolution operators in spaces of functions that are analytic in -convex domains (a description of the general solution of a homogeneous -convolution equation and of systems of such equations, a topological description of the kernel of a -convolution operator, the construction of principal solutions, and a criterion for factorization).","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"11 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":"117228035","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
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