Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N01ABEH002535
B. Loginov, N. Sidorov
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.
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V072N02ABEH002150
É. M. Galeev
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.
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N02ABEH002553
I. Ovsyannikov, L. Shilnikov
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 .
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N02ABEH002132
Yu V Tishin
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.
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N01ABEH001396
V. Temlyakov
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.
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V072N02ABEH002142
V. F. Kirichenko
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).
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N01ABEH001389
I. E. Shparlinskii
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.
形式为f (x) + a, a = 1，…的原始多项式个数的渐近公式， h，其中得到f (x)Fp[x]，对所有固定次多项式f的“平均”，也得到了“稀疏”可因子多项式个数的估计。
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N01ABEH002531
V. Golubyatnikov
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.
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N02ABEH002559
S. Rychkov
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.
{"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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N01ABEH002534
Y. Korobeinik
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).
{"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：