Pub Date : 1992-02-28DOI: 10.1070/SM1992V071N02ABEH001403
I. F. Krasichkov-Ternovskii
A general approach is worked out for problems of complex analysis connected with the transition from local properties of analytic functions (of a single variable) to their global properties.
对于复杂分析问题，从解析函数(单变量)的局部性质到全局性质的转换，提出了一种一般的解决方法。
{"title":"ABSTRACT METHODS FOR A LOCAL DESCRIPTION OF CLOSED SUBMODULES OF ANALYTIC FUNCTIONS","authors":"I. F. Krasichkov-Ternovskii","doi":"10.1070/SM1992V071N02ABEH001403","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001403","url":null,"abstract":"A general approach is worked out for problems of complex analysis connected with the transition from local properties of analytic functions (of a single variable) to their global properties.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"12 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":"132920252","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/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/SM1992V073N02ABEH002556
V. A. Aleksandrov
The possibility of imbedding n-dimensional locally Euclidean metrics in the large in Rn is studied by means of the global inverse function theorem in the forms suggested by Hadamard, John, Levy and Plastock. The imbeddability of conformally Euclidean metrics is studied by means of a theorem of Zorich on the removability of an isolated singularity of a locally quasiconformal mapping.
{"title":"IMBEDDING LOCALLY EUCLIDEAN AND CONFORMALLY EUCLIDEAN METRICS","authors":"V. A. Aleksandrov","doi":"10.1070/SM1992V073N02ABEH002556","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002556","url":null,"abstract":"The possibility of imbedding n-dimensional locally Euclidean metrics in the large in Rn is studied by means of the global inverse function theorem in the forms suggested by Hadamard, John, Levy and Plastock. The imbeddability of conformally Euclidean metrics is studied by means of a theorem of Zorich on the removability of an isolated singularity of a locally quasiconformal mapping.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"41 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":"124483127","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/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}
Pub Date : 1992-02-28DOI: 10.1070/SM1992V073N02ABEH002562
V. F. Akulov, A. Shishkov
Lower bounds are established for the rate of growth of generalized, locally bounded solutions of mixed problems for various classes of quasilinear degenerate parabolic equations both of second and higher orders in unbounded spatial domains.
建立了无界空间域上各类二阶和高阶拟线性退化抛物型方程混合问题的广义、局部有界解的增长率下界。
{"title":"ON ASYMPTOTIC PROPERTIES OF SOLUTIONS OF MIXED PROBLEMS FOR QUASILINEAR PARABOLIC EQUATIONS IN UNBOUNDED DOMAINS","authors":"V. F. Akulov, A. Shishkov","doi":"10.1070/SM1992V073N02ABEH002562","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002562","url":null,"abstract":"Lower bounds are established for the rate of growth of generalized, locally bounded solutions of mixed problems for various classes of quasilinear degenerate parabolic equations both of second and higher orders in unbounded spatial domains.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"33 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":"128097641","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/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/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/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}
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