Pub Date : 1992-02-28DOI: 10.1070/SM1992V072N01ABEH001265
A. Bovdi, I. I. Khripta
The structure of the multiplicative group of a group algebra is studied. The main problem is that of describing the structure of groups whose group algebras over a given field have multiplicative groups satisfying an Engel (or bounded Engel) condition.
{"title":"ENGEL PROPERTIES OF THE MULTIPLICATIVE GROUP OF A GROUP ALGEBRA","authors":"A. Bovdi, I. I. Khripta","doi":"10.1070/SM1992V072N01ABEH001265","DOIUrl":"https://doi.org/10.1070/SM1992V072N01ABEH001265","url":null,"abstract":"The structure of the multiplicative group of a group algebra is studied. The main problem is that of describing the structure of groups whose group algebras over a given field have multiplicative groups satisfying an Engel (or bounded Engel) condition.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"19 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":"122365925","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/SM1992V072N02ABEH001271
P. Katsylo
{"title":"RATIONALITY OF THE MODULI VARIETY OF CURVES OF GENUS 5","authors":"P. Katsylo","doi":"10.1070/SM1992V072N02ABEH001271","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH001271","url":null,"abstract":"","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"66 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":"114577477","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/SM1992V072N02ABEH002143
A. Privalov
An orthogonal trigonometric basis in the space is constructed whose degrees have growth rate .
构造了空间中的正交三角基，其度数具有增长率。
{"title":"ON AN ORTHOGONAL TRIGONOMETRIC BASIS","authors":"A. Privalov","doi":"10.1070/SM1992V072N02ABEH002143","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH002143","url":null,"abstract":"An orthogonal trigonometric basis in the space is constructed whose degrees have growth rate .","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"35 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":"122020321","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/SM1992V073N02ABEH002560
Shakro Tetunashvili
Uniqueness theorems are proved for some multiple function series. A particular consequence of these theorems is the solution of a uniqueness problem for multiple trigonometric series. One result is the following proposition: any countable set is a set of uniqueness (for Pringsheim convergence) of d-fold trigonometric series (d ≥ 2).
{"title":"ON SOME MULTIPLE FUNCTION SERIES AND THE SOLUTION OF THE UNIQUENESS PROBLEM FOR PRINGSHEIM CONVERGENCE OF MULTIPLE TRIGONOMETRIC SERIES","authors":"Shakro Tetunashvili","doi":"10.1070/SM1992V073N02ABEH002560","DOIUrl":"https://doi.org/10.1070/SM1992V073N02ABEH002560","url":null,"abstract":"Uniqueness theorems are proved for some multiple function series. A particular consequence of these theorems is the solution of a uniqueness problem for multiple trigonometric series. One result is the following proposition: any countable set is a set of uniqueness (for Pringsheim convergence) of d-fold trigonometric series (d ≥ 2).","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":"128464153","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/SM1992V071N02ABEH001400
N. V. Ivanov
In this paper all primitive representations of braid groups on strings of surfaces of finite type in groups of permutations of symbols are found. As an application it is proved that the groups of pure braids of surfaces are characteristic subgroups of the braid groups. These results generalize Artin's classical results on Artin's braid groups.
{"title":"PERMUTATION REPRESENTATIONS OF BRAID GROUPS OF SURFACES","authors":"N. V. Ivanov","doi":"10.1070/SM1992V071N02ABEH001400","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001400","url":null,"abstract":"In this paper all primitive representations of braid groups on strings of surfaces of finite type in groups of permutations of symbols are found. As an application it is proved that the groups of pure braids of surfaces are characteristic subgroups of the braid groups. These results generalize Artin's classical results on Artin's braid groups.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"34 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":"128679588","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/SM1992V071N02ABEH001402
A. Chanyshev
It is proved that an associative PI-algebra over a field of characteristic zero that is graded by an arbitrary semigroup and that satisfies the relation an = 0 for all homogeneous elements and is generated by a finite number of its homogeneous components is nilpotent. This generalizes a well-known theorem of M. Nagata.
{"title":"ON NILPOTENCY OF GRADED ASSOCIATIVE ALGEBRAS","authors":"A. Chanyshev","doi":"10.1070/SM1992V071N02ABEH001402","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001402","url":null,"abstract":"It is proved that an associative PI-algebra over a field of characteristic zero that is graded by an arbitrary semigroup and that satisfies the relation an = 0 for all homogeneous elements and is generated by a finite number of its homogeneous components is nilpotent. This generalizes a well-known theorem of M. Nagata.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"54 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":"129278750","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/SM1992V072N02ABEH001414
V. Meshkov
For second-order partial differential equations the question of whether they can have solutions decaying superexponentially at infinity is studied. An example is constructed of an equation Δu = q(x)u on the plane with bounded coefficients q having a nonzero solution decaying superexponentially. This example provides a negative answer to a familiar question of E. M. Landis. These questions are also studied for hyperbolic and parabolic equations on manifolds. An example is constructed of a parabolic equation having a nonzero solution u(x, t) decaying superexponentially as t→∞.
{"title":"ON THE POSSIBLE RATE OF DECAY AT INFINITY OF SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS","authors":"V. Meshkov","doi":"10.1070/SM1992V072N02ABEH001414","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH001414","url":null,"abstract":"For second-order partial differential equations the question of whether they can have solutions decaying superexponentially at infinity is studied. An example is constructed of an equation Δu = q(x)u on the plane with bounded coefficients q having a nonzero solution decaying superexponentially. This example provides a negative answer to a familiar question of E. M. Landis. These questions are also studied for hyperbolic and parabolic equations on manifolds. An example is constructed of a parabolic equation having a nonzero solution u(x, t) decaying superexponentially as t→∞.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"1 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":"129365985","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/SM1992V072N02ABEH001270
V. Samokhin
The time-dependent system of equations describing plane-parallel motion of Ostwald-de Waele media is considered in the approximation of magnetohydrodynamics. The system differs from the classical equations of magnetohydrodynamics by the presence in the leading term of power nonlinearities. The initial boundary value problem is solved with the conditions of diffraction of the physical characteristics on the boundary separating the media. Existence of a generalized solution is proved on the basis of the Faedo-Galerkin method and the method of monotone operators.
{"title":"EXISTENCE OF A SOLUTION OF A MODIFICATION OF A SYSTEM OF EQUATIONS OF MAGNETOHYDRODYNAMICS","authors":"V. Samokhin","doi":"10.1070/SM1992V072N02ABEH001270","DOIUrl":"https://doi.org/10.1070/SM1992V072N02ABEH001270","url":null,"abstract":"The time-dependent system of equations describing plane-parallel motion of Ostwald-de Waele media is considered in the approximation of magnetohydrodynamics. The system differs from the classical equations of magnetohydrodynamics by the presence in the leading term of power nonlinearities. The initial boundary value problem is solved with the conditions of diffraction of the physical characteristics on the boundary separating the media. Existence of a generalized solution is proved on the basis of the Faedo-Galerkin method and the method of monotone operators.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"206 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":"116284287","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/SM1992V071N01ABEH002127
Yulia Karpeshina
Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schr?dinger operator in . An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.
{"title":"PERTURBATION THEORY FORMULAS FOR THE SCHRÖDINGER EQUATION WITH A NONSMOOTH PERIODIC POTENTIAL","authors":"Yulia Karpeshina","doi":"10.1070/SM1992V071N01ABEH002127","DOIUrl":"https://doi.org/10.1070/SM1992V071N01ABEH002127","url":null,"abstract":"Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schr?dinger operator in . An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"43 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":"122019201","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/SM1992V071N02ABEH001404
A. Buslaev, V. Tikhomirov
The authors study the problem of Kolmogorov widths of Sobolev classes Wpr([0, 1]) of functions in the Lq-metric, p ≥ q, and the connected questions of the existence and uniqueness of the spectra of nonlinear equations.
{"title":"SPECTRA OF NONLINEAR DIFFERENTIAL EQUATIONS AND WIDTHS OF SOBOLEV CLASSES","authors":"A. Buslaev, V. Tikhomirov","doi":"10.1070/SM1992V071N02ABEH001404","DOIUrl":"https://doi.org/10.1070/SM1992V071N02ABEH001404","url":null,"abstract":"The authors study the problem of Kolmogorov widths of Sobolev classes Wpr([0, 1]) of functions in the Lq-metric, p ≥ q, and the connected questions of the existence and uniqueness of the spectra of nonlinear equations.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"44 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":"124474449","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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