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A THEOREM ON TWO COMMUTING AUTOMORPHISMS, AND INTEGRABLE DIFFERENTIAL EQUATIONS 两个交换自同构和可积微分方程的定理
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V036N02ABEH002021
O. Bogoyavlenskii
{"title":"A THEOREM ON TWO COMMUTING AUTOMORPHISMS, AND INTEGRABLE DIFFERENTIAL EQUATIONS","authors":"O. Bogoyavlenskii","doi":"10.1070/IM1991V036N02ABEH002021","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002021","url":null,"abstract":"Constructions are found for differential equations in an arbitrary continuous associative algebra that admit an equivalent Lax representation (with spectral parameter) in the space of linear operators acting on . The constructions use commuting automorphisms of . Applications of the main construction are indicated for the construction of integrable Euler equations in the direct sum of the Lie algebras and . Constructions are presented for matrix differential equations admitting a Lax representation with several spectral parameters.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131832427","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: 3
ON THE SPECTRUM OF SUMS OF GENERATORS OF A FINITE GROUP 有限群生成子和的谱
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V037N02ABEH002072
S. Strunkov
{"title":"ON THE SPECTRUM OF SUMS OF GENERATORS OF A FINITE GROUP","authors":"S. Strunkov","doi":"10.1070/IM1991V037N02ABEH002072","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002072","url":null,"abstract":"Let be any finite extension field of the field of rationals, and let and be given natural numbers. It is shown that there are only finitely many isomorphism classes of finite groups on generators such that the spectrum of the element of the algebra lies in .","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121472292","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: 3
TRIPLES OF INFINITE ITERATES OF METRIZABLE FUNCTORS 可度量函子的无限迭代的三元组
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V036N02ABEH002028
V. Fedorchuk
{"title":"TRIPLES OF INFINITE ITERATES OF METRIZABLE FUNCTORS","authors":"V. Fedorchuk","doi":"10.1070/IM1991V036N02ABEH002028","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002028","url":null,"abstract":"The concepts of metrizable, uniformly metrizable, and perfectly metrizable functors are introduced. The triple , , of infinite iterates of a perfectly metrizable functor is defined. The geometric properties of such triples are investigated for the continuous hyperspace functor and the probability measure functor. Bibliography: 14 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124954138","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
ON THE BOUNDARY BEHAVIOR OF FUNCTIONS IN SPACES OF HARDY TYPE hardy型空间中函数的边界行为
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V037N02ABEH002065
V. Krotov
{"title":"ON THE BOUNDARY BEHAVIOR OF FUNCTIONS IN SPACES OF HARDY TYPE","authors":"V. Krotov","doi":"10.1070/IM1991V037N02ABEH002065","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002065","url":null,"abstract":"Let be a topological space with a measure . In the product (or ) simple axioms are used to distinguish a family of domains for approaching the boundary of . Associated with the family is the maximal function The spaces consisting of functions continuous on with are introduced, along with the subspaces of them consisting of the functions having a -limit a.e. The properties of the spaces and the action in them of operators of smoothing type are studied. The results are applied to Hardy spaces of harmonic or holomorphic functions.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125959067","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
CHANGE OF JORDAN STRUCTURE OF G-SELFADJOINT OPERATORS AND SELFADJOINT OPERATOR-VALUED FUNCTIONS UNDER SMALL PERTURBATIONS 小扰动下g自伴随算子和自伴随算子值函数Jordan结构的变化
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V037N02ABEH002068
V. R. Ol'shevskii
{"title":"CHANGE OF JORDAN STRUCTURE OF G-SELFADJOINT OPERATORS AND SELFADJOINT OPERATOR-VALUED FUNCTIONS UNDER SMALL PERTURBATIONS","authors":"V. R. Ol'shevskii","doi":"10.1070/IM1991V037N02ABEH002068","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002068","url":null,"abstract":"The author considers the problem of the change of length of Jordan chains when passing from -selfadjoint operator to -selfadjoint operator , provided is small enough. The role played by the so-called sign characteristics is clarified. The results will carry over to the case of small perturbations of holomorphic selfadjoint operator-valued functions.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127071360","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: 4
DISCRETE REGULARIZATION OF OPTIMAL CONTROL PROBLEMS ON ILL-POSED MONOTONE VARIATIONAL INEQUALITIES 不适定单调变分不等式上最优控制问题的离散正则化
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V037N02ABEH002066
O. A. Liskovets
{"title":"DISCRETE REGULARIZATION OF OPTIMAL CONTROL PROBLEMS ON ILL-POSED MONOTONE VARIATIONAL INEQUALITIES","authors":"O. A. Liskovets","doi":"10.1070/IM1991V037N02ABEH002066","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002066","url":null,"abstract":"The author considers the problem of minimizing an abstract functional which depends on the control and on the solution of an ill-posed variational inequality (v.i.) with a bounded monotone exact operator with the -property (these properties are not needed for approximate operators, nor is the -property in the pseudomonotone case). Solvability of the problem is shown. For its regularization the original v.i. is regularized by means of v.i. with a small step. A number of generalizations are indicated.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133371062","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: 9
ON THE ZEROS OF THE DAVENPORT-HEILBRONN FUNCTION LYING ON THE CRITICAL LINE davenport-heilbronn函数的零点在临界线上
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V036N02ABEH002023
A. A. Karatsuba
{"title":"ON THE ZEROS OF THE DAVENPORT-HEILBRONN FUNCTION LYING ON THE CRITICAL LINE","authors":"A. A. Karatsuba","doi":"10.1070/IM1991V036N02ABEH002023","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002023","url":null,"abstract":"It is proved that at least zeros of the Davenport-Heilbronn function lie on the segment of the critical line. Bibliography: 12 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115698931","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: 32
ADMISSIBILITY OF RULES OF INFERENCE, AND LOGICAL EQUATIONS, IN MODAL LOGICS AXIOMATIZING PROVABILITY 模态逻辑公理化可证明性中推理规则和逻辑方程的容许性
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V036N02ABEH002026
V. Rybakov
{"title":"ADMISSIBILITY OF RULES OF INFERENCE, AND LOGICAL EQUATIONS, IN MODAL LOGICS AXIOMATIZING PROVABILITY","authors":"V. Rybakov","doi":"10.1070/IM1991V036N02ABEH002026","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002026","url":null,"abstract":"This paper examines the modal logics of Godel-Lob (GL) and Solovay (S) - the smallest and the largest modal representations of arithmetic theories. The problem of recognizing the admissibility of inference rules with parameters (and, in particular, without parameters) in GL and S is shown to be decidable; that is, a positive solution is obtained to analogues of a problem of Friedman. The analogue of a problem of Kuznetsov on finite bases of admissible rules for S and GL is solved in the negative sense. Algorithms are found for recognizing the solvability in GL and S of logical equations and for constructing solutions for them.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127219753","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
ON DILATION THEORY AND SPECTRAL ANALYSIS OF DISSIPATIVE SCHRÖDINGER OPERATORS IN WEYL'S LIMIT-CIRCLE CASE weyl极限环情况下耗散schrÖdinger算子的膨胀理论与谱分析
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V036N02ABEH002020
B. P. Allakhverdiev
{"title":"ON DILATION THEORY AND SPECTRAL ANALYSIS OF DISSIPATIVE SCHRÖDINGER OPERATORS IN WEYL'S LIMIT-CIRCLE CASE","authors":"B. P. Allakhverdiev","doi":"10.1070/IM1991V036N02ABEH002020","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002020","url":null,"abstract":"Dissipative Schrodinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114588763","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: 39
ASYMPTOTIC SOLUTION OF A VARIATIONAL INEQUALITY MODELING FRICTION 模拟摩擦的变分不等式的渐近解
Mathematics of The Ussr-izvestiya Pub Date : 1991-04-30 DOI: 10.1070/IM1991V037N02ABEH002067
S. Nazarov
{"title":"ASYMPTOTIC SOLUTION OF A VARIATIONAL INEQUALITY MODELING FRICTION","authors":"S. Nazarov","doi":"10.1070/IM1991V037N02ABEH002067","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002067","url":null,"abstract":"The problem of minimizing the nondifferentiable functional is considered. An asymptotic solution of the corresponding variational inequality is constructed and justified under the assumption that or is a small parameter. Also, formal asymptotic representations are obtained for singular surfaces which characterize a change in the type of boundary conditions. For a modification of the Vishik-Lyusternik method is used, and exponential boundary layers arise. If , then the boundary layer has only power growth; the principal term of the asymptotic expansion of the solution of the problem in a multidimensional region and the complete asymptotic expansion for the case are obtained.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114736971","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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