Pub Date : 1992-06-30DOI: 10.1070/IM1992V038N03ABEH002217
M. Fedoryuk
New classes of Heun's functions that are eigenfunctions of a two-parameter spectral problem with boundary conditions at singular points of Heun's equation are introduced. The asymptotics of the spectrum and of Heun's functions are studied.
{"title":"ASYMPTOTICS OF THE SPECTRUM OF HEUN'S EQUATION AND OF HEUN'S FUNCTIONS","authors":"M. Fedoryuk","doi":"10.1070/IM1992V038N03ABEH002217","DOIUrl":"https://doi.org/10.1070/IM1992V038N03ABEH002217","url":null,"abstract":"New classes of Heun's functions that are eigenfunctions of a two-parameter spectral problem with boundary conditions at singular points of Heun's equation are introduced. The asymptotics of the spectrum and of Heun's functions are studied.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115784363","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 : 1992-06-30DOI: 10.1070/IM1992V038N03ABEH002220
M. Sapir
An algorithm is found that decides, for an arbitrary system of semigroup identities, whether the orders of the finite semigroups satisfying the system are bounded by a function (or a recursive function) of the number of generators.
{"title":"THE RESTRICTED BURNSIDE PROBLEM FOR VARIETIES OF SEMIGROUPS","authors":"M. Sapir","doi":"10.1070/IM1992V038N03ABEH002220","DOIUrl":"https://doi.org/10.1070/IM1992V038N03ABEH002220","url":null,"abstract":"An algorithm is found that decides, for an arbitrary system of semigroup identities, whether the orders of the finite semigroups satisfying the system are bounded by a function (or a recursive function) of the number of generators.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115679591","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 : 1992-06-30DOI: 10.1070/IM1992V038N03ABEH002210
S. Zube
The author constructs mappings between bundles on an elliptic surface and bundles on an elliptic surface that has been modified by a logarithmic transformation. These mappings are applied to the study of the moduli varieties of bundles with c1=0 on elliptic surfaces.
{"title":"LOGARITHMIC TRANSFORMATION OF AN ELLIPTIC SURFACE, AND VECTOR BUNDLES","authors":"S. Zube","doi":"10.1070/IM1992V038N03ABEH002210","DOIUrl":"https://doi.org/10.1070/IM1992V038N03ABEH002210","url":null,"abstract":"The author constructs mappings between bundles on an elliptic surface and bundles on an elliptic surface that has been modified by a logarithmic transformation. These mappings are applied to the study of the moduli varieties of bundles with c1=0 on elliptic surfaces.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121578765","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 : 1992-06-30DOI: 10.1070/IM1992V038N03ABEH002215
A. Tuzhilin
The Morse-type index of a compact p-dimensional minimal submanifold is the index of the second variation of the p-dimensional volume functional. In this paper a definition is given for the index of a noncompact minimal submanifold, and the indices of some two-dimensional minimal surfaces in three-dimensional Euclidean space R3 and in three-dimensional Lobachevsky space H3 are computed. In particular, the indices of all the classic minimal surfaces in R3 are computed: the catenoid, Enneper surfaces, Scherk surfaces, Richmond surfaces, and others. The indices of spherical catenoids in H3 are computed, which completes the computation of the indices of catenoids in H3 (hyperbolic and parabolic catenoids have zero index, that is, they are stable). It is also proved that for a one-parameter family of helicoids in H3 the helicoids are stable for certain values of the parameter.
{"title":"MORSE-TYPE INDICES OF TWO-DIMENSIONAL MINIMAL SURFACES IN R3 AND H3","authors":"A. Tuzhilin","doi":"10.1070/IM1992V038N03ABEH002215","DOIUrl":"https://doi.org/10.1070/IM1992V038N03ABEH002215","url":null,"abstract":"The Morse-type index of a compact p-dimensional minimal submanifold is the index of the second variation of the p-dimensional volume functional. In this paper a definition is given for the index of a noncompact minimal submanifold, and the indices of some two-dimensional minimal surfaces in three-dimensional Euclidean space R3 and in three-dimensional Lobachevsky space H3 are computed. In particular, the indices of all the classic minimal surfaces in R3 are computed: the catenoid, Enneper surfaces, Scherk surfaces, Richmond surfaces, and others. The indices of spherical catenoids in H3 are computed, which completes the computation of the indices of catenoids in H3 (hyperbolic and parabolic catenoids have zero index, that is, they are stable). It is also proved that for a one-parameter family of helicoids in H3 the helicoids are stable for certain values of the parameter.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126589046","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 : 1992-06-30DOI: 10.1070/IM1992V039N03ABEH002247
A. Kochubei
The author constructs and investigates a fundamental solution of Cauchy's problem for a parabolic equation with a -adic space variable and a real time variable. The question of existence and uniqueness of solutions to Cauchy's problem in classes of bounded and increasing functions is considered, and conditions for nonnegativity of the fundamental solution are found. The problem of determining if the solution stabilizes as is solved for a model equation with constant coefficients.
{"title":"PARABOLIC EQUATIONS OVER THE FIELD OF $ p$-ADIC NUMBERS","authors":"A. Kochubei","doi":"10.1070/IM1992V039N03ABEH002247","DOIUrl":"https://doi.org/10.1070/IM1992V039N03ABEH002247","url":null,"abstract":"The author constructs and investigates a fundamental solution of Cauchy's problem for a parabolic equation with a -adic space variable and a real time variable. The question of existence and uniqueness of solutions to Cauchy's problem in classes of bounded and increasing functions is considered, and conditions for nonnegativity of the fundamental solution are found. The problem of determining if the solution stabilizes as is solved for a model equation with constant coefficients.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133974805","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 : 1992-06-30DOI: 10.1070/IM1992V039N03ABEH002242
N. Kruzhilin
It is shown that there exists a Levi-flat surface in with boundary on a given two-dimensional sphere that lies in the boundary of a strictly pseudoconvex domain and is totally real everywhere except at a finite number of elliptic and hyperbolic points.
{"title":"TWO-DIMENSIONAL SPHERES IN THE BOUNDARIES OF STRICTLY PSEUDOCONVEX DOMAINS IN $ mathbb C^2$","authors":"N. Kruzhilin","doi":"10.1070/IM1992V039N03ABEH002242","DOIUrl":"https://doi.org/10.1070/IM1992V039N03ABEH002242","url":null,"abstract":"It is shown that there exists a Levi-flat surface in with boundary on a given two-dimensional sphere that lies in the boundary of a strictly pseudoconvex domain and is totally real everywhere except at a finite number of elliptic and hyperbolic points.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127980163","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 : 1992-06-30DOI: 10.1070/IM1992V038N03ABEH002212
A. Kolesov
Effective conditions are found under which planar relaxation systems of a certain class have cycles with one δ-like component and another component close to discontinuous. A complete asymptotics of the cycles is constructed and the question on their stability is solved.
{"title":"SPECIFIC RELAXATION CYCLES OF SYSTEMS OF LOTKA-VOLTERRA TYPE","authors":"A. Kolesov","doi":"10.1070/IM1992V038N03ABEH002212","DOIUrl":"https://doi.org/10.1070/IM1992V038N03ABEH002212","url":null,"abstract":"Effective conditions are found under which planar relaxation systems of a certain class have cycles with one δ-like component and another component close to discontinuous. A complete asymptotics of the cycles is constructed and the question on their stability is solved.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"254 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116167730","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 : 1992-06-30DOI: 10.1070/IM1992V038N03ABEH002218
A. Sergeev, P. Haĭntsner
It is proved that the extended matrix disk is a domain of holomorphy. This gives a positive answer to a conjecture that is a "compact" analogue of the conjecture on the extended future tube.
{"title":"THE EXTENDED MATRIX DISK IS A DOMAIN OF HOLOMORPHY","authors":"A. Sergeev, P. Haĭntsner","doi":"10.1070/IM1992V038N03ABEH002218","DOIUrl":"https://doi.org/10.1070/IM1992V038N03ABEH002218","url":null,"abstract":"It is proved that the extended matrix disk is a domain of holomorphy. This gives a positive answer to a conjecture that is a \"compact\" analogue of the conjecture on the extended future tube.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124123829","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 : 1992-06-30DOI: 10.1070/IM1992V039N03ABEH002248
V. A. Voevodskii
The author considers Galois group actions on the fundamental groups of curves of hyperbolic type, and proves certain cases of Grothendieck's conjecture about the possibility of recovering a curve from its Galois representation.
{"title":"GALOIS REPRESENTATIONS CONNECTED WITH HYPERBOLIC CURVES","authors":"V. A. Voevodskii","doi":"10.1070/IM1992V039N03ABEH002248","DOIUrl":"https://doi.org/10.1070/IM1992V039N03ABEH002248","url":null,"abstract":"The author considers Galois group actions on the fundamental groups of curves of hyperbolic type, and proves certain cases of Grothendieck's conjecture about the possibility of recovering a curve from its Galois representation.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115431589","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 : 1992-06-30DOI: 10.1070/IM1992V039N03ABEH002244
A. Khrennikov
A theory is developed for superanalytic generalized functions on a superspace over a non-Archimedean Banach superalgebra with trivial annihilator of the odd part. A Gaussian distribution and the Volkenborn distribution are introduced on the non-Archimedean superspace. Existence and uniqueness theorems are proved for the Cauchy problem for linear differential equations with variable coefficients. The Cauchy problem for non-Archimedean superdiffusion, the Schrodinger equation, and the Schrodinger equation for supersymmetric quantum mechanics on a non-Archimedean Riemann surface are considered as applications.
{"title":"GENERALIZED FUNCTIONS ON A NON-ARCHIMEDEAN SUPERSPACE","authors":"A. Khrennikov","doi":"10.1070/IM1992V039N03ABEH002244","DOIUrl":"https://doi.org/10.1070/IM1992V039N03ABEH002244","url":null,"abstract":"A theory is developed for superanalytic generalized functions on a superspace over a non-Archimedean Banach superalgebra with trivial annihilator of the odd part. A Gaussian distribution and the Volkenborn distribution are introduced on the non-Archimedean superspace. Existence and uniqueness theorems are proved for the Cauchy problem for linear differential equations with variable coefficients. The Cauchy problem for non-Archimedean superdiffusion, the Schrodinger equation, and the Schrodinger equation for supersymmetric quantum mechanics on a non-Archimedean Riemann surface are considered as applications.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124374412","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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