Pub Date : 1992-02-28DOI: 10.1070/IM1992V039N01ABEH002230
V. Trofimov
A positive answer is given to the problem of the existence of an upper bound for orders of stabilizers of vertices of connected graphs in vertex-transitive groups of automorphisms, if these stabilizers are finite and, under actions on adjacent vertices, contain the group PSLn(q) as normal subgroups in its natural doubly transitive representation, char Fq>3 (n and q fixed).
{"title":"GRAPHS WITH PROJECTIVE SUBORBITS","authors":"V. Trofimov","doi":"10.1070/IM1992V039N01ABEH002230","DOIUrl":"https://doi.org/10.1070/IM1992V039N01ABEH002230","url":null,"abstract":"A positive answer is given to the problem of the existence of an upper bound for orders of stabilizers of vertices of connected graphs in vertex-transitive groups of automorphisms, if these stabilizers are finite and, under actions on adjacent vertices, contain the group PSLn(q) as normal subgroups in its natural doubly transitive representation, char Fq>3 (n and q fixed).","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"16 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":"130565621","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 : 1991-06-30DOI: 10.1070/IM1991V037N03ABEH002161
L. Pastur, V. Tkachenko
A nonselfadjoint Sturm-Liouville operator () with a periodic potential which can be extended holomorphically to the upper half plane, is considered.
研究了一类具有周期势的非自伴Sturm-Liouville算子，该算子可以全纯地扩展到上半平面。
{"title":"AN INVERSE PROBLEM FOR A CLASS OF ONE-DIMENSIONAL SCHRÖDINGER OPERATORS WITH A COMPLEX PERIODIC POTENTIAL","authors":"L. Pastur, V. Tkachenko","doi":"10.1070/IM1991V037N03ABEH002161","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002161","url":null,"abstract":"A nonselfadjoint Sturm-Liouville operator () with a periodic potential which can be extended holomorphically to the upper half plane, is considered.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117025367","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 : 1991-06-30DOI: 10.1070/IM1991V036N03ABEH002034
A. S. Merkur’ev, A. Suslin
This paper gives a description of the torsion and cotorsion in the Milnor groups and for an arbitrary field . The main result is that, for any natural number with , and the group is uniquely -divisible if . This theorem is a consequence of an analogue of Hilbert's Theorem 90 for relative -groups of extensions of semilocal principal ideal domains. Among consequences of the main result we obtain an affirmative solution of the Milnor conjecture on the bijectivity of the homomorphism , where is the ideal of classes of even-dimensional forms in the Witt ring of the field , as well as a more complete description of the group for all global fields.
{"title":"THE GROUP $ K_3$ FOR A FIELD","authors":"A. S. Merkur’ev, A. Suslin","doi":"10.1070/IM1991V036N03ABEH002034","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002034","url":null,"abstract":"This paper gives a description of the torsion and cotorsion in the Milnor groups and for an arbitrary field . The main result is that, for any natural number with , and the group is uniquely -divisible if . This theorem is a consequence of an analogue of Hilbert's Theorem 90 for relative -groups of extensions of semilocal principal ideal domains. Among consequences of the main result we obtain an affirmative solution of the Milnor conjecture on the bijectivity of the homomorphism , where is the ideal of classes of even-dimensional forms in the Witt ring of the field , as well as a more complete description of the group for all global fields.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129490875","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 : 1991-06-30DOI: 10.1070/IM1991V037N03ABEH002160
V Yu Novokshënov
An asymptotic representation of the general solution of the second Painleve equation is constructed in a sector of the complex -plane. The principal term of the asymptotics is an elliptic function whose modulus and argument are functions of . Explicit expressions of these functions are given, and an approximation as is proved for the initial Painleve function outside a small neighborhood of its lattice of poles.
{"title":"THE BOUTROUX ANSATZ FOR THE SECOND PAINLEVÉ EQUATION IN THE COMPLEX DOMAIN","authors":"V Yu Novokshënov","doi":"10.1070/IM1991V037N03ABEH002160","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002160","url":null,"abstract":"An asymptotic representation of the general solution of the second Painleve equation is constructed in a sector of the complex -plane. The principal term of the asymptotics is an elliptic function whose modulus and argument are functions of . Explicit expressions of these functions are given, and an approximation as is proved for the initial Painleve function outside a small neighborhood of its lattice of poles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"387 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123512173","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 : 1991-06-30DOI: 10.1070/IM1991V037N03ABEH002158
A. Krasil'nikov
It is shown that the identities of a group with nilpotent commutator subgroup are finitely based. It follows that the identities of a connected matrix group over a field are finitely based.
证明了具有幂零换子群的群的恒等式是有限基的。由此得出域上连通矩阵群的恒等式是有限基的。
{"title":"THE IDENTITIES OF A GROUP WITH NILPOTENT COMMUTATOR SUBGROUP ARE FINITELY BASED","authors":"A. Krasil'nikov","doi":"10.1070/IM1991V037N03ABEH002158","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002158","url":null,"abstract":"It is shown that the identities of a group with nilpotent commutator subgroup are finitely based. It follows that the identities of a connected matrix group over a field are finitely based.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129765608","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 : 1991-06-30DOI: 10.1070/IM1991V036N03ABEH002039
V. Stepanov
Weighted estimates (1)are considered, where the constant does not depend on , for fractional Riemann- Liouville integrals and the following problem is examined: find necessary and sufficient conditions on weight functions and under which estimate (1) is valid for all functions for which the right-hand side of (1) is finite. The problem is solved for and . This result is definitive, and it generalizes known results for integral operators when . Bibliography: 19 titles.
{"title":"TWO-WEIGHTED ESTIMATES OF RIEMANN-LIOUVILLE INTEGRALS","authors":"V. Stepanov","doi":"10.1070/IM1991V036N03ABEH002039","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002039","url":null,"abstract":"Weighted estimates (1)are considered, where the constant does not depend on , for fractional Riemann- Liouville integrals and the following problem is examined: find necessary and sufficient conditions on weight functions and under which estimate (1) is valid for all functions for which the right-hand side of (1) is finite. The problem is solved for and . This result is definitive, and it generalizes known results for integral operators when . Bibliography: 19 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129219200","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 : 1991-06-30DOI: 10.1070/IM1991V036N03ABEH002032
A. Krivosheev
A criterion is given, in terms of the Laplace transform of an analytic functional , for the convolution operator , corresponding to this functional, to be an epimorphism, in the case when is an arbitrary convex domain and an arbitrary convex compact set in Cn.
{"title":"A CRITERION FOR THE SOLVABILITY OF NONHOMOGENEOUS CONVOLUTION EQUATIONS IN CONVEX DOMAINS OF Cn","authors":"A. Krivosheev","doi":"10.1070/IM1991V036N03ABEH002032","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002032","url":null,"abstract":"A criterion is given, in terms of the Laplace transform of an analytic functional , for the convolution operator , corresponding to this functional, to be an epimorphism, in the case when is an arbitrary convex domain and an arbitrary convex compact set in Cn.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125556762","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 : 1991-06-30DOI: 10.1070/IM1991V036N03ABEH002031
A. A. Danielyan, B. Levitan
The asymptotic expansion valid outside any angle , 0$ SRC=http://ej.iop.org/images/0025-5726/36/3/A02/tex_im_2031_img4.gif/>, is obtained for the Weyl-Titchmarsh function of the Sturm-Liouville problem on the half-axis with potential . Bibliography: 8 titles.
{"title":"On the Asymptotic Behavior of the Weyl-Titchmarsh m-FUNCTION","authors":"A. A. Danielyan, B. Levitan","doi":"10.1070/IM1991V036N03ABEH002031","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002031","url":null,"abstract":"The asymptotic expansion valid outside any angle , 0$ SRC=http://ej.iop.org/images/0025-5726/36/3/A02/tex_im_2031_img4.gif/>, is obtained for the Weyl-Titchmarsh function of the Sturm-Liouville problem on the half-axis with potential . Bibliography: 8 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133698693","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 : 1991-06-30DOI: 10.1070/IM1991V037N03ABEH002157
V. Kostov
A normal form is given for families of differential forms of nonzero real degree on the real line (in particular, a normal form for families of vector fields on the line), which depend smoothly on the parameters, in the neighborhood of zeros of the coefficient of the form of finite multiplicity (zeros of finite multiplicity of the field).
{"title":"VERSAL DEFORMATIONS OF DIFFERENTIAL FORMS OF REAL DEGREE ON THE REAL LINE","authors":"V. Kostov","doi":"10.1070/IM1991V037N03ABEH002157","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002157","url":null,"abstract":"A normal form is given for families of differential forms of nonzero real degree on the real line (in particular, a normal form for families of vector fields on the line), which depend smoothly on the parameters, in the neighborhood of zeros of the coefficient of the form of finite multiplicity (zeros of finite multiplicity of the field).","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123502011","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 : 1991-06-30DOI: 10.1070/IM1991V036N03ABEH002036
A. Khrennikov
The construction of a general theory of partial differential equations on a superspace is continued in the framework of functional superanalysis. Superanalogues of the spaces and of generalized functions are introduced; a theorem is proved on the existence of a fundamental solution for linear differential equations with constant coefficients on a superspace. In contrast to the scalar case, there exist differential operators not having fundamental solutions. Formulas are obtained for the fundamental solutions of the Laplace operator, the heat conduction operator, the Schrodinger operator, the d'Alembert operator, and the Helmholtz operator on a superspace. There is a discussion of the role of the nilpotence condition for even ghosts in a commutative superalgebra in the construction of a theory of generalized functions.
{"title":"EQUATIONS ON A SUPERSPACE","authors":"A. Khrennikov","doi":"10.1070/IM1991V036N03ABEH002036","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002036","url":null,"abstract":"The construction of a general theory of partial differential equations on a superspace is continued in the framework of functional superanalysis. Superanalogues of the spaces and of generalized functions are introduced; a theorem is proved on the existence of a fundamental solution for linear differential equations with constant coefficients on a superspace. In contrast to the scalar case, there exist differential operators not having fundamental solutions. Formulas are obtained for the fundamental solutions of the Laplace operator, the heat conduction operator, the Schrodinger operator, the d'Alembert operator, and the Helmholtz operator on a superspace. There is a discussion of the role of the nilpotence condition for even ghosts in a commutative superalgebra in the construction of a theory of generalized functions.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130908185","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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