Pub Date : 1991-06-30DOI: 10.1070/IM1991V037N03ABEH002156
V. A. Voevodskii
The author proves a conjecture of Grothendieck concerning the possibility of recovering a normal scheme over a field of finite type over Q from its etale site.
证明了格罗登狄克关于有限型域在Q上从其起始点恢复正规格式的可能性的一个猜想。
{"title":"ÉTALE Topologies of Schemes Over Fields of Finite Type Over Q","authors":"V. A. Voevodskii","doi":"10.1070/IM1991V037N03ABEH002156","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002156","url":null,"abstract":"The author proves a conjecture of Grothendieck concerning the possibility of recovering a normal scheme over a field of finite type over Q from its etale site.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1818 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":"127453175","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/IM1991V037N03ABEH002162
V. S. Pilidi
Criteria are obtained for applicability of approximation methods to a one-dimensional singular integral operator with piecewise continuous coefficients. These methods use families of strongly approximating operators with "cut out" singularity of the Cauchy kernel.
{"title":"CRITERIA FOR UNIFORM INVERTIBILITY OF REGULAR APPROXIMATIONS OF ONE-DIMENSIONAL SINGULAR INTEGRAL OPERATORS WITH PIECEWISE CONTINUOUS COEFFICIENTS","authors":"V. S. Pilidi","doi":"10.1070/IM1991V037N03ABEH002162","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002162","url":null,"abstract":"Criteria are obtained for applicability of approximation methods to a one-dimensional singular integral operator with piecewise continuous coefficients. These methods use families of strongly approximating operators with \"cut out\" singularity of the Cauchy kernel.","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":"124380381","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/IM1991V037N03ABEH002159
L. Kuz'min
The author obtains a new explicit formula for the norm residue symbol in a local cyclotomic field which is especially suitable for work in Zl-extensions. Several applications of this formula to a conjecture on the l-adic regulator are given.
{"title":"NEW EXPLICIT FORMULAS FOR THE NORM RESIDUE SYMBOL, AND THEIR APPLICATIONS","authors":"L. Kuz'min","doi":"10.1070/IM1991V037N03ABEH002159","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002159","url":null,"abstract":"The author obtains a new explicit formula for the norm residue symbol in a local cyclotomic field which is especially suitable for work in Zl-extensions. Several applications of this formula to a conjecture on the l-adic regulator are given.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"15 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113961343","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/IM1991V037N03ABEH002155
A. Babin
Second-order elliptic equations with analytic coefficients and right sides in a domain with piecewise smooth boundary are studied. It is assumed that the boundary is characteristic at all points. Both Lipschitz and non-Lipschitz singularities of the boundary are admitted. It is proved that for large values of the spectral parameter, solutions possess high smoothness even at those points where the boundary has singularities. The results are based on the study of a constructive representation of solutions of the equations in the form of series of analytic functions.
{"title":"ON THE SMOOTHNESS OF SOLUTIONS OF DIFFERENTIAL EQUATIONS AT SINGULAR POINTS OF THE BOUNDARY OF THE DOMAIN","authors":"A. Babin","doi":"10.1070/IM1991V037N03ABEH002155","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002155","url":null,"abstract":"Second-order elliptic equations with analytic coefficients and right sides in a domain with piecewise smooth boundary are studied. It is assumed that the boundary is characteristic at all points. Both Lipschitz and non-Lipschitz singularities of the boundary are admitted. It is proved that for large values of the spectral parameter, solutions possess high smoothness even at those points where the boundary has singularities. The results are based on the study of a constructive representation of solutions of the equations in the form of series of analytic functions.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"519 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":"123124668","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/IM1991V037N03ABEH002163
V. Uspenskiĭ
The free topological group F(X) of an arbitrary metrizable space X is complete in the Weil sense. If Y is a closed subspace of a metrizable space X, then F(Y) is a topological subgroup of F(X).
{"title":"FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES","authors":"V. Uspenskiĭ","doi":"10.1070/IM1991V037N03ABEH002163","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002163","url":null,"abstract":"The free topological group F(X) of an arbitrary metrizable space X is complete in the Weil sense. If Y is a closed subspace of a metrizable space X, then F(Y) is a topological subgroup of F(X).","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"75 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":"124625689","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/IM1991V037N03ABEH002165
V. Rybakov
The author studies the problem of recognizing admissibility of rules of inference of a general form - rules of inference with parameters - in the intuitionistic propositional calculus. Algorithmic and semantic criteria are found for recognizing admissibility of such rules, based on special intuitionistic Kripke models. In particular, Friedman's problem generalized to rules of inference with parameters is solved. These results are applied to recognizing the solvability of logical equations and constructing their solutions.
{"title":"CRITERIA FOR ADMISSIBILITY OF RULES OF INFERENCE WITH PARAMETERS IN THE INTUITIONISTIC PROPOSITIONAL CALCULUS","authors":"V. Rybakov","doi":"10.1070/IM1991V037N03ABEH002165","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002165","url":null,"abstract":"The author studies the problem of recognizing admissibility of rules of inference of a general form - rules of inference with parameters - in the intuitionistic propositional calculus. Algorithmic and semantic criteria are found for recognizing admissibility of such rules, based on special intuitionistic Kripke models. In particular, Friedman's problem generalized to rules of inference with parameters is solved. These results are applied to recognizing the solvability of logical equations and constructing their solutions.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"37 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":"122306400","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/IM1991V036N03ABEH002037
V. Sharko
Stable algebra is developed as needed in Morse theory. New estimates are found for the number of critical points of Morse functions, and conditions are found for the existence of minimal Morse functions on non-simply-connected manifolds.
{"title":"STABLE ALGEBRA IN MORSE THEORY","authors":"V. Sharko","doi":"10.1070/IM1991V036N03ABEH002037","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002037","url":null,"abstract":"Stable algebra is developed as needed in Morse theory. New estimates are found for the number of critical points of Morse functions, and conditions are found for the existence of minimal Morse functions on non-simply-connected manifolds.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"29 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":"131787008","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/IM1991V037N03ABEH002164
A. Kytmanov
Let be a Stein manifold of dimension , let be a domain which is relatively compact in with connected, and let with . It is shown that any CR-function which is defined on extends holomorphically to . A local version of this assertion is also obtained.
{"title":"HOLOMORPHIC EXTENSION OF CR-FUNCTIONS WITH SINGULARITIES ON A HYPERSURFACE","authors":"A. Kytmanov","doi":"10.1070/IM1991V037N03ABEH002164","DOIUrl":"https://doi.org/10.1070/IM1991V037N03ABEH002164","url":null,"abstract":"Let be a Stein manifold of dimension , let be a domain which is relatively compact in with connected, and let with . It is shown that any CR-function which is defined on extends holomorphically to . A local version of this assertion is also obtained.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"22 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":"129346982","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/IM1991V036N03ABEH002035
A. Fomenko, Kh Tsishang
A new topological invariant is constructed which classifies integrable Hamiltonian systems with two degrees of freedom (admitting a Bott integral). A criterion for the equivalence of Bott systems is proved: such systems are topologically equivalent if and only if their topological invariants coincide. The topological invariant is effectively calculated for specific integrable Hamiltonian systems in physics and mechanics.
{"title":"A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM","authors":"A. Fomenko, Kh Tsishang","doi":"10.1070/IM1991V036N03ABEH002035","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002035","url":null,"abstract":"A new topological invariant is constructed which classifies integrable Hamiltonian systems with two degrees of freedom (admitting a Bott integral). A criterion for the equivalence of Bott systems is proved: such systems are topologically equivalent if and only if their topological invariants coincide. The topological invariant is effectively calculated for specific integrable Hamiltonian systems in physics and mechanics.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"24 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":"129992773","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/IM1991V036N03ABEH002033
A. Lavrik
Various types of functional equations for Dirichlet series are examined, and their equivalence is shown.
研究了狄利克雷级数的各种类型的泛函方程，并证明了它们的等价性。
{"title":"FUNCTIONAL EQUATIONS WITH PARAMETER OF ZETA-FUNCTIONS","authors":"A. Lavrik","doi":"10.1070/IM1991V036N03ABEH002033","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002033","url":null,"abstract":"Various types of functional equations for Dirichlet series are examined, and their equivalence is shown.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"8 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":"126820152","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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