Pub Date : 1992-04-30DOI: 10.1070/IM1992V039N02ABEH002235
Y. Korobeinik
The general form of series in exponentials that converge absolutely to zero in complete, Hausdorff, locally convex function spaces is described. The results are applied to the description of kernels of (scalar and matrix) convolution operators and to solving the factorization problem for convolution operators.
{"title":"DESCRIPTION OF THE GENERAL FORM OF NONTRIVIAL EXPANSIONS OF ZERO IN EXPONENTIALS. APPLICATIONS","authors":"Y. Korobeinik","doi":"10.1070/IM1992V039N02ABEH002235","DOIUrl":"https://doi.org/10.1070/IM1992V039N02ABEH002235","url":null,"abstract":"The general form of series in exponentials that converge absolutely to zero in complete, Hausdorff, locally convex function spaces is described. The results are applied to the description of kernels of (scalar and matrix) convolution operators and to solving the factorization problem for convolution operators.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125922417","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 : 1992-04-30DOI: 10.1070/IM1992V038N02ABEH002206
P. Katsylo
The fields of rational functions on the moduli varieties of stable (symplectic) vector bundles over the projective plane are described. As a consequence the rationality of some series of moduli varieties is proved.
描述了在射影平面上稳定(辛)向量束的模变上有理函数的域。从而证明了若干模变级数的合理性。
{"title":"BIRATIONAL GEOMETRY OF MODULI VARIETIES OF VECTOR BUNDLES OVER $ mathbf P^2$","authors":"P. Katsylo","doi":"10.1070/IM1992V038N02ABEH002206","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002206","url":null,"abstract":"The fields of rational functions on the moduli varieties of stable (symplectic) vector bundles over the projective plane are described. As a consequence the rationality of some series of moduli varieties is proved.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126750951","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 : 1992-04-30DOI: 10.1070/IM1992V038N02ABEH002203
I. Taimanov
A proof is given for the theorem of Novikov and the author on the existence of a closed nonselfintersecting extremal for a single-valued functional corresponding to the motion of a charged particle in a strong magnetic field on a Riemannian manifold homeomorphic to the 2-sphere, and an analogue in the case of multivalued functionals is also proved.
{"title":"NONSELFINTERSECTING CLOSED EXTREMALS OF MULTIVALUED OR NOT EVERYWHERE POSITIVE FUNCTIONALS","authors":"I. Taimanov","doi":"10.1070/IM1992V038N02ABEH002203","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002203","url":null,"abstract":"A proof is given for the theorem of Novikov and the author on the existence of a closed nonselfintersecting extremal for a single-valued functional corresponding to the motion of a charged particle in a strong magnetic field on a Riemannian manifold homeomorphic to the 2-sphere, and an analogue in the case of multivalued functionals is also proved.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1709 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129426398","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 : 1992-04-30DOI: 10.1070/IM1992V038N02ABEH002199
V. A. Krasnov
For a nonsingular -dimensional real projective algebraic variety the set of its real points is the union of connected components . Those components give rise to homology classes . In this paper a bound on the number of relations between those homology classes is obtained.
{"title":"ON HOMOLOGY CLASSES DETERMINED BY REAL POINTS OF A REAL ALGEBRAIC VARIETY","authors":"V. A. Krasnov","doi":"10.1070/IM1992V038N02ABEH002199","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002199","url":null,"abstract":"For a nonsingular -dimensional real projective algebraic variety the set of its real points is the union of connected components . Those components give rise to homology classes . In this paper a bound on the number of relations between those homology classes is obtained.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"33 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114105853","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 : 1992-04-30DOI: 10.1070/IM1992V038N02ABEH002202
P. Plotnikov
The problem of solitary waves on the surface of an ideal fluid is considered. By means of a variational principle it is shown that for an infinite set of values of the Froude number this problem has at least two geometrically distinct solutions. Sufficient conditions are formulated for the existence of bifurcations of degenerate critical points of one-parameter families of smooth functionals defined in a normed space.
{"title":"NONUNIQUENESS OF SOLUTIONS OF THE PROBLEM OF SOLITARY WAVES AND BIFURCATION OF CRITICAL POINTS OF SMOOTH FUNCTIONALS","authors":"P. Plotnikov","doi":"10.1070/IM1992V038N02ABEH002202","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002202","url":null,"abstract":"The problem of solitary waves on the surface of an ideal fluid is considered. By means of a variational principle it is shown that for an infinite set of values of the Froude number this problem has at least two geometrically distinct solutions. Sufficient conditions are formulated for the existence of bifurcations of degenerate critical points of one-parameter families of smooth functionals defined in a normed space.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121017954","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 : 1992-04-30DOI: 10.1070/IM1992V038N02ABEH002204
V. Khomich
This paper introduces a new method of representing pseudo-Boolean algebras by implication structures of a special type or by partially ordered sets. This is used to construct four sequences of pseudo-Boolean algebras. Their properties and the properties of the logics prescribed by the sequences are studied. The connection between these logics and the logic consisting of the realizable propositional formulas is established, and a problem posed by Hosoi and Ono is solved.
{"title":"ON SUPERINTUITIONISTIC PROPOSITIONAL LOGICS CONNECTED WITH PARTIALLY ORDERED SETS","authors":"V. Khomich","doi":"10.1070/IM1992V038N02ABEH002204","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002204","url":null,"abstract":"This paper introduces a new method of representing pseudo-Boolean algebras by implication structures of a special type or by partially ordered sets. This is used to construct four sequences of pseudo-Boolean algebras. Their properties and the properties of the logics prescribed by the sequences are studied. The connection between these logics and the logic consisting of the realizable propositional formulas is established, and a problem posed by Hosoi and Ono is solved.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121671523","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 : 1992-04-30DOI: 10.1070/IM1992V039N02ABEH002236
A. Soldatov
A general (not necessarily local) boundary value problem is considered for an elliptic system on the plane of th order containing only leading terms with constant coefficients. By a method of function theory developed for elliptic systems of first order with a constant triangular matrix , ; this problem is reduced to an equivalent system of integrofunctional equations on the boundary. In particular, a criterion that the problem be Noetherian and a formula for its index are obtained in this way. All considerations are carried out in the smooth case when the boundary of the domain has no corner points, while the boundary operators act in spaces of continuous functions.
{"title":"A FUNCTION THEORY METHOD IN BOUNDARY VALUE PROBLEMS IN THE PLANE. I: THE SMOOTH CASE","authors":"A. Soldatov","doi":"10.1070/IM1992V039N02ABEH002236","DOIUrl":"https://doi.org/10.1070/IM1992V039N02ABEH002236","url":null,"abstract":"A general (not necessarily local) boundary value problem is considered for an elliptic system on the plane of th order containing only leading terms with constant coefficients. By a method of function theory developed for elliptic systems of first order with a constant triangular matrix , ; this problem is reduced to an equivalent system of integrofunctional equations on the boundary. In particular, a criterion that the problem be Noetherian and a formula for its index are obtained in this way. All considerations are carried out in the smooth case when the boundary of the domain has no corner points, while the boundary operators act in spaces of continuous functions.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121072623","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 : 1992-04-30DOI: 10.1070/IM1992V038N02ABEH002198
V. A. Iskovskikh, S. Tregub
Generators and relations of the groups of birational automorphisms are described for six classes of (-minimal) rational surfaces. For surfaces with , and , , relations between the already known generators are described, and for surfaces with , , and , , generators and relations are described.
{"title":"ON BIRATIONAL AUTOMORPHISMS OF RATIONAL SURFACES","authors":"V. A. Iskovskikh, S. Tregub","doi":"10.1070/IM1992V038N02ABEH002198","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002198","url":null,"abstract":"Generators and relations of the groups of birational automorphisms are described for six classes of (-minimal) rational surfaces. For surfaces with , and , , relations between the already known generators are described, and for surfaces with , , and , , generators and relations are described.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132357596","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 : 1992-04-30DOI: 10.1070/IM1992V039N02ABEH002237
B. Khabibullin
A general approach is proposed for the description of sets of uniqueness in spaces of entire functions.
给出了描述整个函数空间中唯一性集的一般方法。
{"title":"SETS OF UNIQUENESS IN SPACES OF ENTIRE FUNCTIONS OF A SINGLE VARIABLE","authors":"B. Khabibullin","doi":"10.1070/IM1992V039N02ABEH002237","DOIUrl":"https://doi.org/10.1070/IM1992V039N02ABEH002237","url":null,"abstract":"A general approach is proposed for the description of sets of uniqueness in spaces of entire functions.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122402345","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 : 1992-04-30DOI: 10.1070/IM1992V038N02ABEH002205
V. Kulikov
Let be a complex algebraic hypersurface in not passing through the point . The generators of the fundamental group and the relations among them are described in terms of the real cone over with apex at . This description is a generalization to the algebraic case of Wirtinger's corepresentation of the fundamental group of a knot in . A new proof of Zariski's conjecture about commutativity of the fundamental group for a projective nodal curve is given in the second part of the paper based on the description of the generators and the relations in the group obtained in the first part.
{"title":"THE FUNDAMENTAL GROUP OF THE COMPLEMENT OF A HYPERSURFACE IN $ mathbf C^n$","authors":"V. Kulikov","doi":"10.1070/IM1992V038N02ABEH002205","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002205","url":null,"abstract":"Let be a complex algebraic hypersurface in not passing through the point . The generators of the fundamental group and the relations among them are described in terms of the real cone over with apex at . This description is a generalization to the algebraic case of Wirtinger's corepresentation of the fundamental group of a knot in . A new proof of Zariski's conjecture about commutativity of the fundamental group for a projective nodal curve is given in the second part of the paper based on the description of the generators and the relations in the group obtained in the first part.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115231051","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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