Pub Date : 1992-06-30DOI: 10.1070/IM1992V039N03ABEH002243
N. M. Timofeev
This paper is concerned with the behavior of multiplicative functions on the set , where is a prime and is a nonzero integer. Several results are obtained in which either the average value of a multiplicative function on this set is estimated or its asymptotic behavior is determined. As one application a nontrivial estimate of is found, where , is a sufficiently large prime, and is a character of degree greater than 4.
{"title":"MULTIPLICATIVE FUNCTIONS ON THE SET OF SHIFTED PRIME NUMBERS","authors":"N. M. Timofeev","doi":"10.1070/IM1992V039N03ABEH002243","DOIUrl":"https://doi.org/10.1070/IM1992V039N03ABEH002243","url":null,"abstract":"This paper is concerned with the behavior of multiplicative functions on the set , where is a prime and is a nonzero integer. Several results are obtained in which either the average value of a multiplicative function on this set is estimated or its asymptotic behavior is determined. As one application a nontrivial estimate of is found, where , is a sufficiently large prime, and is a character of degree greater than 4.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"23 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":"132629718","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/IM1992V039N03ABEH002240
M. I. D’yachenko
The author discusses classes of periodic functions of variables that are either piecewise monotonic or piecewise monotonic in the sense of Hardy, and clarifies the connections, for such functions, between the property of belonging to space, , and the convergence of series of their trigonometric Fourier coefficients, We establish the existence, when 1$ SRC=http://ej.iop.org/images/0025-5726/39/3/A02/tex_im_2240_img5.gif/>, of certain results that differ from the one-dimensional case.
{"title":"PIECEWISE MONOTONIC FUNCTIONS OF SEVERAL VARIABLES AND A THEOREM OF HARDY AND LITTLEWOOD","authors":"M. I. D’yachenko","doi":"10.1070/IM1992V039N03ABEH002240","DOIUrl":"https://doi.org/10.1070/IM1992V039N03ABEH002240","url":null,"abstract":"The author discusses classes of periodic functions of variables that are either piecewise monotonic or piecewise monotonic in the sense of Hardy, and clarifies the connections, for such functions, between the property of belonging to space, , and the convergence of series of their trigonometric Fourier coefficients, We establish the existence, when 1$ SRC=http://ej.iop.org/images/0025-5726/39/3/A02/tex_im_2240_img5.gif/>, of certain results that differ from the one-dimensional case.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"27 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132653406","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 : 1992-06-01DOI: 10.1070/IM1992V038N03ABEH002214
E. S. Sinaiskii
The author investigates an algorithm for the construction of a polynomial that realizes the simultaneous approximation of the solution of a boundary value problem and its derivatives with the same rapidity of decrease of the error as for the case of the best uniform polynomial approximation of the function on an interval.
{"title":"SIMULTANEOUS APPROXIMATION OF THE SOLUTION AND ITS DERIVATIVES IN A BOUNDARY VALUE PROBLEM FOR A LINEAR DIFFERENTIAL EQUATION WITH POLYNOMIAL COEFFICIENTS","authors":"E. S. Sinaiskii","doi":"10.1070/IM1992V038N03ABEH002214","DOIUrl":"https://doi.org/10.1070/IM1992V038N03ABEH002214","url":null,"abstract":"The author investigates an algorithm for the construction of a polynomial that realizes the simultaneous approximation of the solution of a boundary value problem and its derivatives with the same rapidity of decrease of the error as for the case of the best uniform polynomial approximation of the function on an interval.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128192279","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/IM1992V038N02ABEH002208
M. Zaidenberg
{"title":"ADDITIONS AND CORRECTIONS TO THE PAPER “ISOTRIVIAL FAMILIES OF CURVES ON AFFINE SURFACES AND CHARACTERIZATION OF THE AFFINE PLANE”","authors":"M. Zaidenberg","doi":"10.1070/IM1992V038N02ABEH002208","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002208","url":null,"abstract":"","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"5 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":"127958507","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/IM1992V039N02ABEH002232
S. I. Adyan, I. G. Lysënok
For any odd number n≥1003, the authors construct an infinite 2-generator group each of whose proper subgroups is contained in a cyclic subgroup of order n. This result strengthens analogous results of Ol'shanskiĭ for prime n>1075 and Atabekyan and Ivanov for odd n>1080. The proof is carried out in the original language of Novikov-Adyan theory. Bibliography: 6 titles.
{"title":"ON GROUPS ALL OF WHOSE PROPER SUBGROUPS ARE FINITE CYCLIC","authors":"S. I. Adyan, I. G. Lysënok","doi":"10.1070/IM1992V039N02ABEH002232","DOIUrl":"https://doi.org/10.1070/IM1992V039N02ABEH002232","url":null,"abstract":"For any odd number n≥1003, the authors construct an infinite 2-generator group each of whose proper subgroups is contained in a cyclic subgroup of order n. This result strengthens analogous results of Ol'shanskiĭ for prime n>1075 and Atabekyan and Ivanov for odd n>1080. The proof is carried out in the original language of Novikov-Adyan theory. Bibliography: 6 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"172 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":"115231618","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/IM1992V039N02ABEH002233
O. Bogoyavlenskii
Systems of differential equations, admitting the Lax representation and extending the systems of hydrodynamic type, connected with the Volterra model and Toda lattice, are presented. A construction of differential operator equations with derivatives of arbitrary order with respect to the variables t and y and possessing a reduction preserving the eigenvalues of the corresponding operator L is suggested. Dynamical systems having a Lax representation and generalizing the Toda lattice are constructed. A construction of integrable Euler equations admitting a Lax representation with n independent spectral parameters and connected with n Riemann surfaces is found.
{"title":"BREAKING SOLITONS. VI. EXTENSION OF SYSTEMS OF HYDRODYNAMIC TYPE","authors":"O. Bogoyavlenskii","doi":"10.1070/IM1992V039N02ABEH002233","DOIUrl":"https://doi.org/10.1070/IM1992V039N02ABEH002233","url":null,"abstract":"Systems of differential equations, admitting the Lax representation and extending the systems of hydrodynamic type, connected with the Volterra model and Toda lattice, are presented. A construction of differential operator equations with derivatives of arbitrary order with respect to the variables t and y and possessing a reduction preserving the eigenvalues of the corresponding operator L is suggested. Dynamical systems having a Lax representation and generalizing the Toda lattice are constructed. A construction of integrable Euler equations admitting a Lax representation with n independent spectral parameters and connected with n Riemann surfaces is found.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"16 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":"124108875","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/IM1992V039N02ABEH002234
A. G. Zavadskii
A complete classification of the indecomposable representations of partially ordered sets of finite growth is given.
给出了有限增长的部分有序集的不可分解表示的完全分类。
{"title":"DIFFERENTIATION ALGORITHM AND CLASSIFICATION OF REPRESENTATIONS","authors":"A. G. Zavadskii","doi":"10.1070/IM1992V039N02ABEH002234","DOIUrl":"https://doi.org/10.1070/IM1992V039N02ABEH002234","url":null,"abstract":"A complete classification of the indecomposable representations of partially ordered sets of finite growth is given.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"72 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":"126167480","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/IM1992V038N02ABEH002201
V. Pidstrigach
A solution is given for the problem of determining smoothness invariants on an algebraic surface from a nonsmooth compact moduli space of instantons. For this a study is made of the deformation of the instanton surface. The results are used to distinguish smoothness on certain algebraic surfaces.
{"title":"DEFORMATIONS OF INSTANTON SURFACES","authors":"V. Pidstrigach","doi":"10.1070/IM1992V038N02ABEH002201","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002201","url":null,"abstract":"A solution is given for the problem of determining smoothness invariants on an algebraic surface from a nonsmooth compact moduli space of instantons. For this a study is made of the deformation of the instanton surface. The results are used to distinguish smoothness on certain algebraic surfaces.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"71 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":"128670434","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/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}
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