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/IM1992V038N02ABEH002207
Yu. P. Krasovskii
A solution of a parabolic equation without an initial condition is determined in terms of the right side in a semi-infinite cylinder. It is assumed that the coefficients of the equation do not depend on time. An estimate of the solution is given in terms of the right side of the equation, which estimate contains a weighted exponential function of time.
{"title":"AN ESTIMATE OF SOLUTIONS OF PARABOLIC PROBLEMS WITHOUT AN INITIAL CONDITION","authors":"Yu. P. Krasovskii","doi":"10.1070/IM1992V038N02ABEH002207","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002207","url":null,"abstract":"A solution of a parabolic equation without an initial condition is determined in terms of the right side in a semi-infinite cylinder. It is assumed that the coefficients of the equation do not depend on time. An estimate of the solution is given in terms of the right side of the equation, which estimate contains a weighted exponential function of time.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"12 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":"134144587","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/IM1992V038N02ABEH002200
A. A. Makhnëv
The following reduction theorem for TI-subgroups is obtained: if a 2-group A is a TI-subgroup of a finite group, then either A is an elementary or cyclic group, or the normal closure of A is a well-known group.
{"title":"A REDUCTION THEOREM FOR TI-SUBGROUPS","authors":"A. A. Makhnëv","doi":"10.1070/IM1992V038N02ABEH002200","DOIUrl":"https://doi.org/10.1070/IM1992V038N02ABEH002200","url":null,"abstract":"The following reduction theorem for TI-subgroups is obtained: if a 2-group A is a TI-subgroup of a finite group, then either A is an elementary or cyclic group, or the normal closure of A is a well-known group.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"40 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":"131689185","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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