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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika最新文献

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An estimate for the sum of a Dirichlet series on an arc of bounded slope 有界斜率弧上狄利克特数列之和的估计值
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-02-12 DOI: 10.26907/0021-3446-2024-1-3-13
T. Belous, A. M. Gaisin, R. A. Gaisin
{"title":"An estimate for the sum of a Dirichlet series on an arc of bounded slope","authors":"T. Belous, A. M. Gaisin, R. A. Gaisin","doi":"10.26907/0021-3446-2024-1-3-13","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-1-3-13","url":null,"abstract":"The article considers the behavior of the sum of the Dirichlet series F(s) = sum nanelambda ns, 0 < lambda n uparrow infty , which converges absolutely in the left half-plane Pi 0, on a curve arbitrarily approaching the imaginary axis — the boundary of this half-plane. We have obtained a solution to the following problem: Under what additional conditions on gamma will the strengthened asymptotic relation be valid in the case when the argument s tends to the imaginary axis along gamma over a sufficiently massive set.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"73 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139842049","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}
引用次数: 0
Theorems on direct and inverse approximation by algebraic polynomials and piecewise polynomials in the spaces Hm(a, b) and Bs2,q(a, b) 代数多项式和片断多项式在空间 Hm(a, b) 和 Bs2,q(a, b) 中的直接逼近和反向逼近定理
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-02-12 DOI: 10.26907/0021-3446-2024-1-14-34
R. Dautov
{"title":"Theorems on direct and inverse approximation by algebraic polynomials and piecewise polynomials in the spaces Hm(a, b) and Bs2,q(a, b)","authors":"R. Dautov","doi":"10.26907/0021-3446-2024-1-14-34","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-1-14-34","url":null,"abstract":"The best estimates for the approximation error of functions, defined on a finite interval, by algebraic polynomials and piecewise polynomial functions are obtained in the case when the errors are measured in the norms of Sobolev and Besov spaces. We indicate the weighted Besov spaces, whose functions satisfy Jackson-type and Bernstein-type inequalities and, as a consequence, direct and inverse approximation theorems. In a number of cases, exact constants are indicated in the estimates.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"85 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139783590","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}
引用次数: 0
Symptotic behavior of solutions of the inhomogeneous Schrödinger equation on noncompact Riemannian manifolds 非紧密黎曼流形上不均匀薛定谔方程解的症状行为
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-02-12 DOI: 10.26907/0021-3446-2024-1-35-49
E. Mazepa, D. K. Ryaboshlikova
{"title":"Symptotic behavior of solutions of the inhomogeneous Schrödinger equation on noncompact Riemannian manifolds","authors":"E. Mazepa, D. K. Ryaboshlikova","doi":"10.26907/0021-3446-2024-1-35-49","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-1-35-49","url":null,"abstract":"The paper studies the behavior of bounded solutions of the inhomogeneous Schrödinger equation on non-compact Riemannian manifolds under a variation of the right side of the equation. Various problems for homogeneous elliptic equations, in particular the Laplace-Beltrami equation and the stationary Schrödinger equation, have been considered by a number of Russian and foreign authors since the second half of the 20th century. In the first part of this paper, an approach to the formulation of boundary value problems based on the introduction of classes of equivalent functions will be developed. The relationship between the solvability of boundary value problems on an arbitrary non-compact Riemannian manifold with variation of inhomogeneity is also established. In the second part of the work, based on the results of the first part, properties of solutions of the inhomogeneous Schrödinger equation on quasi-model manifolds are investigated, and exact conditions for unique solvability of the Dirichlet problem and some other boundary value problems on these manifolds are found.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"67 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139784808","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}
引用次数: 0
Theorems on direct and inverse approximation by algebraic polynomials and piecewise polynomials in the spaces Hm(a, b) and Bs2,q(a, b) 代数多项式和片断多项式在空间 Hm(a, b) 和 Bs2,q(a, b) 中的直接逼近和反向逼近定理
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-02-12 DOI: 10.26907/0021-3446-2024-1-14-34
R. Dautov
{"title":"Theorems on direct and inverse approximation by algebraic polynomials and piecewise polynomials in the spaces Hm(a, b) and Bs2,q(a, b)","authors":"R. Dautov","doi":"10.26907/0021-3446-2024-1-14-34","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-1-14-34","url":null,"abstract":"The best estimates for the approximation error of functions, defined on a finite interval, by algebraic polynomials and piecewise polynomial functions are obtained in the case when the errors are measured in the norms of Sobolev and Besov spaces. We indicate the weighted Besov spaces, whose functions satisfy Jackson-type and Bernstein-type inequalities and, as a consequence, direct and inverse approximation theorems. In a number of cases, exact constants are indicated in the estimates.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"64 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139843524","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}
引用次数: 0
On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates 论等距坐标下 Timoshenko 型各向同性浅壳的非线性边界值问题的可解性问题
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-02-12 DOI: 10.26907/0021-3446-2024-1-50-68
S. Timergaliev
{"title":"On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates","authors":"S. Timergaliev","doi":"10.26907/0021-3446-2024-1-50-68","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-1-50-68","url":null,"abstract":"The solvability of a boundary value problem for a system, which describes the equilibrium state of elastic shallow inhomogeneous isotropic shells with loose edges referred to isometric coordinates in the Timoshenko shear model and consists of five non-linear second-order partial differential equations under given non-linear boundary conditions, is studied. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in Sobolev space, the solvability of this equation is established with the help of the contraction mapping principle.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"48 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139845094","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}
引用次数: 0
Main properties of the Faddeev equation for 2 times 2 operator matrices 2 次 2 算子矩阵的法德夫方程的主要性质
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2023-12-24 DOI: 10.26907/0021-3446-2023-12-53-58
T. H. Rasulov, E. Dilmurodov
{"title":"Main properties of the Faddeev equation for 2 times 2 operator matrices","authors":"T. H. Rasulov, E. Dilmurodov","doi":"10.26907/0021-3446-2023-12-53-58","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-53-58","url":null,"abstract":"In the present paper we consider a 2 times 2 operator matrix H. We construct an analog of the well-known Faddeev equation for the eigenvectors of H and study some important properties of this equation, related with the number of eigenvalues. In particular, the Birman–Schwinger principle for H is proven.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"2014 33","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139160105","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}
引用次数: 0
On the problem of optimal interpolation of functions 关于函数的最优插值问题
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2023-12-24 DOI: 10.26907/0021-3446-2023-12-59-70
K. M. Shadimetov, N. H. Mamatova
{"title":"On the problem of optimal interpolation of functions","authors":"K. M. Shadimetov, N. H. Mamatova","doi":"10.26907/0021-3446-2023-12-59-70","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-59-70","url":null,"abstract":"In this work, the problem of constructing optimal interpolation formulas is discussed. Here, first, an exact upper bound for the error of the interpolation formula in the Sobolev space is calculated. The existence and uniqueness of the optimal interpolation formula, which gives the smallest error, are proved. An algorithm for finding the coefficients of the optimal interpolation formula is given. By implementing this algorithm, the optimal coefficients are found.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"2003 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139160241","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}
引用次数: 0
Rings, matrices over which are representable as the sum of two potent matrices 环，其上的矩阵可表示为两个潜在矩阵之和
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2023-12-24 DOI: 10.26907/0021-3446-2023-12-90-94
A. Abyzov, D. Tapkin
{"title":"Rings, matrices over which are representable as the sum of two potent matrices","authors":"A. Abyzov, D. Tapkin","doi":"10.26907/0021-3446-2023-12-90-94","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-90-94","url":null,"abstract":"This paper investigates conditions under which representability of each element a from the field P as the sum a = f + g, with f q1 = f, g q2 = g and q1, q2 are fixed integers >1, implies a similar representability of each square matrix over the field P. We propose a general approach to solving this problem. As an application we describe fields and commutative rings with 2 is a unit, over which each square matrix is the sum of two 4-potent matrices.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"1992 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139160419","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}
引用次数: 0
Equivalence of computed tomography problem with the problem of recovery of functions by finite convolutions in a scheme of computational (numerical) diameter 计算（数值）直径方案中计算断层扫描问题与有限卷积恢复函数问题的等价性
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2023-12-24 DOI: 10.26907/0021-3446-2023-12-95-102
N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliev, Y. Y. Nurmoldin, G. E. Taugynbayeva, A. Zhubanysheva
{"title":"Equivalence of computed tomography problem with the problem of recovery of functions by finite convolutions in a scheme of computational (numerical) diameter","authors":"N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliev, Y. Y. Nurmoldin, G. E. Taugynbayeva, A. Zhubanysheva","doi":"10.26907/0021-3446-2023-12-95-102","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-95-102","url":null,"abstract":"The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how Computer Science, previously established in the theory of Computational (Numerical) diameter, immediately leads to non-trivial results in Computed Tomography.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"323 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139160931","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}
引用次数: 0
A problem in an unbounded domain with combined Tricomi and Frankl conditions on one boundary characteristic for one class of mixed type equations 一类混合型方程的无界域问题，在一个边界特征上具有特里科米和弗兰克尔组合条件
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2023-12-24 DOI: 10.26907/0021-3446-2023-12-39-52
M. Mirsaburov, R. N. Turaev
{"title":"A problem in an unbounded domain with combined Tricomi and Frankl conditions on one boundary characteristic for one class of mixed type equations","authors":"M. Mirsaburov, R. N. Turaev","doi":"10.26907/0021-3446-2023-12-39-52","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-39-52","url":null,"abstract":"In this work, in an unbounded domain, we prove the cof the problem with combined Tricomi and Frankl conditions on one boundary characteristic for one class of equations of mixed type.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"1994 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139160353","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}
引用次数: 0
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