Pub Date : 2024-02-12DOI: 10.26907/0021-3446-2024-1-3-13
T. Belous, A. M. Gaisin, R. A. Gaisin
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.
文章考虑了迪里希勒数列 F(s) = sum nanelambda ns, 0 < lambda n uparrow infty 的和的行为，它在左半平面 Pi 0 中绝对收敛于任意接近虚轴--这个半平面的边界--的曲线上。我们得到了下面问题的一个解：当参数 s 在一个足够大的集合上沿着 gamma 趋向于虚轴时，在 gamma 的哪些附加条件下，加强的渐近关系将有效。
{"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}
Pub Date : 2024-02-12DOI: 10.26907/0021-3446-2024-1-14-34
R. Dautov
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.
{"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}
Pub Date : 2024-02-12DOI: 10.26907/0021-3446-2024-1-35-49
E. Mazepa, D. K. Ryaboshlikova
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.
{"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}
Pub Date : 2024-02-12DOI: 10.26907/0021-3446-2024-1-14-34
R. Dautov
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.
{"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}
Pub Date : 2024-02-12DOI: 10.26907/0021-3446-2024-1-50-68
S. Timergaliev
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.
{"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}
Pub Date : 2023-12-24DOI: 10.26907/0021-3446-2023-12-53-58
T. H. Rasulov, E. Dilmurodov
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.
在本文中，我们考虑一个 2 次 2 的算子矩阵 H。我们为 H 的特征向量构建了一个著名的 Faddeev 方程，并研究了该方程与特征值数量相关的一些重要性质。特别是，我们证明了 H 的比尔曼-施温格原理。
{"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}
Pub Date : 2023-12-24DOI: 10.26907/0021-3446-2023-12-59-70
K. M. Shadimetov, N. H. Mamatova
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.
{"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}
Pub Date : 2023-12-24DOI: 10.26907/0021-3446-2023-12-90-94
A. Abyzov, D. Tapkin
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.
本文研究了在哪些条件下，场 P 中的每个元素 a 都可以表示为和 a = f + g（f q1 = f，g q2 = g，q1、q2 为大于 1 的固定整数），这意味着场 P 上的每个平方矩阵都具有类似的可表示性。作为应用，我们描述了以 2 为单位的场和交换环，在这些场和交换环上，每个平方矩阵都是两个 4 实矩阵之和。
{"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}
Pub Date : 2023-12-24DOI: 10.26907/0021-3446-2023-12-95-102
N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliev, Y. Y. Nurmoldin, G. E. Taugynbayeva, A. Zhubanysheva
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.
{"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}
Pub Date : 2023-12-24DOI: 10.26907/0021-3446-2023-12-39-52
M. Mirsaburov, R. N. Turaev
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.
{"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}
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