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Bulletin of the Karaganda University-Mathematics最新文献

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Well-posedness criteria for one family of boundary value problems 一族边界值问题的妥善处理标准
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/5-20
P. B. Abdimanapova, S. Temesheva
{"title":"Well-posedness criteria for one family of boundary value problems","authors":"P. B. Abdimanapova, S. Temesheva","doi":"10.31489/2023m4/5-20","DOIUrl":"https://doi.org/10.31489/2023m4/5-20","url":null,"abstract":"This paper considers a family of linear two-point boundary value problems for systems of ordinary differential equations. The questions of existence of its solutions are investigated and methods of finding approximate solutions are proposed. Sufficient conditions for the existence of a family of linear two-point boundary value problems for systems of ordinary differential equations are established. The uniqueness of the solution of the problem under consideration is proved. Algorithms for finding an approximate solution based on modified of the algorithms of the D.S. Dzhumabaev parameterization method are proposed and their convergence is proved. According to the scheme of the parameterization method, the problem is transformed into an equivalent family of multipoint boundary value problems for systems of differential equations. By introducing new unknown functions we reduce the problem under study to an equivalent problem, a Volterra integral equation of the second kind. Sufficient conditions of feasibility and convergence of the proposed algorithm are established, which also ensure the existence of a unique solution of the family of boundary value problems with parameters. Necessary and sufficient conditions for the well-posedness of the family of linear boundary value problems for the system of ordinary differential equations are obtained.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":"75 1‐2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139146122","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
Best approximation by «angle» and the absolute Cesàro summability of double Fourier series 双傅里叶级数的 "角度 "最佳近似和绝对 Cesàro 求和性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/56-65
S. Bitimkhan, O. Mekesh
{"title":"Best approximation by «angle» and the absolute Cesàro summability of double Fourier series","authors":"S. Bitimkhan, O. Mekesh","doi":"10.31489/2023m4/56-65","DOIUrl":"https://doi.org/10.31489/2023m4/56-65","url":null,"abstract":"This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered. In this article, a sufficient condition for the vector index absolute summation method was obtained in terms of the best approximation by «angle» of the functions from Lebesgue space. The theorem that gives a sufficient condition proves the conditions that are sufficient in different cases, which may depend on the parameters. From this proved theorem, a sufficient condition on the term mixed smoothness modulus of the function from Lebesgue space, which is easily obtained by a well-known inequality, is also presented.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":"111 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139146361","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
Representing a second-order Ito equation as an equation with a given force structure 将二阶伊藤方程表示为具有给定力结构的方程
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/119-129
M. Tleubergenov, G. Vassilina, A.A. Abdrakhmanova
{"title":"Representing a second-order Ito equation as an equation with a given force structure","authors":"M. Tleubergenov, G. Vassilina, A.A. Abdrakhmanova","doi":"10.31489/2023m4/119-129","DOIUrl":"https://doi.org/10.31489/2023m4/119-129","url":null,"abstract":"The problem of constructing equivalent equations with a given structure of forces by the given system of stochastic equations is considered. The equivalence of equations in the sense of almost surely is investigated. The paper determines the conditions under which a given system of second-order Ito stochastic differential equations is represented in the form of stochastic Lagrange equations with non-potential forces of a certain structure. Necessary and sufficient conditions for the representability of stochastic equations in the form of stochastic equations with non-potential forces admitting the Rayleigh function are obtained. The obtained results are illustrated by an example of motion of a symmetric satellite in a circular orbit, assuming a change in pitch under the action of gravitational and aerodynamic forces.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 55","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139144515","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
Mixed inverse problem for a Benney–Luke type integro-differential equation with two redefinition functions and parameters 具有两个重新定义函数和参数的本尼-卢克型微分方程的混合逆问题
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/144-162
T. Yuldashev
{"title":"Mixed inverse problem for a Benney–Luke type integro-differential equation with two redefinition functions and parameters","authors":"T. Yuldashev","doi":"10.31489/2023m4/144-162","DOIUrl":"https://doi.org/10.31489/2023m4/144-162","url":null,"abstract":"In this paper, we consider a linear Benney–Luke type partial integro-differential equation of higher order with degenerate kernel and two redefinition functions given at the endpoint of the segment and two parameters. To find these redefinition functions we use two intermediate data. Dirichlet boundary value conditions are used with respect to spatial variable. The Fourier series method of variables separation is applied. The countable system of functional-integral equations is obtained. Theorem on a unique solvability of countable system for functional-integral equations is proved. The method of successive approximations is used in combination with the method of contraction mapping. The triple of solutions of the inverse problem is obtained in the form of Fourier series. Absolutely and uniformly convergences of Fourier series are proved.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139144065","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
Coefficients of multiple Fourier-Haar series and variational modulus of continuity 多重傅立叶-哈尔数列系数和连续性变分模量
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/21-29
T. Akhazhanov, N. Bokayev, D. T. Matin, T. Aktosun
{"title":"Coefficients of multiple Fourier-Haar series and variational modulus of continuity","authors":"T. Akhazhanov, N. Bokayev, D. T. Matin, T. Aktosun","doi":"10.31489/2023m4/21-29","DOIUrl":"https://doi.org/10.31489/2023m4/21-29","url":null,"abstract":"In this paper, we introduce the concept of a variational modulus of continuity for functions of several variables, give an estimate for the sum of the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity, and prove theorems of absolute convergence of series composed of the coefficients of multiple Fourier-Haar series. In this paper, we study the issue of the absolute convergence for multiple series composed of the Fourier-Haar coefficients of functions of several variables of bounded p-variation. We estimate the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity and prove the sufficiency theorem for the condition for the absolute convergence of series composed of the Fourier-Haar coefficients of the considered function class. This paper researches the question: under what conditions, imposed on the variational modulus of continuity of the fractional order of several variables functions, there is the absolute convergence for series composed of the coefficients of multiple Fourier-Haar series.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 47","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139144278","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
Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions 有记忆的开尔文-伏依格方程：解的存在性、唯一性和正则性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/66-78
Kh. Khompysh, N. K. Nugymanova
{"title":"Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions","authors":"Kh. Khompysh, N. K. Nugymanova","doi":"10.31489/2023m4/66-78","DOIUrl":"https://doi.org/10.31489/2023m4/66-78","url":null,"abstract":"In general, the study of inverse problems is realizable only in the case when the corresponding direct problems have the unique solution with some necessary properties such as continuity and regularity. In this paper, we study initial-boundary value problems for the system of 2D-3D nonlinear Kelvin-Voigt equations with memory, which describes a motion of an incompressible homogeneous non-Newtonian fluids with viscoelastic and relaxation properties. The investigation of these direct problems is related to the study of inverse problems for this system, which requires the continuity and regularity of solutions to these direct problems and their derivatives. The system, in addition to the initial condition, is supplemented with one of the boundary conditions: stick and slip boundary conditions. In both cases of these boundary conditions, the global in time existence and uniqueness of strong solutions to these initial-boundary value problems were proved. Moreover, under suitable assumptions on the data, the regularity of solutions and their derivatives were established.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":"100 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139146897","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
Boundary value problems with displacement for one mixed hyperbolic equation of the second order 一个二阶混合双曲方程的带位移的边界值问题
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/41-55
Zh.A. Balkizov
{"title":"Boundary value problems with displacement for one mixed hyperbolic equation of the second order","authors":"Zh.A. Balkizov","doi":"10.31489/2023m4/41-55","DOIUrl":"https://doi.org/10.31489/2023m4/41-55","url":null,"abstract":"The paper studies two nonlocal problems with a displacement for the conjugation of two equations of second-order hyperbolic type, with a wave equation in one part of the domain and a degenerate hyperbolic equation of the first kind in the other part. As a non-local boundary condition in the considered problems, a linear system of FDEs is specified with variable coefficients involving the first-order derivative and derivatives of fractional (in the sense of Riemann-Liouville) orders of the desired function on one of the characteristics and on the line of type changing. Using the integral equation method, the first problem is equivalently reduced to a question of the solvability for the Volterra integral equation of the second kind with a weak singularity; and a question of the solvability for the second problem is equivalently reduced to a question of the solvability for the Fredholm integral equation of the second kind with a weak singularity. For the first problem, we prove the uniform convergence of the resolvent kernel for the resulting Volterra integral equation of the second kind and we prove that its solution belongs to the required class. As to the second problem, sufficient conditions are found for the given functions that ensure the existence of a unique solution to the Fredholm integral equation of the second kind with a weak singularity of the required class. In some particular cases, the solutions are written out explicitly.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 107","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139144950","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
Similarities of Jonsson spectra’s classes 琼森光谱类别的相似性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/130-143
A. Yeshkeyev, O. I. Ulbrikht, G. Urken
{"title":"Similarities of Jonsson spectra’s classes","authors":"A. Yeshkeyev, O. I. Ulbrikht, G. Urken","doi":"10.31489/2023m4/130-143","DOIUrl":"https://doi.org/10.31489/2023m4/130-143","url":null,"abstract":"The study of syntactic and semantic properties of a first-order language, generally speaking, for incomplete theories, is one of the urgent problems of mathematical logic. In this article we study Jonsson theories, which are satisfied by most classical examples from algebra and which, generally speaking, are not complete. A new and relevant method for studying Jonson theories is to study these theories using the concepts of syntactic and semantic similarities. The most invariant concept is the concept of syntactic similarity of theories, because it preserves all the properties of the theories under consideration. The main result of this article is the fact that any perfect Jonson theory which are complete for existential sentences, is syntactically similar to some polygon theory (S-polygon, where S is a monoid). This result extends to the corresponding classes of Jonsson theories from the Jonsson spectrum of an arbitrary model of an arbitrary signature.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":"20 9","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139145328","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
Model-theoretic properties of semantic pairs and e.f.c.p. in Jonsson spectrum 琼森频谱中语义对的模型理论属性和 e.f.c.p.
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/185-193
G. E. Zhumabekova
{"title":"Model-theoretic properties of semantic pairs and e.f.c.p. in Jonsson spectrum","authors":"G. E. Zhumabekova","doi":"10.31489/2023m4/185-193","DOIUrl":"https://doi.org/10.31489/2023m4/185-193","url":null,"abstract":"The article is committed to the study of model-theoretic properties of stable hereditary Jonsson theories, wherein we consider Jonsson theories that retain jonssonnes for any permissible enrichment. The paper proves a generalization of stability that relates stability and classical stability for Jonsson spectrum. This paper introduces new concepts such as “existentially finite cover property” and “semantic pair”. The basic properties of e.f.c.p and semantic pairs in the class of stable perfect Jonsson spectrum are studied.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":"219 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139145344","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 study on new classes of binary soft sets in topological rough approximation space 拓扑粗糙近似空间中的二元软集新类别研究
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/79-94
C. Parvathy, A. Sofia
{"title":"A study on new classes of binary soft sets in topological rough approximation space","authors":"C. Parvathy, A. Sofia","doi":"10.31489/2023m4/79-94","DOIUrl":"https://doi.org/10.31489/2023m4/79-94","url":null,"abstract":"Soft binary relation is used to define new classes of soft sets, namely BR-soft simply open set and BR-soft simply* alpha open set, in topological rough approximation space over two different universes. The defined set provides information on the missing elements of a BR-soft set and can help in simplifying decision making. Approximation operators are defined and the characteristics of the proposed sets are studied with examples. The relationship between the defined sets and other soft sets is brought out. An accuracy check was done to compare the proposed method with other methods. It is identified that the proposed method is more accurate.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 25","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139142391","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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