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Bulletin of the Karaganda University-Mathematics最新文献

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Well-posedness of the initial-boundary value problems for the time-fractional degenerate diffusion equations 时间分数退化扩散方程初边值问题的适定性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/145-151
A. Smadiyeva
{"title":"Well-posedness of the initial-boundary value problems for the time-fractional degenerate diffusion equations","authors":"A. Smadiyeva","doi":"10.31489/2022m3/145-151","DOIUrl":"https://doi.org/10.31489/2022m3/145-151","url":null,"abstract":"This paper deals with the solving of initial-boundary value problems for the one-dimensional linear timefractional diffusion equations with time-degenerate diffusive coefficients t^β with β > 1 − α. The solutions to initial-boundary value problems for the one-dimensional time-fractional degenerate diffusion equations with Riemann-Liouville fractional integral I^1−α_0+,t of order α ∈ (0, 1) and with Riemann-Liouville fractional derivative D^α_0+,t of order α ∈ (0, 1) in the variable, are shown. The solutions to these fractional diffusive equations are presented using the Kilbas-Saigo function Eα,m,l(z). The solution to the problems is discovered by the method of separation of variables, through finding two problems with one variable. Rather, through finding a solution to the fractional problem depending on the parameter t, with the Dirichlet or Neumann boundary conditions. The solution to the Sturm-Liouville problem depends on the variable x with the initial fractional-integral Riemann-Liouville condition. The existence and uniqueness of the solution to the problem are confirmed. The convergence of the solution was evidenced using the estimate for the KilbasSaigo function E_α,m,l(z) from and by Parseval’s identity.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46650934","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: 3
New exact solutions of space-time fractional Schr¨odinger-Hirota equation 时空分数Schr¨odinger-Hirota方程的新精确解
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/17-24
V. Ala
{"title":"New exact solutions of space-time fractional Schr¨odinger-Hirota equation","authors":"V. Ala","doi":"10.31489/2022m3/17-24","DOIUrl":"https://doi.org/10.31489/2022m3/17-24","url":null,"abstract":"In this study, improved Bernoulli sub-equation function method (IBSEFM) is presented to construct the exact solutions of the nonlinear conformable fractional Schr¨odinger-Hirota equation (FSHE). By using the traveling wave transformation FSHE turns into the ordinary differential equation (ODE) and by the aid of symbolic calculation software, new exact solutions are obtained. 2D, 3D figures and contour surfaces acquired from the values of the solutions are plotted. The results show that the proposed method is powerful, effective and straightforward for formulating new solutions to various types of nonlinear fractional partial differential equations in applied sciences.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44734649","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 different look at the soft topological polygroups 软拓扑多群的另一种看法
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/85-97
R. Mousarezaei, B. Davvaz
{"title":"A different look at the soft topological polygroups","authors":"R. Mousarezaei, B. Davvaz","doi":"10.31489/2022m3/85-97","DOIUrl":"https://doi.org/10.31489/2022m3/85-97","url":null,"abstract":"Soft topological polygroups are defined in two different ways. First, it is defined as a usual topology. In the usual topology, there are five equivalent definitions for continuity, but not all of them are necessarily established in soft continuity. Second it is defined as a soft topology including concepts such as soft neighborhood, soft continuity, soft compact, soft connected, soft Hausdorff space and their relationship with soft continuous functions in soft topological polygroups.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41959073","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
Stability of the time-dependent identification problem for delay hyperbolic equations 时滞双曲型方程时变辨识问题的稳定性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/25-34
A. Ashyralyev, B. Haso
{"title":"Stability of the time-dependent identification problem for delay hyperbolic equations","authors":"A. Ashyralyev, B. Haso","doi":"10.31489/2022m3/25-34","DOIUrl":"https://doi.org/10.31489/2022m3/25-34","url":null,"abstract":"Time-dependent and space-dependent source identification problems for partial differential and difference equations take an important place in applied sciences and engineering, and have been studied by several authors. Moreover, the delay appears in complicated systems with logical and computing devices, where certain time for information processing is needed. In the present paper, the time-dependent identification problem for delay hyperbolic equation is investigated. The theorems on the stability estimates for the solution of the time-dependent identification problem for the one dimensional delay hyperbolic differential equation are established. The proofs of these theorems are based on the Dalambert’s formula for the hyperbolic differential equation and integral inequality.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49538431","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
Some Convergent Summation Theorems For Appell’s Function F1 Having Arguments −1, 1/2 具有- 1,1 /2参数的Appell函数F1的收敛求和定理
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/116-123
M. I. Qureshi, M. Baboo, A. Ahmad
{"title":"Some Convergent Summation Theorems For Appell’s Function F1 Having Arguments −1, 1/2","authors":"M. I. Qureshi, M. Baboo, A. Ahmad","doi":"10.31489/2022m3/116-123","DOIUrl":"https://doi.org/10.31489/2022m3/116-123","url":null,"abstract":"In this paper, we obtain some closed forms of hypergeometric summation theorems for Appell’s function of first kind F1 having the arguments −1, 1/2 with suitable convergence conditions, by adjustment of parameters and arguments in generalized form of first, second and third summation theorems of K¨ummer and others.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43070021","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
Existence and smoothness of solutions of a singular differential equation of hyperbolic type 一类双曲型奇异微分方程解的存在性与光滑性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/98-104
M. Muratbekov, Yerik Bayandiyev
{"title":"Existence and smoothness of solutions of a singular differential equation of hyperbolic type","authors":"M. Muratbekov, Yerik Bayandiyev","doi":"10.31489/2022m3/98-104","DOIUrl":"https://doi.org/10.31489/2022m3/98-104","url":null,"abstract":"This paper investigates the question of the existence of solutions to the semiperiodic Dirichlet problem for a class of singular differential equations of hyperbolic type. The problem of smoothness of solutions is also considered, i.e., maximum regularity of solutions. Such a problem will be interesting when the coefficients are strongly growing functions at infinity. For the first time, a weighted coercive estimate was obtained for solutions to a differential equation of hyperbolic type with strongly growing coefficients.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43396388","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 recognizing groups by the bottom layer 论底层群体识别
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/124-131
V. Senashov, I. A. Paraschuk
{"title":"On recognizing groups by the bottom layer","authors":"V. Senashov, I. A. Paraschuk","doi":"10.31489/2022m3/124-131","DOIUrl":"https://doi.org/10.31489/2022m3/124-131","url":null,"abstract":"The article discusses the possibility of recognizing a group by the bottom layer, that is, by the set of its elements of prime orders. The paper gives examples of groups recognizable by the bottom layer, almost recognizable by the bottom layer, and unrecognizable by the bottom layer. Results are obtained for recognizing a group by the bottom layer in the class of infinite groups under some additional restrictions. The notion of recognizability of a group by the bottom layer was introduced by analogy with the recognizability of a group by its spectrum (the set of orders of its elements). It is proved that all finite simple nonAbelian groups are recognizable by spectrum and bottom layer simultaneously in the class of finite simple non-Abelian groups.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46032811","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 priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations 退化热方程不连续系数的Sobolev类Cauchy问题解的先验估计
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/59-69
U.K. Koilyshov, K. Beisenbaeva, S.D. Zhapparova
{"title":"A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations","authors":"U.K. Koilyshov, K. Beisenbaeva, S.D. Zhapparova","doi":"10.31489/2022m3/59-69","DOIUrl":"https://doi.org/10.31489/2022m3/59-69","url":null,"abstract":"Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors. Conjugation problems for time-degenerate equations of the parabolic type with discontinuous coefficients are practically not studied. In this work, in an n-dimensional space, a conjugation problem is considered for a heat equation with discontinuous coefficients which degenerates at the initial moment of time. A fundamental solution to the set problem has been constructed and estimates of its derivatives have been found. With the help of these estimates, in the Sobolev classes, the estimate of the solution to the set problem was obtained.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46214814","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 nonlocal problems in time for subdiffusion equations with the Riemann-Liouville derivatives 关于具有Riemann-Liouville导数的次扩散方程的非局部时间问题
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-06-30 DOI: 10.31489/2022m2/18-37
R. Ashurov, Y. Fayziev
{"title":"On the nonlocal problems in time for subdiffusion equations with the Riemann-Liouville derivatives","authors":"R. Ashurov, Y. Fayziev","doi":"10.31489/2022m2/18-37","DOIUrl":"https://doi.org/10.31489/2022m2/18-37","url":null,"abstract":"Initial boundary value problems with a time-nonlocal condition for a subdiffusion equation with the Riemann-Liouville time-fractional derivatives are considered. The elliptical part of the equation is the Laplace operator, defined in an arbitrary N−dimensional domain Ω with a sufficiently smooth boundary ∂Ω. The existence and uniqueness of the solution to the considered problems are proved. Inverse problems are studied for determining the right-hand side of the equation and a function in a time-nonlocal condition. The main research tool is the Fourier method, so the obtained results can be extended to subdiffusion equations with a more general elliptic operator.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42105254","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: 4
Existentially positive Mustafin theories of S-acts over a group 群上s行为的存在正性Mustafin理论
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-06-30 DOI: 10.31489/2022m2/172-185
A. Yeshkeyev, O. I. Ulbrikht, A. R. Yarullina
{"title":"Existentially positive Mustafin theories of S-acts over a group","authors":"A. Yeshkeyev, O. I. Ulbrikht, A. R. Yarullina","doi":"10.31489/2022m2/172-185","DOIUrl":"https://doi.org/10.31489/2022m2/172-185","url":null,"abstract":"The paper is connected with the study of Jonsson spectrum notion of the fixed class of models of Sacts signature, assuming a group as a monoid of S-acts. The Jonsson spectrum notion is effective when describing theoretical-model properties of algebras classes whose theories admit joint embedding and amalgam properties. It is usually sufficient to consider universal-existential sentences true on models of this class. Up to the present paper, the Jonsson spectrum has tended to deal only with Jonsson theories. The authors of this study define the positive Jonsson spectrum notion, the elements of which can be, non-Jonsson theories. This happens because in the definition of the existentially positive Mustafin theories considered in a given paper involve not only isomorphic embeddings, but also immersions. In this connection, immersions are considered in the definition of amalgam and joint embedding properties. The resulting theories do not necessarily have to be Jonsson. We can observe that the above approach to the Jonsson spectrum study proves to be justified because even in the case of a non-Jonsson theory there exists regular method for finding such Jonsson theory that satisfies previously known notions and results, but that will also be directly related to the existentially positive Mustafin theory in question.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46917815","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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