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Roughness in Fuzzy Cayley Graphs 模糊 Cayley 图中的粗糙度
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/105-118
M.H. Shahzamanian, B. Davvaz
{"title":"Roughness in Fuzzy Cayley Graphs","authors":"M.H. Shahzamanian, B. Davvaz","doi":"10.31489/2023m4/105-118","DOIUrl":"https://doi.org/10.31489/2023m4/105-118","url":null,"abstract":"Rough set theory is a worth noticing approach for inexact and uncertain system modelling. When rough set theory accompanies with fuzzy set theory, which both are a complementary generalization of set theory, they will be attended by potency in theoretical discussions. In this paper a definition for fuzzy Cayley subsets is put forward as well as fuzzy Cayley graphs of fuzzy subsets on groups inspired from the definition of Cayley graphs. We introduce rough approximation of a Cayley graph with respect to a fuzzy normal subgroup. We introduce the approximation rough fuzzy Cayley graphs and fuzzy rough fuzzy Cayley graphs. The last approximation is the mixture of the other approximations. Some theorems and properties are investigated and proved.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":"179 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139145641","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
Iterated discrete Hardy-type inequalities with three weights for a class of matrix operators 一类矩阵算子的三权重迭代离散哈代型不等式
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/163-172
N.S. Zhangabergenova, A.M. Temirhanova
{"title":"Iterated discrete Hardy-type inequalities with three weights for a class of matrix operators","authors":"N.S. Zhangabergenova, A.M. Temirhanova","doi":"10.31489/2023m4/163-172","DOIUrl":"https://doi.org/10.31489/2023m4/163-172","url":null,"abstract":"Iterated Hardy-type inequalities are one of the main objects of current research on the theory of Hardy inequalities. These inequalities have become well-known after study boundedness properties of the multidimensional Hardy operator acting from the weighted Lebesgue space to the local Morrie-type space. In addition, the results of quasilinear inequalities can be applied to study bilinear Hardy inequalities. In the paper, we discussed weighted discrete Hardy-type inequalities containing some quasilinear operators with a matrix kernel where matrix entries satisfy discrete Oinarov condition. The research of weighted Hardy-type inequalities depends on the relations between parameters p, q and θ, so we considered the cases 1 < p ≤ q < θ < ∞ and p ≤ q < θ < ∞, 0 < p ≤1, criteria for the fulfillment of iterated discrete Hardy-type inequalities are obtained. Moreover, an alternative method of proof was shown in the work.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 27","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139144986","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 a boundary problem for the fourth order equation with the third derivative with respect to time 关于时间三阶导数四阶方程的边界问题
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/30-40
Yusufjon P. Apakov, D.M. Meliquzieva
{"title":"On a boundary problem for the fourth order equation with the third derivative with respect to time","authors":"Yusufjon P. Apakov, D.M. Meliquzieva","doi":"10.31489/2023m4/30-40","DOIUrl":"https://doi.org/10.31489/2023m4/30-40","url":null,"abstract":"In this paper, we consider a boundary value problem in a rectangular domain for a fourth-order homogeneous partial differential equation containing the third derivative with respect to time. The uniqueness of the solution of the stated problem is proved by the method of energy integrals. Using the method of separation of variables, the solution of the considered problem is sought as a multiplication of two functions X (x) and Y (y). To determine X (x),we obtain a fourth-order ordinary differential equation with four boundary conditions at the segment boundary [0,p], and for a Y (y) – third-order ordinary differential equation with three boundary conditions at the boundary of the segment [0,q]. Imposing conditions on the given functions, we prove the existence theorem for a regular solution of the problem. The solution of the problem is constructed in the form of an infinite series, and the possibility of term-by-term differentiation of the series with respect to all variables is substantiated. When substantiating the uniform convergence, it is shown that the “small denominator” is different from zero.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139145031","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
Automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication 具有零乘法的有限维津比尔代数的普遍包络代数的自动形态
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/173-184
D. M. Zhangazinova, A. Naurazbekova
{"title":"Automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication","authors":"D. M. Zhangazinova, A. Naurazbekova","doi":"10.31489/2023m4/173-184","DOIUrl":"https://doi.org/10.31489/2023m4/173-184","url":null,"abstract":"In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A. Naurazbekova, using the methods of Gro¨bner-Shirshov bases, constructed the basis of the universal (multiplicative) enveloping algebra U(A) of A. Using this result, the automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication are described.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 13","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139143784","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
Implementation of summation theorems of Andrews and Gessel-Stanton 安德鲁斯和盖塞尔-斯坦顿求和定理的实现
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-12-29 DOI: 10.31489/2023m4/95-104
Mohd. Idris Qureshi, Tafaz Ul, Rahman Shah
{"title":"Implementation of summation theorems of Andrews and Gessel-Stanton","authors":"Mohd. Idris Qureshi, Tafaz Ul, Rahman Shah","doi":"10.31489/2023m4/95-104","DOIUrl":"https://doi.org/10.31489/2023m4/95-104","url":null,"abstract":"Generalized hypergeometric functions and their natural generalizations in one and several variables appear in many mathematical problems and their applications. Solving partial differential equations encountered in many applied problems of mathematics physics is expressed in terms of such generalized hypergeometric functions. In particular, the Srivastava-Daoust double hypergeometric function (S-D function) has proved its practical utility in representing solutions to a wide range of problems in pure and applied mathematics. In this paper, we introduce two general double-series identities involving bounded sequences of arbitrary complex numbers employing the finite summation theorems of Gessel-Stanton and Andrews for terminating 3F2 hypergeometric series with arguments 3/4 and 4/3, respectively. Using these double-series identities, we establish two reduction formulas for the (S-D function) with arguments z, 3z/4 and z, −4z/3 expressed in terms of two generalized hypergeometric function of arguments proportional to z3 and −z3 respectively. All the results mentioned in the paper are verified numerically using Mathematica Program.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":"74 s315","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139145954","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
Compactness of Commutators for Riesz Potential on Local Morrey-type spaces 局部morrey型空间上Riesz势换向子的紧性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-06-30 DOI: 10.31489/2023m2/93-103
D. Matin, T. Akhazhanov, A. Adilkhanov
{"title":"Compactness of Commutators for Riesz Potential on Local Morrey-type spaces","authors":"D. Matin, T. Akhazhanov, A. Adilkhanov","doi":"10.31489/2023m2/93-103","DOIUrl":"https://doi.org/10.31489/2023m2/93-103","url":null,"abstract":"The paper considers Morrey-type local spaces from LM^w_pθ. The main work is the proof of the commutator compactness theorem for the Riesz potential [b, I_α] in local Morrey-type spaces from LM^w1_pθ to LM^w2_qθ. We also give new sufficient conditions for the commutator to be bounded for the Riesz potential [b, I_α] in local Morrey-type spaces from LM^w1_pθ to LM^w2_qθ. In the proof of the commutator compactness theorem for the Riesz potential, we essentially use the boundedness condition for the commutator for the Riesz potential [b, Iα] in local Morrey-type spaces LM^w_pθ, and use the sufficient conditions from the theorem of precompactness of sets in local spaces of Morrey type LM^w_pθ. In the course of proving the commutator compactness theorem for the Riesz potential, we prove lemmas for the commutator ball for the Riesz potential [b, I_α]. Similar results were obtained for global Morrey-type spaces GM^w_pθ and for generalized Morrey spaces M^w_p.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48124149","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 family of definite integrals involving Legendre’s polynomials 一个包含勒让德多项式的定积分族
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-06-30 DOI: 10.31489/2023m2/116-130
M. I. Qureshi, S. Malik, D. Ahmad
{"title":"A family of definite integrals involving Legendre’s polynomials","authors":"M. I. Qureshi, S. Malik, D. Ahmad","doi":"10.31489/2023m2/116-130","DOIUrl":"https://doi.org/10.31489/2023m2/116-130","url":null,"abstract":"The main objective of this article is to provide the analytical solutions (not previously found and not available in the literature) of some problems related with definite integrals integrands of which are the products of the derivatives of Legendre’s polynomials of first kind having different order, with the help of some derivatives of Legendre’s polynomials of first kind P_n(x), Rodrigues formula, Leibnitz’s generalized rule for successive integration by parts and certain values of successive differential coefficients of (x^2 − 1)^r at x = ±1.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48136017","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 weighted integrability of the sum of series with monotone coefficients with respect to multiplicative systems 关于乘法系统单调系数级数和的加权可积性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-06-30 DOI: 10.31489/2023m2/160-168
M.Zh. Turgumbaev, Z. R. Suleimenova, D. I. Tungushbaeva
{"title":"On weighted integrability of the sum of series with monotone coefficients with respect to multiplicative systems","authors":"M.Zh. Turgumbaev, Z. R. Suleimenova, D. I. Tungushbaeva","doi":"10.31489/2023m2/160-168","DOIUrl":"https://doi.org/10.31489/2023m2/160-168","url":null,"abstract":"In this paper, we consider the questions about the weighted integrability of the sum of series with respect to multiplicative systems with monotone coefficients. Conditions are obtained for weight functions that ensure that the sum of such series belongs to the weighted Lebesgue space. The main theorems are proved without the condition that the generator sequence is bounded; in particular, it can be unbounded. In the case of boundedness of the generator sequence, the proved theorems imply an analogue of the well-known Hardy-Littlewood theorem on trigonometric series with monotone coefficients.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48336622","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 of integrodifferential equations under boundary conditions taking into account physical nonlinearity 考虑物理非线性的边界条件下积分微分方程的边值问题
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-06-30 DOI: 10.31489/2023m2/131-141
A. Seitmuratov, N. K. Medeubaev, T.T. Kozhoshov, B.R. Medetbekov
{"title":"Boundary value problems of integrodifferential equations under boundary conditions taking into account physical nonlinearity","authors":"A. Seitmuratov, N. K. Medeubaev, T.T. Kozhoshov, B.R. Medetbekov","doi":"10.31489/2023m2/131-141","DOIUrl":"https://doi.org/10.31489/2023m2/131-141","url":null,"abstract":"When solving integrodifferential equations under boundary conditions, taking into account physical nonlinearity, a broad class of boundary-value problems of oscillations arises associated with various boundary conditions at the edges of a flat element. When taking into account non-stationary external influences, the main parameters is the frequency of natural vibrations of a flat component, taking into account temperature, prestressing, and other factors. The study of such problems, taking into account complicating factors, reduces to solving rather complex problems. The difficulty of solving these problems is due to both the type of equations and the variety. We analyze the results of previous works on the boundary problems of vibrations of plane elements. Possible boundary conditions at the edges of a flat element and the necessary initial conditions for solving particular problems of self-oscillation and forced vibrations, and other problems are considered. The set of equations, boundaries, and initial conditions make it possible to formulate and solve various boundary value problems of vibrations for a flat element. The oscillation equations for a flat element in the form of a plate given in this paper contain viscoelastic operators that describe the viscous behavior of the materials of a flat component. In studying oscillations and wave processes, it is advisable to take the kernels of viscoelastic operators regularly, since only such operators describe instantaneous elasticity and then viscous flow.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46504362","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 Robinson spectrum of the semantic Jonsson quasivariety of unars 关于一元语义Jonsson拟变的Robinson谱
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-06-30 DOI: 10.31489/2023m2/169-178
A. Yeshkeyev, A. R. Yarullina, S.M. Amanbekov, M. T. Kassymetova
{"title":"On Robinson spectrum of the semantic Jonsson quasivariety of unars","authors":"A. Yeshkeyev, A. R. Yarullina, S.M. Amanbekov, M. T. Kassymetova","doi":"10.31489/2023m2/169-178","DOIUrl":"https://doi.org/10.31489/2023m2/169-178","url":null,"abstract":"Given article is devoted to the study of semantic Jonsson quasivariety of universal unars of signature containing only unary functional symbol. The first section of the article consists of basic necessary concepts. There were defined new notions of semantic Jonsson quasivariety of Robinson unars JCU , its elementary theory and semantic model. In order to prove the main result of the article, there were considered Robinson spectrum RSp(JCU ) and its partition onto equivalence classes [∆] by cosemanticness relation. The characteristic features of such equivalence classes [∆] ∈ RSp(JCU ) were analysed. The main result is the following theorem of the existence of: characteristic for every class [∆] the meaning of which is Robinson theories of unars; class [∆] for any arbitrary characteristic; criteria of equivalence of two classes [∆]1, [∆]2. The obtained results can be useful for continuation of the various Jonsson algebras’ research, particularly semantic Jonsson quasivariety of S-acts over cyclic monoid.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45283697","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: 1
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