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Bulletin of the Karaganda University-Mathematics最新文献

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Asymptotic estimations of the solution for a singularly perturbed equation with unlimited boundary conditions 具有无限边界条件的奇摄动方程解的渐近估计
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/20-33
N. Atakhan, K.S. Nurpeisov, K. Konisbayeva
{"title":"Asymptotic estimations of the solution for a singularly perturbed equation with unlimited boundary conditions","authors":"N. Atakhan, K.S. Nurpeisov, K. Konisbayeva","doi":"10.31489/2022m4/20-33","DOIUrl":"https://doi.org/10.31489/2022m4/20-33","url":null,"abstract":"The paper studies a two-point boundary value problem with unlimited boundary conditions for a linear singularly perturbed differential equation. Asymptotic estimates are given for a linearly independent system of solutions of a homogeneous perturbed equation. Auxiliary, so-called boundary functions, the Cauchy function are defined. For sufficiently small values of the parameter, estimates for the Cauchy function and boundary functions are found. An algorithm for constructing the desired solution of the boundary value problem has been developed. A theorem on the solvability of a solution to a boundary value problem is proved. For sufficiently small values of the parameter, an asymptotic estimate for the solution of the inhomogeneous boundary value problem is established. The initial conditions for the degenerate equation are determined. The formula is determined; the phenomena of the initial jump are studied.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45898414","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 Correctness of Boundary Value Problems for the Two-Dimensional Loaded Parabolic Equation 关于二维加载抛物型方程边值问题的正确性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m/34-41
A. Attaev, M. Ramazanov, M.T. Omarov
{"title":"On the Correctness of Boundary Value Problems for the Two-Dimensional Loaded Parabolic Equation","authors":"A. Attaev, M. Ramazanov, M.T. Omarov","doi":"10.31489/2022m/34-41","DOIUrl":"https://doi.org/10.31489/2022m/34-41","url":null,"abstract":"The paper studies the problems of the correctness of setting boundary value problems for a loaded parabolic equation. The a feature of the problems is that the order of the derivative in the loaded term is less than or equal to the order of the differential part of the equation, and the load point moves according to a nonlinear law. At the same time, the distinctive characteristic is that the line, on which the loaded term is set, is at the zero point. On the basis of the study the authors proved the theorems about correctness of the studied boundary value problems.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42737873","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
The Bessel equation on the quantum calculus 量子微积分中的贝塞尔方程
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/132-144
S. Shaimardan, N. Tokmagambetov, Y. Aikyn
{"title":"The Bessel equation on the quantum calculus","authors":"S. Shaimardan, N. Tokmagambetov, Y. Aikyn","doi":"10.31489/2022m3/132-144","DOIUrl":"https://doi.org/10.31489/2022m3/132-144","url":null,"abstract":"A large number of the most diverse problems related to almost all the most important branches of mathematical physics and designed to answer topical technical questions are associated with the use of Bessel functions. This paper introduces a h-difference equation analogue of the Bessel differential equation and investigates the properties of its solution, which is express using the Frobenius method by assuming a generalized power series. The authors find discrete analogue formulas for Bessel function and the h-Neumann function and these are solutions presented by a series with the h-fractional function t^(α)_h. Lastly they obtain the linear dependencies between h-functions Bessel on T_a.","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":"45082085","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
Forcing companions of Jonsson AP-theories Jonsson ap理论的强迫同伴
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/152-163
A. Yeshkeyev, I.O. Tungushbayeva, M. Omarova
{"title":"Forcing companions of Jonsson AP-theories","authors":"A. Yeshkeyev, I.O. Tungushbayeva, M. Omarova","doi":"10.31489/2022m3/152-163","DOIUrl":"https://doi.org/10.31489/2022m3/152-163","url":null,"abstract":"This article is devoted to the study of the forcing companions of the Jonsson AP-theories in the enriched signature. It is proved that the forcing companion of the theory does not change when expanding the theories under consideration, which have some properties, by adding new predicate and constant symbols to the language. The model-theoretic results obtained in this paper in general form are supported by examples from differential algebra. An approach in combining a Jonsson and non-Jonsson theories is demonstrated. In this paper, for the first time in the history of Model Theory. This will allow us to further develop the methods of research of Jonsson theories and expand the apparatus for studying incomplete theories.","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":"43249867","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
Two theorems on estimates for solutions of one class of nonlinear equations in a finite-dimensional space 有限维空间中一类非线性方程解的两个估计定理
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/70-84
B. D. Koshanov, N. Kakharman, R. U. Segizbayeva, Zh.B. Sultangaziyeva
{"title":"Two theorems on estimates for solutions of one class of nonlinear equations in a finite-dimensional space","authors":"B. D. Koshanov, N. Kakharman, R. U. Segizbayeva, Zh.B. Sultangaziyeva","doi":"10.31489/2022m3/70-84","DOIUrl":"https://doi.org/10.31489/2022m3/70-84","url":null,"abstract":"The need to study boundary value problems for elliptic parabolic equations is dictated by numerous practical applications in the theoretical study of the processes of hydrodynamics, electrostatics, mechanics, heat conduction, elasticity theory and quantum physics. In this paper, we obtain two theorems on a priori estimates for solutions of nonlinear equations in a finite-dimensional Hilbert space. The work consists of four items. In the first subsection, the notation used and the statement of the main results are given. In the second subsection, the main lemmas are given. The third section is devoted to the proof of Theorem 1. In the fourth section, Theorem 2 is proved. The conditions of the theorems are such that they can be used in studying a certain class of initial-boundary value problems to obtain strong a priori estimates in the presence of weak a priori estimates. This is the meaning of these theorems.","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":"43071937","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
Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators 一类退化椭圆算子的奇异数估计
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/51-58
Sabit Igisinov, L.D. Zhumaliyeva, A. O. Suleimbekova, Yerik Bayandiyev
{"title":"Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators","authors":"Sabit Igisinov, L.D. Zhumaliyeva, A. O. Suleimbekova, Yerik Bayandiyev","doi":"10.31489/2022m3/51-58","DOIUrl":"https://doi.org/10.31489/2022m3/51-58","url":null,"abstract":"In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure the existence and uniqueness of the solution. The existence, uniqueness, and smoothness of a solution are proved, and estimates are found for singular numbers (s-numbers) and eigenvalues of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration.","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":"42441643","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
Multipliers in weighted Sobolev spaces on the axis 轴上加权Sobolev空间的乘数
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/105-115
A. Myrzagaliyeva
{"title":"Multipliers in weighted Sobolev spaces on the axis","authors":"A. Myrzagaliyeva","doi":"10.31489/2022m3/105-115","DOIUrl":"https://doi.org/10.31489/2022m3/105-115","url":null,"abstract":"This work establishes necessary and sufficient conditions for the boundedness of one variable differential operator acting from a weighted Sobolev space W^l_p,v to a weighted Lebesgue space on the positive real half line. The coefficients of differential operators are often assumed to be pointwise multipliers of function spaces. The author introduces pointwise multipliers in weighted Sobolev spaces; obtains the description of the space of multipliers M(W_1 → W_2) for a pair of weighted Sobolev spaces (W_1, W_2) with weights of general type.","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":"46214053","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
Attractors of 2D Navier–Stokes system of equations in a locally periodic porous medium 局部周期多孔介质中二维Navier-Stokes方程组的吸引子
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/35-50
K. Bekmaganbetov, G. Chechkin, A. Toleubay
{"title":"Attractors of 2D Navier–Stokes system of equations in a locally periodic porous medium","authors":"K. Bekmaganbetov, G. Chechkin, A. Toleubay","doi":"10.31489/2022m3/35-50","DOIUrl":"https://doi.org/10.31489/2022m3/35-50","url":null,"abstract":"This article deals with two-dimensional Navier–Stokes system of equations with rapidly oscillating term in the equations and boundary conditions. Studying the problem in a perforated domain, the authors set homogeneous Dirichlet condition on the outer boundary and the Fourier (Robin) condition on the boundary of the cavities. Under such assumptions it is proved that the trajectory attractors of this system converge in some weak topology to trajectory attractors of the homogenized Navier–Stokes system of equations with an additional potential and nontrivial right hand side in the domain without pores. For this aim, the approaches from the works of A.V. Babin, V.V. Chepyzhov, J.-L. Lions, R. Temam, M.I. Vishik concerning trajectory attractors of evolution equations and homogenization methods appeared at the end of the XX-th century are used. First, we apply the asymptotic methods for formal construction of asymptotics, then, we verify the leading terms of asymptotic series by means of the methods of functional analysis and integral estimates. Defining the appropriate axillary functional spaces with weak topology, we derive the limit (homogenized) system of equations and prove the existence of trajectory attractors for this system. Lastly, we formulate the main theorem and prove it through axillary lemmas.","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":"43658744","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
Construction of stochastic differential equations of motion in canonical variables 正则变量中随机运动微分方程的构造
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/152-162
M. Tleubergenov, G. Vassilina, S.R. Seisenbayeva
{"title":"Construction of stochastic differential equations of motion in canonical variables","authors":"M. Tleubergenov, G. Vassilina, S.R. Seisenbayeva","doi":"10.31489/2022m3/152-162","DOIUrl":"https://doi.org/10.31489/2022m3/152-162","url":null,"abstract":"Galiullin proposed a classification of inverse problems of dynamics for the class of ordinary differential equations (ODE). Considered problem belongs to the first type of inverse problems of dynamics (of the three main types of inverse problems of dynamics): the main inverse problem under the additional assumption of the presence of random perturbations. In this paper Hamilton and Birkhoff equations are constructed according to the given properties of motion in the presence of random perturbations from the class of processes with independent increments. The obtained necessary and sufficient conditions for the solvability of the problem of constructing stochastic differential equations of both Hamiltonian and Birkhoffian structure by the given properties of motion are illustrated by the example of the motion of an artificial Earth satellite under the action of gravitational and aerodynamic forces.","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":"43676995","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
Global solvability of a nonlinear Boltzmann equation 非线性Boltzmann方程的全局可解性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-09-30 DOI: 10.31489/2022m3/4-16
A.Sh. Akysh (Akishev)
{"title":"Global solvability of a nonlinear Boltzmann equation","authors":"A.Sh. Akysh (Akishev)","doi":"10.31489/2022m3/4-16","DOIUrl":"https://doi.org/10.31489/2022m3/4-16","url":null,"abstract":"In this paper, based on the splitting method scheme, the existence and uniqueness theorem on the whole time interval t ∈ [0, T), T ≤ ∞ for the full nonlinear Boltzmann equation in the nonequilibrium case is proved where the intermolecular interactions are hard-sphere molecule and central forces. Considering the existence of a bounded solution in the space C, the strict positivity of the solution to the full nonlinear Boltzmann equation is proved when the initial function is positive. On the basis of this some mathematical justification of the H−theorem of Boltzmann is shown.","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":"48157968","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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