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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki最新文献

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A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation 一种求解多维三阶伪抛物方程第二次初边值问题的数值方法
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210303
M. Beshtokov
{"title":"A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation","authors":"M. Beshtokov","doi":"10.35634/vm210303","DOIUrl":"https://doi.org/10.35634/vm210303","url":null,"abstract":"The work is devoted to the study of the second initial-boundary value problem for a general-form third-order differential equation of pseudoparabolic type with variable coefficients in a multidimensional domain with an arbitrary boundary. In this paper, a multidimensional pseudoparabolic equation is reduced to an integro-differential equation with a small parameter, and a locally one-dimensional difference scheme by A.A. Samarskii is used. Using the maximum principle, an a priori estimate is obtained for the solution of a locally one-dimensional difference scheme in the uniform metric in the $C$ norm. The stability and convergence of the locally one-dimensional difference scheme are proved.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"20 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88874138","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
On sequential traversal of sets 关于集合的顺序遍历
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210310
A. Chentsov, P. Chentsov
{"title":"On sequential traversal of sets","authors":"A. Chentsov, P. Chentsov","doi":"10.35634/vm210310","DOIUrl":"https://doi.org/10.35634/vm210310","url":null,"abstract":"The problem of sequential traversal of megapolises with precedence conditions is investigated; this problem is oriented to mechanical engineering — CNC metal cutting machines. There is the following setting singularity: the terminal component of additive criterion contains the dependence on the starting point. This singularity leads to the fact that the natural solution procedure based on dynamic programming must be applied individually for every starting point. The investigation goal consists in the construction of an optimizing algorithm for determining a complex including a route (a variant of megapolis numbering), a trajectory, and a starting point. The proposed algorithm realizes an idea of directed enumeration of starting points. This algorithm is realized as a program for PC; computations for model examples are made.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"223 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77495001","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 convexity of the reachable set with respect to a part of coordinates at small time intervals 关于可达集在小时间间隔内对部分坐标的凸性
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210204
I. O. Osipov
{"title":"On the convexity of the reachable set with respect to a part of coordinates at small time intervals","authors":"I. O. Osipov","doi":"10.35634/vm210204","DOIUrl":"https://doi.org/10.35634/vm210204","url":null,"abstract":"We investigate the convexity of the reachable sets for some of the coordinates of nonlinear systems with integral constraints on the control at small time intervals. We have proved sufficient convexity conditions in the form of constraints on the asymptotics of the eigenvalues of the Gramian of the controllability of a linearized system for some of the coordinates. There are two nonlinear third-order systems under study as examples. The system linearized along a trajectory generated by zero control is uncontrollable, and the system in the other example is completely controllable. We investigate the sufficient conditions for convexity of projection of reachable sets. Numerical modeling has been carried out, demonstrating the non-convexity of some projections even for small time intervals.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"142 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78351237","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
Integration of the Harry Dym equation with an integral type source 带积分型源的Harry Dym方程的积分
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210209
G. Urazboev, A. Babadjanova, D. R. Saparbaeva
{"title":"Integration of the Harry Dym equation with an integral type source","authors":"G. Urazboev, A. Babadjanova, D. R. Saparbaeva","doi":"10.35634/vm210209","DOIUrl":"https://doi.org/10.35634/vm210209","url":null,"abstract":"In the work, we deduce the evolution of scattering data for a spectral problem associated with the nonlinear evolutionary equation of Harry Dym with a self-consistent source of integral type. The obtained equalities completely determine the scattering data for any $t$, which makes it possible to apply the method of the inverse scattering problem to solve the Cauchy problem for the Harry Dym equation with an integral type source.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"39 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82431611","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
Holomorphic continuation into a matrix ball of functions defined on a piece of its skeleton 全纯延拓成定义在其骨架上的函数矩阵球
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210210
G. Khudayberganov, J. Abdullayev
{"title":"Holomorphic continuation into a matrix ball of functions defined on a piece of its skeleton","authors":"G. Khudayberganov, J. Abdullayev","doi":"10.35634/vm210210","DOIUrl":"https://doi.org/10.35634/vm210210","url":null,"abstract":"The question of the possibility of holomorphic continuation into some domain of functions defined on the entire boundary of this domain has been well studied. The problem of describing functions defined on a part of the boundary that can be extended holomorphically into a fixed domain is attracting more interest. In this article, we reformulate the problem under consideration: Under what conditions can we extend holomorphically to a matrix ball the functions given on a part of its skeleton? We describe the domains into which the integral of the Bochner—Hua Luogeng type for a matrix ball can be extended holomorphically. As the main result, we present the criterion of holomorphic continuation into a matrix ball of functions defined on a part of the skeleton of this matrix ball. The proofs of several results are briefly presented. Some recent advances are highlighted. The results obtained in this article generalize the results of L.A. Aizenberg, A.M. Kytmanov and G. Khudayberganov.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"61 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80480641","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 generalized boundary value problem for a feedback control system with infinite delay 一类无穷时滞反馈控制系统的广义边值问题
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210201
M. Afanasova, V. Obukhovskii, G. Petrosyan
{"title":"On a generalized boundary value problem for a feedback control system with infinite delay","authors":"M. Afanasova, V. Obukhovskii, G. Petrosyan","doi":"10.35634/vm210201","DOIUrl":"https://doi.org/10.35634/vm210201","url":null,"abstract":"We consider a non-local boundary value problem for a feedback control system described by a semilinear functional-differential inclusion of fractional order with infinite delay in a separable Banach space. The general principle of existence of solutions to the problem in terms of the difference from zero of the topological degree of the corresponding vector field is given. We prove a concrete example (Theorem 6) of the implementation of this general principle. The existence of an optimal solution to the posed problem is proved, which minimizes the given lower semicontinuous quality functional.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88907656","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 nonlocal perturbation of the problem on eigenvalues of differentiation operator on a segment 段上微分算子特征值问题的非局部摄动
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210202
N. Imanbaev
{"title":"On nonlocal perturbation of the problem on eigenvalues of differentiation operator on a segment","authors":"N. Imanbaev","doi":"10.35634/vm210202","DOIUrl":"https://doi.org/10.35634/vm210202","url":null,"abstract":"This work is devoted to the construction of a characteristic polynomial of the spectral problem of a first-order differential equation on an interval with a spectral parameter in a boundary value condition with integral perturbation which is an entire analytic function of the spectral parameter. Based on the characteristic polynomial formula, conclusions about the asymptotics of the spectrum of the perturbed spectral problem are established.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"137 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88039926","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: 2
Regularized classical optimality conditions in iterative form for convex optimization problems for distributed Volterra-type systems 分布式volterra型系统凸优化问题的正则经典迭代最优性条件
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210208
V. Sumin, M. I. Sumin
{"title":"Regularized classical optimality conditions in iterative form for convex optimization problems for distributed Volterra-type systems","authors":"V. Sumin, M. I. Sumin","doi":"10.35634/vm210208","DOIUrl":"https://doi.org/10.35634/vm210208","url":null,"abstract":"We consider the regularization of the classical optimality conditions (COCs) — the Lagrange principle and the Pontryagin maximum principle — in a convex optimal control problem with functional constraints of equality and inequality type. The system to be controlled is given by a general linear functional-operator equation of the second kind in the space $L^m_2$, the main operator of the right-hand side of the equation is assumed to be quasinilpotent. The objective functional of the problem is strongly convex. Obtaining regularized COCs in iterative form is based on the use of the iterative dual regularization method. The main purpose of the regularized Lagrange principle and the Pontryagin maximum principle obtained in the work in iterative form is stable generation of minimizing approximate solutions in the sense of J. Warga. Regularized COCs in iterative form are formulated as existence theorems in the original problem of minimizing approximate solutions. They “overcome” the ill-posedness properties of the COCs and are regularizing algorithms for solving optimization problems. As an illustrative example, we consider an optimal control problem associated with a hyperbolic system of first-order differential equations.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"126 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87872661","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: 2
On totally global solvability of evolutionary equation with unbounded operator 具有无界算子的进化方程的全局可解性
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210212
A. Chernov
{"title":"On totally global solvability of evolutionary equation with unbounded operator","authors":"A. Chernov","doi":"10.35634/vm210212","DOIUrl":"https://doi.org/10.35634/vm210212","url":null,"abstract":"Let $X$ be a Hilbert space, $U$ be a Banach space, $Gcolon Xto X$ be a linear operator such that the operator $B_lambda=lambda I-G$ is maximal monotone with some (arbitrary given) $lambdainmathbb{R}$. For the Cauchy problem associated with controlled semilinear evolutionary equation as follows\u0000[x^prime(t)=Gx(t)+fbigl( t,x(t),u(t)bigr),quad tin[0;T];quad x(0)=x_0in X,]\u0000where $u=u(t)colon[0;T]to U$ is a control, $x(t)$ is unknown function with values in $X$, we prove the totally (with respect to a set of admissible controls) global solvability subject to global solvability of the Cauchy problem associated with some ordinary differential equation in the space $mathbb{R}$. Solution $x$ is treated in weak sense and is sought in the space $mathbb{C}_wbigl([0;T];Xbigr)$ of weakly continuous functions. In fact, we generalize a similar result having been proved by the author formerly for the case of bounded operator $G$. The essence of this generalization consists in that postulated properties of the operator $B_lambda$ give us the possibility to construct Yosida approximations for it by bounded linear operators and thus to extend required estimates from “bounded” to “unbounded” case. As examples, we consider initial boundary value problems associated with the heat equation and the wave equation.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"112 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86756790","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: 2
Numerical solution of the inverse boundary value heat transfer problem for an inhomogeneous rod 非均匀杆反边值传热问题的数值解
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-06-01 DOI: 10.35634/vm210207
A. I. Sidikova, A. Sushkov
{"title":"Numerical solution of the inverse boundary value heat transfer problem for an inhomogeneous rod","authors":"A. I. Sidikova, A. Sushkov","doi":"10.35634/vm210207","DOIUrl":"https://doi.org/10.35634/vm210207","url":null,"abstract":"The article is devoted to solving an inverse boundary value problem for a rod consisting of composite materials. In the inverse problem, it is required, using information about the temperature of the heat flow in the media section, to determine the temperature at one of the ends of the rod. The paper presents a method of projection regularization, which made it possible to approximately estimate the error of the obtained solution to the inverse problem. To check the computational efficiency of this method, test calculations were carried out.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":"76 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86455749","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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