Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta最新文献_第2页

Mathematical model of process of sedimentation of multicomponent suspension on the bottom and changes in the composition of bottom materials 多组分悬浮物在底部沉降过程及底部物料组成变化的数学模型

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-11-01 DOI: 10.35634/2226-3594-2022-60-05

A. Sukhinov, A. Chistyakov, A. Atayan, I. Kuznetsova, V. Litvinov, A. Nikitina

{"title":"Mathematical model of process of sedimentation of multicomponent suspension on the bottom and changes in the composition of bottom materials","authors":"A. Sukhinov, A. Chistyakov, A. Atayan, I. Kuznetsova, V. Litvinov, A. Nikitina","doi":"10.35634/2226-3594-2022-60-05","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-60-05","url":null,"abstract":"The paper considers 2D and 3D models of transport of suspended particles, taking into account the following factors: movement of aqueous medium; variable density depending on the suspension concentration; multicomponent character of suspension; changes in bottom geometry as a result of suspension sedimentation. The approximation of the three-dimensional diffusion-convection equation is based on splitting schemes into two-dimensional and one-dimensional problems. In this work, we use discrete analogues of convective and diffusion transfer operators in the case of partial cell occupancy. The geometry of the computational domain is described based on the occupancy function. The difference scheme used is a linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients obtained by minimizing the approximation error. This scheme is designed to solve the problem of impurity transfer at large grid Peclet numbers. Based on the results of numerical experiments, conclusions are drawn about the advantage of the 3D model of multicomponent suspension transport in comparison with the 2D model. Computational experiments have been performed to simulate the process of sedimentation of a multicomponent suspension, as well as its effect on the bottom topography and changes in its composition.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"26 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77873075","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 explicit expression of the solution to the regularizing by Tikhonov optimization problem in terms of the regularization parameter in the finite-dimensional case 有限维正则化参数下Tikhonov优化问题解的显式表达

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-11-01 DOI: 10.35634/2226-3594-2022-60-06

A. Chernov

{"title":"On explicit expression of the solution to the regularizing by Tikhonov optimization problem in terms of the regularization parameter in the finite-dimensional case","authors":"A. Chernov","doi":"10.35634/2226-3594-2022-60-06","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-60-06","url":null,"abstract":"It is well known that using the Tikhonov regularization method for solving operator equations of the first kind one has to minimize a regularized residual functional. The minimizer is determined from so called Euler equation which in finite-dimensional case and at its discretization is written as a one-parametric (depending on the regularization parameter) system of linear algebraic equations of special form. Here, there exist various ways of choosing the regularization parameter. In particular, in the frame of principle of generalized residual, it is necessary to solve the corresponding equation of generalized residual with respect to the regularization parameter. And it implies (when solving this equation numerically), in turn, multifold solving a one-parametric system of linear algebraic equations for arbitrary value of the parameter. In this paper we obtain an explicit simple and effective formula of solution to a one-parametric system for an arbitrary value of the parameter. We give an example of computations by above-mentioned formula and also an example of numerical solution of the Fredholm integral equation of the first kind under usage of this formula which substantiates its effectiveness.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"31 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87088235","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

Algorithms of optimal covering of 2D sets with dynamical metrics 二维动态度量集的最优覆盖算法

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-11-01 DOI: 10.35634/2226-3594-2022-60-04

P. Lebedev, A. Lempert, A. Kazakov

引用次数: 0

Approximate calculation of reachable sets for linear control systems with different control constraints 具有不同控制约束的线性控制系统可达集的近似计算

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-11-01 DOI: 10.35634/2226-3594-2022-60-02

I. Zykov

引用次数: 0

Pursuit-evasion differential games with Gr-constraints on controls 控制上有gr约束的追击-逃避微分对策

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-06

B. Samatov, A. Akbarov, B. I. Zhuraev

{"title":"Pursuit-evasion differential games with Gr-constraints on controls","authors":"B. Samatov, A. Akbarov, B. I. Zhuraev","doi":"10.35634/2226-3594-2022-59-06","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-59-06","url":null,"abstract":"In the paper, a pursuit-evasion differential game is considered when controls of the players are subject to differential constraints in the form of Grönwall's integral inequality. The strategy of parallel pursuit (briefly, $Pi$-strategy) was introduced and used by L.A. Petrosyan to solve simple pursuit problems under phase constraints on the states of the players in the case when control functions of both players are chosen from the class $L_infty$. In the present work, the $Pi$-strategy is constructed for a simple pursuit problem in the cases when control functions of both players are chosen from different classes of the Grönwall type constraints, and sufficient conditions of capture and optimal capture time are found in these cases. To solve the evasion problem, we suggest a control function for the Evader and find sufficient conditions of evasion. In addition, an attainability domain of the players is constructed and its conditions of embedding in respect to time are given. Results of this work continue and extend the works of R. Isaacs, L.A. Petrosyan, B.N. Pshenichnyi, A.A. Chirii, A.A. Azamov and other researchers, including the authors.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"6 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89256566","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 regularization of the Lagrange principle in the optimization problems for linear distributed Volterra type systems with operator constraints 带算子约束的线性分布Volterra型系统优化问题中拉格朗日原理的正则化

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-07

V. Sumin, M. I. Sumin

{"title":"On regularization of the Lagrange principle in the optimization problems for linear distributed Volterra type systems with operator constraints","authors":"V. Sumin, M. I. Sumin","doi":"10.35634/2226-3594-2022-59-07","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-59-07","url":null,"abstract":"Regularization of the classical optimality conditions - the Lagrange principle and the Pontryagin maximum principle - in a convex optimal control problem subject to functional equality and inequality constraints is considered. The controlled system is described by a linear functional-operator equation of second kind of the general form in the space $L_2^m$. The main operator on the right-hand side of the equation is assumed to be quasi-nilpotent. The objective functional to be minimized is strongly convex. The derivation of the regularized classical optimality conditions is based on the use of the dual regularization method. The main purpose of the regularized Lagrange principle and regularized Pontryagin maximum principle is to stably generate minimizing approximate solutions in the sense of J. Warga. As an application of the results obtained for the general linear functional-operator equation of second kind, two examples of concrete optimal control problems related to a system of delay equations and to an integro-differential transport equation are discussed.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"10 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73793497","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 flexibility of constraints system under approximation of optimal control problems 最优控制问题逼近下约束系统的柔性问题

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-08

A. Chernov

引用次数: 0

On one simple pursuit problem of two rigidly coordinated evaders 关于两个刚性协调逃避者的简单追逐问题

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-05

N. Petrov

引用次数: 0

Numerical method for system of space-fractional equations of superdiffusion type with delay and Neumann boundary conditions 具有延迟和Neumann边界条件的超扩散型空间分数阶方程组的数值方法

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-04

M. Ibrahim, V. Pimenov

引用次数: 0

The Savage principle and accounting for outcome in single-criterion nonlinear problem under uncertainty 不确定单准则非线性问题的Savage原理及结果的计算

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-03

V. Zhukovskiĭ, L. Zhukovskaya, S. P. Samsonov, L. Smirnova

{"title":"The Savage principle and accounting for outcome in single-criterion nonlinear problem under uncertainty","authors":"V. Zhukovskiĭ, L. Zhukovskaya, S. P. Samsonov, L. Smirnova","doi":"10.35634/2226-3594-2022-59-03","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-59-03","url":null,"abstract":"In the middle of the last century the American mathematician and statistician professor of Michigan University Leonard Savage (1917-1971) and the well-known economist, professor of Zurich University (Switzerland) Jurg Niehans (1919-2007) independently from each other suggested the approach to decision-making in one-criterion problem under uncertainty (OPU), called the principle of minimax regret. This principle along with Wald principle of guaranteed result (maximin) is playing the most important role in guaranteed under uncertainty decision-making in OPU. The main role in the principle of minimax regret is carrying out the regret function, which determines the Niehans-Savage risk in OPU. Such risk has received the broad extension in practical problems during last years. In the present article we suggest one of possible approaches to finding decision in OPU from the position of a decision-maker, which simultaneously tries to increase the payoff (outcome) and to reduce the risk (i.e., “to kill two birds with one stone in one throw”). As an application, an explicit form of such a solution was immediately found for a linear-quadratic variant of the OPU of a fairly general form.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"47 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91217652","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