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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki最新文献

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On guarantee optimization in control problem with finite set of disturbances 有限扰动控制问题的保证优化
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-12-01 DOI: 10.35634/vm210406
M. Gomoyunov, D. Serkov
{"title":"On guarantee optimization in control problem with finite set of disturbances","authors":"M. Gomoyunov, D. Serkov","doi":"10.35634/vm210406","DOIUrl":"https://doi.org/10.35634/vm210406","url":null,"abstract":"In this paper, we deal with a control problem under conditions of disturbances, which is stated as a problem of optimization of the guaranteed result. Compared to the classical formulation of such problems, we assume that the set of admissible disturbances is finite and consists of piecewise continuous functions. In connection with this additional functional constraint on the disturbance, we introduce an appropriate class of non-anticipative control strategies and consider the corresponding value of the optimal guaranteed result. Under a technical assumption concerning a property of distinguishability of the admissible disturbances, we prove that this result can be achieved by using control strategies with full memory. As a consequence, we establish unimprovability of the class of full-memory strategies. A key element of the proof is a procedure of recovering the disturbance acting in the system, which allows us to associate every non-anticipative strategy with a full-memory strategy providing a close guaranteed result. The paper concludes with an illustrative example.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91353414","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
Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation 多维差分方程解的生成级数各部分的递推关系
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210305
A. Lyapin, S. S. Akhtamova
{"title":"Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation","authors":"A. Lyapin, S. S. Akhtamova","doi":"10.35634/vm210305","DOIUrl":"https://doi.org/10.35634/vm210305","url":null,"abstract":"In this paper, we study the sections of the generating series for solutions to a linear multidimensional difference equation with constant coefficients and find recurrent relations for these sections. As a consequence, a multidimensional analogue of Moivre's theorem on the rationality of sections of the generating series depending on the form of the initial data of the Cauchy problem for a multidimensional difference equation is proved. For problems on the number of paths on an integer lattice, it is shown that the sections of their generating series represent the well-known sequences of polynomials (Fibonacci, Pell, etc.) with a suitable choice of steps.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90943712","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
Sufficient Turing instability conditions for the Schnakenberg system Schnakenberg系统的充分图灵不稳定性条件
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210306
S. Revina, S. Lysenko
{"title":"Sufficient Turing instability conditions for the Schnakenberg system","authors":"S. Revina, S. Lysenko","doi":"10.35634/vm210306","DOIUrl":"https://doi.org/10.35634/vm210306","url":null,"abstract":"A classical reaction-diffusion system, the Schnakenberg system, is under consideration in a bounded domain $Omegasubsetmathbb{R}^m$ with Neumann boundary conditions. We study diffusion-driven instability of a stationary spatially homogeneous solution of this system, also called the Turing instability, which arises when the diffusion coefficient $d$ changes. An analytical description of the region of necessary and sufficient conditions for the Turing instability in the parameter plane is obtained by analyzing the linearized system in diffusionless and diffusion approximations. It is shown that one of the boundaries of the region of necessary conditions is an envelope of the family of curves that bound the region of sufficient conditions. Moreover, the intersection points of two consecutive curves of this family lie on a straight line whose slope depends on the eigenvalues of the Laplace operator and does not depend on the diffusion coefficient. We find an analytical expression for the critical diffusion coefficient at which the stability of the equilibrium position of the system is lost. We derive conditions under which the set of wavenumbers corresponding to neutral stability modes is countable, finite, or empty. It is shown that the semiaxis $d>1$ can be represented as a countable union of half-intervals with split points expressed in terms of the eigenvalues of the Laplace operator; each half-interval is characterized by the minimum wavenumber of loss of stability.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77552008","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
Flows in strongly regular periodic dynamic resource networks 在强规则周期性动态资源网络中流动
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210308
V. Skorokhodov, D.O. Sviridkin
{"title":"Flows in strongly regular periodic dynamic resource networks","authors":"V. Skorokhodov, D.O. Sviridkin","doi":"10.35634/vm210308","DOIUrl":"https://doi.org/10.35634/vm210308","url":null,"abstract":"This paper is devoted to studying the processes of resource allocation in dynamic resource networks. In such networks, the capacities of the arcs depend on time. Resource allocation in the network occurs in discrete time. The resource of each vertex is distributed only between adjacent vertices according to some rules. The study of the processes of resource redistribution in such networks is carried out. The main goal is to develop methods for finding the limit state (distribution) of a resource in a dynamic resource network. It is shown that the approach based on the construction of an auxiliary network is also applicable to reduce the problem of resource allocation in a dynamic network to a similar problem in an auxiliary network. Theorems on the existence of a limit state on an auxiliary graph are proved for strongly regular periodic dynamical networks. To find the limit states, one can use the approaches which are developed for the shortest path problem in dynamic networks.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89047967","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 solving non-homogeneous partial differential equations with right-hand side defined on the grid 求解右手边在网格上定义的非齐次偏微分方程
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210307
L. I. Rubina, O. N. Ul’yanov
{"title":"On solving non-homogeneous partial differential equations with right-hand side defined on the grid","authors":"L. I. Rubina, O. N. Ul’yanov","doi":"10.35634/vm210307","DOIUrl":"https://doi.org/10.35634/vm210307","url":null,"abstract":"An algorithm is proposed for obtaining solutions of partial differential equations with right-hand side defined on the grid ${ x_{1}^{mu}, x_{2}^{mu}, ldots, x_{n}^{mu}}, (mu=1,2,ldots,N)colon f_{mu}=f(x_{1}^{mu}, x_{2}^{mu}, ldots, x_{n}^{mu}).$ Here $n$ is the number of independent variables in the original partial differential equation, $N$ is the number of rows in the grid for the right-hand side, $f=f( x_{1}, x_{2}, ldots, x_{n})$ is the right-hand of the original equation. The algorithm implements a reduction of the original equation to a system of ordinary differential equations (ODE system) with initial conditions at each grid point and includes the following sequence of actions. We seek a solution to the original equation, depending on one independent variable. The original equation is associated with a certain system of relations containing arbitrary functions and including the partial differential equation of the first order. For an equation of the first order, an extended system of equations of characteristics is written. Adding to it the remaining relations containing arbitrary functions, and demanding that these relations be the first integrals of the extended system of equations of characteristics, we arrive at the desired ODE system, completing the reduction. The proposed algorithm allows at each grid point to find a solution of the original partial differential equation that satisfies the given initial and boundary conditions. The algorithm is used to obtain solutions of the Poisson equation and the equation of unsteady axisymmetric filtering at the points of the grid on which the right-hand sides of the corresponding equations are given.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85378756","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
Problem with data on the characteristics for a loaded system of hyperbolic equations 加载双曲方程系统的特性数据问题
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210301
A. Assanova, A. Zholamankyzy
{"title":"Problem with data on the characteristics for a loaded system of hyperbolic equations","authors":"A. Assanova, A. Zholamankyzy","doi":"10.35634/vm210301","DOIUrl":"https://doi.org/10.35634/vm210301","url":null,"abstract":"We consider a problem with data on the characteristics for a loaded system of hyperbolic equations of the second order on a rectangular domain. The questions of the existence and uniqueness of the classical solution of the considered problem, as well as the continuity dependence of the solution on the initial data, are investigated. We propose a new approach to solving the problem with data on the characteristics for the loaded system of hyperbolic equations second order based on the introduction new functions. By introducing new unknown functions the problem is reduced to an equivalent family of Cauchy problems for a loaded system of differential with a parameters and integral relations. An algorithm for finding an approximate solution to the equivalent problem is proposed and its convergence is proved. Conditions for the unique solvability of the problem with data on the characteristics for the loaded system of hyperbolic equations of the second order are established in the terms of coefficient's system.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86038866","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
Asymptotic distribution of hitting times for critical maps of the circle 圆的关键映射命中次数的渐近分布
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210302
Sh. A. Ayupov, A. A. Zhalilov
{"title":"Asymptotic distribution of hitting times for critical maps of the circle","authors":"Sh. A. Ayupov, A. A. Zhalilov","doi":"10.35634/vm210302","DOIUrl":"https://doi.org/10.35634/vm210302","url":null,"abstract":"It is well known that the renormalization group transformation $mathcal{R}$ has a unique fixed point $f_{cr}$ in the space of critical $C^{3}$-circle homeomorphisms with one cubic critical point $x_{cr}$ and the golden mean rotation number $overline{rho}:=frac{sqrt{5}-1}{2}.$ Denote by $Cr(overline{rho})$ the set of all critical circle maps $C^{1}$-conjugated to $f_{cr}.$ Let $fin Cr(overline{rho})$ and let $mu:=mu_{f}$ be the unique probability invariant measure of $f.$ Fix $theta in(0,1).$ For each $ngeq1$ define $c_{n}:=c_{n}(theta)$ such that $mu([x_{cr},c_{n}])=thetacdotmu([x_{cr},f^{q_{n}}(x_{cr})]),$ where $q_{n}$ is the first return time of the linear rotation $f_{overline{rho}}.$ We study convergence in law of rescaled point process of time hitting. We show that the limit distribution is singular w.r.t. the Lebesgue measure.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82196526","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 structure of the singular set of solutions in one class of 3D time-optimal control problems 一类三维时间最优控制问题奇异解集的结构
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210309
A. A. Uspenskii, P. Lebedev
{"title":"On the structure of the singular set of solutions in one class of 3D time-optimal control problems","authors":"A. A. Uspenskii, P. Lebedev","doi":"10.35634/vm210309","DOIUrl":"https://doi.org/10.35634/vm210309","url":null,"abstract":"A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the effectiveness of the developed methods for solving nonsmooth dynamic problems, an example of the numerical-analytical construction of resolving structures of a control problem in terms of speed is given.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82987724","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
Recovery of radial-axial velocity in axisymmetric swirling flows of a viscous incompressible fluid in the Lagrangian consideration of vorticity evolution 考虑涡度演化的拉格朗日条件下粘性不可压缩流体轴对称旋流径向速度的恢复
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210311
E. Prosviryakov
{"title":"Recovery of radial-axial velocity in axisymmetric swirling flows of a viscous incompressible fluid in the Lagrangian consideration of vorticity evolution","authors":"E. Prosviryakov","doi":"10.35634/vm210311","DOIUrl":"https://doi.org/10.35634/vm210311","url":null,"abstract":"Swirling laminar axisymmetric flows of viscous incompressible fluids in a potential field of body forces are considered. The study of flows is carried out in a cylindrical coordinate system. In the flows, the regions in which the axial derivative of the circumferential velocity cannot take on zero value in some open neighborhood (essentially swirling flows) and the regions in which this derivative is equal to zero (the region with layered swirl) are considered separately. It is shown that a well-known method (the method of viscous vortex domains) developed for non-swirling flows can be used for regions with layered swirling. For substantially swirling flows, a formula is obtained for calculating the radial-axial velocity of an imaginary fluid through the circumferential vorticity component, the circumferential circulation of a real fluid, and the partial derivatives of these functions. The particles of this imaginary fluid “transfer” vortex tubes of the radial-axial vorticity component while maintaining the intensity of these tubes, and also “transfer” the circumferential circulation and the product of the circular vorticity component by some function of the distance to the axis of symmetry. A non-integral method for reconstructing the velocity field from the vorticity field is proposed. It is reduced to solving a system of linear algebraic equations in two variables. The obtained result is proposed to be used to extend the method of viscous vortex domains to swirling axisymmetric flows.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87325902","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 projections of products of spaces 关于空间乘积的投影
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2021-09-01 DOI: 10.35634/vm210304
A. Gryzlov
{"title":"On projections of products of spaces","authors":"A. Gryzlov","doi":"10.35634/vm210304","DOIUrl":"https://doi.org/10.35634/vm210304","url":null,"abstract":"We consider dense sets of products of topological spaces. We prove that in the product $Z^c=prodlimits_{alphain 2^omega} Z_{alpha},$ where $Z_alpha=Z$ $(alphain 2^omega),$ there are dense sets such that their countable subsets have projections with additional properties. These properties entail that these dense sets contain no convergent sequences. By these properties we prove that the character of closed sets of the product is uncountable.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82757789","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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