Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki最新文献_第5页

On one problem of controlling the heating of a rod system under uncertainty 关于不确定条件下棒材加热控制问题

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-12-01 DOI: 10.35634/vm220404

I. Izmest'ev, V. Ukhobotov

引用次数: 0

Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane 滚轮赛车在振动平面上直线运动的轨道稳定性研究

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-12-01 DOI: 10.35634/vm220408

E. Artemova, A. Kilin, Yu.V. Korobeinikova

引用次数: 0

Pseudo semi-projective modules and endomorphism rings 伪半投影模与自同态环

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-12-01 DOI: 10.35634/vm220405

N. Ha

引用次数: 0

On totally global solvability of evolutionary Volterra equation of the second kind 第二类进化Volterra方程的全局可解性

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-12-01 DOI: 10.35634/vm220407

A. Chernov

引用次数: 1

On the parametric dependence of the volume of integral funnels and their approximations 积分漏斗体积的参数依赖性及其近似

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220307

V. Ushakov, A. Ershov

{"title":"On the parametric dependence of the volume of integral funnels and their approximations","authors":"V. Ushakov, A. Ershov","doi":"10.35634/vm220307","DOIUrl":"https://doi.org/10.35634/vm220307","url":null,"abstract":"We consider a nonlinear control system in a finite-dimensional Euclidean space and on a finite time interval, which depends on a parameter. Reachable sets and integral funnels of a differential inclusion corresponding to a control system containing a parameter are studied. When studying numerous problems of control theory and differential games, constructing their solutions and estimating errors, various theoretical approaches and associated computational methods are used. The problems mentioned above include, for example, various types of approach problems, the resolving constructions of which can be described quite simply in terms of reachable sets and integral funnels.\u0000In this paper, we study the dependence of reachable sets and integral funnels on a parameter: the degree of this dependence on a parameter is estimated under certain conditions on the control system. The degree of dependence of the integral funnels is investigated for the change in their volume with a change in the parameter. To estimate this dependence, systems of sets in the phase space are introduced that approximate the reachable sets and integral funnels on a given time interval corresponding to a finite partition of this interval. In this case, the degree of dependence of the approximating system of sets on the parameter is first estimated, and then this estimate is used in estimating the dependence of the volume of the integral funnel of the differential inclusion on the parameter. This approach is natural and especially useful in the study of specific applied control problems, in solving which, in the end, one has to deal not with ideal reachable sets and integral funnels, but with their approximations corresponding to a discrete representation of the time interval.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85285937","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

Local antimagic chromatic number for the corona product of wheel and null graphs 轮图与零图的电晕积的局部反幻色数

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220308

Rathinavel Shankar, M. Nalliah

引用次数: 0

On nonlinear metric spaces of functions of bounded variation 关于有界变分函数的非线性度量空间

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220301

V. N. Baranov, V. Rodionov

{"title":"On nonlinear metric spaces of functions of bounded variation","authors":"V. N. Baranov, V. Rodionov","doi":"10.35634/vm220301","DOIUrl":"https://doi.org/10.35634/vm220301","url":null,"abstract":"In the first part of the paper, the nonlinear metric space $langleoverline{rm G}^infty[a,b],drangle$ is defined and studied. It consists of functions defined on the interval $[a,b]$ and taking the values in the extended numeric axis $overline{mathbb R}$. For any $xinoverline{rm G}^infty[a,b]$ and $tin(a,b)$ there are limit numbers $x(t-0),x(t+0) inoverline{mathbb R}$ (and numbers $x(a+0),x(b-0)inoverline{mathbb R}$). The completeness of the space is proved. It is the closure of the space of step functions in the metric $d$. In the second part of the work, the nonlinear space ${rm RL}[a,b]$ is defined and studied. Every piecewise smooth function defined on $[a,b]$ is contained in ${rm RL}[a,b]$. Every function $xin{rm RL}[a,b]$ has bounded variation. All one-sided derivatives (with values in the metric space $langleoverline{mathbb R},varrhorangle$) are defined for it. The function of left-hand derivatives is continuous on the left, and the function of right-hand derivatives is continuous on the right. Both functions extended to the entire interval $[a,b]$ belong to the space $overline{rm G}^infty[a,b]$. In the final part of the paper, two subspaces of the space ${rm RL}[a,b]$ are defined and studied. In subspaces, promising formulations for the simplest variational problems are stated and discussed.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77476025","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

Upper and lower directional derivative sets and differentials of the set valued maps 集值映射的上、下方向导数集和微分

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220304

Nihal Ege, A. Huseyin, N. Huseyin

引用次数: 0

On a boundary value problem for a class of fractional Langevin type differential equations in a Banach space Banach空间中一类分数阶Langevin型微分方程的边值问题

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220305

G. Petrosyan

引用次数: 0

On one inclusion with a mapping acting from a partially ordered set to a set with a reflexive binary relation 在一个包含上，从偏序集合映射到具有自反二元关系的集合

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220302

S. Benarab, E. Panasenko

{"title":"On one inclusion with a mapping acting from a partially ordered set to a set with a reflexive binary relation","authors":"S. Benarab, E. Panasenko","doi":"10.35634/vm220302","DOIUrl":"https://doi.org/10.35634/vm220302","url":null,"abstract":"Set-valued mappings acting from a partially ordered space $X=(X,leq)$ to a set $Y$ on which a reflexive binary relation $vartheta$ is given (this relation is not supposed to be antisymmetric or transitive, i.e., $vartheta$ is not an order in $Y$), are considered. For such mappings, analogues of the concepts of covering and monotonicity are introduced. These concepts are used to study the inclusion $F(x)ni tilde{y},$ where $Fcolon X rightrightarrows Y,$ $tilde{y}in Y.$ It is assumed that for some given $x_0 in X,$ there exists $y_{0} in F(x_{0})$ such that $(tilde{y},y_{0}) in vartheta.$ Conditions for the existence of a solution $xin X$ satisfying the inequality $xleq x_0$ are obtained, as well as those for the existence of minimal and least solutions. The property of stability of solutions of the considered inclusion to changes of the set-valued mapping $F$ and of the element $widetilde{y}$ is also defined and investigated. Namely, the sequence of “perturbed” inclusions $F_i(x)ni tilde{y}_i,$ $iin mathbb{N},$ is assumed, and the conditions of existence of solutions $x_i in X$ such that for any increasing sequence of integers ${i_n}$ there holds $sup_{n in mathbb{N}}{x_{i_{n}}}= x,$ where $x in X$ is a solution of the initial inclusion, are derived.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79168475","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