Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta最新文献_第4页

Stability of regular vortex polygons in Bose-Einstein condensate 玻色-爱因斯坦凝聚中规则涡旋多边形的稳定性

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2020-11-01 DOI: 10.35634/2226-3594-2020-56-02

A. Kilin, E. Artemova

引用次数: 3

Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms 一类一阶常项拟线性方程组非局部可解的充分条件

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2020-05-01 DOI: 10.35634/2226-3594-2020-55-05

M. Dontsova

{"title":"Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms","authors":"M. Dontsova","doi":"10.35634/2226-3594-2020-55-05","DOIUrl":"https://doi.org/10.35634/2226-3594-2020-55-05","url":null,"abstract":"We consider a Cauchy problem for a system of two quasilinear equations of the first order with constant terms. The study of the solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms in the original coordinates is based on the method of an additional argument. Theorems on the local and nonlocal existence and uniqueness of solutions to the Cauchy problem are formulated and proved. We prove the existence and uniqueness of the local solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms, which has the same smoothness with respect to $x$ as the initial functions of the Cauchy problem. Sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms are found; this solution is continued by a finite number of steps from the local solution. The proof of the nonlocal solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms relies on global estimates.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"64 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74072637","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

To the question of optimization of the starting point in the routing problem with restrictions 对带约束的路由问题中起点的优化问题进行了研究

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2020-05-01 DOI: 10.35634/2226-3594-2020-55-09

A. Chentsov, P. Chentsov

{"title":"To the question of optimization of the starting point in the routing problem with restrictions","authors":"A. Chentsov, P. Chentsov","doi":"10.35634/2226-3594-2020-55-09","DOIUrl":"https://doi.org/10.35634/2226-3594-2020-55-09","url":null,"abstract":"We consider the extreme routing problem with an additive criterion, the terminal component of which depends on the starting point. This dependence may be associated, in particular, with the requirement to return to the starting point region after completing the final system of tasks that need to be ordered. The work assumes that the tasks to be performed are related with visiting non-empty finite sets called megacities. In turn, the mentioned visits are associated with the performance of works, the costs of which are involved in the formation of the criterion. Finally, the costs of external movements (between megacities) supplement the formation of an additive criterion to be minimized. It is required to find a global extremum and a solution that includes a starting point, the order of visits to megacities and a specific trajectory of the process. The solution uses widely understood dynamic programming (DP). It is significant that procedures based on DP use starting point. Therefore, enumeration of mentioned points is required. The article proposes an approach to solving the problem of reducing this enumeration through the use of auxiliary DP that are universal with respect to the choice of a starting point. The optimal algorithm was built and implemented on a PC using the aforementioned approach.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"27 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90468196","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 certain analogues of linkedness and supercompactness 关于连接和超紧性的某些类似物

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2020-05-01 DOI: 10.35634/2226-3594-2020-55-08

A. Chentsov

{"title":"On certain analogues of linkedness and supercompactness","authors":"A. Chentsov","doi":"10.35634/2226-3594-2020-55-08","DOIUrl":"https://doi.org/10.35634/2226-3594-2020-55-08","url":null,"abstract":"Natural generalizations of properties of the family linkedness and the topological space supercompactness are considered. We keep in mind reinforced linkedness when nonemptyness of intersection of preassigned number of sets from a family is postulated. Analogously, supercompactness is modified: it is postulated the existence of an open subbasis for which, from every covering (by sets of the subbasis), it is possible to extract a subcovering with a given number of sets (more precisely, not more than a given number). It is clear that among all families having the reinforced linkedness, one can distinguish families that are maximal in ordering by inclusion. Under natural and (essentially) “minimal”' conditions imposed on the original measurable structure, among the mentioned maximal families with reinforced linkedness, ultrafilters are certainly contained. These ultrafilters form subspaces in the sense of natural topologies corresponding conceptually to schemes of Wallman and Stone. In addition, maximal families with reinforced linkedness, when applying topology of the Wallman type, have the above-mentioned property generalizing supercompactness. Thus, an analogue of the superextension of the $T_1$-space is realized. The comparability of “Wallman”' and “Stone”' topologies is established. As a result, bitopological spaces (BTS) are realized; for these BTS, under equipping with analogous topologies, ultrafilter sets are subspaces. It is indicated that some cases exist when the above-mentioned BTS is nondegenerate in the sense of the distinction for forming topologies. At that time, in the case of “usual” linkedness (this is a particular case of reinforced linkedness), very general classes of spaces are known for which the mentioned BTS are degenerate (the cases when origial set, i.e., “unit”' is equipped with an algebra of sets or a topology).","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"57 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75912608","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

Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables 具有凸积分质量指标的奇摄动最优控制问题解的渐近展开式，该问题的终端部分加性地依赖于慢变量和快变量

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2020-05-01 DOI: 10.35634/2226-3594-2020-55-03

A. R. Danilin, A. A. Shaburov

{"title":"Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables","authors":"A. R. Danilin, A. A. Shaburov","doi":"10.35634/2226-3594-2020-55-03","DOIUrl":"https://doi.org/10.35634/2226-3594-2020-55-03","url":null,"abstract":"The paper deals with the problem of optimal control with a Boltz-type quality index over a finite time interval for a linear steady-state control system in the class of piecewise continuous controls with smooth control constraints. In particular, we study the problem of controlling the motion of a system of small mass points under the action of a bounded force. The terminal part of the convex integral quality index additively depends on slow and fast variables, and the integral term is a strictly convex function of control variable. If the system is completely controllable, then the Pontryagin maximum principle is a necessary and sufficient condition for optimality. The main difference between this study and previous works is that the equation contains the zero matrix of fast variables and, thus, the results of A.B. Vasilieva on the asymptotic of the fundamental matrix of a control system are not valid. However, the linear steady-state system satisfies the condition of complete controllability. The article shows that problems of optimal control with a convex integral quality index are more regular than time-optimal problems.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"31 5 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90294357","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

Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature 一类具有目标集边界曲率跳跃的时间最优控制问题散射曲线的构造

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2020-05-01 DOI: 10.35634/2226-3594-2020-55-07

P. Lebedev, A. A. Uspenskii

{"title":"Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature","authors":"P. Lebedev, A. A. Uspenskii","doi":"10.35634/2226-3594-2020-55-07","DOIUrl":"https://doi.org/10.35634/2226-3594-2020-55-07","url":null,"abstract":"We consider a time-optimal control problem on the plane with a circular vectogram of velocities and a non-convex target set with a boundary having a finite number of points of discontinuity of curvature. We study the problem of identifying and constructing scattering curves that form a singular set of the optimal result function in the case when the points of discontinuity of curvature have one-sided curvatures of different signs. It is shown that these points belong to pseudo-vertices that are characteristic points of the boundary of the target set, which are responsible for the generation of branches of a singular set. The structure of scattering curves and the optimal trajectories starting from them, which fall in the neighborhood of the pseudo-vertex, is investigated. A characteristic feature of the case under study is revealed, consisting in the fact that one pseudo-vertex can generate two different branches of a singular set. The equation of the tangent to the smoothness points of the scattering curve is derived. A scheme is proposed for constructing a singular set, based on the construction of integral curves for first-order differential equations in normal form, the right-hand sides of which are determined by the geometry of the boundary of the target in neighborhoods of the pseudo-vertices. The results obtained are illustrated by the example of solving the control problem when the target set is a one-dimensional manifold.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"29 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89463346","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

The routing problems with optimization of the starting point: dynamic programming 带优化起点的路径问题:动态规划

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2019-12-09 DOI: 10.20537/2226-3594-2019-54-08

Chentsov Aleksandr Georgievich, Chentsov Pavel Aleksandrovich

引用次数: 2

Persecution of rigidly coordinated evaders in a linear problem with fractional derivatives and a simple matrix 具有分数阶导数和简单矩阵的线性问题中刚性协调逃避者的迫害

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2019-11-01 DOI: 10.20537/2226-3594-2019-54-04

A. I. Machtakova

引用次数: 0

On the supercompactness of ultrafilter space with the topology of Wallman type Wallman型拓扑下超滤空间的超紧性

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2019-11-01 DOI: 10.20537/2226-3594-2019-54-07

A. Chentsov

引用次数: 2

On the spectrum of a relativistic Landau Hamiltonian with a periodic electric potential 具有周期电势的相对论性朗道哈密顿谱

IF 0.4

Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2019-11-01 DOI: 10.20537/2226-3594-2019-54-01

L. I. Danilov

引用次数: 0