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Invariants of Fifth-Order Homogeneous Systems with Dissipation 带耗散的五阶均相系统的不变式
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701466
M. V. Shamolin
{"title":"Invariants of Fifth-Order Homogeneous Systems with Dissipation","authors":"M. V. Shamolin","doi":"10.1134/S1064562423701466","DOIUrl":"10.1134/S1064562423701466","url":null,"abstract":"<p>New cases of integrable fifth-order dynamical systems that are homogeneous with respect to some of the variables are obtained, in which a system on the tangent bundle of a two-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"506 - 513"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Upper Bound for the Competitive Facility Location Problem with Demand Uncertainty 具有需求不确定性的竞争性设施选址问题的上限
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423600318
V. L. Beresnev, A. A. Melnikov
{"title":"Upper Bound for the Competitive Facility Location Problem with Demand Uncertainty","authors":"V. L. Beresnev,&nbsp;A. A. Melnikov","doi":"10.1134/S1064562423600318","DOIUrl":"10.1134/S1064562423600318","url":null,"abstract":"<p>We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenarios. The problem of finding the best solutions for the parties is formulated as a discrete bilevel mathematical programming problem. A procedure for computing an upper bound for the objective function on solution subsets is suggested. The procedure could be employed in implicit enumeration schemes capable of computing an optimal solution for the problem under study. Within the procedure, additional constraints (cuts) iteratively augment the high-point relaxation of the initial bilevel problem, which strengthens the relaxation and improves the upper bound’s quality. A new procedure for generating such cuts is proposed, which allows us to construct the strongest cuts without enumerating the parameters encoding them.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"438 - 442"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Barenblatt–Zeldovich Intermediate Asymptotics 论巴伦布拉特-塞尔多维奇中间渐近线
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701351
V. A. Kostin, D. V. Kostin, A. V. Kostin
{"title":"On Barenblatt–Zeldovich Intermediate Asymptotics","authors":"V. A. Kostin,&nbsp;D. V. Kostin,&nbsp;A. V. Kostin","doi":"10.1134/S1064562423701351","DOIUrl":"10.1134/S1064562423701351","url":null,"abstract":"<p>The concept of intermediate asymptotics for the solution of an evolution equation with initial data and a related solution obtained without initial conditions was introduced by G.N. Barenblatt and Ya.B. Zeldovich in the context of extending the concept of strict determinism in statistical physics and quantum mechanics. Here, according to V.P. Maslov, to axiomatize the mathematical theory, we need to know the conditions satisfied by the initial data of the problem. We show that the correct solvability of a problem without initial conditions for fractional differential equations in a Banach space is a necessary, but not sufficient, condition for intermediate asymptotics. Examples of intermediate asymptotics are given.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"454 - 458"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multidimensional Cubature Formulas with Superpower Convergence 具有超强收敛性的多维立体公式
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701478
A. A. Belov, M. A. Tintul
{"title":"Multidimensional Cubature Formulas with Superpower Convergence","authors":"A. A. Belov,&nbsp;M. A. Tintul","doi":"10.1134/S1064562423701478","DOIUrl":"10.1134/S1064562423701478","url":null,"abstract":"<p>In many applications, multidimensional integrals over the unit hypercube arise, which are calculated using Monte Carlo methods. The convergence of the best of them turns out to be quite slow. In this paper, fundamentally new cubature formulas with superpower convergence based on improved Korobov grids and a special variable substitution are proposed. A posteriori error estimates are constructed, which are nearly indistinguishable from the actual accuracy. Examples of calculations illustrating the advantages of the proposed methods are given.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"514 - 518"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and Relaxation of Solutions for a Differential Inclusion with Maximal Monotone Operators and Perturbations 具有最大单调算子和扰动的微分包容的解的存在性和松弛性
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701399
A. A. Tolstonogov
{"title":"Existence and Relaxation of Solutions for a Differential Inclusion with Maximal Monotone Operators and Perturbations","authors":"A. A. Tolstonogov","doi":"10.1134/S1064562423701399","DOIUrl":"10.1134/S1064562423701399","url":null,"abstract":"<p>A differential inclusion with a time-dependent maximal monotone operator and a perturbation is studied in a separable Hilbert space. The perturbation is the sum of a time-dependent single-valued operator and a multivalued mapping with closed nonconvex values. A particular feature of the single-valued operator is that its sum with the identity operator multiplied by a positive square-integrable function is a monotone operator. The multivalued mapping is Lipschitz continuous with respect to the phase variable. We prove the existence of a solution and the density in the corresponding topology of the solution set of the initial inclusion in the solution set of the inclusion with a convexified multivalued mapping. For these purposes, new distances between maximal monotone operators are introduced.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"477 - 480"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimation of Tetrahedron Degeneration in a Tetrahedral Partition of Three-Dimensional Space 三维空间四面体分区中的四面体退化估算
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701363
Yu. A. Kriksin,  V. F. Tishkin
{"title":"Estimation of Tetrahedron Degeneration in a Tetrahedral Partition of Three-Dimensional Space","authors":"Yu. A. Kriksin,&nbsp; V. F. Tishkin","doi":"10.1134/S1064562423701363","DOIUrl":"10.1134/S1064562423701363","url":null,"abstract":"<p>Based on the geometric characteristics of a tetrahedron, quantitative estimates of its degeneracy are proposed and their relationship with the condition number of local bases generated by the edges emerging from a single vertex is established. The concept of the tetrahedron degeneracy index is introduced in several versions, and their practical equivalence to each other is established. To assess the quality of a particular tetrahedral partition, we propose calculating the empirical distribution function of the degeneracy index on its tetrahedral elements. An irregular model triangulation (tetrahedralization or tetrahedral partition) of three-dimensional space is proposed, depending on a control parameter that determines the quality of its elements. The coordinates of the tetrahedra vertices of the model triangulation tetrahedra are the sums of the corresponding coordinates of the nodes of some given regular mesh and random increments to them. For various values of the control parameter, the empirical distribution function of the tetrahedron degeneracy index is calculated, which is considered as a quantitative characteristic of the quality of tetrahedra in the triangulation of a three-dimensional region.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"459 - 465"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Stability Estimate in the Source Problem for the Radiative Transfer Equation 辐射传递方程源问题中的稳定性估算
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S106456242370134X
V. G. Romanov
{"title":"A Stability Estimate in the Source Problem for the Radiative Transfer Equation","authors":"V. G. Romanov","doi":"10.1134/S106456242370134X","DOIUrl":"10.1134/S106456242370134X","url":null,"abstract":"<p>A stability estimate for the solution of a source problem for the stationary radiative transfer equation is given. It is supposed that the source has an isotropic distribution. Earlier, stability estimates for this problem were found in a partial case of the emission tomography problem with a vanishing scattering operator and for the complete transfer equation under additional difficult-to-check conditions imposed on the absorption coefficient and the scattering kernel. In this work, we suggest a new fairly simple approach for obtaining a stability estimate for the problem under the consideration. The transfer equation is considered in a circle of the two-dimension space. In the forward problem, it is assumed that incoming radiation is absent. In the inverse problem of recovering the unknown source, data on solutions of the forward problem related to outgoing radiation are given on a portion of the boundary. The obtained result can be used to estimate the total density of distributed radiation sources.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"450 - 453"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Operator Group Generated by a One-Dimensional Dirac System 一维狄拉克系统产生的算子组
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701430
A. M. Savchuk, I. V. Sadovnichaya
{"title":"Operator Group Generated by a One-Dimensional Dirac System","authors":"A. M. Savchuk,&nbsp;I. V. Sadovnichaya","doi":"10.1134/S1064562423701430","DOIUrl":"10.1134/S1064562423701430","url":null,"abstract":"<p>In this paper, we construct a strongly continuous operator group generated by a one-dimensional Dirac operator acting in the space <span>(mathbb{H} = {{left( {{{L}_{2}}[0,pi ]} right)}^{2}})</span>. The potential is assumed to be summable. It is proved that this group is well-defined in the space <span>(mathbb{H})</span> and in the Sobolev spaces <span>(mathbb{H}_{U}^{theta })</span>, <span>(theta &gt; 0)</span>, with a fractional index of smoothness θ and boundary conditions <i>U</i>. Similar results are proved in the spaces <span>({{left( {{{L}_{mu }}[0,pi ]} right)}^{2}})</span>, <span>(mu in (1,infty ))</span>. In addition, we obtain estimates for the growth of the group as <span>(t to infty )</span>.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"490 - 492"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of a Maximum of Time-Averaged Harvesting in the KPP Model on Sphere with Permanent and Impulse Harvesting 具有永久和脉冲收获的球面 KPP 模型中时间平均收获最大值的存在性
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701387
E. V. Vinnikov, A. A. Davydov, D. V. Tunitsky
{"title":"Existence of a Maximum of Time-Averaged Harvesting in the KPP Model on Sphere with Permanent and Impulse Harvesting","authors":"E. V. Vinnikov,&nbsp;A. A. Davydov,&nbsp;D. V. Tunitsky","doi":"10.1134/S1064562423701387","DOIUrl":"10.1134/S1064562423701387","url":null,"abstract":"<p>A distributed renewable resource of any nature is considered on a two-dimensional sphere. Its dynamics is described by a model of the Kolmogorov–Petrovsky–Piskunov–Fisher type, and the exploitation of this resource is carried out by constant or periodic impulse harvesting. It is shown that, after choosing an admissible exploitation strategy, the dynamics of the resource tend to limiting dynamics corresponding to this strategy and there is an admissible harvesting strategy that maximizes the time-averaged harvesting of the resource.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"472 - 476"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conditional Cost Function and Necessary Optimality Conditions for Infinite Horizon Optimal Control Problems 无限视界最优控制问题的条件成本函数和必要最优条件
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423600586
S. M. Aseev
{"title":"Conditional Cost Function and Necessary Optimality Conditions for Infinite Horizon Optimal Control Problems","authors":"S. M. Aseev","doi":"10.1134/S1064562423600586","DOIUrl":"10.1134/S1064562423600586","url":null,"abstract":"<p>An infinite horizon optimal control problem with general endpoint constraints is reduced to a family of standard problems on finite time intervals containing the conditional cost of the phase vector as a terminal term. A new version of the Pontryagin maximum principle containing an explicit characterization of the adjoint variable is obtained for the problem with a general asymptotic endpoint constraint. In the case of the problem with a free final state, this approach leads to a normal form version of the maximum principle formulated completely in the terms of the conditional cost function.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"425 - 430"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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