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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Numerical-Statistical Investigation of Superexponential Growth of Mean Particle Flow with Multiplication in a Homogeneous Random Medium 均质随机介质中平均粒子流倍增超指数增长的数值统计研究
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S106456242370148X
G. A. Mikhailov, G. Z. Lotova
{"title":"Numerical-Statistical Investigation of Superexponential Growth of Mean Particle Flow with Multiplication in a Homogeneous Random Medium","authors":"G. A. Mikhailov,&nbsp;G. Z. Lotova","doi":"10.1134/S106456242370148X","DOIUrl":"10.1134/S106456242370148X","url":null,"abstract":"<p>A new correlative-grid approximation of a homogeneous random field is introduced for an effective numerical-analytical investigation of the superexponential growth of the mean particle flow with multiplication in a random medium. The complexity of particle trajectory realization is independent of the correlation scale. Test computations for a critical ball with isotropic scattering showed high accuracy of the corresponding mean flow estimates. For the correlative-grid approximation of a random density field, the possibility of Gaussian asymptotics of the mean particle multiplication rate as the correlation scale decreases is justified.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411750","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
Bernstein Inequality for the Riesz Derivative of Fractional Order Less Than Unity of Entire Functions of Exponential Type 指数型全函数小于整数阶的里兹衍的伯恩斯坦不等式
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701491
A. O. Leont’eva
{"title":"Bernstein Inequality for the Riesz Derivative of Fractional Order Less Than Unity of Entire Functions of Exponential Type","authors":"A. O. Leont’eva","doi":"10.1134/S1064562423701491","DOIUrl":"10.1134/S1064562423701491","url":null,"abstract":"<p>We consider Bernstein inequality for the Riesz derivative of order <span>(0 &lt; alpha &lt; 1)</span> of entire function of exponential type in the uniform norm on the real line. The interpolation formula is obtained for this operator; this formula has non-equidistant nodes. By means of this formula, the exact Bernstein inequality is found for all <span>(0 &lt; alpha &lt; 1)</span>, namely, the extremal entire function and the sharp constant are written out.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884765","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
Mathematical Modeling of Plasma Transport in a Helical Magnetic Field 螺旋磁场中等离子体传输的数学建模
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-03-14 DOI: 10.1134/S1064562423701508
G. G. Lazareva, I. P. Oksogoeva, A. V. Sudnikov
{"title":"Mathematical Modeling of Plasma Transport in a Helical Magnetic Field","authors":"G. G. Lazareva,&nbsp;I. P. Oksogoeva,&nbsp;A. V. Sudnikov","doi":"10.1134/S1064562423701508","DOIUrl":"10.1134/S1064562423701508","url":null,"abstract":"<p>The paper presents the results of mathematical modeling of plasma transport in a spiral magnetic field using new experimental data obtained at the SMOLA trap created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences. Plasma confinement in the trap is carried out by transmitting a pulse from a magnetic field with helical symmetry to a rotating plasma. A new mathematical model is based on a stationary plasma transport equation in an axially symmetric formulation. The distribution of the plasma concentration obtained by numerical simulation confirmed the confinement effect obtained in the experiment. The dependences of the integral characteristics of the plasma on the depth of corrugation of the magnetic field, diffusion, and plasma potential are obtained. The mathematical model is intended to predict plasma confinement parameters in designing traps with a spiral magnetic field.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884533","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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