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Stabilized Scheme for Calculating Radiation Transfer in the P1 Approximation
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-11-11 DOI: 10.1134/S1064562424601495
B. N. Chetverushkin, O. G. Olkhovskaya, V. A. Gasilov
{"title":"Stabilized Scheme for Calculating Radiation Transfer in the P1 Approximation","authors":"B. N. Chetverushkin,&nbsp;O. G. Olkhovskaya,&nbsp;V. A. Gasilov","doi":"10.1134/S1064562424601495","DOIUrl":"10.1134/S1064562424601495","url":null,"abstract":"<p>We consider interpolation-characteristic schemes approximating the radiative transfer equation corresponding to the <span>({{P}_{1}})</span> model. The model equations are modified by adjusting the rate of radiation energy transfer. This correction can reduce the influence of nonphysical effects in calculating radiative heat transfer in a medium with nonuniform opacity.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"393 - 398"},"PeriodicalIF":0.5,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108567","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
Analytic Method for Solving One Class of Nonlinear Equations
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-11-11 DOI: 10.1134/S1064562424601392
Yu. S. Popkov
{"title":"Analytic Method for Solving One Class of Nonlinear Equations","authors":"Yu. S. Popkov","doi":"10.1134/S1064562424601392","DOIUrl":"10.1134/S1064562424601392","url":null,"abstract":"<p>An analytical approximate method for calculating multidimensional integrals of analytic functions is proposed, in which the integrand is approximated by a power series. This approach transforms the original system of nonlinear equations with integral components into a system of equations with a polynomial left-hand side. To solve equations of this class, an analytical method based on abstract power series is developed. A recurrent procedure is developed for the analytical solution of this class of nonlinear equations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"404 - 407"},"PeriodicalIF":0.5,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108562","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
An Exact Quadratic Algorithm for the Shortest Tree Transformation
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-29 DOI: 10.1134/S1064562424702259
K. Yu. Gorbunov, V. A. Lyubetsky
{"title":"An Exact Quadratic Algorithm for the Shortest Tree Transformation","authors":"K. Yu. Gorbunov,&nbsp;V. A. Lyubetsky","doi":"10.1134/S1064562424702259","DOIUrl":"10.1134/S1064562424702259","url":null,"abstract":"<p>The article proposes a new exact algorithm of quadratic complexity that solves the problem of the shortest transformation (“alignment”) of one weighted tree into another, taking into account arbitrary costs of operations on trees. Three operations are considered: adding vertex deletions to an edge or root of a tree and shifting a subtree with deletions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"373 - 378"},"PeriodicalIF":0.5,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110135","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 Supplement to Krasovskii’s Unification Method in Differential Game Theory
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-29 DOI: 10.1134/S1064562424601604
V. N. Ushakov, A. M. Tarasyev, A. A. Ershov
{"title":"A Supplement to Krasovskii’s Unification Method in Differential Game Theory","authors":"V. N. Ushakov,&nbsp;A. M. Tarasyev,&nbsp;A. A. Ershov","doi":"10.1134/S1064562424601604","DOIUrl":"10.1134/S1064562424601604","url":null,"abstract":"<p>The paper deals with the game problem of approach for a conflict-controlled system in a finite-dimensional Euclidean space at a fixed moment of time. The approximate calculation of the solvability sets for the considered approach game is studied. A method is proposed for approximate calculation of solvability sets on the basis of a unification model, which supplements Krasovskii’s unification method in the theory of differential games.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"386 - 392"},"PeriodicalIF":0.5,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110134","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
Construction of Smooth Source–Sink Arcs in the Space of Diffeomorphisms of a Two-Dimensional Sphere
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-29 DOI: 10.1134/S1064562424702260
E. V. Nozdrinova, O. V. Pochinka, E. V. Tsaplina
{"title":"Construction of Smooth Source–Sink Arcs in the Space of Diffeomorphisms of a Two-Dimensional Sphere","authors":"E. V. Nozdrinova,&nbsp;O. V. Pochinka,&nbsp;E. V. Tsaplina","doi":"10.1134/S1064562424702260","DOIUrl":"10.1134/S1064562424702260","url":null,"abstract":"<p>It is well known that the mapping class group of the two-dimensional sphere <span>({{mathbb{S}}^{2}})</span> is isomorphic to the group <span>({{mathbb{Z}}_{2}} = { - 1, + 1} )</span>. At the same time, the class +1(–1) contains all orientation-preserving (orientation-reversing) diffeomorphisms and any two diffeomorphisms of the same class are diffeotopic, that is, they are connected by a smooth arc of diffeomorphisms. On the other hand, each class of maps contains structurally stable diffeomorphisms. It is obvious that in the general case, the arc connecting two diffeotopic structurally stable diffeomorphisms undergoes bifurcations that destroy structural stability. In this direction, it is particular interesting in the question of the existence of a connecting them stable arc – an arc pointwise conjugate to arcs in some of its neighborhood. In general, diffeotopic structurally stable diffeomorphisms of the 2-sphere are not connected by a stable arc. In this paper, the simplest structurally stable diffeomorphisms (source–sink diffeomorphisms) of the 2-sphere are considered. The non-wandering set of such diffeomorphisms consists of two hyperbolic points: the source and the sink. In this paper, the existence of an arc connecting two such orientation-preserving (orientation-reversing) diffeomorphisms and consisting entirely of source-sink diffeomorphisms is constructively proved.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"379 - 385"},"PeriodicalIF":0.5,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110148","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
Addition to the Article “A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise” 对文章 "复杂性的新频谱测量及其在噪声中检测信号的能力 "的补充
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-20 DOI: 10.1134/S1064562424702247
A. A. Galyaev, V. G. Babikov, P. V. Lysenko, L. M. Berlin
{"title":"Addition to the Article “A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise”","authors":"A. A. Galyaev,&nbsp;V. G. Babikov,&nbsp;P. V. Lysenko,&nbsp;L. M. Berlin","doi":"10.1134/S1064562424702247","DOIUrl":"10.1134/S1064562424702247","url":null,"abstract":"<p>An addition to the article “A new spectral measure of complexity and its capabilities for detecting signals in noise” is presented.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 1","pages":"369 - 371"},"PeriodicalIF":0.5,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679664","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 the Accuracy of Calculating Invariants in Centered Rarefaction Waves and in Their Influence Area 论计算居中的稀释波及其影响区域中的不变量的准确性
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-20 DOI: 10.1134/S1064562424702211
V. V. Ostapenko, E. I. Polunina, N. A. Khandeeva
{"title":"On the Accuracy of Calculating Invariants in Centered Rarefaction Waves and in Their Influence Area","authors":"V. V. Ostapenko,&nbsp;E. I. Polunina,&nbsp;N. A. Khandeeva","doi":"10.1134/S1064562424702211","DOIUrl":"10.1134/S1064562424702211","url":null,"abstract":"<p>We perform a comparative analysis of the accuracy of second-order TVD (Total Variation Diminishing), third-order RBM (Rusanov–Burstein–Mirin), and fifth-order in space and third-order in time A-WENO (Alternative Weighted Essentially Non-Oscillatory) difference schemes for solving a special Cauchy problem for shallow water equations with discontinuous initial data. The exact solution of this problem contains a centered rarefaction wave, but does not contain a shock wave. It is shown that in the centered rarefaction wave and its influence area, the solutions of these three schemes converge with different orders to different invariants of the exact solution. This leads to a decrease in the accuracy of these schemes when they used to calculate the vector of base variables of the considered Cauchy problem. The P-form of the first differential approximation of the difference schemes is used for theoretical justification of these numerical results.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 1","pages":"349 - 356"},"PeriodicalIF":0.5,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679672","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
Getting over Wide Obstacles by a Multi-Legged Robot 多腿机器人跨越宽阔障碍物
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-20 DOI: 10.1134/S1064562424601136
Yu. F. Golubev
{"title":"Getting over Wide Obstacles by a Multi-Legged Robot","authors":"Yu. F. Golubev","doi":"10.1134/S1064562424601136","DOIUrl":"10.1134/S1064562424601136","url":null,"abstract":"<p>An upper estimate for the maximum width of a forbidden foothold zone that a multi-legged walking robot can overcome in static stability mode is presented. By using mathematical models of six- and four-legged robots, it is shown that the estimate cannot be improved. For this purpose, foot placement sequences are formed for which the estimate is attained. The dependence of the maximum width of the zone on the body length is found for the six-legged robot model.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 1","pages":"328 - 336"},"PeriodicalIF":0.5,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679671","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
Semi-Analytical Solution of Brent Equations 布伦特方程的半解析解法
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-20 DOI: 10.1134/S1064562424702223
I. E. Kaporin
{"title":"Semi-Analytical Solution of Brent Equations","authors":"I. E. Kaporin","doi":"10.1134/S1064562424702223","DOIUrl":"10.1134/S1064562424702223","url":null,"abstract":"<p>A parametrization of Brent equations is proposed which leads to a several times reduction of the number of unknowns and equations. The arising equations are solved numerically using a nonlinear least squares method. Matrix multiplication algorithms that are faster than previously known ones are obtained. In particular, <span>((4,4,4;48))</span>- and <span>((2,4,5;32))</span>-algorithms are found.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 1","pages":"318 - 322"},"PeriodicalIF":0.5,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679555","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 a Dini Type Blow-Up Condition for Solutions of Higher Order Nonlinear Differential Inequalities 论高阶非线性微分不等式解的迪尼型炸裂条件
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-10-20 DOI: 10.1134/S1064562424601276
A. A. Kon’kov, A. E. Shishkov
{"title":"On a Dini Type Blow-Up Condition for Solutions of Higher Order Nonlinear Differential Inequalities","authors":"A. A. Kon’kov,&nbsp;A. E. Shishkov","doi":"10.1134/S1064562424601276","DOIUrl":"10.1134/S1064562424601276","url":null,"abstract":"<p>We obtain a Dini type blow-up condition for solutions of the differential inequality <span>(sumlimits_{|alpha | = m} {{partial }^{alpha }}{{a}_{alpha }}(x,u) geqslant g({text{|}}u{text{|)}};{text{in}};{kern 1pt} {{mathbb{R}}^{n}},)</span> where <span>(m,n geqslant 1)</span> are integers and <span>({{a}_{alpha }})</span> and <i>g</i> are some functions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 1","pages":"308 - 311"},"PeriodicalIF":0.5,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679665","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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