Pub Date : 2024-09-13DOI: 10.1134/s1064562424601434
M. V. Shamolin
Abstract
New cases of integrable ninth-order dynamical systems that are homogeneous in terms of some of their variables are presented, in which a system on the tangent bundle of a four-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 it generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.
{"title":"New Cases of Integrable Ninth-Order Conservative and Dissipative Dynamical Systems","authors":"M. V. Shamolin","doi":"10.1134/s1064562424601434","DOIUrl":"https://doi.org/10.1134/s1064562424601434","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>New cases of integrable ninth-order dynamical systems that are homogeneous in terms of some of their variables are presented, in which a system on the tangent bundle of a four-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 it generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142181030","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}
Pub Date : 2024-09-13DOI: 10.1134/s1064562424601148
S. I. Uvarov
Abstract
This paper is devoted to the localisation of random 3-CNF formulas that are polynomially solvable by the resolution algorithm. It is shown that random formulas with the number of clauses proportional to the square of the number of variables, are polynomially solvable with probability close to unity when the proportionality coefficient exceeds the found threshold.
{"title":"Sufficient Condition for Polynomial Solvability of Random 3-CNF Formulas","authors":"S. I. Uvarov","doi":"10.1134/s1064562424601148","DOIUrl":"https://doi.org/10.1134/s1064562424601148","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper is devoted to the localisation of random 3-CNF formulas that are polynomially solvable by the resolution algorithm. It is shown that random formulas with the number of clauses proportional to the square of the number of variables, are polynomially solvable with probability close to unity when the proportionality coefficient exceeds the found threshold.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223729","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}
Pub Date : 2024-09-13DOI: 10.1134/s106456242470217x
N. N. Avdeev, R. E. Zvolinskii, E. M. Semenov, A. S. Usachev
Abstract
Criteria for a Banach limit to belong to the discrete or continuous part of the set of Banach limits are presented. The diameters and radii of these parts are found.
摘要 提出了巴拿赫极限属于巴拿赫极限集合离散或连续部分的标准。求出了这些部分的直径和半径。
{"title":"The Set of Banach Limits and Its Discrete and Continuous Subsets","authors":"N. N. Avdeev, R. E. Zvolinskii, E. M. Semenov, A. S. Usachev","doi":"10.1134/s106456242470217x","DOIUrl":"https://doi.org/10.1134/s106456242470217x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Criteria for a Banach limit to belong to the discrete or continuous part of the set of Banach limits are presented. The diameters and radii of these parts are found.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142181031","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}
Pub Date : 2024-08-29DOI: 10.1134/s1064562424702156
V. B. Betelin, V. A. Galkin
Abstract
The tasks of analyzing and visualizing the dynamics of viscous incompressible flows of complex geometry based on traditional grid and projection methods are associated with significant requirements for computer performance necessary to achieve the set goals. To reduce the computational load in solving this class of problems, it is possible to apply algorithms for constructing artificial neural networks (ANNs) using exact solutions of the Navier–Stokes equations on a given set of spatial regions as training sets. An ANN is implemented to construct flows in regions that are complexes made up of training sets of standard axisymmetric domains (cylinders, balls, etc.). To reduce the amount of calculations in the case of 3D problems, invariant flow manifolds of lower dimensions are used. This makes it possible to identify the structure of solutions in detail. It is established that typical invariant regions of such flows are figures of rotation, in particular, ones homeomorphic to the torus, which form the structure of a topological bundle, for example, in a ball, cylinder, and general complexes composed of such figures. The structures of flows obtained by approximation based on the simplest 3D unsteady vortex flows are investigated. Classes of exact solutions of the incompressible Navier–Stokes system in bounded regions of ({{mathbb{R}}_{3}}) are distinguished based on the superposition of the above-mentioned topological bundles. Comparative numerical experiments suggest that the application of the proposed class of ANNs can significantly speed up the computations, which allows the use of low-performance computers.
{"title":"Construction of an Artificial Neural Network for Solving the Incompressible Navier–Stokes Equations","authors":"V. B. Betelin, V. A. Galkin","doi":"10.1134/s1064562424702156","DOIUrl":"https://doi.org/10.1134/s1064562424702156","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The tasks of analyzing and visualizing the dynamics of viscous incompressible flows of complex geometry based on traditional grid and projection methods are associated with significant requirements for computer performance necessary to achieve the set goals. To reduce the computational load in solving this class of problems, it is possible to apply algorithms for constructing artificial neural networks (ANNs) using exact solutions of the Navier–Stokes equations on a given set of spatial regions as training sets. An ANN is implemented to construct flows in regions that are complexes made up of training sets of standard axisymmetric domains (cylinders, balls, etc.). To reduce the amount of calculations in the case of 3D problems, invariant flow manifolds of lower dimensions are used. This makes it possible to identify the structure of solutions in detail. It is established that typical invariant regions of such flows are figures of rotation, in particular, ones homeomorphic to the torus, which form the structure of a topological bundle, for example, in a ball, cylinder, and general complexes composed of such figures. The structures of flows obtained by approximation based on the simplest 3D unsteady vortex flows are investigated. Classes of exact solutions of the incompressible Navier–Stokes system in bounded regions of <span>({{mathbb{R}}_{3}})</span> are distinguished based on the superposition of the above-mentioned topological bundles. Comparative numerical experiments suggest that the application of the proposed class of ANNs can significantly speed up the computations, which allows the use of low-performance computers.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142181063","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}
Pub Date : 2024-08-29DOI: 10.1134/s1064562424702168
V. I. Berdyshev
Abstract
We propose ways of acting an observer f when tracking an object (t) moving in ({{mathbb{R}}^{3}}) along the shortest trajectory (mathcal{T}) bypassing a collection ({ {{G}_{i}}} ) of convex sets. The object has high-speed miniobjects threatening the observer. The tracking methods depend on the geometric properties of ({{G}_{i}}) and (mathcal{T}). The observer’s task is to track the motion of the object over as long a segment of (mathcal{T}) as possible.
Abstract We propose ways of acting an observer f when tracking an object (t) moving in ({{mathbb{R}}^{3}}) along the shortest trajectory (mathcal{T}) bypassing a collection ({{G}_{i}}) of convex sets.物体有高速小物体威胁观察者。跟踪方法取决于 ({{G}_{i}}) 和 (mathcal{T}) 的几何特性。观察者的任务是在尽可能长的(mathcal{T})段上跟踪物体的运动。
{"title":"Methods for Tracking an Object Moving in $${{mathbb{R}}^{3}}$$ under Conditions of Its Counteraction","authors":"V. I. Berdyshev","doi":"10.1134/s1064562424702168","DOIUrl":"https://doi.org/10.1134/s1064562424702168","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We propose ways of acting an observer <i>f</i> when tracking an object <span>(t)</span> moving in <span>({{mathbb{R}}^{3}})</span> along the shortest trajectory <span>(mathcal{T})</span> bypassing a collection <span>({ {{G}_{i}}} )</span> of convex sets. The object has high-speed miniobjects threatening the observer. The tracking methods depend on the geometric properties of <span>({{G}_{i}})</span> and <span>(mathcal{T})</span>. The observer’s task is to track the motion of the object over as long a segment of <span>(mathcal{T})</span> as possible.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142181032","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}
Pub Date : 2024-08-09DOI: 10.1134/s1064562424702120
A. Arutyunov, S. Zhukovskiy
{"title":"On the Existence and Estimates of Inverse Functions in the Degenerate Case","authors":"A. Arutyunov, S. Zhukovskiy","doi":"10.1134/s1064562424702120","DOIUrl":"https://doi.org/10.1134/s1064562424702120","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141923020","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}
Pub Date : 2024-08-09DOI: 10.1134/s1064562424702132
I. Kashchenko, S. A. Kashchenko, I. N. Maslenikov
{"title":"Stability of Solutions to the Logistic Equation with Delay, Diffusion, and Nonclassical Boundary Conditions","authors":"I. Kashchenko, S. A. Kashchenko, I. N. Maslenikov","doi":"10.1134/s1064562424702132","DOIUrl":"https://doi.org/10.1134/s1064562424702132","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141924725","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}
Pub Date : 2024-08-09DOI: 10.1134/s1064562424702144
E. Kugushev, T. Salnikova
{"title":"Generalization of Jacobi’s Theorem on the Last Multiplier","authors":"E. Kugushev, T. Salnikova","doi":"10.1134/s1064562424702144","DOIUrl":"https://doi.org/10.1134/s1064562424702144","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141924166","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}
Pub Date : 2024-08-09DOI: 10.1134/s1064562424601239
N. S. Romanovskiy
{"title":"On Elementary Theory of Completion of Solvable Baumslag–Solitar Group","authors":"N. S. Romanovskiy","doi":"10.1134/s1064562424601239","DOIUrl":"https://doi.org/10.1134/s1064562424601239","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141921320","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}
Pub Date : 2024-07-31DOI: 10.1134/s1064562424702090
B. N. Chetverushkin, V. A. Sudakov, Yu. P. Titov
Abstract
An original method for processing large factor models based on graph condensation using machine learning models and artificial neural networks is developed. The proposed mathematical apparatus can be used to plan and manage complex organizational and technical systems, to optimize large socioeconomic objects of national scale, and to solve problems of preserving the health of the nation (searching for compatibility of medications and optimizing health care resources).
{"title":"Graph Condensation for Large Factor Models","authors":"B. N. Chetverushkin, V. A. Sudakov, Yu. P. Titov","doi":"10.1134/s1064562424702090","DOIUrl":"https://doi.org/10.1134/s1064562424702090","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An original method for processing large factor models based on graph condensation using machine learning models and artificial neural networks is developed. The proposed mathematical apparatus can be used to plan and manage complex organizational and technical systems, to optimize large socioeconomic objects of national scale, and to solve problems of preserving the health of the nation (searching for compatibility of medications and optimizing health care resources).</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862689","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号