Contemporary Mathematics. Fundamental Directions最新文献_第5页

Topological Conjugacy of Gradient-Like Flows on Surfaces and Efficient Algorithms for Its Distinguition 曲面上类梯度流的拓扑共轭性及其判别算法

Contemporary Mathematics. Fundamental Directions Pub Date : 2022-09-08 DOI: 10.22363/2413-3639-2022-68-3-467-487

V. Kruglov

{"title":"Topological Conjugacy of Gradient-Like Flows on Surfaces and Efficient Algorithms for Its Distinguition","authors":"V. Kruglov","doi":"10.22363/2413-3639-2022-68-3-467-487","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-3-467-487","url":null,"abstract":"Gradient-like flows on surfaces have simple dynamics, which inspired many mathematicians to search for invariants of their topological equivalence. Under assumptions of different generality on the class of gradient-like flows under consideration, such classical invariants as the Leontovich- Mayer scheme, the Peixoto graph, the equipped Peixoto graph, the two-color Wang graph, the threecolor Oshemkov-Sharko graph, the Fleitas circular scheme, etc. were obtained. Thus, the problem of classifying gradient-like flows on surfaces from the point of view of topological equivalence has been solved in an exhaustive way. In recent works by Kruglov, Malyshev, and Pochinka, it was proved that for gradient-like flows the topological equivalence classes coincide with the topological conjugacy classes. The obtained result allows us to use any invariants of their equivalence for topological conjugacy of gradient-like flows. The present study is a review of the results on topological conjugacy of gradient-like flows on surfaces and efficient algorithms for its distinguishing, that is, algorithms whose running time is limited by some polynomial on the length of the input information.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129783847","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: 4

On the Completeness of Eigenfunctions of One 5th-Order Differential Operator 一类五阶微分算子特征函数的完备性

Contemporary Mathematics. Fundamental Directions Pub Date : 2022-06-06 DOI: 10.22363/2413-3639-2022-68-2-338-375

V. Rykhlov

{"title":"On the Completeness of Eigenfunctions of One 5th-Order Differential Operator","authors":"V. Rykhlov","doi":"10.22363/2413-3639-2022-68-2-338-375","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-2-338-375","url":null,"abstract":"In this paper, we fully solve the problem of the completeness of the eigenfunctions of an ordinary 5th-order differential operator in the space of square-summable functions on the segment [0, 1] generated by the simplest differential expression ( y^{(5)} ) and two-point two-term boundary conditions (alpha_v y^{(v−1)}(0) + beta_v \u0000y^{(v−1)}(1) = 0) and (v = \u0000overline{1, 5}), under the main assumption (alpha_v ne 0), (v = overline{1, 5}) or (beta_v ne 0), (v = overline{1, 5}) (in this case, without loss of generality, we can assume that all (alpha_v) or all (beta_v) , respectively, are equal to one). The classical methods of studying completeness, which go back to well-known articles by M. V. Keldysh, A. P. Khromov, A. A. Shkalikov, and many others, are not applicable to the operator under consideration. These methods are based on “good” estimates for the spectral parameter of the used generating functions (“classical”) for the system of eigenfunctions and associated functions. In the case of a strong irregularity of the operator under consideration, these «classical» generating functions have too large rate of grows in the spectral parameter. To solve the problem of multiple completeness, we propose a new approach that uses a special parametric solution that generalizes «classical» generating functions. The main idea of this approach is to select the parameters of this special solution to construct generating functions that are no longer «classical» with suitable estimates in terms of the spectral parameter. Such a selection for the operator under consideration turned out to be possible, although rather nontrivial, which allowed us to follow the traditional scheme of proving the completeness of the system of eigenfunctions in the space of square-summable functions on the segment [0, 1].","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122374252","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: 0

Stochastic Equations and Inclusions with Mean Derivatives and Their Applications 随机方程和包含均值导数及其应用

Contemporary Mathematics. Fundamental Directions Pub Date : 2022-06-06 DOI: 10.22363/2413-3639-2022-68-2-191-337

Y. Gliklikh

引用次数: 0

Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis 一类Hammerstein型非线性积分方程解在整轴上的渐近性质

Contemporary Mathematics. Fundamental Directions Pub Date : 2022-06-06 DOI: 10.22363/2413-3639-2022-68-2-376-391

K. Khachatryan, H. S. Petrosyan

引用次数: 0

Systems of Matrix Differential Equations for Surfaces 曲面的矩阵微分方程组

Contemporary Mathematics. Fundamental Directions Pub Date : 2022-04-20 DOI: 10.22363/2413-3639-2022-68-1-70-79

K. Muminov, R. A. Gafforov

引用次数: 0

Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay 时滞非平稳控制系统阻尼问题解的平滑性

Contemporary Mathematics. Fundamental Directions Pub Date : 2022-04-20 DOI: 10.22363/2413-3639-2022-68-1-14-24

A. S. Adkhamova

引用次数: 0

Weierstrass Polynomials in Estimates of Oscillatory Integrals 振动积分估计中的Weierstrass多项式

Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-4-668-692

I. Ikromov, A. Sadullaev

引用次数: 0

Deficiency Indices of Block Jacobi Matrices: Survey 块雅可比矩阵的缺陷指数:综述

Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-2-237-254

V. Budyka, M. Malamud, K. A. Mirzoev

引用次数: 3

Nonexistence of Nontrivial Weak Solutions of Some Nonlinear Inequalities with Gradient Nonlinearity 一类梯度非线性非线性不等式非平凡弱解的不存在性

Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-1-1-13

V. E. Admasu, E. Galakhov, O. Salieva

引用次数: 1

In Memory of Nikolay Dmitrievich Kopachevsky, a Mathematician and a Human 纪念尼古拉·德米特里耶维奇·科帕切夫斯基，一个数学家和一个人

Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-2-193-207

V. Voytitsky, A. Muratov, Yulia S. Pashkova, P. A. Starkov, T. Suslina, D. Tsvetkov

引用次数: 0