Proceedings of the Steklov Institute of Mathematics最新文献_第7页

Comparison and Polyhedral Properties of Valid Inequalities for a Polytope of Schedules for Servicing Identical Requests 为相同请求提供服务的多面体时间表的有效不等式的比较和多面体性质

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060202

R. Yu. Simanchev, I. V. Urazova

引用次数: 0

Polynomial-Time Approximability of the Asymmetric Problem of Covering a Graph by a Bounded Number of Cycles 用有界循环数覆盖图的非对称问题的多项式时间逼近性

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s008154382306010x

M. Yu. Khachai, E. D. Neznakhina, K. V. Ryzhenko

{"title":"Polynomial-Time Approximability of the Asymmetric Problem of Covering a Graph by a Bounded Number of Cycles","authors":"M. Yu. Khachai, E. D. Neznakhina, K. V. Ryzhenko","doi":"10.1134/s008154382306010x","DOIUrl":"https://doi.org/10.1134/s008154382306010x","url":null,"abstract":"Recently, O. Svensson and V. Traub have provided the first proof of the polynomial-time approximability of the asymmetric traveling salesman problem (ATSP) in the class of constant-factor approximation algorithms. Just as the famous Christofides–Serdyukov algorithm for the symmetric routing problems, these breakthrough results, applied as a “black box,” have opened an opportunity for developing the first constant-factor polynomial-time approximation algorithms for several related combinatorial problems. At the same time, problems have been revealed in which this simple approach, based on reducing a given instance to one or more auxiliary ATSP instances, does not succeed. In the present paper, we extend the Svensson–Traub approach to the wider class of problems related to finding a minimum-weight cycle cover of an edge-weighted directed graph with an additional constraint on the number of cycles. In particular, it is shown for the first time that the minimum weight cycle cover problem with at most (k) cycles admits polynomial-time approximation with constant factor (max{22+varepsilon,4+k}) for arbitrary (varepsilon>0).\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757264","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

Fejér-Type Iterative Processes in the Constrained Quadratic Minimization Problem 受约束二次最小化问题中的费耶尔式迭代过程

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s008154382306024x

V. V. Vasin

引用次数: 0

Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data 具有终端凸性能指标和初始数据扰动的最优控制问题解的渐近性

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s008154382306007x

A. R. Danilin, O. O. Kovrizhnykh

引用次数: 0

Young Duality of Variational Inequalities. An Application for the Analysis of Interactions in Production Networks 变分不等式的年轻对偶性。生产网络互动分析的应用

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060172

N. K. Obrosova, A. A. Shananin

引用次数: 0

Sharp Carlson Type Inequalities with Many Weights 多权重的尖锐卡尔森型不等式

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060184

K. Yu. Osipenko

引用次数: 0

On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups” 从 "有限群图集 "看有限群中的无穷子群与简单群的交集

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060251

V. I. Zenkov

引用次数: 0

A Bicomposition of Conical Projections 圆锥投影的二重组合

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060160

E. A. Nurminski

引用次数: 0

On Operator Inclusions in Spaces with Vector-Valued Metrics 论具有矢量值度量的空间中的算子夹杂物

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060196

E. A. Panasenko

{"title":"On Operator Inclusions in Spaces with Vector-Valued Metrics","authors":"E. A. Panasenko","doi":"10.1134/s0081543823060196","DOIUrl":"https://doi.org/10.1134/s0081543823060196","url":null,"abstract":"We consider an inclusion (widetilde{y}in F(x)) with a multivalued mapping acting in spaces with vector-valued metrics\u0000whose values are elements of cones in Banach spaces and can be infinite. A statement about the existence of a solution (xin X)\u0000and an estimate of its deviation from a given element (x_{0}in X) in a vector-valued metric are obtained. This result extends\u0000the known theorems on similar operator equations and inclusions in metric spaces and in the spaces with (n)-dimensional metric\u0000to a more general case and, applied to particular classes of functional equations and inclusions, allows to get less restrictive,\u0000compared to known, solvability conditions as well as more precise estimates of solutions. We apply this result to the integral inclusion\u0000(widetilde{y}(t)in f(t,intop_{a}^{b}varkappa(t,s)x(s),ds,x(t)), tin[a, b],)\u0000where the function (widetilde{y}) is measurable, the mapping (f) satisfies the Carathéodory conditions, and the solution (x) is\u0000required to be only measurable (the integrability of (x) is not assumed).\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889097","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 Submodularity and K $$mathfrak{F}$$ -Subnormality in Finite Groups 论有限群中的次模性和 K $$mathfrak{F}$ -次规范性

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060159

V. S. Monakhov, I. L. Sokhor

{"title":"On Submodularity and K $$mathfrak{F}$$ -Subnormality in Finite Groups","authors":"V. S. Monakhov, I. L. Sokhor","doi":"10.1134/s0081543823060159","DOIUrl":"https://doi.org/10.1134/s0081543823060159","url":null,"abstract":"Let (mathfrak{F}) be a formation, and let (G) be a finite group. A subgroup (H) of (G) is called (mathrm{K}mathfrak{F})-subnormal (submodular) in (G) if there is a subgroup chain (H=H_{0}leq H_{1}leqmathinner{ldotpldotpldotp}leq H_{n-1}leq H_{n}=G) such that, for every (i) either (H_{i}) is normal in (H_{i+1}) or (H_{i+1}^{mathfrak{F}}leq H_{i}) ((H_{i}) is a modular subgroup of (H_{i+1}), respectively). We prove that, in a group, a primary subgroup is submodular if and only if it is (mathrm{K}mathfrak{U}_{1})-subnormal. Here (mathfrak{U}_{1}) is a formation of all supersolvable groups of square-free exponent. Moreover, for a solvable subgroup-closed formation (mathfrak{F}), every solvable (mathrm{K}mathfrak{F})-subnormal subgroup of a group (G) is contained in the solvable radical of (G). We also obtain a series of applications of these results to the investigation of groups factorized by (mathrm{K}mathfrak{F})-subnormal and submodular subgroups.\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889099","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