Proceedings of the Steklov Institute of Mathematics最新文献_第6页

Examples of Nonpronormal Relatively Maximal Subgroups of Finite Simple Groups 有限简单群的非正则相对最大子群实例

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060135

B. Li, D. O. Revin

引用次数: 0

Reconstruction of a Function Analytic in a Disk from the Boundary Values of Its Real Part Using Interpolation Wavelets 利用插值小波从实部边界值重构圆盘中的解析函数

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060068

N. I. Chernykh

{"title":"Reconstruction of a Function Analytic in a Disk from the Boundary Values of Its Real Part Using Interpolation Wavelets","authors":"N. I. Chernykh","doi":"10.1134/s0081543823060068","DOIUrl":"https://doi.org/10.1134/s0081543823060068","url":null,"abstract":"For a function (f(z)) analytic in a disk, a method of approximate reconstruction from known (or arbitrarily specified) boundary values of its real part (under the condition of its continuity) using interpolation wavelets is proposed; the method is easy to implement numerically. Despite the fact that there are known exact analytical formulas for solving this problem, the explicit formulas for approximating the function (f(z)) proposed here are much easier to apply in practice, since the previously known exact formulas lead to the necessity to apply numerical integration methods when calculating convolutions of functions with Poisson or Schwartz kernels. For the approximations used in this paper, effective upper bounds are obtained for the error of approximation of functions analytic in the disk by interpolation wavelets in the spaces (L_{p}(0,2pi)) for any (pgeq 2). These estimates can be used to find the parameters of the wavelets from a desired accuracy of recovering the function (f(z)). Note that if the real part of (f(z)) is continuous on the boundary of the disk, the continuity of (f(z)) in the closure of the disk cannot be guaranteed; that is why it is impossible to estimate the approximation error for (f(z)) in the uniform metric (for (p=infty)) in the general case.\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757090","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 Generalized Translation Operator Generated by the Sinc Function on an Interval 由区间上的 Sinc 函数生成的广义平移算子

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060032

V. V. Arestov, M. V. Deikalova

引用次数: 0

Optimization of the Optimal Value Function in Problems of Convex Parametric Programming 优化凸参数编程问题中的最优值函数

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060111

O. V. Khamisov

引用次数: 0

Periodic Groups with One Finite Nontrivial Sylow 2-Subgroup 有一个有限非小 Sylow 2 子群的周期群

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060147

D. V. Lytkina, V. D. Mazurov

{"title":"Periodic Groups with One Finite Nontrivial Sylow 2-Subgroup","authors":"D. V. Lytkina, V. D. Mazurov","doi":"10.1134/s0081543823060147","DOIUrl":"https://doi.org/10.1134/s0081543823060147","url":null,"abstract":"The following results are proved. Let (d) be a natural number, and let (G) be a group of finite even exponent such that each of its finite subgroups is contained in a subgroup isomorphic to the direct product of (m) dihedral groups, where (mleq d). Then (G) is finite (and isomorphic to the direct product of at most (d) dihedral groups). Next, suppose that (G) is a periodic group and (p) is an odd prime. If every finite subgroup of (G) is contained in a subgroup isomorphic to the direct product (D_{1}times D_{2}), where (D_{i}) is a dihedral group of order (2p^{r_{i}}) with natural (r_{i}), (i=1,2), then (G=M_{1}times M_{2}), where (M_{i}=langle H_{i},trangle), (t_{i}) is an element of order (2), (H_{i}) is a locally cyclic (p)-group, and (h^{t_{i}}=h^{-1}) for every (hin H_{i}), (i=1,2). Now, suppose that (d) is a natural number and (G) is a solvable periodic group such that every of its finite subgroups is contained in a subgroup isomorphic to the direct product of at most (d) dihedral groups. Then (G) is locally finite and is an extension of an abelian normal subgroup by an elementary abelian (2)-subgroup of order at most (2^{2d}).\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757097","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

Minimizing Sequences in a Constrained DC Optimization Problem 受约束直流优化问题中的序列最小化

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060214

A. S. Strekalovsky

{"title":"Minimizing Sequences in a Constrained DC Optimization Problem","authors":"A. S. Strekalovsky","doi":"10.1134/s0081543823060214","DOIUrl":"https://doi.org/10.1134/s0081543823060214","url":null,"abstract":"A smooth nonconvex optimization problem is considered, where the equality and inequality constraints and the objective function are given by DC functions. First, the original problem is reduced to an unconstrained problem with the help of I. I. Eremin’s exact penalty theory, and the objective function of the penalized problem also turns out to be a DC function. Necessary and sufficient conditions for minimizing sequences of the penalized problem are proved. On this basis, a “theoretical method” for constructing a minimizing sequence in the penalized problem with a fixed penalty parameter is proposed and the convergence of the method is proved. A well-known local search method and its properties are used for developing a new global search scheme based on global optimality conditions with a varying penalty parameter. The sequence constructed using the global search scheme turns out to be minimizing in the “limit” penalized problem, and each of its terms (z^{k+1}) turns out to be an approximately critical vector for the local search method and an approximate solution of the current penalized problem ((mathcal{P}_{k})triangleq(mathcal{P}_{sigma_{k}})). Finally, under an additional condition of “approximate feasibility,” the constructed sequence turns out to be minimizing for the original problem with DC constraints.\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757440","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 Graph with a Locally Projective Vertex-Transitive Group of Automorphisms Aut( $$Fi_{22}$$ ) Which Has a Nontrivial Stabilizer of a Ball of Radius $$2$$ 具有半径为 $$2$$ 的球的非小稳定子的局部投影顶点-传递自整定群 Aut( $$Fi_{22}$$ ) 的图形

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060238

V. I. Trofimov

引用次数: 0

A Study of New Methods for Localizing Discontinuity Lines on Extended Correctness Classes 扩展正确性类上定位不连续线的新方法研究

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-02-12 DOI: 10.1134/s0081543823060020

A. L. Ageev, T. V. Antonova

{"title":"A Study of New Methods for Localizing Discontinuity Lines on Extended Correctness Classes","authors":"A. L. Ageev, T. V. Antonova","doi":"10.1134/s0081543823060020","DOIUrl":"https://doi.org/10.1134/s0081543823060020","url":null,"abstract":"We consider the ill-posed problem of finding the position of the discontinuity lines of a function of two variables.\u0000It is assumed that the function is smooth outside the lines of discontinuity but has a discontinuity of the first kind on the line.\u0000At each node of a uniform grid with step (tau), the mean values of the perturbed function on a square with side (tau) are known.\u0000The perturbed function approximates the exact function in the space (L_{2}(mathbb{R}^{2})). The perturbation level (delta) is assumed\u0000to be known. Previously, the authors investigated (accuracy estimates were obtained) global discrete regularizing algorithms\u0000for approximating the set of lines of discontinuity of a noisy function provided that the line of discontinuity of the exact function\u0000satisfies the local Lipschitz condition. In this paper, we introduce a one-sided Lipschitz condition and formulate a new, wider\u0000correctness class. New methods for localizing discontinuity lines are constructed that work on an extended class of functions.\u0000A convergence theorem is proved, and estimates of the approximation error and other important characteristics of the algorithms\u0000are obtained. It is shown that the new methods determine the position of the discontinuity lines with guarantee in situations\u0000where the standard methods do not work.\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889037","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

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":null,"pages":null},"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