Proceedings of the Steklov Institute of Mathematics最新文献_第10页

Integral Inequalities for Entire Functions of Exponential Type in Morrey Spaces 莫雷空间中指数型全函数的积分不等式

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-01 DOI: 10.1134/s008154382305005x

引用次数: 0

Riemann–Liouville Space of Fractional Potentials on the Half-Line 半线上分数势的黎曼-刘维尔空间

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-01 DOI: 10.1134/s0081543823050073

引用次数: 0

Closed Mappings and Construction of Extension Models 封闭映射与扩展模型的构建

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-01 DOI: 10.1134/s0081543823060056

{"title":"Closed Mappings and Construction of Extension Models","authors":"","doi":"10.1134/s0081543823060056","DOIUrl":"https://doi.org/10.1134/s0081543823060056","url":null,"abstract":"<h3>Abstract</h3> The problem of reachability in a topological space is studied under constraints of asymptotic nature arising from weakening the requirement that the image of a solution belong to a given set. The attraction set that arises in this case in the topological space is a regularization of certain kind for the image of the preimage of the mentioned set (the image and the preimage are defined for generally different mappings). When constructing natural compact extensions of the reachability problem with constraints of asymptotic nature generated by a family of neighborhoods of a fixed set, the case was studied earlier where the topological space in which the results of one or another choice of solution are realized satisfies the axiom (T_{2}) . In the present paper, for a number of statements related to compact extensions, it is possible to use for this purpose a (T_{1}) space, which seems to be quite important from a theoretical point of view, since it is possible to find out the exact role of the axiom (T_{2}) in questions related to correct extensions of reachability problems. We study extension models using ultrafilters of a broadly understood measurable space with detailing of the main elements in the case of a reachability problem in the space of functionals with the topology of a Tychonoff power of the real line with the usual (|cdot|) -topology. The general constructions of extension models are illustrated by an example of a nonlinear control problem with state constraints. ","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757098","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

Asset Tokenization and Related Problems 资产代币化及相关问题

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-01 DOI: 10.1134/s0081543823060081

引用次数: 0

On Constants in the Bernstein–Szegő Inequality for the Weyl Derivative of Order Less Than Unity of Trigonometric Polynomials and Entire Functions of Exponential Type in the Uniform Norm 论统一规范中三角多项式和指数型全函数小于统一阶的韦尔导数的伯恩斯坦-塞格不等式中的常数

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-01 DOI: 10.1134/s0081543823060123

{"title":"On Constants in the Bernstein–Szegő Inequality for the Weyl Derivative of Order Less Than Unity of Trigonometric Polynomials and Entire Functions of Exponential Type in the Uniform Norm","authors":"","doi":"10.1134/s0081543823060123","DOIUrl":"https://doi.org/10.1134/s0081543823060123","url":null,"abstract":"<h3>Abstract</h3> The Weyl derivative (fractional derivative) (f_{n}^{(alpha)}) of real nonnegative order (alpha) is considered on the set (mathscr{T}_{n}) of trigonometric polynomials (f_{n}) of order (n) with complex coefficients. The constant in the Bernstein–Szegő inequality ({|}f_{n}^{(alpha)}costheta+tilde{f}_{n}^{(alpha)}sintheta{| }leq B_{n}(alpha,theta)|f_{n}|) in the uniform norm is studied. This inequality has been well studied for (alphageq 1) : G. T. Sokolov proved in 1935 that it holds with the constant (n^{alpha}) for all (thetainmathbb{R}) . For (0<alpha<1) , there is much less information about (B_{n}(alpha,theta)) . In this paper, for (0<alpha<1) and (thetainmathbb{R}) , we establish the limit relation (lim_{ntoinfty}B_{n}(alpha,theta)/n^{alpha}=mathcal{B}(alpha,theta)) , where (mathcal{B}(alpha,theta)) is the sharp constant in the similar inequality for entire functions of exponential type at most (1) that are bounded on the real line. The value (theta=-pialpha/2) corresponds to the Riesz derivative, which is an important particular case of the Weyl–Szegő operator. In this case, we derive exact asymptotics for the quantity (B_{n}(alpha)=B_{n}(alpha,-pialpha/2)) as (ntoinfty) . ","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757089","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

Periodic and Solitary Waves and Nondissipative Discontinuity Structures in Electromagnetic Hydrodynamics in the Case of Wave Resonance 波共振情况下电磁流体力学中的周期波和孤波以及非耗散不连续结构

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-09-01 DOI: 10.1134/s008154382304003x

I. B. Bakholdin

引用次数: 0

Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves 长波和短波共振情况下周期成分辐射的对流调制不稳定性

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-09-01 DOI: 10.1134/s0081543823040107

引用次数: 0

Andrei Gennad’evich Kulikovskii: On the occasion of his 90th birthday 安德烈-根纳季耶维奇-库里科夫斯基在他 90 岁生日之际

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-09-01 DOI: 10.1134/s0081543823040016

Editorial Board

引用次数: 0

Longitudinal–Torsional Waves in Nonlinear Elastic Rods 非线性弹性杆中的纵扭波

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-09-01 DOI: 10.1134/s0081543823040132

引用次数: 0

Linear and Nonlinear Development of Bending Perturbations in a Fluid-Conveying Pipe with Variable Elastic Properties 具有可变弹性特性的输液管弯曲扰动的线性和非线性发展

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-09-01 DOI: 10.1134/s0081543823040028

{"title":"Linear and Nonlinear Development of Bending Perturbations in a Fluid-Conveying Pipe with Variable Elastic Properties","authors":"","doi":"10.1134/s0081543823040028","DOIUrl":"https://doi.org/10.1134/s0081543823040028","url":null,"abstract":" <h3>Abstract</h3> We consider bending vibrations of a fluid-conveying pipe resting on an elastic foundation with nonuniform elasticity coefficient. Previously A. G. Kulikovskii showed analytically that the elasticity parameters can be distributed in such a way that at every point the system is either locally stable or convectively unstable. In this case, despite the absence of local absolute instability, there exists a global growing mode whose formation is associated with the points of internal reflection of waves. In the present paper, we perform a numerical simulation of the development of the initial perturbation in such a system. In the linear formulation we demonstrate how the perturbation is transformed into a growing eigenmode after a series of reflections and passages through a region of local instability. In the nonlinear formulation, where the nonlinear tension of the pipe is taken into account within the von Kármán model, we show that the perturbation growth is limited; in this case the vibrations acquire a quasi-chaotic character but do not leave the region bounded by the internal reflection points determined by the linearized problem. ","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138821470","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