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Chebyshevskii Sbornik最新文献

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About the continuity of one operation with convex compacts in finite-dimensional normed spaces 关于有限维赋范空间中凸紧一运算的连续性
Chebyshevskii Sbornik Pub Date : 2022-11-07 DOI: 10.22405/2226-8383-2022-23-5-152-160
A. Galstyan
{"title":"About the continuity of one operation with convex compacts in finite-dimensional normed spaces","authors":"A. Galstyan","doi":"10.22405/2226-8383-2022-23-5-152-160","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-5-152-160","url":null,"abstract":"In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite-dimensional normed spaces, in the case when both compact sets are non-empty convex subsets, such an operation is continuous in the topology generated by the Hausdorff metric. The question of the continuous dependence of the described intersection on the radius of the neighborhood arose as a by-product of the development of the theory of extremal networks. However, it turned out to be interesting in itself, suggesting various generalizations. Therefore, it was decided to publish it separately.","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"160 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86446542","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: 1
The Fermat-Torricelli problem in the case of three-point sets in normed planes 范数平面上三点集的费马-托里拆利问题
Chebyshevskii Sbornik Pub Date : 2022-10-09 DOI: 10.22405/2226-8383-2022-23-5-72-86
D. A. Ilyukhin
{"title":"The Fermat-Torricelli problem in the case of three-point sets in normed planes","authors":"D. A. Ilyukhin","doi":"10.22405/2226-8383-2022-23-5-72-86","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-5-72-86","url":null,"abstract":"In the paper the Fermat-Torricelli problem is considered. The problem asks a point minimizing the sum of distances to arbitrarily given points in d-dimensional real normed spaces. Various generalizations of this problem are outlined, current methods of solving and some recent results in this area are presented. The aim of the article is to find an answer to the following question: in what norms on the plane is the solution of the Fermat-Torricelli problem unique for any three points. The uniqueness criterion is formulated and proved in the work, in addition, the application of the criterion on the norms set by regular polygons, the so-called lambda planes, is shown.","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"163 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86393753","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: 1
Reducing smooth functions to normal forms near critical points 在临界点附近将光滑函数化简为正规形式
Chebyshevskii Sbornik Pub Date : 2022-06-01 DOI: 10.22405/2226-8383-2022-23-5-101-116
A. S. Orevkova
{"title":"Reducing smooth functions to normal forms near critical points","authors":"A. S. Orevkova","doi":"10.22405/2226-8383-2022-23-5-101-116","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-5-101-116","url":null,"abstract":"The paper is devoted to\"uniform\"reduction of smooth functions on 2-manifolds to canonical form near critical points by some coordinate changes in some neighbourhoods of these points. For singularity types $E_6,E_8$ and $A_n$, we explicitly construct such coordinate changes and estimate from below (in terms of $C^r$-norm of the function) the radius of a required neighbourhood.","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"98 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86493019","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
Research Institute for Mathematics and Mechanics of Moscow University (to the 100𝑡ℎ anniversaryof the foundation of the Institute) 莫斯科大学数学与力学研究所(至100𝑡研究所成立100周年)
Chebyshevskii Sbornik Pub Date : 2022-01-01 DOI: 10.22405/2226-8383-2022-23-3-269-281
S. Demidov
{"title":"Research Institute for Mathematics and Mechanics of Moscow University (to the 100𝑡ℎ anniversaryof the foundation of the Institute)","authors":"S. Demidov","doi":"10.22405/2226-8383-2022-23-3-269-281","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-3-269-281","url":null,"abstract":"","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78613957","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
Margarita Babkenovna Nalbandyan and her research on the History of Mathematics in Russia(for the 90trh anniversary of her birth) 玛格丽塔·巴克诺芙娜·纳尔班扬及其对俄罗斯数学史的研究(纪念她诞辰90周年)
Chebyshevskii Sbornik Pub Date : 2022-01-01 DOI: 10.22405/2226-8383-2022-23-2-219-231
Yu. S. Nalbandyan
{"title":"Margarita Babkenovna Nalbandyan and her research on the History of Mathematics in Russia(for the 90trh anniversary of her birth)","authors":"Yu. S. Nalbandyan","doi":"10.22405/2226-8383-2022-23-2-219-231","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-2-219-231","url":null,"abstract":"","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80007395","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
Recognition of anomalies of an a priori unknown type 识别先验未知类型的异常
Chebyshevskii Sbornik Pub Date : 2022-01-01 DOI: 10.22405/2226-8383-2022-23-5-227-240
A. Ivanov, G. Nosovskiy, V. Kibkalo, M. Nikulin, F. Y. Popelensky, D. Fedoseev, V. Gribushin, V. Zlobin, S.S. Kuzin, I. Mazurenko
{"title":"Recognition of anomalies of an a priori unknown type","authors":"A. Ivanov, G. Nosovskiy, V. Kibkalo, M. Nikulin, F. Y. Popelensky, D. Fedoseev, V. Gribushin, V. Zlobin, S.S. Kuzin, I. Mazurenko","doi":"10.22405/2226-8383-2022-23-5-227-240","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-5-227-240","url":null,"abstract":"","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80170892","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
Generalized Dirichlet problem for a two-dimensional lattice of Dirichlet approximations 二维点阵Dirichlet近似的广义Dirichlet问题
Chebyshevskii Sbornik Pub Date : 2022-01-01 DOI: 10.22405/2226-8383-2022-23-1-83-105
N. N. Dobrovol'skii, M. N. Dobrovol’skii, V. N. Chubarikov, I. Rebrova, N. M. Dobrovol’skii
{"title":"Generalized Dirichlet problem for a two-dimensional lattice of Dirichlet approximations","authors":"N. N. Dobrovol'skii, M. N. Dobrovol’skii, V. N. Chubarikov, I. Rebrova, N. M. Dobrovol’skii","doi":"10.22405/2226-8383-2022-23-1-83-105","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-1-83-105","url":null,"abstract":"","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79298147","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
Yuri Valentinovich Nesterenko(to the 75th anniversary) 尤里·瓦伦蒂诺维奇·涅斯捷连科(致75周年纪念)
Chebyshevskii Sbornik Pub Date : 2022-01-01 DOI: 10.22405/2226-8383-2022-23-1-10-20
A. I. Shafarevich, A. Fomenko, V. N. Chubarikov, A. Ivanov, V.G. Chirsky, V. Bernik, V. Bykovskii, A. Galochkin, S. Demidov, S. Gashkov, A. Nizhnikov, A. Fomin, E. I. Deza, A. Kanel-Belov, N. Dobrovolsky, N. N. Dobrovolsky, I. Rebrova, V. Salikhov
{"title":"Yuri Valentinovich Nesterenko(to the 75th anniversary)","authors":"A. I. Shafarevich, A. Fomenko, V. N. Chubarikov, A. Ivanov, V.G. Chirsky, V. Bernik, V. Bykovskii, A. Galochkin, S. Demidov, S. Gashkov, A. Nizhnikov, A. Fomin, E. I. Deza, A. Kanel-Belov, N. Dobrovolsky, N. N. Dobrovolsky, I. Rebrova, V. Salikhov","doi":"10.22405/2226-8383-2022-23-1-10-20","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-1-10-20","url":null,"abstract":"","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81858754","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
The Ritz method for solving partial differential equations using number-theoretic grids 用数论网格求解偏微分方程的里兹方法
Chebyshevskii Sbornik Pub Date : 2022-01-01 DOI: 10.22405/2226-8383-2022-23-5-117-129
A. V. Rodionov
{"title":"The Ritz method for solving partial differential equations using number-theoretic grids","authors":"A. V. Rodionov","doi":"10.22405/2226-8383-2022-23-5-117-129","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-5-117-129","url":null,"abstract":"","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80359447","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
Generalizations of some integral inequalities for Riemann-Liouville operator Riemann-Liouville算子若干积分不等式的推广
Chebyshevskii Sbornik Pub Date : 2022-01-01 DOI: 10.22405/2226-8383-2022-23-2-161-169
M. Sofrani, A. Senouci
{"title":"Generalizations of some integral inequalities for Riemann-Liouville operator","authors":"M. Sofrani, A. Senouci","doi":"10.22405/2226-8383-2022-23-2-161-169","DOIUrl":"https://doi.org/10.22405/2226-8383-2022-23-2-161-169","url":null,"abstract":"","PeriodicalId":37492,"journal":{"name":"Chebyshevskii Sbornik","volume":"116 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87800044","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
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