Pub Date : 2022-11-07DOI: 10.22405/2226-8383-2022-23-5-152-160
A. Galstyan
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.
{"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}
Pub Date : 2022-10-09DOI: 10.22405/2226-8383-2022-23-5-72-86
D. A. Ilyukhin
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.
{"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}
Pub Date : 2022-06-01DOI: 10.22405/2226-8383-2022-23-5-101-116
A. S. Orevkova
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.
{"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}
Pub Date : 2022-01-01DOI: 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}
Pub Date : 2022-01-01DOI: 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}
Pub Date : 2022-01-01DOI: 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}
Pub Date : 2022-01-01DOI: 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}
Pub Date : 2022-01-01DOI: 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}
Pub Date : 2022-01-01DOI: 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}
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