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Title: | On properties of intersection of α-sets О свойствах пересечения α-множеств |
Authors: | Ershov, A. A. Kuvshinov, O. A. |
Issue Date: | 2020 |
Publisher: | Udmurt State University |
Citation: | Ershov A. A. On properties of intersection of α-sets / A. A. Ershov, O. A. Kuvshinov. — DOI 10.35634/2226-3594-2020-55-06 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2020. — Vol. 55. — P. 79-92. |
Abstract: | In this paper, we study the properties of α-sets, which are one of the generalizations of convex sets. In the first part of the paper, the equivalence of two definitions of α-sets in the plane is proved. The second part of the work is devoted to the experimental study of the properties of simply connected intersections of α-sets. It follows from the results of numerical experiments that the value α of the measure of nonconvexity in a simply connected intersection of two α-sets can be greater than the initial value of α in intersected sets even when these values are very close to zero. Based on these results, we can hypothesize that, firstly, such an increase in the value of α is possible with an arbitrarily small initial α for intersected sets, secondly, this increase is limited by a linear function of the initial value of α. © 2020 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. All rights reserved. |
Keywords: | GENERALIZED CONVEX SET INTERSECTION OF SETS Α-SET |
URI: | http://elar.urfu.ru/handle/10995/102692 |
Access: | info:eu-repo/semantics/openAccess |
RSCI ID: | 42949302 |
SCOPUS ID: | 85093876710 |
WOS ID: | 000547994700006 |
PURE ID: | 13199898 |
ISSN: | 22263594 |
DOI: | 10.35634/2226-3594-2020-55-06 |
metadata.dc.description.sponsorship: | The reported study was funded by RFBR according to the research project no. 18–01–00221 A. The work was supported by Act 211 Government of the Russian Federation, contract no. 02.A03.21.0006. |
Appears in Collections: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
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