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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.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85093876710
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.
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