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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2020, Volume 55, Pages 79–92
DOI: https://doi.org/10.35634/2226-3594-2020-55-06 (Mi iimi392) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On properties of intersection of $\alpha$-sets

A. A. Ershovab, O. A. Kuvshinovb

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620219, Russia
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DOI: https://doi.org/10.35634/2226-3594-2020-55-06
Abstract: In this paper, we study the properties of $\alpha$-sets, which are one of the generalizations of convex sets. In the first part of the paper, the equivalence of two definitions of $\alpha$-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 $\alpha$-sets. It follows from the results of numerical experiments that the value $\alpha$ of the measure of nonconvexity in a simply connected intersection of two $\alpha$-sets can be greater than the initial value of $\alpha$ 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 $\alpha$ is possible with an arbitrarily small initial $\alpha$ for intersected sets, secondly, this increase is limited by a linear function of the initial value of $\alpha$.
Keywords: generalized convex set, $\alpha$-set, intersection of sets.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00221_�
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
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.
Received: 10.02.2020
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 52A01, 11H16
Language: Russian
Citation: A. A. Ershov, O. A. Kuvshinov, “On properties of intersection of $\alpha$-sets”, Izv. IMI UdGU, 55 (2020), 79–92
Citation in format AMSBIB
\Bibitem{ErsKuv20}
\by A.~A.~Ershov, O.~A.~Kuvshinov
\paper On properties of intersection of $\alpha$-sets
\jour Izv. IMI UdGU
\yr 2020
\vol 55
\pages 79--92
\mathnet{http://mi.mathnet.ru/iimi392}
\crossref{https://doi.org/10.35634/2226-3594-2020-55-06}
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    		Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
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