О свойствах пересечения α-множеств
| Autor: | O.A. Kuvshinov, A.A. Ershov |
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| Jazyk: | ruština |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Izv. Inst. Mat. Inform. Udmurt. Gos. Univ. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta |
| Popis: | 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. 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. |
| Databáze: | OpenAIRE |
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