Scientific publications

В.Н. Ушаков, О.А. Кувшинов.

α*- множества в конечномерных евклидовых пространствах и их свойства

// Математическая Теория Игр и ее Приложения, т. 18, в. 1. 2026. C. 47-114

Vladimir N. Ushakov, Oleg A. Kuvshinov. α*- sets in finite-dimensional euclidean spaces and their properties // Mathematical game theory and applications. Vol 18. No 1. 2026. Pp. 47-114

Keywords: convex set in Rⁿ, convex hull in Rⁿ, α in Rⁿ, α*-set in Rⁿ, α*-hyperplane in Rⁿ, α*-separability

The concept of α*-sets in finite-dimensional Euclidean space is given, which is a generalization of the concept of α*-sets and convex sets in finite-dimensional Euclidean space. This concept arose in connection with the study of nonconvex reachability sets of some nonlinear controlled systems in a finite-dimensional Euclidean space. The paper examines the concept of α*-sets as applied to some sets in finite-dimensional Euclidean space and in particular to fractals in the space R². The issues related to the topic of α*-separability of nonconvex sets in finite-dimensional Euclidean spaces are considered.

Indexed at RSCI, RSCI (WS)

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Last modified: April 8, 2026