Том 71
№ 9

All Issues

Stefanchuk M. V.

Articles: 2
Article (Ukrainian)

Generalizations of the shadow problem

Stefanchuk M. V., Zelinskii Yu. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 6. - pp. 757-763

We solve the shadow problem in the n-dimensional Euclidean space $N^n$ for a family of sets obtained from any convex domain with nonempty interior with the help of parallel translations and homotheties. We determine the number of balls with centers on the sphere, sufficient for giving a shadow in the $n$-dimensional complex (hypercomplex) space.

Article (Russian)

Generalized convex sets and the problem of shadow

Stefanchuk M. V., Vyhovs'ka I. Yu., Zelinskii Yu. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1658-1666

The problem of shadow is solved. It is equivalent to the problem of finding conditions for a point to belong to a generalized convex hull of a family of compact sets.