Titlebook: Excursions into Combinatorial Geometry; Vladimir Boltyanski,Horst Martini,Petru S. Soltan Textbook 1997 Springer-Verlag Berlin Heidelberg

GIST

OPINE

DAMP

Homothetic covering and illumination,e problems are equivalent for compact, convex bodies, whereas they differ from each other in the unbounded case. Among these four problems, the central one is the question for the minimal number of smaller homothets of a convex body . ⊂ R. which are sufficient to cover.. In addition, the problem of

Climate

Combinatorial geometry of belt bodies, the class of zonoids. (For zonoids and their fascinating properties, the reader is referred to the surveys [S-W], [G-W], [Bk 1], and [Mar 4].) Moreover, the class of belt bodies is dense in the family of all compact, convex bodies. Nevertheless, solutions of combinatorial problems for zonoids [Ba 1

透明

噱头

https://doi.org/10.1007/978-94-009-3867-0Borsuk considered this question for two-dimensional sets and for the n-dimensional ball . ⊂ R.. One motivation for these investigations was given by the famous theorem of Borsuk and Ulam, referring to continuous mappings of the .-sphere into R..

glowing

Armory

The Short-Time Fourier Transform,n . such that .(.,.) =∥ . − . ∥ for any ., . ∈ .. Finally, we say that a metric . is . if the set . = { . ∈ . : .(., .) ≤ 1 { is bounded in . . The problem is to describe a condition under which a metric . in . is normable.

Corporeal

,Borsuk’s partition problem,Borsuk considered this question for two-dimensional sets and for the n-dimensional ball . ⊂ R.. One motivation for these investigations was given by the famous theorem of Borsuk and Ulam, referring to continuous mappings of the .-sphere into R..

arboretum

Combinatorial geometry of belt bodies,er, the class of belt bodies is dense in the family of all compact, convex bodies. Nevertheless, solutions of combinatorial problems for zonoids [Ba 1, Ba 2, Mar 2, B-SP 5, B-SP 6] can be extended to belt bodies. The aim of this chapter is the explanation of combinatorial properties of belt bodies, cf. also [B-M 1].