Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets (Mathematics and Its Applications) par Pallaschke, Diethard Ernst; Urbanski, R.: New (2010)

A propos de cet article

N� de r�f. du vendeur I-9789048161492

D�tails bibliographiques

Titre: Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets (Mathematics and Its Applications)
�diteur: Springer
Date de parution: 2010
Langue: anglais
ISBN � 10 chiffres: 9048161495
ISBN � 13 chiffres: 9789048161492
Reliure: Couverture souple
�tat de l'article: New

A propos de ce titre

Synopsis

The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the R�dstr�m-H�rmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity. In the first three chapters of the book the basic facts about convexity, mixed volumes and the R�dstr�m-H�rmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs.

Pr�sentation de l'�diteur

The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the R�dstr�m-H�rmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity. In the first three chapters of the book the basic facts about convexity, mixed volumes and the R�dstr�m-H�rmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs.

Les informations fournies dans la section � A propos du livre � peuvent faire r�f�rence � une autre �dition de ce titre.