Pairs of Compact Convex Sets - Fractional Arithmetic with Convex Sets

Pairs of compact convex sets arise in the quasidifferential calculus of V.F. Demyanov and A.M. Rubinov as sub- and superdifferentials of quasidifferen tiable functions (see [26]) and in the formulas for the numerical evaluation of the Aumann-Integral which were recently introduced in a series of papers by R. Baier and F. Lempio (see [4], [5], [10] and [9]) and R. Baier and E.M. Farkhi [6], [7], [8]. In the field of combinatorial convexity G. Ewald et al. [36] used an interesting construction called virtual polytope, which can also be represented as a pair of polytopes for the calculation of the combinatorial Picard group of a fan. Since in all mentioned cases the pairs of compact con vex sets are not uniquely determined, minimal representations are of special to the existence of minimal pairs of compact importance. A problem related convex sets is the existence of reduced pairs of convex bodies, which has been studied by Chr. Bauer (see [14]).

Sommario

I Convexity.- 1 Convex Sets and Sublinearity.- 2 Topological Vector Spaces.- 3 Compact Convex Sets.- II Minimal Pairs.- 4 Minimal Pairs of Convex Sets.- 5 The Cardinality of Minimal Pairs.- 6 Minimality under Constraints.- 7 Symmetries.- 8 Decompositions.- 9 Invariants.- 10 Applications.- III Semigroups.- 11 Fractions.- 12 Piecewise Linear Functions.- Open Questions.- List of Symbols.

Riassunto

Deals with the theory of pairs of compact convex sets. This book also talks about 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 Radstrom-Hormander Theory.

Dettagli sul prodotto

• Autori: D. Pallaschke, Diethard Pallaschke, Diethard Erns Pallaschke, Diethard Ernst Pallaschke, R Urbanski, R. Urbanski, Ryszard Urbanski
• Editore: Springer Netherlands
• Lingue: Inglese
• Formato: Copertina rigida
• Pubblicazione: 30.06.2009
• EAN: 9781402009389
• ISBN: 978-1-4020-0938-9
• Pagine: 295
• Dimensioni: 171 mm x 22 mm x 242 mm
• Peso: 617 g
• Illustrazioni: XII, 295 p.
• Serie: Mathematics and Its Applications; Mathematics and Its Applications
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Geometria; Optimierung, B, Optimization, Diskrete Mathematik, minimum, Interaction, Mathematics and Statistics, Discrete Mathematics, Discrete geometry, Convex and Discrete Geometry, Mathematical optimization, Sets, functions, symmetric relation, semigroup, Prime number, cardinality