Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets: 548 - Brossura

Pallaschke, Diethard Ernst; Urbanski, R.

Brossura

ISBN 10: 9048161495 ISBN 13: 9789048161492

Casa editrice: Springer, 2010

Riassunto

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]).

Su questo libro

Contenuti

Preface. 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. Index. Bibliography.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2010
• ISBN 10: 9048161495
• ISBN 13: 9789048161492
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 308