Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets by Diethard Ernst PallaschkePairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets by Diethard Ernst Pallaschke

Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets

byDiethard Ernst Pallaschke, R. Urbanski

Paperback | December 8, 2010

Pricing and Purchase Info

$164.20 online 
$191.95 list price save 14%
Earn 821 plum® points

Prices and offers may vary in store

Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

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]).
Title:Pairs of Compact Convex Sets: Fractional Arithmetic with Convex SetsFormat:PaperbackDimensions:295 pages, 23.5 × 15.5 × 0.07 inPublished:December 8, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048161495

ISBN - 13:9789048161492

Reviews

Table of Contents

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.