Pairs of Compact Convex Sets
Fractional Arithmetic with Convex Sets
(Sprache: Englisch)
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...
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Klappentext zu „Pairs of Compact 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]).
Inhaltsverzeichnis zu „Pairs of Compact Convex Sets “
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.
Bibliographische Angaben
- Autoren: Diethard Pallaschke , Ryszard Urbanski
- 2002, 295 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer Netherlands
- ISBN-10: 1402009380
- ISBN-13: 9781402009389
- Erscheinungsdatum: 31.10.2002
Sprache:
Englisch
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