Pairs of Compact Convex Sets
Fractional Arithmetic with Convex Sets
Seiten
2002
Kluwer Academic Publishers (Verlag)
9781402009389 (ISBN)
Kluwer Academic Publishers (Verlag)
9781402009389 (ISBN)
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.
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]).
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]).
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.
| Erscheint lt. Verlag | 31.10.2002 |
|---|---|
| Reihe/Serie | Mathematics and Its Applications ; 548 | Mathematics and Its Applications ; 548 |
| Zusatzinfo | XII, 295 p. |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-13 | 9781402009389 / 9781402009389 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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