Pairs of Compact Convex Sets
Fractional Arithmetic with Convex Sets
Seiten
2010
|
Softcover reprint of hardcover 1st ed. 2003
Springer (Verlag)
978-90-481-6149-2 (ISBN)
Springer (Verlag)
978-90-481-6149-2 (ISBN)
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 | 8.12.2010 |
|---|---|
| Reihe/Serie | Mathematics and Its Applications ; 548 |
| Zusatzinfo | XII, 295 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 90-481-6149-5 / 9048161495 |
| ISBN-13 | 978-90-481-6149-2 / 9789048161492 |
| Zustand | Neuware |
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