Pairs of Compact Convex Sets

Fractional Arithmetic with Convex Sets
2003
ISBN: 978-1-4020-0938-9
Verlag: Springer Netherlands

Buch, Englisch, Band 548, 295 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1360 g

Reihe: Mathematics and Its Applications

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]).

Zielgruppe

Research

Autoren/Hrsg.

Urbanski, R.

Pallaschke, Diethard Ernst

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Operations Research Spieltheorie

Inhaltsverzeichnis

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.