| Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets Contributor(s): Pallaschke, Diethard Ernst (Author), Urbanski, R. (Author) |
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ISBN: 9048161495 ISBN-13: 9789048161492 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Analytic - Medical - Mathematics | Set Theory |
| Dewey: 516.08 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.65" H x 6.14" W x 9.21" (0.96 lbs) 295 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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]). |