Pairs of compact convex sets : fractional arithmetic with convex sets

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Bibliographic Information

Pairs of compact convex sets : fractional arithmetic with convex sets

by Diethard Pallaschke and Ryszard Urbański

(Mathematics and its applications, v. 548)

Kluwer Academic, c2002

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Note

Includes bibliographical references (p. 287-295) and index

Description and Table of Contents

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]).

Table of Contents

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.

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Details

  • NCID
    BA59750479
  • ISBN
    • 1402009380
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xii, 295 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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