Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets (Mathematics and Its Applications)
Pallaschke, Diethard Ernst; Urbanski, R.
ISBN 10: 9048161495 ISBN 13: 9789048161492
Editorial: Springer, 2010
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The book is devoted to the theory of pairs of compact convex sets and in particular to 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 Rådström-Hörmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity. In the first three chapters of the book the basic facts about convexity, mixed volumes and the Rådström-Hörmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs.
Reseña del editor: 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]).
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Título: Pairs of Compact Convex Sets: Fractional ...
Editorial: Springer
Año de publicación: 2010
Encuadernación: Encuadernación de tapa blanda
Condición: New
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Pairs of Compact Convex Sets
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Springer Netherlands, 2010
ISBN 10: 9048161495
ISBN 13: 9789048161492
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. Decompo. Nº de ref. del artículo: 5820001
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Pairs of Compact Convex Sets | Fractional Arithmetic with Convex Sets
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Springer Netherland, 2010
ISBN 10: 9048161495
ISBN 13: 9789048161492
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Taschenbuch. Condición: Neu. Pairs of Compact Convex Sets | Fractional Arithmetic with Convex Sets | R. Urbanski (u. a.) | Taschenbuch | xii | Englisch | 2010 | Springer Netherland | EAN 9789048161492 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Nº de ref. del artículo: 107245372
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Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets (Mathematics and Its Applications)
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Pairs of Compact Convex Sets
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Springer Netherlands, Springer Netherlands Dez 2010, 2010
ISBN 10: 9048161495
ISBN 13: 9789048161492
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Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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]).Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 308 pp. Englisch. Nº de ref. del artículo: 9789048161492
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Pairs of Compact Convex Sets
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Springer Netherlands Dez 2010, 2010
ISBN 10: 9048161495
ISBN 13: 9789048161492
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Librería: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Alemania
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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]). 308 pp. Englisch. Nº de ref. del artículo: 9789048161492
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Pairs of Compact Convex Sets : Fractional Arithmetic With Convex Sets
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Pairs of Compact Convex Sets : Fractional Arithmetic With Convex Sets
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Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets (Mathematics and Its Applications)
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Pairs of Compact Convex Sets : Fractional Arithmetic with Convex Sets
Publicado por
Springer Netherlands, 2010
ISBN 10: 9048161495
ISBN 13: 9789048161492
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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]). Nº de ref. del artículo: 9789048161492
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