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Lieferstatus:	i.d.R. innert 5-10 Tagen versandfertig
Veröffentlichung:	November 1996
Genre:	Schulbücher
	beltbody / Combinatorics / coveringproblems / d-convexity / Geometrie / Graph / h-convexity / hellydimension / Kombinatorik / Optimierung / set / Variationsrechnung mehr...
ISBN:	9783540613411
EAN-Code:	9783540613411
Verlag:	Springer
Einband:	Kartoniert
Sprache:	English
Dimensionen:	H 235 mm / B 155 mm / D 24 mm
Gewicht:	663 gr
Seiten:	440
Bewertung:	Titel bewerten / Meinung schreiben

Inhalt:

I. Convexity.- ?Convex sets.- ?Faces and supporting hyperplanes.- ?Polarity.- ?Direct sum decompositions.- ?The lower semicontinuity of the operator "exp".- ?Convex cones.- ?The Farkas Lemma and its generalization.- ?Separable systems of convex cones.- II. d-Convexity in normed spaces.- ?The definition of d-convex sets.- ? Support properties of d-convex sets.- ? Properties of d-convex flats.- ? The join of normed spaces.- ? Separability of d-convex sets.- ? The Helly dimension of a set family.- ? d-Star-shaped sets.- III. H-convexity.- ? The functional md for vector systems.- ? The ?-displacement Theorem.- ? Lower semicontinuity of the functional md.- ? The definition of H-convex sets.- ? Upper semicontinuity of the H-convex hull.- ? Supporting cones of H-convex bodies.- ? The Helly Theorem for H-convex sets.- ? Some applications of H-convexity.- ? Some remarks on connection between d-convexity and H-convexity.- IV. The Sz?efalvi-Nagy Problem.- ? The Theorem of Sz?efalvi-Nagy and its generalization.- ? Description of vector systems with md H = 2 that are not one-sided.- ? The 2-systems without particular vectors.- ? The 2-system with particular vectors.- ? The compact, convex bodies with md M = 2.- ? Centrally symmetric bodies.- V. Borsuk's partition problem.- ? Formulation of the problem and a survey of results.- ? Bodies of constant width in Euclidean and normed spaces.- ? Borsuk's problem in normed spaces.- VI. Homothetic covering and illumination.- ? The main problem and a survey of results.- ? The hypothesis of Gohberg-Markus-Hadwiger.- ? The infinite values of the functional b, b2032;, c, c2032;,.- ? Inner illumination of convex bodies.- ?Estimates for the value of the functional p(K).- VII. Combinatorial geometry of belt bodies.- ? The integral respresentation of zonoids.- ? Belt vectors of a compact, convex body.- ? Definition of belt bodies.- ? Solution of the illumination problem for belt bodies.- ? Solution of the Sz?efalvi-Nagy problem for belt bodies.- ? Minimal fixing systems.- VIII. Some research problems.- Author Index.- List of Symbols.