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Directed Sets and Differences of Convex Compact Sets

Titelangaben

Baier, Robert ; Farkhi, E.:
Directed Sets and Differences of Convex Compact Sets.
In: Polis, Michael P. ; Dontchev, Asen L. ; Kall, Peter ; Lasiecka, Irena ; Olbrot, Andrzej W. (Hrsg.): Systems modelling and optimization : Proceedings of the 18th IFIP TC7 Conference held in Detroit, Michigan, July 22-25, 1997. - Boca Raton : Chapman & Hall , 1999 . - S. 135-143 . - (Chapman & Hall/CRC Research Notes in Mathematics Series ; 396 )
ISBN 0-8493-0607-8

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Abstract

This paper is devoted to directed sets and differences of convex compact sets. The authors use the specific parametrization of convex compact sets via their support functions and consider the supporting faces as lower-dimensional convex sets. Extending this approach they define a directed set as a pair of mappings that associate to each unit direction an (n-1)-dimensional directed set and a scalar function determining the position of this face in |R^n.
The main differences of the authors' approach to other existing embeddings are that there are no equivalence classes and, secondly, that differences of directed convex sets in |R^n are not real-valued functions of n arguments. The authors provide an application, by giving an example of set-valued interpolation where nonconvex visualizations of directed sets appear as results.

Weitere Angaben

Publikationsform: Aufsatz in einem Buch
Begutachteter Beitrag: Ja
Zusätzliche Informationen: Contents:
1. Introduction
2. Directed Intervals
3. Directed Sets
4. Applications and Numerical Example
Keywords: convex sets in n dimensions; set-valued maps; set-valued interpolation; interval arithmetic; set-valued analysis
Fachklassifikationen: Mathematics Subject Classification Code: 52A20 (49M25 65D05 65G30 93B03 49J53 54C60)
Institutionen der Universität: Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 19 Feb 2021 07:01
Letzte Änderung: 06 Mai 2021 11:22
URI: https://eref.uni-bayreuth.de/id/eprint/63207