Non-Connected Convexities and Applications 2002 ed. [Kõva köide]

Cristescu (mathematics, Aurel Vlaicu U. of Arad, Romania) and Lupsa (mathematics, Babes-Bolyai U. of Cluj-Napoca, Romania) propose two classifications of convexity properties for sets, both starting from the internal mechanism of defining them. The volume's 13 chapters cover the fields of non-connected convexity properties; convexity with respect to a set; convexity with respect to behaviors; convexity with respect to a set and two behaviors; convexities defined by means of distance functions; induced convexity; convexity defined by means of given functions; classification of the convexity properties; applications in pattern recognition; alternative theorems and integer convex sets; various types of generalized convex functions; applications in optimization; and applications in pharmacoeconomics. Written in charmingly clunky but fairly understandable English. Annotation c. Book News, Inc., Portland, OR (booknews.com)

The notion of convex set, known according to its numerous applications in linear spaces due to its connectivity which leads to separation and support properties, does not imply, in fact, necessarily, the connectivity. This aspect of non-connectivity hidden under the convexity is discussed in this book. The property of non-preserving the connectivity leads to a huge extent of the domain of convexity. The book contains the classification of 100 notions of convexity, using a generalised convexity notion, which is the classifier, ordering the domain of concepts of convex sets. Also, it opens the wide range of applications of convexity in non-connected environment. Applications in pattern recognition, in discrete programming, with practical applications in pharmaco-economics are discussed. Both the synthesis part and the applied part make the book useful for more levels of readers. Audience: Researchers dealing with convexity and related topics, young researchers at the beginning of their approach to convexity, PhD and master students.