Overview

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, necessarily, the connectivity. This aspect of non-connectivity hidden under the convexity is discussed in this text. The property of non-preserving the connectivity leads to a huge extent of the domain of convexity. This book contains the classification of 100 notions of convexity, using a generalized 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 environments. Applications in pattern recognition, in discrete programming, with practical applications in pharmaco-economics are discussed. Both the synthesis part and the applied part should make the book useful for more levels of readers.

Full Product Details

Author:   G. Cristescu ,  L. Lupsa
Publisher:   Kluwer Academic Publishers
Imprint:   Kluwer Academic Publishers
Edition:   2002 ed.
Volume:   68
Dimensions:   Width: 15.60cm , Height: 2.20cm , Length: 23.40cm
Weight:   1.600kg
ISBN:  

9781402006241

ISBN 10:   1402006241
Pages:   368
Publication Date:   31 May 2002
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

Table of contents. Preface. Acknowledgements. Main notations. Part 1: Non-connected convexity properties. 1. The fields of non-connected convexity properties. 2. Convexity with respect to a set. 3. Behaviours. Convexity with respect to a behaviour. 4. Convexity with respect to a set and two behaviours. 5. Convexities defined by means of distance functions. 6. Induced convexity. 7. Convexity defined by means of given functions. 8. Classification of the convexity properties. Part 2: Applications. 9. Applications in pattern recognition. 10. Alternative theorems and integer convex sets. 11. Various types of generalised convex functions and main properties. 12. Applications in optimisation. 13. Applications in pharmaco-economics. References. Authors index. Subject index. Figures index. Tables index.

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