Dictionary of Distances

Elena Deza, Michel Marie Deza

410 pages, parution le 15/10/2006

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Résumé

This book comes out of need and urgency (expressed especially in areas of Information Retrieval with respect to Image, Audio, Internet and Biology) to have a working tool to compare data. The book will provide powerful resource for all researchers using Mathematics as well as for mathematicians themselves. In the time when over-specialization and terminology fences isolate researchers, this Dictionary try to be "centripedal" and "oikoumeni", providing some access and altitude of vision but without taking the route of scientific vulgarisation. This attempted balance is the main philosophy of this Dictionary which defined its structure and style.

Key features:

- Unicity: it is the first book treating the basic notion of Distance in whole generality. - Interdisciplinarity: this Dictionary is larger in scope than majority of thematic dictionaries. - Encyclopedicity: while an Encyclopedia of Distances seems now too difficult to produce, this book (by its scope, short introductions and organization) provides the main material for it and for future tutorials on some parts of this material. - Applicability: the distances, as well as distance-related notions and paradigms, are provided in ready-to-use fashion. - Worthiness: the need and urgency for such dictionary was great in several huge areas, esp. Information Retrieval, Image Analysis, Speech Recognition and Biology. - Accessibility: the definitions are easy to locate by subject or, in Index, by alphabetic order; the introductions and definitions are reader-friendly and maximally independent one from another; still the text is structured, in the 3D HTML style, by hyperlink-like boldfaced references to similar definitions.

Sommaire

Mathematics of Distances
- General Definitions
- Topological Spaces
- Generalizations of Metric Spaces
- Metric Transforms
- Metrics on Normed Structures
Geometry and Distances
- Distances in Geometry
- Riemannian and Hermitian Metrics
- Distances on Surfaces and Knots
- Distances on Convex Bodies, Cones, and Simplicial Complexes
Distances in Classical Mathematics
- Distances in Algebra
- Distances on Strings and Permutations
- Distances on Numbers, Polynomials, and Matrices
- Distances in Functional Analysis
- Distances in Probability Theory
Distances in Applied Mathematics
- Distances in Graph Theory
- Distances in Coding Theory
- Distances and Similarities in Data Analysis
- Distances in Mathematical Engineering
Computer-related Distances
- Distances on Real and Digital Planes
- Voronoi Diagram Distances
- Image and Audio Distances
- Distances in Internet and Similar Networks
Distances in Natural Sciences
- Distances in Biology
- Distances in Physics and Chemistry
- Distances in Geography, Geophysics, and Astronomy
- Distances in Cosmology ad Theory of Relativity
Real-world Distances
- Length Measures and Scales
- Non-mathematical and Figurative Meaning of Distance

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Elsevier
Auteur(s)	Elena Deza, Michel Marie Deza
Parution	15/10/2006
Nb. de pages	410
Format	17 x 25
Couverture	Relié
Poids	875g
Intérieur	Noir et Blanc
EAN13	9780444520876