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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.
- 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.
- Covers a large range of subjects in pure and applied mathematics
- Designed to be easily applied--the distances and distance-related notions and paradigms are ready to use
- Helps users quickly locate definitions by subject or in alphabetical order; stand-alone entries include references to other entries and sources for further investigation
Researchers, students and general public interested in Science.
I. Mathematics of Distances
- General Definitions
- Topological Spaces
- Generalizations of Metric Spaces
- Metric Transforms
- Metrics on Normed Structures
II. Geometry and Distances
- Distances in Geometry
- Riemannian and Hermitian Metrics
- Distances on Surfaces and Knots
- Distances on Convex Bodies, Cones, and Simplicial Complexes
III. 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
IV. Distances in Applied Mathematics
- Distances in Graph Theory
- Distances in Coding Theory
- Distances and Similarities in Data Analysis
- Distances in Mathematical Engineering
V. Computer-related Distances
- Distances on Real and Digital Planes
- Voronoi Diagram Distances
- Image and Audio Distances
- Distances in Internet and Similar Networks
VI. 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
VII. Real-world Distances
- Length Measures and Scales
- Non-mathematical and Figurative Meaning of Distance
- No. of pages:
- © Elsevier Science 2006
- 3rd October 2006
- Elsevier Science
- Hardcover ISBN:
- eBook ISBN:
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