Dictionary of Distances

ISBN-13: 9780444520876 / Angielski / Twarda / 2006 / 412 str.

Michel-Marie Deza; Elena Deza

Opis

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.

* 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

Spis treści

PrefaceI. Mathematics of Distances1. General Definitions2. Topological Spaces3. Generalizations of Metric Spaces4. Metric Transforms5. Metrics on Normed StructuresII. Geometry and Distances6. Distances in Geometry7. Riemannian and Hermitian Metrics8. Distances on Surfaces and Knots9. Distances on Convex Bodies, Cones, and Simplicial ComplexesIII. Distances in Classical Mathematics10. Distances in Algebra11. Distances on Strings and Permutations12. Distances on Numbers, Polynomials, and Matrices13. Distances in Functional Analysis14. Distances in Probability TheoryIV. Distances in Applied Mathematics15. Distances in Graph Theory16. Distances in Coding Theory17. Distances and Similarities in Data Analysis18. Distances in Mathematical EngineeringV. Computer-related Distances19. Distances on Real and Digital Planes20. Voronoi Diagram Distances21. Image and Audio Distances22. Distances in Internet and Similar NetworksVI. Distances in Natural Sciences23. Distances in Biology24. Distances in Physics and Chemistry25. Distances in Geography, Geophysics, and Astronomy26. Distances in Cosmology ad Theory of RelativityVII. Real-world Distances27. Length Measures and Scales28. Non-mathematical and Figurative Meaning of Distance