Dictionary of Distances

1st Edition

Authors: Michel-Marie Deza Elena Deza
Hardcover ISBN: 9780444520876
eBook ISBN: 9780080465548
Imprint: Elsevier Science
Published Date: 3rd October 2006
Page Count: 412
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Description

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.

Key Features

  • 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

Readership

Researchers, students and general public interested in Science.

Table of Contents

Preface
I. Mathematics of Distances

  1. General Definitions
  2. Topological Spaces
  3. Generalizations of Metric Spaces
  4. Metric Transforms
  5. Metrics on Normed Structures
    II. Geometry and Distances
  6. Distances in Geometry
  7. Riemannian and Hermitian Metrics
  8. Distances on Surfaces and Knots
  9. Distances on Convex Bodies, Cones, and Simplicial Complexes
    III. Distances in Classical Mathematics
  10. Distances in Algebra
  11. Distances on Strings and Permutations
  12. Distances on Numbers, Polynomials, and Matrices
  13. Distances in Functional Analysis
  14. Distances in Probability Theory
    IV. Distances in Applied Mathematics
  15. Distances in Graph Theory
  16. Distances in Coding Theory
  17. Distances and Similarities in Data Analysis
  18. Distances in Mathematical Engineering
    V. Computer-related Distances
  19. Distances on Real and Digital Planes
  20. Voronoi Diagram Distances
  21. Image and Audio Distances
  22. Distances in Internet and Similar Networks
    VI. Distances in Natural Sciences
  23. Distances in Biology
  24. Distances in Physics and Chemistry
  25. Distances in Geography, Geophysics, and Astronomy
  26. Distances in Cosmology ad Theory of Relativity
    VII. Real-world Distances
  27. Length Measures and Scales
  28. Non-mathematical and Figurative Meaning of Distance

Details

No. of pages:
412
Language:
English
Copyright:
© Elsevier Science 2006
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080465548
Hardcover ISBN:
9780444520876

About the Author

Michel-Marie Deza

Elena Deza