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
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