『Dictionary of Distances』

Elena Deza and Michel Marie Deza

(2006年10月刊行,Elsevier,Amsterdam, xvi + 391 pp. + 4 color plates, ISBN:9780444520876版元ページ



さまざまな学問領域で用いられている「距離概念」の総覧.数量分類学あり,多様体論あり,もちろん系統推定論あり.それにしても,400ページもの本が1冊書けるほど,さまざまな距離が世の中にはあるということか.

版元ページ著者サイト(M. -M. Deza).著者サイトからは目次および両端章(pdf)を入手できる.




【目次】
Preface iii

I. Mathematics of Distances 3

 1. General Definitions
 2. Topological Spaces
 3. Generalizations of Metric Spaces
 4. Metric Transforms
 5. Metrics on Normed Structures

II. Geometry and Distances 73

 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 145

 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 203

 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 253

 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 305

 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 361

 27. Length Measures and Scales
 28. Non-mathematical and Figurative Meaning of Distance


Bibliography 395
Index 404