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 iiiI. Mathematics of Distances 3
1. General Definitions
2. Topological Spaces
3. Generalizations of Metric Spaces
4. Metric Transforms
5. Metrics on Normed StructuresII. 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 ComplexesIII. 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 TheoryIV. 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 EngineeringV. 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 NetworksVI. 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 RelativityVII. Real-world Distances 361
27. Length Measures and Scales
28. Non-mathematical and Figurative Meaning of Distance
Bibliography 395
Index 404