Dictionary of Distances (eBook)
412 Seiten
Elsevier Science (Verlag)
978-0-08-046554-8 (ISBN)
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
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 "e;centripedal"e; and "e;oikoumeni"e;, 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
Front cover 1
Preface 8
Contents 12
Part I. Mathematics of Distances 18
Chapter 1. General Definitions 19
1.1. Basic definitions 19
1.2. Main distance-related notions 24
1.3. General distances 38
Chapter 2. Topological Spaces 48
Chapter 3. Generalizations of Metric Spaces 53
3.1. m-metrics 53
3.2. Indefinite metrics 54
3.3. Topological generalizations 55
3.4. Beyond numbers 57
Chapter 4. Metric Transforms 61
4.1. Metrics on the same set 61
4.2. Metrics on set extensions 63
4.3. Metrics on other sets 65
Chapter 5. Metrics on Normed Structures 67
Part II. Geometry and Distances 78
Chapter 6. Distances in Geometry 79
6.1. Geodesic Geometry 79
6.2. Projective Geometry 83
6.3. Affine Geometry 88
6.4. Non-Euclidean Geometry 90
Chapter 7. Riemannian and Hermitian Metrics 98
7.1. Riemannian metrics and generalizations 98
7.2. Riemannian metrics in Information Theory 111
7.3. Hermitian metrics and generalizations 116
Chapter 8. Distances on Surfaces and Knots 128
8.1. General surface metrics 128
8.2. Intrinsic metrics on surfaces 133
8.3. Distances on knots 137
Chapter 9. Distances on Convex Bodies, Cones, and Simplicial Complexes 139
9.1. Distances on convex bodies 139
9.2. Distances on cones 144
9.3. Distances on simplicial complexes 146
Part III. Distances in Classical Mathematics 150
Chapter 10. Distances in Algebra 151
10.1. Group metrics 151
10.2. Metrics on binary relations 158
10.3. Lattice metrics 160
Chapter 11. Distances on Strings and Permutations 163
11.1. Distances on general strings 164
11.2. Distances on permutations 168
Chapter 12. Distances on Numbers, Polynomials, and Matrices 171
12.1. Metrics on numbers 171
12.2. Metrics on polynomials 175
12.3. Metrics on matrices 176
Chapter 13. Distances in Functional Analysis 182
13.1. Metrics on function spaces 182
13.2. Metrics on linear operators 189
Chapter 14. Distances in Probability Theory 193
14.1. Distances on random variables 194
14.2. Distances on distribution laws 195
Part IV. Distances in Applied Mathematics 206
Chapter 15. Distances in Graph Theory 207
15.1. Distances on vertices of a graph 208
15.2. Distance-defined graphs 212
15.3. Distances on graphs 214
15.4. Distances on trees 219
Chapter 16. Distances in Coding Theory 224
16.1. Minimum distance and relatives 225
16.2. Main coding distances 228
Chapter 17. Distances and Similarities in Data Analysis 234
17.1. Similarities and distances for numerical data 235
17.2. Relatives of Euclidean distance 238
17.3. Similarities and distances for binary data 240
17.4. Correlation similarities and distances 243
Chapter 18. Distances in Mathematical Engineering 247
18.1. Motion planning distances 247
18.2. Cellular automata distances 251
18.3. Distances in Control Theory 251
18.4. MOEA distances 253
Part V. Computer-Related Distances 256
Chapter 19. Distances on Real and Digital Planes 257
19.1. Metrics on real plane 257
19.2. Digital metrics 265
Chapter 20. Voronoi Diagram Distances 270
20.1. Classical Voronoi generation distances 271
20.2. Plane Voronoi generation distances 273
20.3. Other Voronoi generation distances 276
Chapter 21. Image and Audio Distances 279
21.1. Image distances 279
21.2. Audio distances 290
Chapter 22. Distances in Internet and Similar Networks 296
22.1. Scale-free networks 296
22.2. Network-based semantic distances 298
22.3. Distances in Internet and Web 300
Part VI. Distances in Natural Sciences 304
Chapter 23. Distances in Biology 305
23.1. Genetic distances for gene-frequency data 306
23.2. Distances for DNA data 309
23.3. Distances for protein data 311
23.4. Other biological distances 313
Chapter 24. Distances in Physics and Chemistry 318
24.1. Distances in Physics 318
24.2. Distances in Chemistry 323
Chapter 25. Distances in Geography, Geophysics, and Astronomy 326
25.1. Distances in Geography and Geophysics 326
25.2. Distances in Astronomy 329
Chapter 26. Distances in Cosmology and Theory of Relativity 335
26.1. Distances in Cosmology 335
26.2. Distances in Theory of Relativity 341
Part VII. Real-World Distances 358
Chapter 27. Length Measures and Scales 359
27.1. Length scales 359
27.2. Orders of magnitude for length 363
Chapter 28. Non-Mathematical and Figurative Meaning of Distance 367
28.1. Remoteness-related distances 367
28.2. Vision-related distances 374
28.3. Equipment distances 377
28.4. Miscellany 381
References 388
Subject Index 395
| Erscheint lt. Verlag | 16.11.2006 |
|---|---|
| Sprache | englisch |
| Themenwelt | Sachbuch/Ratgeber |
| Schulbuch / Wörterbuch ► Lexikon / Chroniken | |
| Mathematik / Informatik ► Informatik ► Datenbanken | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| ISBN-10 | 0-08-046554-4 / 0080465544 |
| ISBN-13 | 978-0-08-046554-8 / 9780080465548 |
| Haben Sie eine Frage zum Produkt? |
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