Dictionary of Distances:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2006
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 391 S. Ill. |
| ISBN: | 0444520872 9780444520876 |
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Record in the Search Index
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| adam_text | Contents
Preface vii
PART I. MATHEMATICS OF DISTANCES
Chapter 1. General Definitions 2
1.1. Basic definitions 2
1.2. Main distance-related notions 7
1.3. General distances 21
Chapter 2. Topological Spaces 31
Chapter 3. Generalizations of Metric Spaces 36
3.1. m-metrics 36
3.2. Indefinite metrics 37
3.3. Topological generalizations 38
3.4. Beyond numbers 40
Chapter 4. Metric Transforms 44
4.1. Metrics on the same set 44
4.2. Metrics on set extensions 46
4.3. Metrics on other sets 48
Chapter 5. Metrics on Normed Structures 50
PART IL GEOMETRY AND DISTANCES
Chapter 6. Distances in Geometry 62
6.1. Geodesic Geometry 62
6.2. Projective Geometry 66
xi
6.3. Affine Geometry 71
6.4. Non-Euclidean Geometry 73
Chapter 7. Riemannian and Hermitian Metrics 81
7.1. Riemannian metrics and generalizations 81
7.2. Riemannian metrics in Information Theory 94
7.3. Hermitian metrics and generalizations 99
Chapter 8. Distances on Surfaces and Knots 111
8.1. General surface metrics 111
8.2. Intrinsic metrics on surfaces 116
8.3. Distances on knots 120
Chapter 9. Distances on Convex Bodies, Cones, and Simplirial Complexes 122
9.1. Distances on convex bodies 122
9.2. Distances on cones 127
9.3. Distances on simplicial complexes 129
PART III. DISTANCES IN CLASSICAL MATHEMATICS
Chapter 10. Distances in Algebra 134
10.1. Group metrics 134
10.2. Metrics on binary relations 141
10.3. Lattice metrics 143
Chapter 11. Distances on Strings and Permutations 146
11.1. Distances on general strings 147
11.2. Distances on permutations 151
Chapter 12. Distances on Niunbers, Polynomials, and Matrices 154
12.1. Metrics on numbers 154
12.2. Metrics on polynomials 158
12.3. Metrics on matrices 159
Chapter 13. Distances in Functional Analysis 165
13.1. Metrics on function Spaces 165 j
j
13.2. Metrics on linear Operators 1?2
Chapter 14. Distances in Probability Theory 176
14.1. Distances on random variables 177
14.2. Distances on distribution laws 178
PART IV. DISTANCES IN APPLIED MATHEMATICS
Chapter 15. Distances in Graph Theory 190
15.1. Distances on vertices of a graph 191
15.2. Distance-defined graphs 195
15.3. Distances on graphs 197
15.4. Distances on trees 202
Chapter 16. Distances in Coding Theory 207
16.1. Minimum distance and relatives 208
16.2. Main coding distances 211
Chapter 17. Distances and Similarities in Data Analysis 217
17.1. Similarities and distances for numerical data 218
17.2. Relatives of Euclidean distance 221
17.3. Similarities and distances for binary data 223
17.4. Correlation similarities and distances 226
Chapter 18. Distances in Mathematical Engineering 230
18.1. Motion planning distances 230
18.2. Cellular automata distances 234
18.3. Distances in Control Theory 234
18.4. MOEA distances 236
PART V. COMPUTER-RELATED DISTANCES
Chapter 19. Distances on Real and Digital Planes 240
19.1. Metricson real plane 240
19.2. Digital metrics 248
Chapter 20. Voronoi Diagram Distances 253
20.1. Classical Voronoi generation distances 254
20.2. Plane Voronoi generation distances 256
20.3. Other Voronoi generation distances 259
Chapter21. Image and Audio Distances 262
21.1. Image distances 262
21.2. Audio distances 273
Chapter 22. Distances in Internet and Similar Networks 279
22.1. Scale-free networks 279
22.2. Network-based semantic distances 281
22.3. Distances in Internet and Web 283
PART VI. DISTANCES IN NATURAL SCIENCES
Chapter 23. Distances in Biology 288
23.1. Genetic distances for gene-frequency data 289
23.2. Distances for DNA data 292
23.3. Distances for protein data 294
23.4. Other biological distances 296
Chapter 24. Distances in Physics and Chemistry 301
24.1. Distances in Physics 301
24.2. Distances in Chemistry 306
Chapter 25. Distances in Geography, Geophysics, and Astronomy 309
25.1. Distances in Geography and Geophysics 309
25.2. Distances in Astronomy 312
Chapter 26. Distances in Cosmology and Theory of Relativity 318
26.1. Distances in Cosmology 318
26.2. Distances in Theory of Relativity 324
PART VII. REAL-WORLD DISTANCES
Chapter 27. Length Measures and Scales 342
27.1. Length scales 342
27.2. Orders of magnitude for length 346
Chapter 28. Non-Mathematical and Figurative Meaning of Distance 350
28.1. Remoteness-related distances 350
28.2. Vision-related distances 357
28.3. Equipment distances 360
28.4. Miscellany 364
References 371
Subject Index 378
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| institution | BVB |
| isbn | 0444520872 9780444520876 |
| language | English |
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| owner | DE-523 DE-634 |
| owner_facet | DE-523 DE-634 |
| physical | XV, 391 S. Ill. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Elsevier |
| record_format | marc |
| spelling | Deza, Elena 1961- Verfasser (DE-588)1027553648 aut Dictionary of Distances Elena Deza ; Michel-Marie Deza 1. ed. Amsterdam [u.a.] Elsevier 2006 XV, 391 S. Ill. txt rdacontent n rdamedia nc rdacarrier Abstand (DE-588)4228463-6 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Abstandsmessung (DE-588)4195923-1 gnd rswk-swf Abstand (DE-588)4228463-6 s Angewandte Mathematik (DE-588)4142443-8 s Metrischer Raum (DE-588)4169745-5 s Abstandsmessung (DE-588)4195923-1 s 1\p DE-604 Deza, Michel-Marie Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017241115&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Deza, Elena 1961- Deza, Michel-Marie Dictionary of Distances Abstand (DE-588)4228463-6 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Metrischer Raum (DE-588)4169745-5 gnd Abstandsmessung (DE-588)4195923-1 gnd |
| subject_GND | (DE-588)4228463-6 (DE-588)4142443-8 (DE-588)4169745-5 (DE-588)4195923-1 |
| title | Dictionary of Distances |
| title_auth | Dictionary of Distances |
| title_exact_search | Dictionary of Distances |
| title_full | Dictionary of Distances Elena Deza ; Michel-Marie Deza |
| title_fullStr | Dictionary of Distances Elena Deza ; Michel-Marie Deza |
| title_full_unstemmed | Dictionary of Distances Elena Deza ; Michel-Marie Deza |
| title_short | Dictionary of Distances |
| title_sort | dictionary of distances |
| topic | Abstand (DE-588)4228463-6 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Metrischer Raum (DE-588)4169745-5 gnd Abstandsmessung (DE-588)4195923-1 gnd |
| topic_facet | Abstand Angewandte Mathematik Metrischer Raum Abstandsmessung |
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