Encyclopedia of Distances:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Edition: | 1. Aufl. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 590 S. Ill. |
| ISBN: | 9783642002335 |
Staff View
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Record in the Search Index
| _version_ | 1804138837088141312 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PART I MATHEMATICS OF DISTANCES 1 GENERAL DEFINITIONS 3
1.1 BASIC DEFINITIONS 3
1.2 MAIN DISTANCE-RELATED NOTIONS 11
1.3 METRIC NUMERICAL INVARIANTS 19
1.4 METRIC MAPPINGS 30
1.5 GENERAL DISTANCES 40
2 TOPOLOGICAL SPACES 59
3 GENERALIZATIONS OF METRIC SPACES 67
3.1 M-METRICS 67
3.2 INDEFINITE METRICS 68
3.3 TOPOLOGICAL GENERALIZATIONS 69
3.4 BEYOND NUMBERS 72
4 METRIC TRANSFORMS 79
4.1 METRICS ON THE SAME SET 79
4.2 METRICS ON SET EXTENSIONS 82
4.3 METRICS ON OTHER SETS 85
5 METRICS ON NORMED STRUCTURES 89
PART II GEOMETRY AND DISTANCES
6 DISTANCES IN GEOMETRY 103
6.1 GEODESIC GEOMETRY 103
6.2 PROJECTIVE GEOMETRY 110
6.3 AFFINE GEOMETRY 115
6.4 NON-EUCLIDEAN GEOMETRY 117
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/992310148
DIGITALISIERT DURCH
IMAGE 2
XUE CONTENTS
7 RIEMANNIAN AND HERMITIAN METRICS 127
7.1 RIEMANNIAN METRICS AND GENERALIZATIONS 128
7-2 RIEMANNIAN METRICS IN INFORMATION THEORY 143
7.3 HERMITIAN METRICS AND GENERALIZATIONS 148
8 DISTANCES ON SURFACES AND KNOTS 161
8.1 GENERAL SURFACE METRICS 161
8.2 INTRINSIC METRICS ON SURFACES 167
8.3 DISTANCES ON KNOTS 170
9 DISTANCES ON CONVEX BODIES, CONES, AND SIMPLICIAL COMPLEXES 173
9.1 DISTANCES ON CONVEX BODIES 173
9.2 DISTANCES ON CONES 179
9.3 DISTANCES ON SIMPLICIAL COMPLEXES 181
PART III DISTANCES IN CLASSICAL MATHEMATICS
10 DISTANCES IN ALGEBRA 187
10.1 GROUP METRICS 187
10.2 METRICS ON BINARY RELATIONS 196
10.3 METRICS ON LATTICES.. 197
11 DISTANCES ON STRINGS AND PERMUTATIONS 201
11.1 DISTANCES ON GENERAL STRINGS 202
11.2 DISTANCES ON PERMUTATIONS 210
12 DISTANCES ON NUMBERS, POLYNOMIALS, AND MATRICES 215 12.1 METRICS ON
NUMBERS 215
12.2 METRICS ON POLYNOMIALS 220
12.3 METRICS ON MATRICES 221
13 DISTANCES IN FUNCTIONAL ANALYSIS 229
13.1 METRICS ON FUNCTION SPACES 229
13.2 METRICS ON LINEAR OPERATORS 236
14 DISTANCES IN PROBABILITY THEORY 241
14.1 DISTANCES ON RANDOM VARIABLES 242
14.2 DISTANCES ON DISTRIBUTION LAWS 243
PART IV DISTANCES IN APPLIED MATHEMATICS
15 DISTANCES IN GRAPH THEORY 257
15.1 DISTANCES ON VERTICES OF A GRAPH 258
15.2 DISTANCE-DEFINED GRAPHS 264
IMAGE 3
CONTENTS XIII
15.3 DISTANCES ON GRAPHS 271
15.4 DISTANCES ON TREES 278
16 DISTANCES IN CODING THEORY 285
16.1 MINIMUM DISTANCE AND RELATIVES 286
16.2 MAIN CODING DISTANCES 289
17 DISTANCES AND SIMILARITIES IN DATA ANALYSIS 297
17.1 SIMILARITIES AND DISTANCES FOR NUMERICAL DATA 298
17.2 RELATIVES OF EUCLIDEAN DISTANCE 301
17.3 SIMILARITIES AND DISTANCES FOR BINARY DATA 304
17.4 CORRELATION SIMILARITIES AND DISTANCES 307
18 DISTANCES IN MATHEMATICAL ENGINEERING 311
18.1 MOTION PLANNING DISTANCES 311
18.2 CELLULAR AUTOMATA DISTANCES 315
18.3 DISTANCES IN CONTROL THEORY 316
18.4 MOEA DISTANCES 318
PART V COMPUTER-RELATED DISTANCES
19 DISTANCES ON REAL AND DIGITAL PLANES 323
19.1 METRICS ON REAL PLANE 323
19.2 DIGITAL METRICS 332
20 VORONOI DIAGRAM DISTANCES 339
20.1 CLASSICAL VORONOI GENERATION DISTANCES 340
20.2 PLANE VORONOI GENERATION DISTANCES 342
20.3 OTHER VORONOI GENERATION DISTANCES 346
21 IMAGE AND AUDIO DISTANCES 349
21.1 IMAGE DISTANCES 349
21.2 AUDIO DISTANCES 362
22 DISTANCES IN INTERNET AND SIMILAR NETWORKS 371
22.1 SCALE-FREE NETWORKS 371
22.2 NETWORK-BASED SEMANTIC DISTANCES 374
22.3 DISTANCES IN INTERNET AND WEB 376
PART VI DISTANCES IN NATURAL SCIENCES
23 DISTANCES IN BIOLOGY 385
23.1 GENETIC DISTANCES FOR GENE-FREQUENCY DATA 387
23.2 DISTANCES FOR DNA/RNA DATA 391
IMAGE 4
XIV CONTENTS
23.3 DISTANCES FOR PROTEIN DATA 400
23.4 OTHER BIOLOGICAL DISTANCES 404
24 DISTANCES IN PHYSICS AND CHEMISTRY 419
24.1 DISTANCES IN PHYSICS 419
24.2 DISTANCES IN CHEMISTRY AND CRYSTALLOGRAPHY 436
25 DISTANCES IN GEOGRAPHY, GEOPHYSICS, AND ASTRONOMY 445 25.1 DISTANCES
IN GEOGRAPHY AND GEOPHYSICS 445
25.2 DISTANCES IN ASTRONOMY 456
26 DISTANCES IN COSMOLOGY AND THEORY OF RELATIVITY 465 26.1 DISTANCES IN
COSMOLOGY 465
26.2 DISTANCES IN THEORY OF RELATIVITY 473
PART VII REAL-WORLD DISTANCES
27 LENGTH MEASURES AND SCALES 495
27.1 LENGTH SCALES 495
27.2 ORDERS OF MAGNITUDE FOR LENGTH 503
28 DISTANCES IN APPLIED SOCIAL SCIENCES 509
28.1 DISTANCES IN PSYCHOLOGY AND SOCIOLOGY 509
28.2 DISTANCES IN ECONOMICS AND HUMAN GEOGRAPHY 514 28.3 DISTANCES IN
PERCEPTION, COGNITION AND LANGUAGE 522 28.4 DISTANCES IN PHILOSOPHY,
RELIGION AND ART 530
29 OTHER DISTANCES 537
29.1 DISTANCES IN MEDICINE, ANTROPOMETRY AND SPORT 537 29.2 EQUIPMENT
DISTANCES 546
29.3 MISCELLANY 554
REFERENCES 563
INDEX 571
|
| any_adam_object | 1 |
| author | Deza, Michel 1939- Deza, Elena 1961- |
| author_GND | (DE-588)118064495 (DE-588)1027553648 |
| author_facet | Deza, Michel 1939- Deza, Elena 1961- |
| author_role | aut aut |
| author_sort | Deza, Michel 1939- |
| author_variant | m d md e d ed |
| building | Verbundindex |
| bvnumber | BV035406655 |
| classification_rvk | SK 280 |
| classification_tum | MAT 519f MAT 546f |
| ctrlnum | (OCoLC)633544257 (DE-599)DNB992310148 |
| dewey-full | 510.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.3 |
| dewey-search | 510.3 |
| dewey-sort | 3510.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| isbn | 9783642002335 |
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| physical | XIV, 590 S. Ill. |
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| spelling | Deza, Michel 1939- Verfasser (DE-588)118064495 aut Encyclopedia of Distances Michel Marie Deza ; Elena Deza 1. Aufl. Berlin [u.a.] Springer 2009 XIV, 590 S. Ill. txt rdacontent n rdamedia nc rdacarrier Metrik Mathematik (DE-588)4193458-1 gnd rswk-swf Abstand (DE-588)4228463-6 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Abstand (DE-588)4228463-6 s Metrik Mathematik (DE-588)4193458-1 s Metrischer Raum (DE-588)4169745-5 s 1\p DE-604 DE-604 Deza, Elena 1961- Verfasser (DE-588)1027553648 aut Erscheint auch als Online-Ausgabe 978-3-642-00234-2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017327208&sequence=000001&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, Michel 1939- Deza, Elena 1961- Encyclopedia of Distances Metrik Mathematik (DE-588)4193458-1 gnd Abstand (DE-588)4228463-6 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4193458-1 (DE-588)4228463-6 (DE-588)4169745-5 |
| title | Encyclopedia of Distances |
| title_auth | Encyclopedia of Distances |
| title_exact_search | Encyclopedia of Distances |
| title_full | Encyclopedia of Distances Michel Marie Deza ; Elena Deza |
| title_fullStr | Encyclopedia of Distances Michel Marie Deza ; Elena Deza |
| title_full_unstemmed | Encyclopedia of Distances Michel Marie Deza ; Elena Deza |
| title_short | Encyclopedia of Distances |
| title_sort | encyclopedia of distances |
| topic | Metrik Mathematik (DE-588)4193458-1 gnd Abstand (DE-588)4228463-6 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Metrik Mathematik Abstand Metrischer Raum |
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