Gespeichert in:
| Titel: | Encyclopedia of distances |
|---|---|
| Von: |
Michel Marie Deza ; Elena Deza
|
| Person: |
Deza, Michel
1939- Verfasser aut Deza, Elena 1961- |
| Hauptverfassende: | , |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2013
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | http://deposit.dnb.de/cgi-bin/dokserv?id=4059539&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025484473&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XVIII, 650 S. Ill. 25 cm |
| ISBN: | 9783642309571 3642309577 9783642309588 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819336604146204672 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PART I MATHEMATICS O F DISTANCES 1 GENERAL DEFINITIONS 3
1.1 BASIC DEFINITIONS 3
1.2 MAIN DISTANCE-RELATED NOTIONS 11
1.3 METRIC NUMERICAL INVARIANTS 21
1.4 METRIC MAPPINGS 33
1.5 GENERAL DISTANCES 43
2 TOPOLOGICAL SPACES 59
3 GENERALIZATIONS O F METRIC SPACES 67
3.1 RA-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 109
6.3 AFFINE GEOMETRY 114
6.4 NON-EUCLIDEAN GEOMETRY 116
7 RIEMANNIAN AND HERMITIAN METRICS 125
7.1 RIEMANNIAN METRICS AND GENERALIZATIONS 126
X V
HTTP://D-NB.INFO/1023420988
IMAGE 2
XVI C O N T E N T S
7.2 RIEMANNIAN METRICS IN INFORMATION THEORY 141
7.3 HERMITIAN METRICS AND GENERALIZATIONS 144
8 DISTANCES ON SURFACES AND KNOTS 157
8.1 GENERAL SURFACE METRICS 157
8.2 INTRINSIC METRICS ON SURFACES 162
8.3 DISTANCES ON KNOTS 166
9 DISTANCES ON CONVEX BODIES, CONES, AND SIMPLICIAL COMPLEXES . . . 1 69
9.1 DISTANCES ON CONVEX BODIES 169
9.2 DISTANCES ON CONES 174
9.3 DISTANCES ON SIMPLICIAL COMPLEXES 177
PART III DISTANCES IN CLASSICAL MATHEMATICS
10 DISTANCES IN ALGEBRA 183
10.1 GROUP METRICS 183
10.2 METRICS ON BINARY RELATIONS 191
10.3 METRICS ON LATTICES 193
11 DISTANCES ON STRINGS AND PERMUTATIONS 197
11.1 DISTANCES ON GENERAL STRINGS 198
11.2 DISTANCES ON PERMUTATIONS 206
12 DISTANCES ON NUMBERS, POLYNOMIALS, AND MATRICES 209
12.1 METRICS ON NUMBERS 209
12.2 METRICS ON POLYNOMIALS 213
12.3 METRICS ON MATRICES 215
13 DISTANCES IN FUNCTIONAL ANALYSIS 223
13.1 METRICS ON FUNCTION SPACES 223
13.2 METRICS ON LINEAR OPERATORS 229
14 DISTANCES IN PROBABILITY THEORY 233
14.1 DISTANCES ON RANDOM VARIABLES 234
14.2 DISTANCES ON DISTRIBUTION LAWS 235
PART IV DISTANCES IN APPLIED MATHEMATICS
15 DISTANCES IN GRAPH THEORY 249
15.1 DISTANCES ON THE VERTICES O F A GRAPH 250
15.2 DISTANCE-DEFINED GRAPHS 257
15.3 DISTANCES ON GRAPHS 267
15.4 DISTANCES ON TREES 274
16 DISTANCES IN CODING THEORY 279
16.1 MINIMUM DISTANCE AND RELATIVES 280
16.2 MAIN CODING DISTANCES 283
IMAGE 3
CONTENTS X V I I
17 DISTANCES AND SIMILARITIES IN DATA ANALYSIS 291
17.1 SIMILARITIES AND DISTANCES FOR NUMERICAL DATA 292
17.2 RELATIVES OF EUCLIDEAN DISTANCE 295
17.3 SIMILARITIES AND DISTANCES FOR BINARY DATA 297
17.4 CORRELATION SIMILARITIES AND DISTANCES 301
18 DISTANCES IN SYSTEMS AND MATHEMATICAL ENGINEERING 307
18.1 DISTANCES IN STATE TRANSITION AND DYNAMICAL SYSTEMS 307
18.2 DISTANCES IN CONTROL THEORY 312
18.3 MOTION PLANNING DISTANCES 314
18.4 MOEA DISTANCES 319
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 345
21 IMAGE AND AUDIO DISTANCES 349
21.1 IMAGE DISTANCES 349
21.2 AUDIO DISTANCES 362
22 DISTANCES IN NETWORKS 371
22.1 SCALE-FREE NETWORKS 371
22.2 NETWORK-BASED SEMANTIC DISTANCES 375
22.3 DISTANCES IN INTERNET AND WEB 378
PART VI DISTANCES IN NATURAL SCIENCES
23 DISTANCES IN BIOLOGY 387
23.1 GENETIC DISTANCES 390
23.2 DISTANCES FOR DNA/RNA AND PROTEIN DATA 401
23.3 DISTANCES IN ECOLOGY, BIOGEOGRAPHY, ETHOLOGY 411
23.4 OTHER BIOLOGICAL DISTANCES 423
24 DISTANCES IN PHYSICS AND CHEMISTRY 435
24.1 DISTANCES IN PHYSICS 435
24.2 DISTANCES IN CHEMISTRY AND CRYSTALLOGRAPHY 457
25 DISTANCES IN EARTH SCIENCE AND ASTRONOMY 465
25.1 DISTANCES IN GEOGRAPHY 465
25.2 DISTANCES IN GEOPHYSICS 474
25.3 DISTANCES IN ASTRONOMY 483
IMAGE 4
XV111
CONTENTS
26 DISTANCES IN COSMOLOGY AND THEORY OF RELATIVITY 497
26.1 DISTANCES IN COSMOLOGY 497
26.2 DISTANCES IN THEORY OF RELATIVITY 506
PART VII REAL-WORLD DISTANCES
27 LENGTH MEASURES AND SCALES 529
27.1 LENGTH SCALES 529
27.2 ORDERS OF MAGNITUDE FOR LENGTH 539
28 DISTANCES IN APPLIED SOCIAL SCIENCES 545
28.1 DISTANCES IN PERCEPTION AND PSYCHOLOGY 545
28.2 DISTANCES IN ECONOMICS AND HUMAN GEOGRAPHY 554
28.3 DISTANCES IN SOCIOLOGY AND LANGUAGE 565
28.4 DISTANCES IN PHILOSOPHY, RELIGION AND ART 574
29 OTHER DISTANCES 587
29.1 DISTANCES IN MEDICINE, ANTHROPOMETRY AND SPORT 587
29.2 EQUIPMENT DISTANCES 600
29.3 MISCELLANY 611
REFERENCES 619
INDEX 627
F O
|
| 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 | BV040657658 |
| classification_rvk | SK 280 SK 600 |
| ctrlnum | (OCoLC)823306884 (DE-599)DNB1023420988 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040657658 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:19:52Z |
| institution | BVB |
| isbn | 9783642309571 3642309577 9783642309588 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025484473 |
| oclc_num | 823306884 |
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| owner_facet | DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | XVIII, 650 S. Ill. 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Deza, Michel 1939- Deza, Elena 1961- Encyclopedia of distances Abstand (DE-588)4228463-6 gnd Metrischer Raum (DE-588)4169745-5 gnd Metrik Mathematik (DE-588)4193458-1 gnd |
| subject_GND | (DE-588)4228463-6 (DE-588)4169745-5 (DE-588)4193458-1 |
| 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 | Abstand (DE-588)4228463-6 gnd Metrischer Raum (DE-588)4169745-5 gnd Metrik Mathematik (DE-588)4193458-1 gnd |
| topic_facet | Abstand Metrischer Raum Metrik Mathematik |
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