Relational mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
132 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 567 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9780521762687 |
Internformat
MARC
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|---|---|---|---|
| 001 | BV037236273 | ||
| 003 | DE-604 | ||
| 005 | 20111130 | ||
| 007 | t | ||
| 008 | 110218s2011 ad|| |||| 00||| eng d | ||
| 020 | |a 9780521762687 |c (hbk.) £60.00 |9 978-0-521-76268-7 | ||
| 035 | |a (OCoLC)682120617 | ||
| 035 | |a (DE-599)BSZ329991574 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
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| 100 | 1 | |a Schmidt, Gunther |d 1939- |e Verfasser |0 (DE-588)12940893X |4 aut | |
| 245 | 1 | 0 | |a Relational mathematics |c Gunther Schmidt |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2011 | |
| 300 | |a XIII, 567 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 132 | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Relation |g Mathematik |0 (DE-588)4177675-6 |2 gnd |9 rswk-swf |
| 653 | |a Computer science / Mathematics | ||
| 653 | |a Operations research / Mathematics | ||
| 689 | 0 | 0 | |a Relation |g Mathematik |0 (DE-588)4177675-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Encyclopedia of mathematics and its applications |v 132 |w (DE-604)BV000903719 |9 132 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021149856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-021149856 | ||
Datensatz im Suchindex
| _version_ | 1804143844019666944 |
|---|---|
| adam_text | Contents
Notes
on illustrations page
ix
Preface
xi
1
Introduction
1
PART I REPRESENTATIONS OF RELATIONS
2
Sets, subsets, and elements
5
2.1
Set representation
6
2.2
Element representation
8
2.3
Subset representation
9
3
Relations
15
3.1
Relation representation
15
3.2
Relations describing graphs
19
3.3
Relations generated by cuts
23
3.4
Relations generated randomly
25
3.5
Function representation
26
3.6
Permutation representation
28
3.7
Partition representation
31
PART II OPERATIONS AND CONSTRUCTIONS
4
Algebraic operations on relations
35
4.1
Typing relations
35
4.2
Boolean operations
37
4.3
Relational operations proper
38
4.4
Composite operations
43
5
Order and function: the standard view
49
5.1
Functions
49
5.2
Mappings and points
57
5.3
Order and strictorder
61
Contents
70
76
80
84
91
91
94
98
99
101
103
106
107
107
127
131
135
140
148
150
152
8 Relation
algebra
157
8.1
Laws of
relation
algebra
157
8.2
Visualizing the algebraic laws
159
8.3
Elementary properties of relations
165
8.4
Cancellation properties of residuals and cones
167
8.5
Cancellation properties of the symmetric quotient
171
8.6
Tarski rule and Point Axiom
181
9
Orders and lattices
183
9.1
Maxima and minima
183
9.2
Bounds and cones
185
9.3
Least and greatest elements
187
9.4
Greatest lower and least upper bounds
188
9.5
Lattices
190
10
Rectangles, fringes, inverses
200
10.1
Non-enlargeable rectangles
200
10.2
Independent pairs and covering pairs of sets
206
5.4
Equivalence and quotient
5.5
Transitive closure
5.6
Congruences
5.7
Homomorphisms
Relations and vectors
6.1
Domain and codomain
6.2
Rectangular zones
6.3
Independent pair of sets and covering pair of sets
6.4
Reducing vectors
6.5
Progressively infinite subsets
6.6
Stable and
absorbant
sets
Domain construction
7.1
Domains of ground type
7.2
Direct product
7.3
Direct sum
7.4
Quotient domain
7.5
Subset extrusion
7.6
Direct power
7.7
Domain permutation
7.8
Remarks on further constructions
7.9
Equivalent representations
PART
III ALGEBRA
10.3
Fringes
10.4
Difunctional relations
10.5
Ferrers
relations
10.6
Block-transitive
relations
10.7
Inverses
Concept
analysis
11.1
Row and column spaces
11.2
Factorizations
11.3
Concept
lattices
11.4
Closure and contact
11.5
Completion of an ordering
PART
IV APPLICATH
Contents
vii
210
220
232
242
247
11
Concept analysis
251
251
257
268
276
293
12
Orderings:
an advanced view
303
12.1
Additional properties of
orderings
304
12.2
The hierarchy of
orderings
308
12.3
Block-transitive strictorders
312
12.4
Order extensions
315
12.5
Relating preference and utility
323
12.6
Intervalorders and interval graphs
332
13
Preference and indifference
349
13.1
Duality
349
13.2
Modelling indifference
352
13.3
Modelling thresholds
356
13.4
Preference structures
359
14
Aggregating preferences
368
14.1
Modelling preferences
368
14.2
Introductory example
369
14.3
Relational measures
371
14.4
Relational integration
376
14.5
Defining relational measures
379
14.6
De
Morgan triples
387
15
Relational graph theory
396
15.1
Reducibility and
irreducibili
ty
396
15.2
Homogeneous difunctional relations
403
15.3
Subsets characterized by relational properties
408
16
Standard Galois mechanisms
415
16.1
Galois iteration
415
16.2
Termination
417
viii Contents
16.3 Games 422
16.4
Specialization to kernels
426
16.5
Matching and assignment
428
16.6
Konig s Theorems
435
PART V ADVANCED TOPICS
17
Mathematical applications
441
17.1
Multi-coverings
441
17.2
Covering of graphs and path equivalence
444
17.3
Homomorphism and Isomorphism Theorems
445
17.4
Further mathematical snippets
452
18
Implication structures
461
18.1
Attribute dependency
461
18.2
Examples of implication closures
472
19
Power operations
483
19.1
Existential image and power transpose
483
19.2
Simulation and bisimulation
494
19.3
State transition dynamics
501
Appendix A Notation
511
Appendix
В
Proofs postponed from Part II
516
Appendix
С
Algebraic visualization
524
Appendix
D
Historical annotations
531
References
549
Symbols
558
Index
561
|
| any_adam_object | 1 |
| author | Schmidt, Gunther 1939- |
| author_GND | (DE-588)12940893X |
| author_facet | Schmidt, Gunther 1939- |
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| bvnumber | BV037236273 |
| classification_rvk | SK 150 |
| ctrlnum | (OCoLC)682120617 (DE-599)BSZ329991574 |
| dewey-full | 004.0151 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004.0151 |
| dewey-search | 004.0151 |
| dewey-sort | 14.0151 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV037236273 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:07Z |
| institution | BVB |
| isbn | 9780521762687 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021149856 |
| oclc_num | 682120617 |
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| owner | DE-11 DE-706 DE-19 DE-BY-UBM DE-473 DE-BY-UBG |
| owner_facet | DE-11 DE-706 DE-19 DE-BY-UBM DE-473 DE-BY-UBG |
| physical | XIII, 567 S. Ill., graph. Darst. 24 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Schmidt, Gunther 1939- Verfasser (DE-588)12940893X aut Relational mathematics Gunther Schmidt 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2011 XIII, 567 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 132 Informatik Mathematik Relation Mathematik (DE-588)4177675-6 gnd rswk-swf Computer science / Mathematics Operations research / Mathematics Relation Mathematik (DE-588)4177675-6 s DE-604 Encyclopedia of mathematics and its applications 132 (DE-604)BV000903719 132 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021149856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmidt, Gunther 1939- Relational mathematics Encyclopedia of mathematics and its applications Informatik Mathematik Relation Mathematik (DE-588)4177675-6 gnd |
| subject_GND | (DE-588)4177675-6 |
| title | Relational mathematics |
| title_auth | Relational mathematics |
| title_exact_search | Relational mathematics |
| title_full | Relational mathematics Gunther Schmidt |
| title_fullStr | Relational mathematics Gunther Schmidt |
| title_full_unstemmed | Relational mathematics Gunther Schmidt |
| title_short | Relational mathematics |
| title_sort | relational mathematics |
| topic | Informatik Mathematik Relation Mathematik (DE-588)4177675-6 gnd |
| topic_facet | Informatik Mathematik Relation Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021149856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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