Transfiniteness for graphs, electrical networks and random walks:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 235 - 238 |
| Beschreibung: | X, 246 S. graph. Darst. |
| ISBN: | 3764338180 0817638180 |
Internformat
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| 245 | 1 | 0 | |a Transfiniteness for graphs, electrical networks and random walks |c Armen H. Zemanian |
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| 650 | 4 | |a Transfinite numbers | |
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Datensatz im Suchindex
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| adam_text | ARMEN H. ZEMANIAN TRANSFINITENESS FOR GRAPHS, ELECTRICAL NETWORKS, AND
RANDOM WALKS 1996 BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE
VII ACKNOWLEDGMENTS X 1 INTRODUCTION 1 1.1 NOTATIONS AND TERMINOLOGY 1
1.2 CONVENTIONAL GRAPHS * A POOR START 5 1.3 O-GRAPHS , 9 1.4 WHY
TRANSFINITENESS? 12 2 TRANSFINITE GRAPHS 19 2.1 1-GRAPHS 20 2.2
/I-GRAPHS 29 2.3 CD-GRAPHS 36 2.4 W-GRAPHS 42 2.5 GRAPHS OF HIGHER RANKS
45 3 CONNECTEDNESS 47 3.1 TRANSFINITE CONNECTEDNESS 48 3.2 A
TRANSITIVITY CRITERION FOR TRANSFINITE CONNECTEDNESS ... 53 3.3 ABOUT
NODES AND PATHS 57 3.4 ^-SEQUENCES 60 3.5 ANOTHER TRANSITIVITY CRITERION
FOR TRANSFINITE CONNECTEDNESS 71 3.6 THE CARDINALITY OF THE BRANCH SET
74 4 FINITELY STRUCTURED TRANSFINITE GRAPHS 79 4.1 SUBSECTION AND CORES
81 4.2 A GENERALIZATION OF KONIG S LEMMA 87 4.3 ISOLATING SETS AND CUTS
93 4.4 CONTRACTIONS 100 4.5 FINITELY STRUCTURED ^-GRAPHS 104 4.6
SPANNING TREES 109 5 TRANSFINITE ELECTRICAL NETWORKS 115 5.1 KIRCHHOFF S
LAWS, TELLEGEN S EQUATION, AND OHM S LAW . . 116 5.2 THE VOLTAGE-CURRENT
REGIME 126 5.3 CONDITIONS LEGITIMIZING KIRCHHOFF S LAWS 138 VI CONTENTS
5.4 THE REGIME INDUCED BY A PURE CURRENT SOURCE 143 5.5 NODE VOLTAGES
149 6 PERMISSIVELY FINITELY STRUCTURED NETWORKS 157 6.1 PERMISSIVELY
FINITELY STRUCTURED ^-NETWORKS 158 6.2 EXCITATIONS BY PURE SOURCES 160
6.3 MAXIMUM PRINCIPLES FOR NODE VOLTAGES AND BRANCH CURRENTS 170 7
TRANSFINITE RANDOM WALKS 183 7.1 THE NASH-WILLIAMS RULE 184 7.2
TRANSFINITE WALKS 189 7.3 TRANSFINITE RANDOM WALKS * THE GENERAL IDEA
196 7.4 REACHING A BORDERING NODE 202 7.5 LEAVING A/3-NODE 207 7.6 FROM
A /3-NODE TO A (3- ADJACENT (/3+)-NODE 214 7.7 WANDERING ON A ^-NETWORK
215 APPENDIX A: ORDINAL AND CARDINAL NUMBERS 222 APPENDIX B: SUMMABLE
SERIES 229 APPENDIX C: IRREDUCIBLE AND REVERSIBLE MARKOV CHAINS . . 232
BIBLIOGRAPHY 235 INDEX OF SYMBOLS 239 INDEX 241
|
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| id | DE-604.BV010720666 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:57:48Z |
| institution | BVB |
| isbn | 3764338180 0817638180 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007158760 |
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| owner_facet | DE-29T DE-11 |
| physical | X, 246 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Zemanian, Armen H. 1925- Verfasser (DE-588)134263340 aut Transfiniteness for graphs, electrical networks and random walks Armen H. Zemanian Boston [u.a.] Birkhäuser 1996 X, 246 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 235 - 238 Graph theory Transfinite numbers Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Unendlicher Graph (DE-588)4390888-3 gnd rswk-swf Elektrisches Netzwerk (DE-588)4014214-0 gnd rswk-swf Unendlicher Graph (DE-588)4390888-3 s Elektrisches Netzwerk (DE-588)4014214-0 s Irrfahrtsproblem (DE-588)4162442-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007158760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zemanian, Armen H. 1925- Transfiniteness for graphs, electrical networks and random walks Graph theory Transfinite numbers Irrfahrtsproblem (DE-588)4162442-7 gnd Unendlicher Graph (DE-588)4390888-3 gnd Elektrisches Netzwerk (DE-588)4014214-0 gnd |
| subject_GND | (DE-588)4162442-7 (DE-588)4390888-3 (DE-588)4014214-0 |
| title | Transfiniteness for graphs, electrical networks and random walks |
| title_auth | Transfiniteness for graphs, electrical networks and random walks |
| title_exact_search | Transfiniteness for graphs, electrical networks and random walks |
| title_full | Transfiniteness for graphs, electrical networks and random walks Armen H. Zemanian |
| title_fullStr | Transfiniteness for graphs, electrical networks and random walks Armen H. Zemanian |
| title_full_unstemmed | Transfiniteness for graphs, electrical networks and random walks Armen H. Zemanian |
| title_short | Transfiniteness for graphs, electrical networks and random walks |
| title_sort | transfiniteness for graphs electrical networks and random walks |
| topic | Graph theory Transfinite numbers Irrfahrtsproblem (DE-588)4162442-7 gnd Unendlicher Graph (DE-588)4390888-3 gnd Elektrisches Netzwerk (DE-588)4014214-0 gnd |
| topic_facet | Graph theory Transfinite numbers Irrfahrtsproblem Unendlicher Graph Elektrisches Netzwerk |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007158760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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