MARC details
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06699cam a2200793Mi 4500 |
| 001 - CONTROL NUMBER |
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ocn794328387 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20240925133650.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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m d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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120528s2012 si ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
EBLCP |
| Language of cataloging |
eng |
| Description conventions |
pn |
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EBLCP |
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OCLCQ |
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LGG |
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CDX |
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YDXCP |
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IDEBK |
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AZU |
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DEBSZ |
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OCLCQ |
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OCLCO |
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OCLCQ |
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OCLCF |
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OCLCQ |
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AGLDB |
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ZCU |
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OCLCQ |
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MERUC |
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OCLCQ |
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NJR |
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OCLCQ |
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ICG |
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OCLCQ |
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OCLCQ |
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OCLCL |
| 019 ## - |
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793804765 |
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794902663 |
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817084746 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781848168770 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1848168772 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1280669063 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781280669064 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Canceled/invalid ISBN |
1848168764 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Canceled/invalid ISBN |
9781848168763 |
| 024 8# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
ebc919092 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
457191 |
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(N$T) |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)794328387 |
| Canceled/invalid control number |
(OCoLC)793804765 |
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(OCoLC)794902663 |
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(OCoLC)817084746 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA199 .S36 2012 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
005000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
034000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBKA |
| Source |
bicssc |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515 |
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515.72 |
| 049 ## - LOCAL HOLDINGS (OCLC) |
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| Holding library |
MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Schott, Rene. |
| 9 (RLIN) |
108878 |
| 245 10 - TITLE STATEMENT |
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| Title |
Operator Calculus on Graphs : |
| Remainder of title |
Theory and Applications in Computer Science. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc. |
Singapore : |
| Name of publisher, distributor, etc. |
World Scientific, |
| Date of publication, distribution, etc. |
2012. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource (428 pages) |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Preface; Acknowledgments; Contents; Combinatorial Algebras and Their Properties; 1. Introduction; 1.1 Notational Preliminaries; 2. Combinatorial Algebra; 2.1 Six Group and Semigroup Algebras; 2.1.1 The group of blades Bp, q; 2.1.1.1 Involutions; 2.1.1.2 The n-dimensional hypercube Qn; 2.1.2 The abelian blade group Bp, q sym; 2.1.3 The null blade semigroup; 2.1.4 The abelian null blade semigroup sym; 2.1.5 The semigroup of idempotent blades idem; 2.1.6 The path semigroup n; 2.1.7 Summary; 2.1.7.1 Algebras I-IV; 2.1.7.2 Algebra V; 2.1.7.3 Algebra VI; 2.2 Clifford and Grassmann Algebras. |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
2.2.1 Grassmann (exterior) algebras2.2.2 Clifford algebras; 2.2.3 Operator calculus on Clifford algebras; 2.3 The Symmetric Clifford Algebra sym; 2.4 The Idempotent-Generated Algebra idem; 2.5 The n-Particle Zeon Algebra nil; 2.6 Generalized Zeon Algebras; 3. Norm Inequalities on Clifford Algebras; 3.1 Norms on C p; q; 3.2 Generating Functions; 3.3 Clifford Matrices and the Clifford-Frobenius Norm; 3.4 Powers of Clifford Matrices; Combinatorics and Graph Theory; 4. Specialized Adjacency Matrices; 4.1 Essential Graph Theory; 4.2 Clifford Adjacency Matrices; 4.3 Nilpotent Adjacency Matrices. |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
4.3.1 Euler circuits4.3.2 Conditional branching; 4.3.3 Time-homogeneous random walks on finite graphs; 5. Random Graphs; 5.1 Preliminaries; 5.2 Cycles in Random Graphs; 5.3 Convergence of Moments; 6. Graph Theory and Quantum Probability; 6.1 Concepts; 6.1.1 Operators as random variables; 6.1.2 Operators as adjacency matrices; 6.2 From Graphs to Quantum Random Variables; 6.2.1 Nilpotent adjacency operators in infinite spaces; 6.2.2 Decomposition of nilpotent adjacency operators; 6.3 Connected Components in Graph Processes; 6.3.1 Algebraic preliminaries; 6.3.2 Connected components. |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
6.3.2.1 (k, d)-components6.3.3 Second quantization of graph processes; 7. Geometric Graph Processes; 7.1 Preliminaries; 7.2 Dynamic Graph Processes; 7.2.1 Vertex degrees in Gn; 7.2.2 Energy and Laplacian energy of geometric graphs; 7.2.3 Convergence conditions and a limit theorem; 7.3 Time-Homogeneous Walks on Random Geometric Graphs; Probability on Algebraic Structures; 8. Time-Homogeneous Random Walks; 8.1 sym and Random Walks on Hypercubes; 8.2 Multiplicative Walks on C p, q; 8.2.1 Walks on directed hypercubes; 8.2.2 Random walks on directed hypercubes with loops. |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
8.2.3 Properties of multiplicative walks8.3 Induced Additive Walks on C p, q; 8.3.1 Variance of N; 8.3.2 Variance of; 8.3.3 Central limit theorems; 9. Dynamic Walks in Clifford Algebras; 9.1 Preliminaries; 9.2 Expectation; 9.3 Limit Theorems; 9.3.1 Conditions for convergence; 9.3.2 Induced additive walks; 9.3.3 Central limit theorem; 10. Iterated Stochastic Integrals; 10.1 Preliminaries; 10.2 Stochastic Integrals in; 10.3 Graph-Theoretic Iterated Stochastic Integrals; 10.3.1 Functions on partitions; 10.3.2 The Clifford evolution matrix; 10.3.3 Orthogonal polynomials. |
| 500 ## - GENERAL NOTE |
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| General note |
11. Partition-Dependent Stochastic Measures. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with pack. |
| 588 0# - SOURCE OF DESCRIPTION NOTE |
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| Source of description note |
Print version record. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references (pages 399-406) and index. |
| 590 ## - LOCAL NOTE (RLIN) |
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| Local note |
Added to collection customer.56279.3 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Calculus, Operational. |
| 9 (RLIN) |
140135 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Graph theory. |
| 9 (RLIN) |
1324 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Quantum statistics. |
| 9 (RLIN) |
14132 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Computer science. |
| 9 (RLIN) |
941 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Calcul symbolique. |
| 9 (RLIN) |
140136 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Statistique quantique. |
| 9 (RLIN) |
77041 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Informatique. |
| 9 (RLIN) |
14930 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Calculus. |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
71168 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Mathematical Analysis. |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
71169 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Calculus, Operational |
| Source of heading or term |
fast |
| 9 (RLIN) |
140135 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Computer science |
| Source of heading or term |
fast |
| 9 (RLIN) |
941 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Graph theory |
| Source of heading or term |
fast |
| 9 (RLIN) |
1324 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Quantum statistics |
| Source of heading or term |
fast |
| 9 (RLIN) |
14132 |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Staples, G. Stacey. |
| 9 (RLIN) |
634844 |
| 758 ## - |
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has work: |
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Operator calculus on graphs (Text) |
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https://id.oclc.org/worldcat/entity/E39PCGhJmjYQmbPJkqVyYRXgXd |
| -- |
https://id.oclc.org/worldcat/ontology/hasWork |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Print version: |
| Main entry heading |
Schott, Rene. |
| Title |
Operator Calculus on Graphs : Theory and Applications in Computer Science. |
| Place, publisher, and date of publication |
Singapore : World Scientific, ©2012 |
| International Standard Book Number |
9781848168763 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
EBSCOhost |
| Uniform Resource Identifier |
<a href="https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457191">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457191</a> |
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Coutts Information Services |
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COUT |
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22579785 |
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EBL - Ebook Library |
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EBLB |
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EBL919092 |
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EBSCOhost |
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EBSC |
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457191 |
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ProQuest MyiLibrary Digital eBook Collection |
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IDEB |
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364599 |
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YBP Library Services |
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YANK |
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7466854 |
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92 |
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N$T |