Description: Transfiniteness by Armen H. Zemanian The idea of two branches being connected only through transfinite paths,that is, only through paths having infinitely many branches was never invoked, or so it appears from a perusal of various surveys of infinite graphs [17], [20], [29], [32]. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description "What good is a newborn baby?" Michael Faradays reputed response when asked, "What good is magnetic induction?" But, it must be admitted that a newborn baby may die in infancy. What about this one- the idea of transfiniteness for graphs, electrical networks, and random walks? At least its bloodline is robust. Those subjects, along with Cantors transfinite numbers, comprise its ancestry. There seems to be general agreement that the theory of graphs was born when Leonhard Euler published his solution to the "Konigsberg bridge prob lem" in 1736 [8]. Similarly, the year of birth for electrical network theory might well be taken to be 184 7, when Gustav Kirchhoff published his volt age and current laws [ 14]. Ever since those dates until just a few years ago, all infinite undirected graphs and networks had an inviolate property: Two branches either were connected through a finite path or were not connected at all. The idea of two branches being connected only through transfinite paths,that is, only through paths having infinitely many branches was never invoked, or so it appears from a perusal of various surveys of infinite graphs [17], [20], [29], [32]. Our objective herein is to explore this idea and some of its ramifications. It should be noted however that directed graphs having transfinite paths have appeared in set theory [6, Section 4. Table of Contents 1 Introduction.- 2 Transfinite Graphs.- 3 Connectedness.- 4 Finitely Structured Transfinite Graphs.- 5 Transfinite Electrical Networks.- 6 Permissively Finitely Structured Networks.- 7 Transfinite Random Walks.- Appendix A: Ordinal and Cardinal Numbers.- Appendix B: Summable Series.- Appendix C: Irreducible and Reversible Markov Chains.- Index of Symbols. Long Description "What good is a newborn baby?" Michael Faradays reputed response when asked, "What good is magnetic induction?" But, it must be admitted that a newborn baby may die in infancy. What about this one- the idea of transfiniteness for graphs, electrical networks, and random walks? At least its bloodline is robust. Those subjects, along with Cantors transfinite numbers, comprise its ancestry. There seems to be general agreement that the theory of graphs was born when Leonhard Euler published his solution to the "Konigsberg bridge prob Details ISBN0817638180 Author Armen H. Zemanian Language English ISBN-10 0817638180 ISBN-13 9780817638184 Media Book Format Hardcover Year 1996 Residence Stony Brook, US Affiliation State University of New York, Stony Brook Short Title TRANSFINITENESS 1996/E Subtitle For Graphs, Electrical Networks, and Random Walks Pages 246 Imprint Birkhauser Boston Inc Place of Publication Secaucus Country of Publication United States DOI 10.1007/b57816;10.1007/978-1-4612-0767-2 AU Release Date 1996-01-01 NZ Release Date 1996-01-01 US Release Date 1996-01-01 UK Release Date 1996-01-01 Publisher Birkhauser Boston Inc Edition Description 1996 ed. Edition 1996th Publication Date 1996-01-01 Alternative 9781461268949 DEWEY 510 Illustrations X, 246 p. Audience General We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96239895;
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Format: Hardcover
Language: English
ISBN-13: 9780817638184
Author: Armen H. Zemanian
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Book Title: Transfiniteness
