Pristine Transfinite Graphs and Permissive Electrical Networks

Armen H. Zemanian

ISBN 10: 1461266416 / ISBN 13: 9781461266419

Verlag: Birkhäuser Boston, Birkhäuser Boston Nov 2012, 2012

Beschreibung

This item is printed on demand - Print on Demand Titel. Neuware -A transfinite graph or electrical network of the first rank isobtained conceptually by connecting conventionally infinite graphs andnetworks together at their infinite extremities. This process can berepeated to obtain a hierarchy of transfiniteness whose ranks increasethrough the countable ordinals. This idea, which is of recent originhas enriched the theories of graphs and networks with radically newconstructs and research problems.The book provides a more accessible introduction to the subject thatthough sacrificing some generality, captures the essential ideas oftransfiniteness for graphs and networks. Thus, for example, someresults concerning discrete potentials and random walks on transfinitenetworks can now be presented more concisely. Conversely, thesimplifications enable the development of many new results that werepreviously unavailable.Topics and features: \*A simplified exposition provides an introductionto transfiniteness for graphs and networks.\*Various results forconventional graphs are extended transfinitely. \*Minty's powerfulanalysis of monotone electrical networks is also extendedtransfinitely.\*Maximum principles for node voltages in lineartransfinite networks are established. \*A concise treatment of randomwalks on transfinite networks is developed. \*Conventional theory isexpanded with radically new constructs.Mathematicians, operations researchers and electrical engineers, inparticular, graph theorists, electrical circuit theorists, andprobabalists will find an accessible exposition of an advancedsubject.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 200 pp. Englisch. Bestandsnummer des Verkäufers 9781461266419

Bibliografische Details

Titel: Pristine Transfinite Graphs and Permissive ...

Verlag: Birkhäuser Boston, Birkhäuser Boston Nov 2012

Erscheinungsdatum: 2012

Einband: Taschenbuch

Zustand: Neu

Über diesen Titel

Inhaltsangabe:

Transfiniteness is an abstract mathematical concept that is extended by the author to the very real world of graphs and networks and the idea of random walks, topics of particular interest to circuits and systems network research. The book will be of interest to mathematicians in probability and computer science as well as to electrical engineers, circuits engineers and other physical scientists.

Críticas:

"Transfinite graphs and networks have already been studied in two prior books by the same author. The purpose of the present volume is twofold. First, it is to include a variety of new results that have since been obtained. Second, it is to present a much simpler exposition of the subject. The previous works aimed at generality with a variety of difficulties resulting from the complexity of the subject. The present much simpler exposition sacrifices some generality, but captures the essential ideas of transfiniteness for graphs and networks.... Overall, the author has done excellent work in presenting this complex subject."

―Mathematical Reviews

"Transfiniteness is an abstract mathematical concept that is extended by the author to the very real world of graphs and networks and the idea of random walks, topics of particular interest to circuits and systems network research.... Mathematicians, operations researchers and electrical engineers, in particular, graph theorists, electrical circuit theorists, and probabalists will find an accessible exposition of an advanced subject."

―Zentralblatt MATH