Skip to main content
SpringerLink
Log in
Birkhäuser

Pristine Transfinite Graphs and Permissive Electrical Networks

  • Book
  • © 2001

Overview

Authors:
  1. Armen H. Zemanian

    1. Electrical Engineering Department, University at Stony Brook, Stony Brook, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Armen H. Zemanian
    Pages 1-16

  3. Pristine Transfinite Graphs

    • Armen H. Zemanian
    Pages 17-28

  4. Some Transfinite Graph Theory

    • Armen H. Zemanian
    Pages 29-52

  5. Permissive Transfinite Networks

    • Armen H. Zemanian
    Pages 53-80

  6. Linear Networks; Tellegen Regimes

    • Armen H. Zemanian
    Pages 81-103

  7. Monotone Networks; Kirchhoff Regimes

    • Armen H. Zemanian
    Pages 105-134

  8. Some Maximum Principles

    • Armen H. Zemanian
    Pages 135-147

  9. Transfinite Random Walks

    • Armen H. Zemanian
    Pages 149-171

  10. Back Matter

    Pages 173-183
    Download chapter PDF
Back to top

Keywords

About this book

A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional graphs are extended transfinitely. *Minty's powerful analysis of monotone electrical networks is also extended transfinitely.*Maximum principles for node voltages in linear transfinite networks are established. *A concise treatment of random walks on transfinite networks is developed. *Conventional theory is expanded with radically new constructs. Mathematicians, operations researchers and electrical engineers, in particular, graph theorists, electrical circuit theorists, and probabalists will find an accessible exposition of an advanced subject.

Reviews

"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

Authors and Affiliations

  • Electrical Engineering Department, University at Stony Brook, Stony Brook, USA

    Armen H. Zemanian

Bibliographic Information

  • Book Title: Pristine Transfinite Graphs and Permissive Electrical Networks

  • Authors: Armen H. Zemanian

  • DOI: https://doi.org/10.1007/978-1-4612-0163-2

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2001

  • Hardcover ISBN: 978-0-8176-4194-8Published: 21 December 2000

  • Softcover ISBN: 978-1-4612-6641-9Published: 01 November 2012

  • eBook ISBN: 978-1-4612-0163-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XI, 183

  • Topics: Discrete Mathematics, Electrical Engineering, Complexity, Control, Robotics, Mechatronics

Publish with us

Policies and ethics

Back to top

Search

Navigation