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Graphs and Networks : Transfinite and Nonstandard /

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This self-contained book examines results on transfinite graphs and networks achieved through a continuing research effort during the past several years. These new results, covering the mathematical theory of electrical circuits, are different from those presented in two previously published books b...

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Bibliographic Details
Main Author: Zemanian, A. H. (Armen H.)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint : Birkhäuser, 2004.
Subjects:
Mathematics.
Mathematical physics.
Engineering mathematics.
Telecommunication.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Preface
  • Some Preliminaries
  • Transfinite Graphs
  • Connectedness, Trees, and Hypergraphs
  • Ordinal Distances in Transfinite Graphs
  • Walk-Based Transfinite Graphs and Networks
  • Hyperreal Currents and Voltages in Transfinite Networks
  • Hyperreal Transients in Transfinite RLC Networks
  • Nonstandard Graphs and Networks
  • Appendix A: Some Elements of Nonstandard Analysis
  • Appendix B: The Fibonacci Numbers
  • Appendix C: A Laplace Transform for an Artificial RC Cable
  • References
  • Index of Symbols
  • Subject Index.