Authors:
- New results, covering the mathematical theory of electrical circuits, are different from those presented in two previously published books by the author
- The growing and presently substantial number of mathematicians working in nonstandard analysis will be attracted by the novel application of the analysis employed in the work
- Appeals to a diverse readership, including graduate students, electrical engineers, mathematicians, and physicists working on infinite electrical networks
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
Reviews
"The book presents almost everything that has been achieved so far in the relatively new field of transfinite graphs and electrical networks. In the first two chapters, the reader is familiarized with transfinite graphs and with the symbols and notations used in the book.... The last chapter is dedicated to the approach of nonstandard analysis applied to transfinite graphs. The book must be appreciated especially because new results in the field of transfinite graphs are also included. Therefore, I find this book a welcome addition to the literature." —Zentralblatt MATH
"For about thirty years Zemanian has been developing a theory of infinite electrical networks. This book is the latest in a series of books...on the subject. The subject is necessarily abstract and sophisticated because infinite objects are the main objects of discourse.... The first few chapters are important not only to remind the reader of the terms, but also to give an improved or alternate treatment of some earlier results.… There does not yet seem to be a large following of researchers in this area, but it seems very attractive and ripe for investigation. It’s intriguing to see the connections between set theory and electrical network problems.... To understand these concepts fully the reader must consult the book under review. The reviewer highly recommends devoting the effort needed to understand these original and surprising concepts." —SIAM Review
Authors and Affiliations
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Department of Electrical Engineering, State University of New York at Stony Brook, Stony Brook, USA
Armen H. Zemanian
Bibliographic Information
Book Title: Graphs and Networks
Book Subtitle: Transfinite and Nonstandard
Authors: Armen H. Zemanian
DOI: https://doi.org/10.1007/978-0-8176-8178-4
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2004
Softcover ISBN: 978-0-8176-4292-1Published: 13 May 2004
eBook ISBN: 978-0-8176-8178-4Published: 06 December 2012
Edition Number: 1
Number of Pages: XII, 202
Topics: Applications of Mathematics, Information and Communication, Circuits, Mathematical Methods in Physics, Mathematical and Computational Engineering, Communications Engineering, Networks, Signal, Image and Speech Processing