Over the past two decades a general mathematical theory of infinite electrical networks has been developed. This is the first book to present the salient features of this theory in a coherent exposition. Using the basic tools of functional analysis and graph theory, the author presents the fundamental developments of the past two decades and discusses applications to other areas of mathematics. The first half of the book presents existence and uniqueness theorems for both infinite-power and finite-power voltage-current regimes, and the second half discusses methods for solving problems in...
Over the past two decades a general mathematical theory of infinite electrical networks has been developed. This is the first book to present the sali...
"What good is a newborn baby?" Michael Faraday's 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 Cantor's 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...
"What good is a newborn baby?" Michael Faraday's reputed response when asked, "What good is magnetic induction?" But, it must be admitted that a newbo...
Scientia Gratiii Scientiae It is now thirteen years since the first book that discusses transfinite graphs and elec trical networks appeared 50]. This was followed by two more books 51] and 54] which compiled results from an ongoing research effort on that subject. Why then is a fourth book, this one, being offered? Simply because still more has been achieved beyond that appearing in those prior books. An exposition of these more recent re sults is the purpose of this book. The idea of transfiniteness for graphs and networks appeared as virgin research territory about seventeen years ago....
Scientia Gratiii Scientiae It is now thirteen years since the first book that discusses transfinite graphs and elec trical networks appeared 50]. Thi...
