Transfinite electrical networks

Author

Zemanian, A.H.

Author_Institution

Dept. of Electr. Eng., State Univ. of New York, Stony Brook, NY, USA

Volume

46

Issue

1

fYear

1999

fDate

1/1/1999 12:00:00 AM

Firstpage

59

Lastpage

70

Abstract

This is a tutorial/survey paper that provides an explanation of “transfinite electrical networks.” The theory of such networks has been developing only over the past decade, and undoubtedly much is yet to be discovered. It is quite abstract, and its mathematics is complicated. In this work we try to facilitate an understanding of its main ideas without encumbering comprehension with too much mathematical jargon. Instead, definitions and arguments are heuristically presented, and many examples are given. Transfiniteness for electrical networks is a radical generalization of conventional network theory, which opens up an entirely new area of research. It may be of interest to mathematical circuit theorists but will disappoint those looking for practical applications

Keywords

circuit theory; graph theory; heuristic definitions; mathematical circuit theory; network theory; transfinite electrical networks; Circuits; Embryo; Extremities; Graph theory; H infinity control; Mathematics; Network theory (graphs); Spirals;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.739185

Filename

739185