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Acta Applicandae

Book review

Author(s) Marinov, C.A.
Neittaanmaki, P.
Title Mathematical Models in Electrical Circuits: Theory and Applications
Publisher Kluwer Academic Publishers
Year of publication 1991
Reviewed by Doina Tatar

Dissipative operators occur everywhere in science and technique, especially in the research on mathematical models of electrical and electronic circuits. The theory of dissipative operators is starting to make serious headway in understanding things like: nonlinear networks with transistors, mixed-type circuits with distributed and lumped parameters and digital integrated circuits. There are hundreds of papers on this topic though a systematic treatise appears to be lacking.

The rough contents are as follows: Ch. I, Dissipative operators and differential equations on Banach space (introduction of mathematical tools as theory of monotone operators); Ch. II, Lumped parameter approach of nonlinear networks with transistors (lumped parameter circuits with nonlinearly modelled bipolar transistors); Ch. III, 1^p solutions of countable infinite systems of equations and applications to electrical circuits (circuits containing an infinite number of lumped parameters where transistors are also present); Ch IV, Mixed-type circuits with distributed and lumped parameters as correct models for integrated structures; Ch. V, Asymptotic behaviour of mixed-type circuits, Delay time predicting; Ch. VI, Numerical approximation of mixed models for digital itegrated circuits (a very large class of circuits in which distribuited parameter elements, modelled by degenerate Telegraph Equations, are connected with lumped resistive and capacitive elements).

The authors are most well known as researcher and professors. Their scientific works are well appreciated among the scientific connunity. This is a valuable book which all experts in electrical circuits would like to have within reach and are well admissed to purchase this volume.