Infinite Electrical Networks

Author : Armen H. Zemanian
Publisher : Cambridge University Press
ISBN 13 : 0521401534
Total Pages : 328 pages
Book Rating : 4.31/5 ( download)

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Download or read book Infinite Electrical Networks written by Armen H. Zemanian and published by Cambridge University Press. This book was released on 1991-11-29 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition.

Author : Armen H. Zemanian
Publisher : Springer Science & Business Media
ISBN 13 : 1461201632
Total Pages : 189 pages
Book Rating : 4.32/5 ( download)

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Download or read book Pristine Transfinite Graphs and Permissive Electrical Networks written by Armen H. Zemanian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a relatively accessible introduction to its subject that captures the essential ideas of transfiniteness for graphs and networks.

Author : Paolo M. Soardi
Publisher : Springer
ISBN 13 : 3540487980
Total Pages : 199 pages
Book Rating : 4.82/5 ( download)

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Download or read book Potential Theory on Infinite Networks written by Paolo M. Soardi and published by Springer. This book was released on 2006-11-15 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Author : Victor Anandam
Publisher : Springer Science & Business Media
ISBN 13 : 3642213995
Total Pages : 152 pages
Book Rating : 4.91/5 ( download)

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Download or read book Harmonic Functions and Potentials on Finite or Infinite Networks written by Victor Anandam and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.

Author : A. Henderson
Publisher : Elsevier
ISBN 13 : 148328011X
Total Pages : 417 pages
Book Rating : 4.10/5 ( download)

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Download or read book Electrical Networks written by A. Henderson and published by Elsevier. This book was released on 2014-05-12 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electrical Networks focuses on the principles, methodologies, practices, and approaches involved in electrical networks, including transformers, polarity, Zobel networks, and Fourier series. The book first elaborates on d.c. currents and voltages and varying currents and voltages. Discussions focus on voltage and current sources, energy and power, voltage and current division, star-delta transformation, direction and polarity, periodical quantities, capacitors and inductors, and energy stored in capacitors and inductors. The manuscript then takes a look at some properties of networks and magnetic coupled inductors. Topics include equivalent circuits for magnetic coupled coils, voltage and the current transformer, mutual induction, impedance transformation, current direction, voltage polarity and the mode of winding, polar diagrams, resonance, and Zobel networks. The publication examines networks containing switches, complex frequency, and Fourier series. Considerations include frequency spectrum, finite Fourier series, capacitor discharges over a resistor, natural oscillations, and discontinuity. The monograph is a valuable source of information for electricians and researchers interested in electrical networks.

Author : Peter G. Doyle
Publisher : American Mathematical Soc.
ISBN 13 : 1614440220
Total Pages : 159 pages
Book Rating : 4.22/5 ( download)

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Download or read book Random Walks and Electric Networks written by Peter G. Doyle and published by American Mathematical Soc.. This book was released on 1984-12-31 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.

Author : Armen H. Zemanian
Publisher : Springer Science & Business Media
ISBN 13 : 0817681787
Total Pages : 207 pages
Book Rating : 4.84/5 ( download)

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Download or read book Graphs and Networks written by Armen H. Zemanian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book examines results on transfinite graphs and networks achieved through continued research effort over the past several years. These new results, covering the mathematical theory of electrical circuits, are different from those presented in two previously published books by the author, Transfiniteness for Graphs, Electrical Networks, and Random Walks and Pristine Transfinite Graphs and Permissive Electrical Networks. Specific topics covered include connectedness ideas, distance ideas, and nontransitivity of connectedness. The book will appeal to a diverse readership, including graduate students, electrical engineers, mathematicians, and physicists working on infinite electrical networks. Moreover, the growing and presently substantial number of mathematicians working in nonstandard analysis may well be attracted by the novel application of the analysis employed in the work.

Author : Jorgensen Palle
Publisher : World Scientific
ISBN 13 : 9813202149
Total Pages : 564 pages
Book Rating : 4.46/5 ( download)

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Download or read book Non-commutative Analysis written by Jorgensen Palle and published by World Scientific. This book was released on 2017-01-24 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : Armen H. Zemanian
Publisher : Springer Science & Business Media
ISBN 13 : 1461207673
Total Pages : 252 pages
Book Rating : 4.72/5 ( download)

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Download or read book Transfiniteness written by Armen H. Zemanian and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 network theory might well be taken to be 184 7, when Gustav Kirchhoff published his volt age and current laws [ 14]. Ever since those dates until just a few years ago, all infinite undirected graphs and networks had an inviolate property: Two branches either were connected through a finite path or were not connected at all. The idea of two branches being connected only through transfinite paths, that is, only through paths having infinitely many branches was never invoked, or so it appears from a perusal of various surveys of infinite graphs [17], [20], [29], [32]. Our objective herein is to explore this idea and some of its ramifications. It should be noted however that directed graphs having transfinite paths have appeared in set theory [6, Section 4.

Author : Sophia L. Kalpazidou
Publisher : Springer Science & Business Media
ISBN 13 : 147573929X
Total Pages : 206 pages
Book Rating : 4.99/5 ( download)

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Download or read book Cycle Representations of Markov Processes written by Sophia L. Kalpazidou and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. This expanded second edition adds new advances, which reveal wide-ranging interpretations of cycle representations such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The text includes chapter summaries as well as a number of detailed illustrations.