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Graphs and Networks
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.
Realizability Theory for Continuous Linear Systems
Concise exposition of realizability theory as applied to continous linear systems, specifically to the operators generated by physical systems as mappings of stimuli into responses. Many problems included.
Transfiniteness
"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 curr...
Pristine Transfinite Graphs and Permissive Electrical Networks
This volume provides a relatively accessible introduction to its subject that captures the essential ideas of transfiniteness for graphs and networks.
Distribution Theory and Transform Analysis
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution...
Cycle Representations of Markov Processes
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.
GENERALIZED INTEGRAL TRANSFORMS OF DISTRIBUTIONS
1.1 Introduction In recent years, integral transforms have become essential working tools of every engineer and applied scientist. The Laplace transform, which undoubtedly is the most familiar example, is being suited to solving boundary value problems. The classical methods of solution of initial and boundary value problems in physics and engineering sciences have their roots in Fourier’s pioneering work. An alternative approach through integral transforms methods emerged primarily through Heaviside’s efforts on operational techniques. In addition to being of great theoretical interest to mathematicians, integral transform methods have been found to provide easy and effective ways of so...
Circuits, Systems and Signal Processing
This book is a collection of tutorial-like chapters on all core topics of signals and systems and the electronic circuits. All the topics dealt with in the book are parts of the core syllabi of standard programs in Electrical Engineering, Electrical and Computer Engineering, and Electronics and Telecommunication Engineering domains. This book is intended to serve as a secondary reader or supplementary text for core courses in the area of signals and systems, electronic circuits, and analog and digital signal processing. When studying or teaching a particular topic, the students and instructors of such courses would find it interesting and worthwhile to study the related tutorial chapter in this book in order to enhance their understanding of the fundamentals, simplification of procedures, alternative approaches and relation to other associated topics. In addition, the book can also be used as a primary or secondary text in short-term or refresher courses, and as a self-study guide for professionals wishing to gain a comprehensive review of the signals and systems domain.
Fourteen Papers Translated from the Russian
Covers a range of topics including integral representations, complex analysis, differential equations, and functional analysis.
