Background
Zemanian, Armen Humpartsoum was born on April 16, 1925 in Bridgewater, Massachusetts, United States. Son of Parsegh and Filor (Paparian) Zemanian.
("What good is a newborn baby?" Michael Faraday's reputed ...)
"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 probĀ 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 voltĀ 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.
http://www.amazon.com/gp/product/0817638180/?tag=2022091-20
( This volume provides a relatively accessible introducti...)
This volume provides a relatively accessible introduction to its subject that captures the essential ideas of transfiniteness for graphs and networks.
http://www.amazon.com/gp/product/0817641947/?tag=2022091-20
( Concise exposition of realizability theory as applied t...)
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.
http://www.amazon.com/gp/product/0486688232/?tag=2022091-20
("What good is a newborn baby?" Michael Faraday's reputed ...)
"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 probĀ 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 voltĀ 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.
http://www.amazon.com/gp/product/146126894X/?tag=2022091-20
( This self-contained book examines results on transfinit...)
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.
http://www.amazon.com/gp/product/0817642927/?tag=2022091-20
(Over the past two decades a general mathematical theory o...)
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 infinite cascades and grids. A notable feature is the recent invention of transfinite networks, roughly analogous to Cantor's extension of the natural numbers to the transfinite ordinals. The last chapter is a survey of applications to exterior problems of partial differential equations, random walks on infinite graphs, and networks of operators on Hilbert spaces. The jump in complexity from finite electrical networks to infinite ones is comparable to the jump in complexity from finite-dimensional to infinite-dimensional spaces. Many of the questions that are conventionally asked about finite networks are presently unanswerable for infinite networks, while questions that are meaningless for finite networks crop up for infinite ones and lead to surprising results, such as the occasional collapse of Kirchoff's laws in infinite regimes. Some central concepts have no counterpart in the finite case, as for example the extremities of an infinite network, the perceptibility of infinity, and the connections at infinity.
http://www.amazon.com/gp/product/0521401534/?tag=2022091-20
mathematician electrical engineer
Zemanian, Armen Humpartsoum was born on April 16, 1925 in Bridgewater, Massachusetts, United States. Son of Parsegh and Filor (Paparian) Zemanian.
Bachelor of Electrical Engineering, City College of New York, 1947. Doctor of Science in Engineering, New York University, 1953. Professor (honorary), Dubna University, Russia, 1996.
Tutor, City College of New York, 1947-1948; engineer, The Maintenance Company. New York City, 1948-1952; from assistant to associate professor, New York University, 1952-1962; professor, State University of New York, Stony Brook, 1962-1983; leading professor, State University of New York, Stony Brook, 1983-1998; distinguished professor, State University of New York, Stony Brook, since 1998.
( Concise exposition of realizability theory as applied t...)
("What good is a newborn baby?" Michael Faraday's reputed ...)
("What good is a newborn baby?" Michael Faraday's reputed ...)
( This volume provides a relatively accessible introducti...)
( This self-contained book examines results on transfinit...)
(Over the past two decades a general mathematical theory o...)
Fellow Institute of Electrical and Electronics Engineers, Institute of Electrical and Electronics Engineers Circuits and Systems Society (Golden Jubilee medal 2000), American Mathematics Society, Russian Academy Natural Sciences (foreign. Kapitsa Gold medal 1996), Armenian Academy of Sciences (foreign), Armenian Academy Engineers (foreign), Sigma Xi, Tau Beta Pi, Eta Kappa Nu.
Married Edna Odell Williamson Zemanian, July 12, 1958. Children: Peter, Thomas, Lewis, Susan.