leondumoulin.nl: Graphs and Networks: Transfinite and Nonstandard: Armen H. Zemanian.
Table of contents
- Graphs and Networks - E-bok - Armen H Zemanian () | Bokus
- by Zemanian, Armen H
- Transfinite Graphs and Electrical Networks
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 [8]. Similarly, the year of birth for electrical network theory might well be taken to be 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.
Graphs and Networks - E-bok - Armen H Zemanian () | Bokus
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. Pristine transfinite graphs and permissive electrical networks by A.
H Zemanian Book 4 editions published in in English and held by WorldCat member libraries worldwide "Pristine Transfinite Graphs and Permissive Electrical Networks provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks.
Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. On the other hand, the simplifications enable the development of many new results that were previously unavailable. H Zemanian Book 6 editions published in in English and held by WorldCat member libraries worldwide This self-contained book examines results on transfinite graphs and networks achieved through a continuing research effort during the past several years.
by Zemanian, Armen H
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. Two initial chapters present the preliminary theory summarizing all essential ideas needed for the book and will relieve the reader from any need to consult those prior books.
Subsequent chapters are devoted entirely to novel results and cover: Transfinite and Nonstandard 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.
The applications of generalized functions. A collection of papers presented at the Symposium on "The Applications of Generalized Functions" by Symposium on "The Applications of Generalized Functions" 3 editions published in in English and held by WorldCat member libraries worldwide.
Teoria dystrybucji i analiza transformat: H Zemanian 6 editions published between and in English and Polish and held by 23 WorldCat member libraries worldwide This well-known text provides a relatively elementary introduction to distribution theory and describes generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems.
Transfinite Graphs and Electrical Networks
Suitable for a graduate course for engineering and science students or for an advanced undergraduate course for mathematics majors. The distributional Hankel transformation by A. H Zemanian Book 2 editions published in in English and held by 5 WorldCat member libraries worldwide The Hankel transformation is generalized in a distributional way, something that apparently has not been done before.
Two different procedures are used to accomplish this. In the first procedure a topological linear space of testing functions is constructed for which the mu-th order Hankel transformation is a topological automorphism. The dual space consists of the mu-th order Hankel-transformable distributions. The distributional Hankel transformation is then defined by generalizing a variation of Parseval's formula.
It turns out that the distributions to which this transformation may be applied must be of slow growth. The second procedure yields a more general result in that there is no restriction on the rate of growth of the distributions that are to be transformed. Here again, Parseval's formula is used to define the generalized Hankel transformation, but in contrast to the previous case the testing functions for the distributions under consideration are required to have bounded supports.
The Hankel transforms then turn out to be continuous linear functionals on certain classes of analytic functions.
- The Constructor: Poems.
- November Rose: A Speech on Death (Winner of the 2008 Independent Publisher Book Award).
- Hidden Agenda.
- La regina dei Caraibi di Emilio Salgari (Italian Edition)?
- Everliving.
- Collecting the 1939 New York World's Fair.
- Not A Good Look (Fab Life)!
Several applications to differential equations containing Bessel-type differential operators are also given. Realizability theory for continuos linear systems by A. H Zemanian 1 edition published in in English and held by 4 WorldCat member libraries worldwide. The distributional Laplace and Mellin transformations by A. H Zemanian Book 2 editions published in in English and held by 4 WorldCat member libraries worldwide A new method of developing the distributional Laplace and Mellin transformations is devised.
It simplifies a number of proofs and derivations for various properties of these transformations and provides greater facility in manipulating specific distributional transforms. A time domain characterization of rational positive-real matrices by A. H Zemanian Book 4 editions published in in English and held by 4 WorldCat member libraries worldwide Necessary and sufficient conditions for a matrix W s to be positive-real are established, which characterize the universe Laplace transform of W s in terms of nonnegative-definite distribution and their orders.
In the first two chapters, the reader is familiarized with transfinite graphs and with the symbols and notations used in the book The last chapter is dedicated to the approach of nonstandard analysis applied to transfinite graphs. The book must be appreciated especially because new results in the field of transfinite graphs are also included. Therefore, I find this book a welcome addition to the literature.
This book is the latest in a series of books The subject is necessarily abstract and sophisticated because infinite objects are the main objects of discourse The first few chapters are important not only to remind the reader of the terms, but also to give an improved or alternate treatment of some earlier results There does not yet seem to be a large following of researchers in this area, but it seems very attractive and ripe for investigation.
It's intriguing to see the connections between set theory and electrical network problems To understand these concepts fully the reader must consult the book under review. The reviewer highly recommends devoting the effort needed to understand these original and surprising concepts.