The Mathematics Of Finite Networks
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Author | : Michael Rudolph |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2022-05-12 |
Genre | : Computers |
ISBN | : 1009287834 |
Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to understand the potential applications of operator graph theory.
Author | : Michael Rudolph |
Publisher | : Cambridge University Press |
Total Pages | : 355 |
Release | : 2022-05-12 |
Genre | : Computers |
ISBN | : 1107134439 |
Offers an exact, non-asymptotic approach to studying large-scale features of finite networks that arise in real applications.
Author | : Robert G. Busacker |
Publisher | : |
Total Pages | : 320 |
Release | : 1965 |
Genre | : Mathematics |
ISBN | : |
Author | : Paolo M. Soardi |
Publisher | : Springer |
Total Pages | : 199 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540487980 |
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 | : Bernd Heinrich |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 212 |
Release | : 1987-12-31 |
Genre | : Mathematics |
ISBN | : 311272089X |
No detailed description available for "Finite Difference Methods on Irregular Networks".
Author | : Armen H. Zemanian |
Publisher | : Springer Science & Business Media |
Total Pages | : 207 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681787 |
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 | : Paul Slepian |
Publisher | : Springer Science & Business Media |
Total Pages | : 205 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 364287424X |
In this book we attempt to develop the fundamental results of resistive network analysis, based upon a sound mathematical structure. The axioms upon which our development is based are Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law. In order to state these axioms precisely, and use them in the development of our network analysis, an elaborate mathematical structure is introduced, involving concepts of graph theory, linear algebra, and one dimensional algebraic topology. The graph theory and one dimensional algebraic topology used are developed from first principles; the reader needs no background in these subjects. However, we do assume that the reader has some familiarity with elementary linear algebra. It is now stylish to teach elementary linear algebra at the sophomore college level, and we feel that the require ment that the reader should be familiar with elementary linear algebra is no more demanding than the usual requirement in most electrical engineering texts that the reader should be familiar with calculus. In this book, however, no calculus is needed. Although no formal training in circuit theory is needed for an understanding of the book, such experience would certainly help the reader by presenting him with familiar examples relevant to the mathematical abstractions introduced. It is our intention in this book to exhibit the effect of the topological properties of the network upon the branch voltages and branch currents, the objects of interest in network analysis.
Author | : HEINRICH |
Publisher | : Birkhäuser |
Total Pages | : 207 |
Release | : 2013-03-13 |
Genre | : Science |
ISBN | : 3034871961 |
The finite difference and finite element methods are powerful tools for the approximate solution of differential equations governing diverse physical phenomena, and there is extensive literature on these discre tization methods. In the last two decades, some extensions of the finite difference method to irregular networks have been described and applied to solving boundary value problems in science and engineering. For instance, "box integration methods" have been widely used in electro nics. There are several papers on this topic, but a comprehensive study of these methods does not seem to have been attempted. The purpose of this book is to provide a systematic treatment of a generalized finite difference method on irregular networks for solving numerically elliptic boundary value problems. Thus, several disadvan tages of the classical finite difference method can be removed, irregular networks of triangles known from the finite element method can be applied, and advantageous properties of the finite difference approxima tions will be obtained. The book is written for advanced undergraduates and graduates in the area of numerical analysis as well as for mathematically inclined workers in engineering and science. In preparing the material for this book, the author has greatly benefited from discussions and collaboration with many colleagues who are concerned with finite difference or (and) finite element methods.
Author | : Armen H. Zemanian |
Publisher | : Cambridge University Press |
Total Pages | : 328 |
Release | : 1991-11-29 |
Genre | : Mathematics |
ISBN | : 0521401534 |
This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition.
Author | : W.D. Wallis |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2003-11-06 |
Genre | : Computers |
ISBN | : 9780817642709 |
This concisely written text in finite mathematics gives a sequential, distinctly applied presentation of topics, employing a pedagogical approach that is ideal for freshmen and sophomores in business, the social sciences, and the liberal arts. The work opens with a brief review of sets and numbers, followed by an introduction to data sets, counting arguments, and the Binomial Theorem, which sets the foundation for elementary probability theory and some basic statistics. Further chapters treat graph theory as it relates to modelling, matrices and vectors, and linear programming. Requiring only two years of high school algebra, this book's many examples and illuminating problem sets - with selected solutions - will appeal to a wide audience of students and teachers.