The Mathematics of Finite Networks PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Mathematics of Finite Networks PDF full book. Access full book title The Mathematics of Finite Networks by Michael Rudolph. Download full books in PDF and EPUB format.
Author: Michael Rudolph
Publisher: Cambridge University Press
ISBN: 1009287834
Category : Computers
Languages : en
Pages :
Get Book Here
Book Description
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
ISBN: 1009287834
Category : Computers
Languages : en
Pages :
Get Book Here
Book Description
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
ISBN: 1107134439
Category : Computers
Languages : en
Pages : 355
Get Book Here
Book Description
Offers an exact, non-asymptotic approach to studying large-scale features of finite networks that arise in real applications.
Author: Robert G. Busacker
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 320
Get Book Here
Book Description
Author: Paolo M. Soardi
Publisher: Springer
ISBN: 3540487980
Category : Mathematics
Languages : en
Pages : 199
Get Book Here
Book Description
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: Armen H. Zemanian
Publisher: Springer Science & Business Media
ISBN: 0817681787
Category : Mathematics
Languages : en
Pages : 207
Get Book Here
Book Description
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: Bernd Heinrich
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311272089X
Category : Mathematics
Languages : en
Pages : 212
Get Book Here
Book Description
No detailed description available for "Finite Difference Methods on Irregular Networks".
Author: Paul Slepian
Publisher: Springer Science & Business Media
ISBN: 364287424X
Category : Science
Languages : en
Pages : 205
Get Book Here
Book Description
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
ISBN: 3034871961
Category : Science
Languages : en
Pages : 207
Get Book Here
Book Description
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
ISBN: 0521401534
Category : Mathematics
Languages : en
Pages : 328
Get Book Here
Book Description
This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition.
Author: Martin Anthony
Publisher: SIAM
ISBN: 089871480X
Category : Computers
Languages : en
Pages : 137
Get Book Here
Book Description
This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.
