Operator Calculus On Graphs
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| Author | : René Schott |
| Publisher | : World Scientific |
| Total Pages | : 428 |
| Release | : 2012 |
| Genre | : Computers |
| ISBN | : 1848168764 |
This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.
| Author | : Michael Rudolph |
| Publisher | : |
| Total Pages | : |
| Release | : 2022 |
| Genre | : COMPUTERS |
| ISBN | : 9781316466919 |
"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 | : Leo J. Grady |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 371 |
| Release | : 2010-07-23 |
| Genre | : Computers |
| ISBN | : 1849962901 |
This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.
| Author | : B. V. Rajarama Bhat |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 337 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821808214 |
This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of C*-algebras and von Neumann algebras, together with recent work on the classification of C*-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.
| Author | : Arthur Erdelyi |
| Publisher | : Courier Corporation |
| Total Pages | : 114 |
| Release | : 2013-07-24 |
| Genre | : Mathematics |
| ISBN | : 0486316327 |
Suitable for advanced undergraduates and graduate students, this brief monograph examines elementary and convergence theories of convolution quotients, differential equations involving operator functions, exponential functions of operators. Solutions. 1962 edition.
| Author | : Ilwoo Cho |
| Publisher | : CRC Press |
| Total Pages | : 446 |
| Release | : 2013-09-11 |
| Genre | : Mathematics |
| ISBN | : 146659019X |
This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical objects. It also covers tools and methods from a variety of mathematical areas, including algebra, operator theory, and combinatorics, and offers numerous applications of fractal theory, entropy theory, K-theory, and index 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 | : Markus Haase |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 399 |
| Release | : 2006-08-18 |
| Genre | : Mathematics |
| ISBN | : 3764376988 |
This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
| Author | : Gregors Krabbe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461343925 |
Since the publication of an article by G. DoETSCH in 1927 it has been known that the Laplace transform procedure is a reliable sub stitute for HEAVISIDE's operational calculus*. However, the Laplace transform procedure is unsatisfactory from several viewpoints (some of these will be mentioned in this preface); the most obvious defect: the procedure cannot be applied to functions of rapid growth (such as the 2 function tr-+-exp(t)). In 1949 JAN MIKUSINSKI indicated how the un necessary restrictions required by the Laplace transform can be avoided by a direct approach, thereby gaining in notational as well as conceptual simplicity; this approach is carefully described in MIKUSINSKI's textbook "Operational Calculus" [M 1]. The aims of the present book are the same as MIKUSINSKI's [M 1]: a direct approach requiring no un-necessary restrictions. The present operational calculus is essentially equivalent to the "calcul symbolique" of distributions having left-bounded support (see 6.52 below and pp. 171 to 180 of the textbook "Theorie des distributions" by LAURENT SCHWARTZ).
| Author | : Nobuaki Obata |
| Publisher | : Springer |
| Total Pages | : 141 |
| Release | : 2017-02-17 |
| Genre | : Science |
| ISBN | : 9811035067 |
This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs.This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.
