Representations Of Discrete Functions
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Representations Of Discrete Functions
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Author : Tsutomu Sasao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Representations Of Discrete Functions written by Tsutomu Sasao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Representations of Discrete Functions is an edited volume containing 13 chapter contributions from leading researchers with a focus on the latest research results. The first three chapters are introductions and contain many illustrations to clarify concepts presented in the text. It is recommended that these chapters are read first. The book then deals with the following topics: binary decision diagrams (BDDs), multi-terminal binary decision diagrams (MTBDDs), edge-valued binary decision diagrams (EVBDDs), functional decision diagrams (FDDs), Kronecker decision diagrams (KDDs), binary moment diagrams (BMDs), spectral transform decision diagrams (STDDs), ternary decision diagrams (TDDs), spectral transformation of logic functions, other transformations oflogic functions, EXOR-based two-level expressions, FPRM minimization with TDDs and MTBDDs, complexity theories on FDDs, multi-level logic synthesis, and complexity of three-level logic networks. Representations of Discrete Functions is designed for CAD researchers and engineers and will also be of interest to computer scientists who are interested in combinatorial problems. Exercises prepared by the editors help make this book useful as a graduate level textbook.
Representation Of Lie Groups And Special Functions
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Author : N.Ja. Vilenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Representation Of Lie Groups And Special Functions written by N.Ja. Vilenkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. For research mathematicians, physicists and engineers.
Representations Of Multiple Valued Logic Functions
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Author : Radomir S. Stankovic
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Representations Of Multiple Valued Logic Functions written by Radomir S. Stankovic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.
Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them. Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms
Representation Of Lie Groups And Special Functions
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Author : Naum I︠A︡kovlevich Vilenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-11-30
Representation Of Lie Groups And Special Functions written by Naum I︠A︡kovlevich Vilenkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-30 with Mathematics categories.
This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations.This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given.The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory.For research mathematicians, physicists and engineers.
Spectral Logic And Its Applications For The Design Of Digital Devices
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Author : Mark G. Karpovsky
language : en
Publisher: John Wiley & Sons
Release Date : 2008-07-14
Spectral Logic And Its Applications For The Design Of Digital Devices written by Mark G. Karpovsky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-14 with Computers categories.
Spectral techniques facilitate the design and testing of today's increasingly complex digital devices There is heightened interest in spectral techniques for the design of digital devices dictated by ever increasing demands on technology that often cannot be met by classical approaches. Spectral methods provide a uniform and consistent theoretic environment for recent achievements in this area, which appear divergent in many other approaches. Spectral Logic and Its Applications for the Design of Digital Devices gives readers a foundation for further exploration of abstract harmonic analysis over finite groups in the analysis, design, and testing of digital devices. After an introduction, this book provides the essential mathematical background for discussing spectral methods. It then delves into spectral logic and its applications, covering: * Walsh, Haar, arithmetic transform, Reed-Muller transform for binary-valued functions and Vilenkin-Chrestenson transform, generalized Haar, and other related transforms for multiple-valued functions * Polynomial expressions and decision diagram representations for switching and multiple-value functions * Spectral analysis of Boolean functions * Spectral synthesis and optimization of combinational and sequential devices * Spectral methods in analysis and synthesis of reliable devices * Spectral techniques for testing computer hardware This is the authoritative reference for computer science and engineering professionals and researchers with an interest in spectral methods of representing discrete functions and related applications in the design and testing of digital devices. It is also an excellent text for graduate students in courses covering spectral logic and its applications.
Decision Diagram Techniques For Micro And Nanoelectronic Design Handbook
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Author : Svetlana N. Yanushkevich
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Decision Diagram Techniques For Micro And Nanoelectronic Design Handbook written by Svetlana N. Yanushkevich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Technology & Engineering categories.
Decision diagram (DD) techniques are very popular in the electronic design automation (EDA) of integrated circuits, and for good reason. They can accurately simulate logic design, can show where to make reductions in complexity, and can be easily modified to model different scenarios. Presenting DD techniques from an applied perspective, Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook provides a comprehensive, up-to-date collection of DD techniques. Experts with more than forty years of combined experience in both industrial and academic settings demonstrate how to apply the techniques to full advantage with more than 400 examples and illustrations. Beginning with the fundamental theory, data structures, and logic underlying DD techniques, they explore a breadth of topics from arithmetic and word-level representations to spectral techniques and event-driven analysis. The book also includes abundant references to more detailed information and additional applications. Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook collects the theory, methods, and practical knowledge necessary to design more advanced circuits and places it at your fingertips in a single, concise reference.
Automorphic Representations And L Functions For The General Linear Group Volume 2
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Author : Dorian Goldfeld
language : en
Publisher: Cambridge University Press
Release Date : 2011-04-21
Automorphic Representations And L Functions For The General Linear Group Volume 2 written by Dorian Goldfeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-21 with Mathematics categories.
This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.
Automorphic Forms Representations And L Functions
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Author : Armand Borel
language : en
Publisher: American Mathematical Soc.
Release Date : 1979-06-30
Automorphic Forms Representations And L Functions written by Armand Borel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-06-30 with Mathematics categories.
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Generalized Functions Volume 6
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Author : I. M. Gel′fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-19
Generalized Functions Volume 6 written by I. M. Gel′fand and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The unifying theme of Volume 6 is the study of representations of the general linear group of order two over various fields and rings of number-theoretic nature, most importantly over local fields (p-adic fields and fields of power series over finite fields) and over the ring of adeles. Representation theory of the latter group naturally leads to the study of automorphic functions and related number-theoretic problems. The book contains a wealth of information about discrete subgroups and automorphic representations, and can be used both as a very good introduction to the subject and as a valuable reference.
Integrating Research On The Graphical Representation Of Functions
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Author : Thomas A. Romberg
language : en
Publisher: Routledge
Release Date : 1993
Integrating Research On The Graphical Representation Of Functions written by Thomas A. Romberg and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Education categories.
First Published in 1993. Routledge is an imprint of Taylor & Francis, an informa company.