Lattice Functions And Equations
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Lattice Functions And Equations
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Author : Sergiu Rudeanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lattice Functions And Equations written by Sergiu Rudeanu 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.
One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations.
Green S Function Estimates For Lattice Schrodinger Operators And Applications Am 158
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Author : Jean Bourgain
language : en
Publisher: Princeton University Press
Release Date : 2005
Green S Function Estimates For Lattice Schrodinger Operators And Applications Am 158 written by Jean Bourgain and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."
Metaharmonic Lattice Point Theory
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2011-05-09
Metaharmonic Lattice Point Theory written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-09 with Mathematics categories.
Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of
Logic Functions And Equations
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Author : Christian Posthoff
language : en
Publisher: Springer
Release Date : 2018-12-31
Logic Functions And Equations written by Christian Posthoff and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-31 with Computers categories.
The expanded and updated 2nd edition of this classic text offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science. The approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. Updated throughout, some major additions for the 2nd edition include: - an expanded introductory section on logic equations; - a new chapter on sets, lattices, and classes of logic functions; - a new chapter about SAT-problems; - a new chapter about methods to solve extremely complex problems; and - an expanded section with new decomposition methods utilizing the Boolean Differential Calculus extended to lattices of logic functions. The book provides insight into applications across binary arithmetic, coding, complexity, logic design, programming, computer architecture, and artificial intelligence. Based on the extensive teaching experience of the authors, Logic Functions and Equations is highly recommended for a one- or two-semester course in computer science and related programs. It provides straightforward high-level access to these methods and enables sophisticated applications, elegantly bridging the gap between mathematics and the theoretical foundations of computer science.
Boolean Functions And Equations
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Author : Sergiu Rudeanu
language : en
Publisher:
Release Date : 1974
Boolean Functions And Equations written by Sergiu Rudeanu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Algebra, Boolean categories.
Algebras Lattices Varieties
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Author : Ralph N. McKenzie
language : en
Publisher: American Mathematical Society
Release Date : 2018-07-09
Algebras Lattices Varieties written by Ralph N. McKenzie and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Mathematics categories.
This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
A Continuum Limit Of The Toda Lattice
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Author : Percy Deift
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
A Continuum Limit Of The Toda Lattice written by Percy Deift 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 1998 with Mathematics categories.
In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A novel feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.
Lattice Gas Methods For Partial Differential Equations
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Author : Gary Doolen
language : en
Publisher: CRC Press
Release Date : 2019-03-01
Lattice Gas Methods For Partial Differential Equations written by Gary Doolen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-01 with Mathematics categories.
Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.
Jacobi Operators And Completely Integrable Nonlinear Lattices
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Author : Gerald Teschl
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Jacobi Operators And Completely Integrable Nonlinear Lattices written by Gerald Teschl 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 2000 with Differentiable dynamical systems categories.
This volume serves as an introduction and reference source on spectral and inverse theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.
Algebraic Analysis Of Solvable Lattice Models
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Author : Michio Jimbo
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Algebraic Analysis Of Solvable Lattice Models written by Michio Jimbo 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 1994 with Mathematics categories.
Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin 1/2 XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the XXX model is briefly discussed, and the book closes with a discussion of other types of models and related works.