Lattice Functions And Equations

Author : Sergiu Rudeanu
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447102410

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Lattice Functions and Equations by Sergiu Rudeanu Pdf

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.

Author : Ralph N. McKenzie,George F. McNulty,Walter F. Taylor
Publisher : American Mathematical Society
Page : 386 pages
File Size : 49,8 Mb
Release : 2018-07-09
Category : Mathematics
ISBN : 9781470442958

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Algebras, Lattices, Varieties by Ralph N. McKenzie,George F. McNulty,Walter F. Taylor Pdf

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.

Author : Jean Bourgain
Publisher : Princeton University Press
Page : 183 pages
File Size : 42,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780691120980

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Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158) by Jean Bourgain Pdf

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."

Author : Ignazio Licata and Sauro Succi
Publisher : MDPI
Page : 291 pages
File Size : 40,8 Mb
Release : 2018-07-17
Category : Electronic books
ISBN : 9783038423065

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Non-Linear Lattice by Ignazio Licata and Sauro Succi Pdf

This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy

Author : Gary Doolen
Publisher : CRC Press
Page : 584 pages
File Size : 54,8 Mb
Release : 2019-03-01
Category : Mathematics
ISBN : 9780429697494

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Lattice Gas Methods For Partial Differential Equations by Gary Doolen Pdf

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.

Author : Willi Freeden
Publisher : CRC Press
Page : 467 pages
File Size : 43,6 Mb
Release : 2011-05-09
Category : Mathematics
ISBN : 9781439861851

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Metaharmonic Lattice Point Theory by Willi Freeden Pdf

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

Author : Sergiu Rudeanu
Publisher : Unknown
Page : 472 pages
File Size : 50,9 Mb
Release : 1974
Category : Algebra, Boolean
ISBN : UCSD:31822012636833

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Boolean Functions and Equations by Sergiu Rudeanu Pdf

Author : Percy Deift,Kenneth T-R McLaughlin
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 44,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806913

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A Continuum Limit of the Toda Lattice by Percy Deift,Kenneth T-R McLaughlin Pdf

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.

Author : Lynne M. Butler
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 48,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821826003

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Subgroup Lattices and Symmetric Functions by Lynne M. Butler Pdf

This work presents foundational research on two approaches to studying subgroup lattices of finite abelian $p$-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schutzenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.

Author : Gerald Teschl
Publisher : American Mathematical Soc.
Page : 373 pages
File Size : 54,6 Mb
Release : 2000
Category : Differentiable dynamical systems
ISBN : 9780821819401

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Jacobi Operators and Completely Integrable Nonlinear Lattices by Gerald Teschl Pdf

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.

Author : Dieter A. Wolf-Gladrow
Publisher : Springer
Page : 314 pages
File Size : 51,9 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540465867

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Lattice-Gas Cellular Automata and Lattice Boltzmann Models by Dieter A. Wolf-Gladrow Pdf

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

Author : Morikazu Toda
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642832192

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Theory of Nonlinear Lattices by Morikazu Toda Pdf

Soliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.

Author : Christian Posthoff,Bernd Steinbach
Publisher : Springer
Page : 511 pages
File Size : 43,5 Mb
Release : 2018-12-31
Category : Computers
ISBN : 9783030024208

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Logic Functions and Equations by Christian Posthoff,Bernd Steinbach Pdf

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.

Author : Michio Jimbo,Tetsuji Miwa
Publisher : American Mathematical Soc.
Page : 182 pages
File Size : 40,6 Mb
Release : 1994
Category : Mathematics
ISBN : 082188929X

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Algebraic Analysis of Solvable Lattice Models by Michio Jimbo,Tetsuji Miwa Pdf

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.

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 47,5 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.