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Author : Jan Smit,Pierre Baal
Publisher : Unknown
Page : 996 pages
File Size : 52,7 Mb
Release : 1993
Category : Gauge fields (Physics)
ISBN : OSU:32435032135055
Author : George Grätzer
Publisher : Springer Nature
Page : 440 pages
File Size : 53,8 Mb
Release : 2023-03-23
Category : Mathematics
ISBN : 9783031290633
The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years. It features the author’s signature “Proof-by-Picture” method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include: an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions complete proofs, an extensive bibliography and index, and over 180 illustrations additional chapters covering new results of the last seven years, increasing the size of this edition to 430 pages, 360 statements, and 262 references This text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions: “[This] monograph...is an exceptional work in lattice theory, like all the contributions by this author. The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. — Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." — Mathematical Reviews
Author : Sharpe Stephen R
Publisher : World Scientific
Page : 340 pages
File Size : 53,8 Mb
Release : 1995-12-21
Category : Electronic
ISBN : 9789814549387
These six lecture courses provide the background necessary in the understanding of the application of lattice methods to phenomenology, and give examples of interesting applications. The first three introduce the necessary techniques: chiral perturbation theory, heavy quark effective field theory, and lattice gauge theory. The remaining three describe how these techniques are used, mainly in lattice simulations, in the study of interesting phenomenological questions: vacuum structure, finite temperature QCD, and electroweak matrix elements. What distinguishes this volume from others is its focus on providing the background necessary for us to understand the methods and the significance of lattice gauge theory research.
Author : G. Grätzer
Publisher : Birkhäuser
Page : 392 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034876339
In the first half of the nineteenth century, George Boole's attempt to formalize propositional logic led to the concept of Boolean algebras. While investigating the axiomatics of Boolean algebras at the end of the nineteenth century, Charles S. Peirce and Ernst Schröder found it useful to introduce the lattice concept. Independently, Richard Dedekind's research on ideals of algebraic numbers led to the same discov ery. In fact, Dedekind also introduced modularity, a weakened form of distri butivity. Although some of the early results of these mathematicians and of Edward V. Huntington are very elegant and far from trivial, they did not attract the attention of the mathematical community. It was Garrett Birkhoff's work in the mid-thirties that started the general develop ment of lattice theory. In a brilliant series of papers he demonstrated the importance of lattice theory and showed that it provides a unifying framework for hitherto unrelated developments in many mathematical disciplines. Birkhoff himself, Valere Glivenko, Karl Menger, John von Neumann, Oystein Ore, and others had developed enough of this new field for Birkhoff to attempt to "seIl" it to the general mathematical community, which he did with astonishing success in the first edition of his Lattice Theory. The further development of the subject matter can best be followed by com paring the first, second, and third editions of his book (G. Birkhoff [1940], [1948], and [1967]).
Author : Anonim
Publisher : Unknown
Page : 518 pages
File Size : 48,8 Mb
Release : 1993
Category : Aeronautics
ISBN : MINN:31951P00314322A
Author : Yuri B. Suris
Publisher : Springer Science & Business Media
Page : 1118 pages
File Size : 50,7 Mb
Release : 2003-06-20
Category : Mathematics
ISBN : 3764369957
An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.
Author : K. Motizuki
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 47,7 Mb
Release : 1986-10-31
Category : Science
ISBN : 9027721718
The structural phase transition is one of the most fundamental problems in solid state physics. Layered transition-metal dichalcogenides provide us with a most exciting area for the study of structural phase transitions that are associated with the charge density wave (CDW). A large variety of structural phase transitions, such as commensurate and incommensurate transitions, and the physical proper ties related to the formation of a CDW, have been an object of intense study made for many years by methods employing modem microscopic techniques. Rather recently, efforts have been devoted to the theoretical understanding of these experimental results. Thus, McMillan, for example, has developed an elegant phenomenological theory on the basis of the Landau free energy expansion. An extension of McMillan's theory has provided a successful understanding of the successive phase transitions observed in the IT- and 2H-compounds. In addition, a microscopic theory of lattice instability, lattice dynamics, and lattice distortion in the CDW state of the transition-metal dichalcogenides has been developed based on their electronic structures. As a result, the driving force of the CDW formation in the IT- and 2H-compounds has become clear. Furthermore, the effect of lattice fluctuations on the CDW transition and on the anomalous behavior of various physical properties has been made clear microscopically.
Author : Jan Smit
Publisher : Cambridge University Press
Page : 285 pages
File Size : 49,6 Mb
Release : 2023-07-31
Category : Science
ISBN : 9781009402743
Author : George Grätzer,Friedrich Wehrung
Publisher : Springer
Page : 472 pages
File Size : 44,7 Mb
Release : 2014-08-27
Category : Mathematics
ISBN : 9783319064130
George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.
Author : E Gava,Antonio Masiero,Kumar Shiv Narain,Seifallah Randjbar-daemi,Qaisar Shafi
Publisher : World Scientific
Page : 494 pages
File Size : 51,9 Mb
Release : 1994-06-28
Category : Electronic
ISBN : 9789814551649
This symposium was organized in order to discuss recent developments and future perspectives in intermediate-energy heavy-ion physics. The subjects included sub-barrier fusion, superheavy elements, fission; halo, skin nuclei; multi-fragmentation, collective flow, compression; properties of hot nuclei; high spin and exotic nuclear shapes; nuclear astrophysics; applications; facilities.
Author : Geoffrey R. Grimmett
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 55,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662039816
Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.
Author : Anonim
Publisher : Unknown
Page : 934 pages
File Size : 54,5 Mb
Release : 1994
Category : Physics
ISBN : UOM:39015027829848
Author : Arjeh M. Cohen,Hans Cuypers,Hans Sterk
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 50,8 Mb
Release : 1998-12-15
Category : Computers
ISBN : 3540634800
This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.
Author : David Lavis,George M. Bell
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 45,9 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783662100202
Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.
Author : Willi Freeden,Martin Gutting
Publisher : CRC Press
Page : 501 pages
File Size : 43,6 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351764766
In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.