The Congruences of a Finite Lattice: A "proof-By-Picture " Approach, Grдtzer George

Автор: Gr?tzer
Название: Lattice Theory: Special Topics and Applications
ISBN: 331944235X ISBN-13(EAN): 9783319442358
Издательство: Springer
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Описание: George Gr?tzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Gr?tzer 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, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.

Автор: Simon Barry
Название: The Statistical Mechanics of Lattice Gases, Volume I
ISBN: 0691607915 ISBN-13(EAN): 9780691607917
Издательство: Wiley
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Описание: A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of such models as the Ising and Heisenberg, an area in which scientists have made enormous strides during the past twenty-five years. This first volume addresses, among many topics, the mathematical backgroun

Автор: David Lavis; George M. Bell
Название: Statistical Mechanics of Lattice Systems
ISBN: 3642084117 ISBN-13(EAN): 9783642084119
Издательство: Springer
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Описание: 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 multi particle 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 2) are princi- pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this 1 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 include some of our discussion of exact results in this volume and some in Volume 2. The other main area of discussion in this volume is mean-field theory leading to closed- form approximations. Although this is known not to give reliable results close to a critical region, it often provides a good qualitative picture for phase dia- grams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available.

Автор: Ekkehard Kr?tzel
Название: Lattice Points
ISBN: 9027727333 ISBN-13(EAN): 9789027727336
Издательство: Springer
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Автор: David A. Lavis
Название: Equilibrium Statistical Mechanics of Lattice Models
ISBN: 9402405046 ISBN-13(EAN): 9789402405040
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Описание: The latter is applied to a general analysis of eight-vertex models yielding as special cases the two-dimensional Ising model and the six-vertex model. The use of the De Neef-Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts model.

Автор: George Gr?tzer; B.A. Davey; R. Freese; B. Ganter;
Название: General Lattice Theory
ISBN: 3764369965 ISBN-13(EAN): 9783764369965
Издательство: Springer
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Описание: "Gratzer`s `General Lattice Theory` has become the lattice theorist`s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields.

Автор: Borwein
Название: Lattice Sums Then and Now
ISBN: 1107039908 ISBN-13(EAN): 9781107039902
Издательство: Cambridge Academ
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Описание: For over a century lattice sums have been studied by mathematicians and scientists in diverse areas of science, in some cases unwittingly duplicating previous work. Here, at last, is a comprehensive overview of the substantial body of knowledge that now exists on lattice sums and their applications.

Автор: Grigore Calugareanu
Название: Lattice Concepts of Module Theory
ISBN: 9048155304 ISBN-13(EAN): 9789048155309
Издательство: Springer
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Описание: It became more and more usual, from, say, the 1970s, for each book on Module Theory, to point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly modular) lattices. This was justified by the nowadays widely accepted perception that the structure of a module over a ring is best understood in terms of the lattice struc- ture of its submodule lattice. Citing Louis H. Rowen "this important example (the lattice of all the submodules of a module) is the raison d'etre for the study of lattice theory by ring theorists." Indeed, many module-theoretic results can be proved by using lattice theory alone. The purpose of this book is to collect and present all and only the results of this kind, although for this purpose one must develop some significant lattice theory. The results in this book are of the following categories: the folklore of Lattice Theory (to be found in each Lattice Theory book), module- theoretic results generalized in (modular, and possibly compactly gen- erated) lattices (to be found in some 6 to 7 books published in the last 20 years), very special module-theoretic results generalized in lattices (e. g., purity in Chapter 9 and several dimensions in Chapter 13, to be found mostly in 27], respectively, 34] and 18]) and some new con- cepts (e. g.

Автор: A.M. Glass; W.C. Holland
Название: Lattice-Ordered Groups
ISBN: 9401075247 ISBN-13(EAN): 9789401075244
Издательство: Springer
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Автор: George Gr?tzer; Friedrich Wehrung
Название: Lattice Theory: Special Topics and Applications
ISBN: 3319064126 ISBN-13(EAN): 9783319064123
Издательство: Springer
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Описание: George Gratzer`s Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Gratzer.

Автор: Bibak, Khodakhast
Название: Restricted Congruences in Computing
ISBN: 0367496038 ISBN-13(EAN): 9780367496036
Издательство: Taylor&Francis
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Описание: As the first book of its kind, this book is devoted to studying congruences, their problems and applications. The book will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

Автор: J. Urbanowicz; Kenneth S. Williams
Название: Congruences for L-Functions
ISBN: 0792363795 ISBN-13(EAN): 9780792363798
Издательство: Springer
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Описание: Provides a comprehensive treatment of research carried out on congruences involving the values of L-functions (attached to quadratic characters) at certain special values. This book presents in a unified way congruences found by many authors over the years, from the classical ones of Gauss and Dirichlet to Gras and Vehara.