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Lattice Duality
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Book Synopsis Topological Duality for Distributive Lattices by : Mai Gehrke
Download or read book Topological Duality for Distributive Lattices written by Mai Gehrke and published by Cambridge University Press. This book was released on 2024-02-29 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing Stone–Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Book Synopsis General Lattice Theory by : George Grätzer
Download or read book General Lattice Theory written by George Grätzer and published by Springer Science & Business Media. This book was released on 2002-11-21 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Grätzer’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. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS
Book Synopsis Lattice Gauge Theories And Monte Carlo Simulations by : Claudio Rebbi
Download or read book Lattice Gauge Theories And Monte Carlo Simulations written by Claudio Rebbi and published by World Scientific. This book was released on 1983-07-01 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the most up-to-date review on Lattice Gauge Theories and Monte Carlo Simulations. It consists of two parts. Part one is an introductory lecture on the lattice gauge theories in general, Monte Carlo techniques and on the results to date. Part two consists of important original papers in this field. These selected reprints involve the following: Lattice Gauge Theories, General Formalism and Expansion Techniques, Monte Carlo Simulations. Phase Structures, Observables in Pure Gauge Theories, Systems with Bosonic Matter Fields, Simulation of Systems with Fermions.
Book Synopsis Continuous Lattices and Domains by : G. Gierz
Download or read book Continuous Lattices and Domains written by G. Gierz and published by Cambridge University Press. This book was released on 2003-03-06 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Linear Programming Duality by : Achim Bachem
Download or read book Linear Programming Duality written by Achim Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an elementary introduction to the theory of oriented matroids. The way oriented matroids are intro- duced emphasizes that they are the most general - and hence simplest - structures for which linear Programming Duality results can be stated and proved. The main theme of the book is duality. Using Farkas' Lemma as the basis the authors start withre- sults on polyhedra in Rn and show how to restate the essence of the proofs in terms of sign patterns of oriented ma- troids. Most of the standard material in Linear Programming is presented in the setting of real space as well as in the more abstract theory of oriented matroids. This approach clarifies the theory behind Linear Programming and proofs become simpler. The last part of the book deals with the facial structure of polytopes respectively their oriented matroid counterparts. It is an introduction to more advanced topics in oriented matroid theory. Each chapter contains suggestions for furt- herreading and the references provide an overview of the research in this field.
Book Synopsis A Compendium of Continuous Lattices by : G. Gierz
Download or read book A Compendium of Continuous Lattices written by G. Gierz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematics book with six authors is perhaps a rare enough occurrence to make a reader ask how such a collaboration came about. We begin, therefore, with a few words on how we were brought to the subject over a ten-year period, during part of which time we did not all know each other. We do not intend to write here the history of continuous lattices but rather to explain our own personal involvement. History in a more proper sense is provided by the bibliography and the notes following the sections of the book, as well as by many remarks in the text. A coherent discussion of the content and motivation of the whole study is reserved for the introduction. In October of 1969 Dana Scott was lead by problems of semantics for computer languages to consider more closely partially ordered structures of function spaces. The idea of using partial orderings to correspond to spaces of partially defined functions and functionals had appeared several times earlier in recursive function theory; however, there had not been very sustained interest in structures of continuous functionals. These were the ones Scott saw that he needed. His first insight was to see that - in more modern terminology - the category of algebraic lattices and the (so-called) Scott-continuous functions is cartesian closed.
Book Synopsis Axioms For Lattices And Boolean Algebras by : R Padmanabhan
Download or read book Axioms For Lattices And Boolean Algebras written by R Padmanabhan and published by World Scientific. This book was released on 2008-08-11 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of equational axioms emerged initially with the axiomatic approach to Boolean algebras, groups, and rings, and later in lattices. This unique research monograph systematically presents minimal equational axiom-systems for various lattice-related algebras, regardless of whether they are given in terms of “join and meet” or other types of operations such as ternary operations. Each of the axiom-systems is coded in a handy way so that it is easy to follow the natural connection among the various axioms and to understand how to combine them to form new axiom systems.A new topic in this book is the characterization of Boolean algebras within the class of all uniquely complemented lattices. Here, the celebrated problem of E V Huntington is addressed, which — according to G Gratzer, a leading expert in modern lattice theory — is one of the two problems that shaped a century of research in lattice theory. Among other things, it is shown that there are infinitely many non-modular lattice identities that force a uniquely complemented lattice to be Boolean, thus providing several new axiom systems for Boolean algebras within the class of all uniquely complemented lattices. Finally, a few related lines of research are sketched, in the form of appendices, including one by Dr Willian McCune of the University of New Mexico, on applications of modern theorem-proving to the equational theory of lattices.
Book Synopsis Statistical Mechanics by : Franz Schwabl
Download or read book Statistical Mechanics written by Franz Schwabl and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique and consistent mathematical treatise contains a deductive description of equilibrium statistics and thermodynamics. The most important elements of non-equilibrium phenomena are also treated. In addition to the fundamentals, the text tries to show how large the area of statistical mechanics is and how many applications can be found here. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications in critical dynamics, as well as fundamental thoughts of irreversibility are discussed. The text will be useful for advanced students in physics and other sciences who have profound knowledge of quantum mechanics.
Book Synopsis Equilibrium Statistical Mechanics of Lattice Models by : David A. Lavis
Download or read book Equilibrium Statistical Mechanics of Lattice Models written by David A. Lavis and published by Springer. This book was released on 2015-01-31 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg--Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi--Hijmans--De Boer hierarchy of approximations. In Part III the use of algebraic, transformation and decoration methods to obtain exact system information is considered. This is followed by an account of the use of transfer matrices for the location of incipient phase transitions in one-dimensionally infinite models and for exact solutions for two-dimensionally infinite systems. 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 treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. 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. The use of Pad\'e, differential and algebraic approximants to locate and analyze second- and first-order transitions is described. The realization of the ideas of scaling theory by the renormalization group is presented together with treatments of various approximation schemes including phenomenological renormalization. Part V of the book contains a collection of mathematical appendices intended to minimise the need to refer to other mathematical sources.
Book Synopsis Selected Papers Of Morikazu Toda by : Miki Wadati
Download or read book Selected Papers Of Morikazu Toda written by Miki Wadati and published by World Scientific. This book was released on 1993-10-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers of Dr Morikazu Toda. The papers are arranged in chronological order of publishing dates. Among Dr Toda's many contributions, his works on liquids and nonlinear lattice dynamics should be mentioned. The one-dimensional lattice where nearest neighboring particles interact through an exponential potential is called the Toda lattice which is a miracle and indeed a jewel in theoretical physics. The papers in this volume can be grouped into five subjects: statistical mechanics, theory of liquids and solutions, lattice dynamics, Toda lattice and soliton theory and its applications.
Book Synopsis J. Michael Dunn on Information Based Logics by : Katalin Bimbo
Download or read book J. Michael Dunn on Information Based Logics written by Katalin Bimbo and published by Springer. This book was released on 2016-04-02 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.
Book Synopsis Foundations of Intelligent Systems by : Yinglin Wang
Download or read book Foundations of Intelligent Systems written by Yinglin Wang and published by Springer Science & Business Media. This book was released on 2011-11-25 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Sixth International Conference on Intelligent System and Knowledge Engineering presents selected papers from the conference ISKE 2011, held December 15-17 in Shanghai, China. This proceedings doesn’t only examine original research and approaches in the broad areas of intelligent systems and knowledge engineering, but also present new methodologies and practices in intelligent computing paradigms. The book introduces the current scientific and technical advances in the fields of artificial intelligence, machine learning, pattern recognition, data mining, information retrieval, knowledge-based systems, knowledge representation and reasoning, multi-agent systems, natural-language processing, etc. Furthermore, new computing methodologies are presented, including cloud computing, service computing and pervasive computing with traditional intelligent methods. The proceedings will be beneficial for both researchers and practitioners who want to utilize intelligent methods in their specific research fields. Dr. Yinglin Wang is a professor at the Department of Computer Science and Engineering, Shanghai Jiao Tong University, China; Dr. Tianrui Li is a professor at the School of Information Science and Technology, Southwest Jiaotong University, China.
Book Synopsis Exactly Solved Models by : Fa Yueh Wu
Download or read book Exactly Solved Models written by Fa Yueh Wu and published by World Scientific. This book was released on 2009 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: Organized into topics ranging from lattice models in condensed matter physics to graph theory in mathematics. This title presents an overview of each of the topics and a look at how crucial developments emerged.
Book Synopsis Orders: Description and Roles by : M. Pouzet
Download or read book Orders: Description and Roles written by M. Pouzet and published by Elsevier. This book was released on 1984-01-01 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orders: Description and Roles
Book Synopsis Statistical Models for the Fracture of Disordered Media by : H.J. Herrmann
Download or read book Statistical Models for the Fracture of Disordered Media written by H.J. Herrmann and published by Elsevier. This book was released on 2014-06-28 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the beginning of the century the technological desire to master the fracture of metals, concrete or polymers has boosted research and has left behind an overwhelming amount of literature. In a field where it seems difficult to say anything simple and new, the editors and authors of this book have managed to do just that.The approach to fracture taken here was not conceived by mechanical engineers or material scientists. It is essentially the by-product of exciting developments that have occurred in the last ten to fifteen years within a branch of theoretical physics, called statistical physics. Concepts such as ``percolation'' and ``fractals'', as models for the properties of fracture are not often considered by engineers. A particular aim of this volume is to emphasize the fundamental role disorder plays in the breaking process.The main scope of the volume is pedagogical and is at the same time an overview of fracture mechanics for physicists and an introduction to new concepts of statistical physics for mechanics and engineers. To this end the first half of the book consists of introductory chapters and the second half contains the results that have emerged from this new approach.
Book Synopsis Algebras and Orders by : Ivo G. Rosenberg
Download or read book Algebras and Orders written by Ivo G. Rosenberg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.
Book Synopsis The Modern Algebra of Information Retrieval by : Sándor Dominich
Download or read book The Modern Algebra of Information Retrieval written by Sándor Dominich and published by Springer Science & Business Media. This book was released on 2008-04-03 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a unique approach to information retrieval by laying down the foundations for a modern algebra of information retrieval based on lattice theory. All major retrieval methods developed so far are described in detail, along with Web retrieval algorithms, and the author shows that they all can be treated elegantly in a unified formal way, using lattice theory as the one basic concept. The book’s presentation is characterized by an engineering-like approach.
