Lattice Theory Special Topics And Applications
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Lattice Theory Special Topics And Applications
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Author : George Grätzer
language : en
Publisher: Springer
Release Date : 2014-08-27
Lattice Theory Special Topics And Applications written by George Grätzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.
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.
Lattice Theory Special Topics And Applications
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Author : George Grätzer
language : en
Publisher: Birkhäuser
Release Date : 2016-10-08
Lattice Theory Special Topics And Applications written by George Grätzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-08 with Mathematics categories.
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, 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.
Lattice Theory Foundation
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Author : George Grätzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-14
Lattice Theory Foundation written by George Grätzer 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 2011-02-14 with Mathematics categories.
This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews
Algebraic Methods In General Rough Sets
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Author : A. Mani
language : en
Publisher: Springer
Release Date : 2019-01-11
Algebraic Methods In General Rough Sets written by A. Mani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-11 with Mathematics categories.
This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value.
Relational And Algebraic Methods In Computer Science
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Author : Uli Fahrenberg
language : en
Publisher: Springer Nature
Release Date : 2021-10-22
Relational And Algebraic Methods In Computer Science written by Uli Fahrenberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-22 with Computers categories.
This book constitutes the proceedings of the 19th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2021, which took place in Marseille, France, during November 2-5, 2021. The 29 papers presented in this book were carefully reviewed and selected from 35 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
Transactions On Rough Sets Xxii
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Author : James F. Peters
language : en
Publisher: Springer Nature
Release Date : 2020-12-16
Transactions On Rough Sets Xxii written by James F. Peters and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-16 with Computers categories.
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XXII in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.
Representations Of Algebras
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Author : Graham J. Leuschke
language : en
Publisher: American Mathematical Soc.
Release Date : 2018
Representations Of Algebras written by Graham J. Leuschke 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 2018 with Mathematics categories.
Contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held in August 2016, at Syracuse University. This volume includes three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories.
A Primer Of Subquasivariety Lattices
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Author : Kira Adaricheva
language : en
Publisher: Springer Nature
Release Date : 2022-08-18
A Primer Of Subquasivariety Lattices written by Kira Adaricheva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-18 with Mathematics categories.
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theories and implicational theories in languages that may, or may not, contain equality. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator. As an application of this new approach, it is shown that completely distributive lattices with a dually compact least element are subquasivariety lattices. The book contains many examples to illustrate these principles, as well as open problems. Ultimately this new approach gives readers a set of tools to investigate classes of lattices that can be represented as subquasivariety lattices.
Lattices Applied To Coding For Reliable And Secure Communications
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Author : Sueli I.R. Costa
language : en
Publisher: Springer
Release Date : 2018-04-02
Lattices Applied To Coding For Reliable And Secure Communications written by Sueli I.R. Costa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-02 with Mathematics categories.
This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.
The Congruences Of A Finite Lattice
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Author : George Grätzer
language : en
Publisher: Birkhäuser
Release Date : 2016-06-29
The Congruences Of A Finite Lattice written by George Grätzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-29 with Mathematics categories.
This is a self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method. Key features: * Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions * Contains complete proofs, an extensive bibliography and index, and over 140 illustrations * This new edition includes two new parts on Planar Semimodular Lattices and The Order of Principle Congruences, covering the research of the last 10 years The book is appropriate for a one-semester graduate course in lattice theory, and it is a practical reference for researchers studying lattices. Reviews of the first edition: "There exist a lot of interesting results in this area of lattice theory, and some of them are presented in this book. [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. Moreover, the author provides a series of companion lectures which help the reader to approach the Proof-by-Picture sections." (Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007) "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. [I]n addition to giving the full formal details of the proofs, the author chooses a somehow more pedagogical way that he calls Proof-by-Picture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. 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