Search results for: lattice-theory-foundation

Lattice Theory Foundation

Author : George Grätzer
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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

Lattice Theory Special Topics and Applications

Author : George Grätzer
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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.

General Lattice Theory

Author : George Grätzer
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"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

Lattice Theory

Author : George Grätzer
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This three-volume-set comprises the complete lattice theory project. Volume 1 of the set, Lattice Theory: Foundation, is the revised and enlarged third edition of General Lattice Theory. It focuses on introducing the field and covers the fundamental concepts and results. The two Special Topics and Applications volumes (volumes 2 and 3 of the set), jointly edited by George Grätzer and Friedrich Wehrung, update the reader on some of the vast areas not in Foundation. Volume 1 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. Volume 2 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.

Canadian Journal of Mathematics

Author :
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Theoretical Metallography

Author : Ulrich Dehlinger
File Size : 23.62 MB
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Employment in Professional Mathematical Work in Industry and Government

Author : United States. Bureau of Labor Statistics
File Size : 34.76 MB
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Foundations of probability theory statistical inference and statistical theories of science

Author : William Leonard Harper
File Size : 54.74 MB
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Introduction to Lattices and Order

Author : B. A. Davey
File Size : 28.40 MB
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This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

Field Theory on the Lattice

Author : Alain Billoire
File Size : 29.39 MB
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Formal Concept Analysis

Author : Bernhard Ganter
File Size : 30.38 MB
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This first textbook on formal concept analysis gives a systematic presentation of the mathematical foundations and their relations to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. The mathematical foundations are treated thoroughly and are illuminated by means of numerous examples, making the basic theory readily accessible in compact form.

The Journal of Fuzzy Mathematics

Author :
File Size : 47.20 MB
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Positive Operators and Semigroups on Banach Lattices

Author : Caribbean Mathematics Foundation
File Size : 22.25 MB
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Proceedings of a Caribbean Mathematics Foundation Conference 1990

Trends in Lattice Theory

Author : Garrett Birkhoff
File Size : 67.62 MB
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Mathematical Morphology

Author : Laurent Najman
File Size : 80.60 MB
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Mathematical Morphology allows for the analysis and processing of geometrical structures using techniques based on the fields of set theory, lattice theory, topology, and random functions. It is the basis of morphological image processing, and finds applications in fields including digital image processing (DSP), as well as areas for graphs, surface meshes, solids, and other spatial structures. This book presents an up-to-date treatment of mathematical morphology, based on the three pillars that made it an important field of theoretical work and practical application: a solid theoretical foundation, a large body of applications and an efficient implementation. The book is divided into five parts and includes 20 chapters. The five parts are structured as follows: Part I sets out the fundamental aspects of the discipline, starting with a general introduction, followed by two more theory-focused chapters, one addressing its mathematical structure and including an updated formalism, which is the result of several decades of work. Part II extends this formalism to some non-deterministic aspects of the theory, in particular detailing links with other disciplines such as stereology, geostatistics and fuzzy logic. Part III addresses the theory of morphological filtering and segmentation, featuring modern connected approaches, from both theoretical and practical aspects. Part IV features practical aspects of mathematical morphology, in particular how to deal with color and multivariate data, links to discrete geometry and topology, and some algorithmic aspects; without which applications would be impossible. Part V showcases all the previously noted fields of work through a sample of interesting, representative and varied applications.

Foundation of Euclidean and Non Euclidean Geometries According to F Klein

Author : László Rédei
File Size : 67.79 MB
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Science and Engineering on Supercomputers

Author : Eric J. Pitcher
File Size : 71.85 MB
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Dimensions of ring theory

Author :
File Size : 67.41 MB
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Lattice Dynamics

Author : Richard Fisher Wallis
File Size : 88.16 MB
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The Welch Foundation Annual Report

Author : Robert A. Welch Foundation
File Size : 24.27 MB
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