Hyperidentities Boolean And De Morgan Structures

Author : Yuri Movsisyan
Publisher : World Scientific
Page : 561 pages
File Size : 50,7 Mb
Release : 2022-09-20
Category : Mathematics
ISBN : 9789811254932

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Hyperidentities: Boolean And De Morgan Structures by Yuri Movsisyan Pdf

Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.

Author : Anonim
Publisher : Unknown
Page : 1100 pages
File Size : 40,8 Mb
Release : 2001
Category : Mathematics
ISBN : UVA:X006170285

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Mathematical Reviews by Anonim Pdf

Author : Dietlinde Lau
Publisher : Springer Science & Business Media
Page : 668 pages
File Size : 40,8 Mb
Release : 2006-11-23
Category : Mathematics
ISBN : 9783540360230

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Function Algebras on Finite Sets by Dietlinde Lau Pdf

Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.

Author : B. Plotkin
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401108201

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Universal Algebra, Algebraic Logic, and Databases by B. Plotkin Pdf

Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.

Author : Raymond Balbes
Publisher : Unknown
Page : 316 pages
File Size : 42,7 Mb
Release : 2011-11-23
Category : Lattices, Distributive
ISBN : 098380110X

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Distributive Lattices by Raymond Balbes Pdf

Discussing the foundations of the theory of distributive lattices and the techniques used in this field, this resource also presents a number of special topics to which the theory is applied. In developing the theory, the authors have made use of the methods and tools of universal algebra and elementary category theory.

Author : Jörg Koppitz,Klaus Denecke
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 47,5 Mb
Release : 2006-02-10
Category : Mathematics
ISBN : 0387308040

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M-Solid Varieties of Algebras by Jörg Koppitz,Klaus Denecke Pdf

A complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on solid varieties of semirings and semigroups. The book aims to develop the theory of solid varieties as a system of mathematical discourse that is applicable in several concrete situations. A unique feature of this book is the use of Galois connections to integrate different topics.

Author : Anonim
Publisher : Academic Press
Page : 370 pages
File Size : 42,5 Mb
Release : 1982-10-07
Category : Mathematics
ISBN : 0080874231

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Rings That are Nearly Associative by Anonim Pdf

Rings That are Nearly Associative

Author : Michael Farber,Markus Burger
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 51,5 Mb
Release : 2007
Category : Robotics
ISBN : 9780821842461

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Topology and Robotics by Michael Farber,Markus Burger Pdf

Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.

Author : Klaus Denecke,S L Wismath
Publisher : CRC Press
Page : 334 pages
File Size : 44,9 Mb
Release : 2000-08-08
Category : Mathematics
ISBN : 905699235X

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Hyperidentities and Clones by Klaus Denecke,S L Wismath Pdf

Theories and results on hyperidentities have been published in various areas of the literature over the last 18 years. Hyperidentities and Clones integrates these into a coherent framework for the first time. The author also includes some applications of hyperidentities to the functional completeness problem in multiple-valued logic and extends the general theory to partial algebras. The last chapter contains exercises and open problems with suggestions for future work in this area of research. Graduate students and mathematical researchers will find Hyperidentities and Clones a thought-provoking and illuminating text that offers a unique opportunity to study the topic in one source.

Author : Peter Fletcher,William F. Lindgren
Publisher : Routledge
Page : 233 pages
File Size : 50,6 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781351420297

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Quasi-Uniform Spaces by Peter Fletcher,William F. Lindgren Pdf

Since quasi-uniform spaces were defined in 1948, a diverse and widely dispersed literatureconcerning them has emerged. In Quasi-Uniform Spaces, the authors present a comprehensivestudy of these structures, together with the theory of quasi-proximities. In additionto new results unavailable elsewhere, the volume unites fundamental materialheretofore scattered throughout the literature.Quasi-Uniform Spaces shows by example that these structures provide a natural approachto the study of point-set topology. It is the only source for many results related to completeness,and a primary source for the study of both transitive and quasi-metric spaces.Included are H. Junnila's analogue of Tamano's theorem, J. Kofner's result showing thatevery GO space is transitive, and R. Fox's example of a non-quasi-metrizable r-space. Inaddition to numerous interesting problems mentioned throughout the text , 22 formalresearch problems are featured. The book nurtures a radically different viewpoint oftopology , leading to new insights into purely topological problems.Since every topological space admits a quasi-uniformity, the study of quasi-uniformspaces can be seen as no less general than the study of topological spaces. For such study,Quasi-Uniform Spaces is a necessary, self-contained reference for both researchers andgraduate students of general topology . Information is made particularly accessible withthe inclusion of an extensive index and bibliography .

Author : François Labourie
Publisher : Unknown
Page : 152 pages
File Size : 47,8 Mb
Release : 2013
Category : Mathematics
ISBN : UCSD:31822040876443

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Lectures on Representations of Surface Groups by François Labourie Pdf

The subject of these notes is the character variety of representations of a surface group in a Lie group. The author emphasizes the various points of view (combinatorial, differential, and algebraic) and is interested in the description of its smooth points, symplectic structure, volume and connected components. He also shows how a three manifold bounded by the surface leaves a trace in this character variety. These notes were originally designed for students with only elementary knowledge of differential geometry and topology. In the first chapters, the author does not focus on the details of the differential geometric constructions and refers to classical textbooks, while in the more advanced chapters proofs occasionally are provided only for special cases where they convey the flavor of the general arguments. These notes might also be used by researchers entering this fast expanding field as motivation for further studies. The concluding paragraph of every chapter provides suggestions for further research.

Author : George M. Bergman
Publisher : Springer
Page : 572 pages
File Size : 43,6 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9783319114781

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An Invitation to General Algebra and Universal Constructions by George M. Bergman Pdf

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Author : Stanley I. Grossman
Publisher : Academic Press
Page : 1177 pages
File Size : 46,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262437

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Calculus by Stanley I. Grossman Pdf

Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis. This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics include the sequences of real numbers, dot product, arc length as a parameter, quadric surfaces, higher-order partial derivatives, and Green's theorem in the plane. This publication is a good source for students learning calculus.

Author : Vieri Benci,Mauro Di Nasso
Publisher : World Scientific
Page : 346 pages
File Size : 48,8 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9789813276604

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How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers by Vieri Benci,Mauro Di Nasso Pdf

'This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.'CHOICEThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis.The basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory.The book also provides a comprehensive exposition of the Theory of Numerosity, a new way of counting (countable) infinite sets that maintains the ancient Euclid's Principle: 'The whole is larger than its parts'. The book is organized into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.

Author : I. N. Herstein
Publisher : Unknown
Page : 247 pages
File Size : 52,9 Mb
Release : 1976
Category : Rings with involution
ISBN : 0226328066

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Rings with Involution by I. N. Herstein Pdf