Prolegomena of Hypergroup Theory PDF Download

Author: Piergiulio Corsini
Publisher:
ISBN:
Category : Hypergroups
Languages : en
Pages : 224

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Author: P. Corsini
Publisher: Springer Science & Business Media
ISBN: 1475737149
Category : Mathematics
Languages : en
Pages : 333

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Book Description
This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6) automata; 7) cryptography; 8) median algebras, relation algebras; 9) combinatorics; 10) codes; 11) artificial intelligence; 12) probabilities. Audience: Graduate students and researchers.

Author: Bijan Davvaz
Publisher: World Scientific
ISBN: 9811249407
Category : Mathematics
Languages : en
Pages : 300

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Book Description
The book presents an updated study of hypergroups, being structured on 12 chapters in starting with the presentation of the basic notions in the domain: semihypergroups, hypergroups, classes of subhypergroups, types of homomorphisms, but also key notions: canonical hypergroups, join spaces and complete hypergroups. A detailed study is dedicated to the connections between hypergroups and binary relations, starting from connections established by Rosenberg and Corsini. Various types of binary relations are highlighted, in particular equivalence relations and the corresponding quotient structures, which enjoy certain properties: commutativity, cyclicity, solvability.A special attention is paid to the fundamental beta relationship, which leads to a group quotient structure. In the finite case, the number of non-isomorphic Rosenberg hypergroups of small orders is mentioned. Also, the study of hypergroups associated with relations is extended to the case of hypergroups associated to n-ary relations. Then follows an applied excursion of hypergroups in important chapters in mathematics: lattices, Pawlak approximation, hypergraphs, topology, with various properties, characterizations, varied and interesting examples. The bibliography presented is an updated one in the field, followed by an index of the notions presented in the book, useful in its study.

Author: Smarandache, Florentin
Publisher: IGI Global
ISBN: 1668434970
Category : Mathematics
Languages : en
Pages : 333

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Book Description
Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

Author: Adesina Abdul Akeem Agboola
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 11

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The objective of this paper is to introduce the concept of neutrosophic hypergroup and present some of its elementary properties.

Author: Paul-Hermann Zieschang
Publisher: Springer Nature
ISBN: 3031394895
Category : Mathematics
Languages : en
Pages : 398

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Book Description
This book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition), and this condition defines the so-called Coxeter hypergroups. Coxeter hypergroups can be treated in a similar way to Coxeter groups. On the other hand, their regular actions are mathematically equivalent to buildings (in the sense of Jacques Tits). A similar equivalence is discussed for twin buildings. The primary audience for the monograph will be researchers working in Algebra and/or Algebraic Combinatorics, in particular on association schemes.

Author: Bijan Davvaz
Publisher: World Scientific
ISBN: 9814425303
Category : Mathematics
Languages : en
Pages : 209

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Book Description
This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics.

Author: Bijan Davvaz
Publisher: Academic Press
ISBN: 0128099259
Category : Mathematics
Languages : en
Pages : 164

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Book Description
Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject. Offers the first book devoted to the semihypergroup theory Presents an introduction to recent progress in the theory of semihypergroups Covers most of the mathematical ideas and techniques required in the study of semihypergroups Employs the notion of fundamental relations to connect semihypergroups to semigroups

Author: Cristina Flaut
Publisher: Springer
ISBN: 3030000842
Category : Technology & Engineering
Languages : en
Pages : 576

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Book Description
This book concisely presents a broad range of models and theories on social systems. Because of the huge spectrum of topics involving social systems, various issues related to Mathematics, Statistics, Teaching, Social Science, and Economics are discussed. In an effort to introduce the subject to a wider audience, this volume, part of the series “Studies in Systems, Decision and Control”, equally addresses the needs of mathematicians, statisticians, sociologists and philosophers. The studies examined here are divided into four parts. The first part, “Perusing the Minds Behind Scientific Discoveries”, traces the winding path of Syamal K. Sen and Ravi P. Agarwal’s scholarship throughout history, and most importantly, the thought processes that allowed each of them to master their subject. The second part covers “Theories in Social Systems” and the third discusses “Models in Social Systems”, while the fourth and final part is dedicated to “Mathematical Methods in the Social Sciences”. Given its breadth of coverage, the book will offer inquisitive readers a valuable point of departure for exploring these rich, vast, and ever-expanding fields of knowledge.

Author: Antonio Maturo
Publisher: Springer
ISBN: 3319405853
Category : Computers
Languages : en
Pages : 426

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Book Description
The papers collected in this volume focus on new perspectives on individuals, society, and science, specifically in the field of socio-economic systems. The book is the result of a scientific collaboration among experts from “Alexandru Ioan Cuza” University of Iaşi (Romania), “G. d’Annunzio” University of Chieti-Pescara (Italy), "University of Defence" of Brno (Czech Republic), and "Pablo de Olavide" University of Sevilla (Spain). The heterogeneity of the contributions presented in this volume reflects the variety and complexity of social phenomena. The book is divided in four Sections as follows. The first Section deals with recent trends in social decisions. Specifically, it aims to understand which are the driving forces of social decisions. The second Section focuses on the social and public sphere. Indeed, it is oriented on recent developments in social systems and control. Trends in quantitative theories and models are described in Section 3, where many new formal, mathematical-statistical tools for modelling complex social phenomena are presented. Finally, Section 4 shows integrative theories and models; particularly, it deals with the ethical, cultural and political approaches to social science, the pedagogical methods, and the relationship between literature, politics, religion and society. The book is addressed to sociologists, philosophers, mathematicians, statisticians, people interested in ethics, and specialists in the fields of communication, social, and political sciences.