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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: Bijan Davvaz
Publisher: World Scientific
ISBN: 9811249407
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
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: 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: Jie Meng
Publisher:
ISBN: 9788972821175
Category : Algebra
Languages : en
Pages : 294
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Book Description
Author: Javad Mashreghi
Publisher: American Mathematical Soc.
ISBN: 9780821848791
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Hilbert spaces of analytic functions are currently a very active field of complex analysis. The Hardy space is the most senior member of this family. However, other classes of analytic functions such as the classical Bergman space, the Dirichlet space, the de Branges-Rovnyak spaces, and various spaces of entire functions, have been extensively studied. This provides an account of the latest developments in the field of analytic function theory.
Author: Bijan Davvaz
Publisher: Springer
ISBN: 3319147625
Category : Technology & Engineering
Languages : en
Pages : 250
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Book Description
This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors’ past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduate and graduate students.
Author: Constantin Nastasescu
Publisher: Springer Science & Business Media
ISBN: 9783540207467
Category : Mathematics
Languages : ja
Pages : 324
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Book Description
The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-
Author: Bijan Davvaz
Publisher: Academic Press
ISBN: 0128099259
Category : Mathematics
Languages : en
Pages : 166
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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: C. Nastasescu
Publisher: Springer
ISBN: 3540384782
Category : Mathematics
Languages : en
Pages : 159
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Book Description
Anesthesia Student Survival Guide: A Case-Based Approach is an indispensable introduction to the specialty. This concise, easy-to-read, affordable handbook is ideal for medical students, nursing students, and others during the anesthesia rotation. Written in a structured prose format and supplemented with many diagrams, tables, and algorithms, this pocket-sized guide contains essential material covered on the USMLE II-III and other licensing exams. The editors, who are academic faculty at Harvard Medical School, summarize the essential content with 32 informative and compelling case studies designed to help students apply new concepts to real situations. Pharmacology, basic skills, common procedures and anesthesia subspecialties are covered, too, with just the right amount of detail for an introductory text. The unique book also offers a section containing career advice and insider tips on how to receive good evaluations from supervising physicians. With its combination of astute clinical instruction, basic science explanation, and practical tips from physicians that have been there before, this handbook is your one-stop guide to a successful anesthesia rotation.
Author: C. Nastasescu
Publisher: Elsevier
ISBN: 0080960162
Category : Mathematics
Languages : en
Pages : 352
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Book Description
This book is aimed to be a ‘technical’ book on graded rings. By ‘technical’ we mean that the book should supply a kit of tools of quite general applicability, enabling the reader to build up his own further study of non-commutative rings graded by an arbitrary group. The body of the book, Chapter A, contains: categorical properties of graded modules, localization of graded rings and modules, Jacobson radicals of graded rings, the structure thedry for simple objects in the graded sense, chain conditions, Krull dimension of graded modules, homogenization, homological dimension, primary decomposition, and more. One of the advantages of the generality of Chapter A is that it allows direct applications of these results to the theory of group rings, twisted and skew group rings and crossed products. With this in mind we have taken care to point out on several occasions how certain techniques may be specified to the case of strongly graded rings. We tried to write Chapter A in such a way that it becomes suitable for an advanced course in ring theory or general algebra, we strove to make it as selfcontained as possible and we included several problems and exercises. Other chapters may be viewed as an attempt to show how the general techniques of Chapter A can be applied in some particular cases, e.g. the case where the gradation is of type Z. In compiling the material for Chapters B and C we have been guided by our own research interests. Chapter 6 deals with commutative graded rings of type 2 and we focus on two main topics: artihmeticallygraded domains, and secondly, local conditions for Noetherian rings. In Chapter C we derive some structural results relating to the graded properties of the rings considered. The following classes of graded rings receive special attention: fully bounded Noetherian rings, birational extensions of commutative rings, rings satisfying polynomial identities, and Von Neumann regular rings. Here the basic idea is to derive results of ungraded nature from graded information. Some of these sections lead naturally to the study of sheaves over the projective spectrum Proj(R) of a positively graded ring, but we did not go into these topics here. We refer to [125] for a noncommutative treatment of projective geometry, i.e. the geometry of graded P.I. algebras.
Author: Madeleine Al-Tahan
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 15
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Book Description
Hyperstructure theory, an 86 years old theory, has been of great interest for many algebraists where their researches were divided in to two categories: theory and applications. On the other hand, neutrosophic theory which is the study of neutralities, was introduced and developed by F. Smarandache in 1995 as an extension of dialectics. The purpose of this paper is to study some connections between the two theories: Neutrosophy and hyperstructures. In this regard, we define neutrosophic quadruple Hv-rings, neutrosophic quadruple Hv-subrings, and neutrosophic quadruple homomorphism and study their various properties.
