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Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 248 pages
File Size : 49,9 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9781599732268
Author : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache
Publisher : Infinite Study
Page : 209 pages
File Size : 43,5 Mb
Release : 2015
Category : Algebras, Linear
ISBN : 9781599733685
In this book authors for the first time construct non-associative algebraic structures on the MOD planes. Using MOD planes we can construct infinite number of groupoids for a fixed m and all these MOD groupoids are of infinite cardinality. Special identities satisfied by these MOD groupoids build using the six types of MOD planes are studied. Further, the new concept of special pseudo zero of these groupoids are defined, described and developed. Also conditions for these MOD groupoids to have special elements like idempotent, special pseudo zero divisors and special pseudo nilpotent are obtained. Further non-associative MOD rings are constructed using MOD groupoids and commutative rings with unit. That is the MOD groupoid rings gives infinitely many non-associative ring. These rings are analysed for substructures and special elements. This study is new and innovative and several open problems are suggested.
Author : W. B. Vasantha Kandasamy,Florentin Smarandache,Moon Kumar Chetry
Publisher : Infinite Study
Page : 242 pages
File Size : 40,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9781599731254
This book defines new classes of groupoids, like matrix groupoid, polynomial groupoid, interval groupoid, and polynomial groupoid.An interesting feature of this book is that introduces 77 new definitions substantiated and described by 426 examples and 150 theorems.
Author : Madad Khan, Florentin Smarandache, Saima Anis
Publisher : Infinite Study
Page : 210 pages
File Size : 46,8 Mb
Release : 2015-04-01
Category : Electronic
ISBN : 9781599733470
We extend now for the first time the AG-groupoid to the Neutrosophic AG-groupoid. A neutrosophic AG-groupoid is a neutrosophic algebraic structure that lies between a neutrosophic groupoid and a neutrosophic commutative semigroup.
Author : W. B. Vasantha Kandasamy
Publisher : Unknown
Page : 242 pages
File Size : 41,6 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1461913675
Author : Florentin Smarandache
Publisher : Infinite Study
Page : 232 pages
File Size : 50,9 Mb
Release : 2016-11-12
Category : Mathematics
ISBN : 9781599734682
This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.
Author : W.B. Vasantha Kandansamy, Florentin Smarandache
Publisher : Infinite Study
Page : 210 pages
File Size : 54,5 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9781599731407
Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 50,9 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9781599732732
Study of algebraic structures built using [0, n) looks to be one of interesting and innovative research. Here we define two types of groupoids using [0, n), both of them are of infinite order. It is an open conjecture to find whether this new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity and so on.
Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
Page : 151 pages
File Size : 50,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9781599732220
Author : Volodymyr Nekrashevych
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 40,9 Mb
Release : 2015-08-21
Category : Duality theory (Mathematics)
ISBN : 9781470415440
The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc. The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid G there is a naturally defined dual groupoid G⊤ acting on the Gromov boundary of a Cayley graph of G. The groupoid G⊤ is also hyperbolic and such that (G⊤)⊤ is equivalent to G. Several classes of examples of hyperbolic groupoids and their applications are discussed.
Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
Page : 157 pages
File Size : 46,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9781599730332
In this book the new notion of interval semirings are introduced. New structures like interval groups are used to construct interval group semirings. Further non-associative interval semirings are constructed using loops and groupoids. We have given 284 examples, 118 problems are proposed ¿ some of them at the research level.The main keywords are interval semirings, interval groups, interval matrix semirings, interval groupoid semirings, neutrosophic interval semirings, and loop interval semirings.
Author : Madad Khan, Florentin Smarandache, Tariq Aziz
Publisher : Infinite Study
Page : 112 pages
File Size : 53,8 Mb
Release : 2015-05-01
Category : Fuzzy sets
ISBN : 9781599733401
Author : Mumtaz Ali,Florentin Smarandache, Muhammad Shabir
Publisher : Infinite Study
Page : 20 pages
File Size : 52,9 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 8210379456XXX
Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic groupoid and their generalization with the discuissionf of some of their characteristics
Author : Alan Paterson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217749
In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.
Author : Ruy Exel,David R. Pitts
Publisher : Springer Nature
Page : 161 pages
File Size : 46,6 Mb
Release : 2022-10-18
Category : Mathematics
ISBN : 9783031055133
This book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces. Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the Kumjian–Renault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the Kumjian–Renault theory to a much broader class of C*-algebras. This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.
