Non Associative Algebraic Structures Using Finite Complex Numbers

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Non Associative Algebraic Structures Using Finite Complex Numbers

Author : W.B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 159973169X
Total Pages : 215 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Non Associative Algebraic Structures Using Finite Complex Numbers by : W.B. Vasantha Kandasamy, Florentin Smarandache

Download or read book Non Associative Algebraic Structures Using Finite Complex Numbers written by W.B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors have used the concept of finite complex modulo integers to construct non associative algebraic structures like groupoids, loops and quasi-loops.Using these structures we built non associative complex matrix groupoids and complex polynomial groupoids.The authors suggest over 300 problems and some are at the research level.

Complex Numbers

Author : Wilfred Halliday Cockcroft
Publisher :
ISBN 13 :
Total Pages : 198 pages
Book Rating : 4.:/5 (4 download)

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Book Synopsis Complex Numbers by : Wilfred Halliday Cockcroft

Download or read book Complex Numbers written by Wilfred Halliday Cockcroft and published by . This book was released on 1972 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Associative Algebraic Structures on MOD Planes

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599733684
Total Pages : 212 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Non-Associative Algebraic Structures on MOD Planes by : W. B. Vasantha Kandasamy

Download or read book Non-Associative Algebraic Structures on MOD Planes written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2015 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Encyclopedia of Neutrosophic Researchers, 1st volume

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599734680
Total Pages : 232 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis The Encyclopedia of Neutrosophic Researchers, 1st volume by : Florentin Smarandache

Download or read book The Encyclopedia of Neutrosophic Researchers, 1st volume written by Florentin Smarandache and published by Infinite Study. This book was released on 2016-11-12 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599731797
Total Pages : 152 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers by : W. B. Vasantha Kandasamy, Florentin Smarandache

Download or read book Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we explore the possibility of extending the natural operations on reals to intervals and matrices. The extension to intervals makes us define a natural class of intervals in which we accept [a, b], a greater than b. Further, we introduce a complex modulo integer in Z_n (n, a positive integer) and denote it by iF with iF^2 = n-1.

Smarandache Special Elements in Multiset Semigroups

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599735644
Total Pages : 244 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Smarandache Special Elements in Multiset Semigroups by : W. B. Vasantha Kandasamy

Download or read book Smarandache Special Elements in Multiset Semigroups written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authors in this book study the notion of Smarandache element in multiset semigroups. It is important to keep on record that we define four operations on multisets viz. +, X, union and intersection in a free way. Thus all sets finite or infinite order contribute to infinite order multisets and the semigroup under any of these operations is of infinite order.

Non Associative Linear Algebras

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599731762
Total Pages : 233 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Non Associative Linear Algebras by : W. B. Vasantha Kandasamy, Florentin Smarandache

Download or read book Non Associative Linear Algebras written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical and Symbolic Computation

Author : Maria Amélia Ramos Loja
Publisher : MDPI
ISBN 13 : 3039363026
Total Pages : 140 pages
Book Rating : 4.0/5 (393 download)

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Book Synopsis Numerical and Symbolic Computation by : Maria Amélia Ramos Loja

Download or read book Numerical and Symbolic Computation written by Maria Amélia Ramos Loja and published by MDPI. This book was released on 2020-06-22 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive set of articles reflecting on the application of symbolic and/or numerical computation in a range of scientific areas within the fields of engineering and science. These articles constitute extended versions of communications presented at the 4th International Conference on Numerical and Symbolic Computation—SYMCOMP 2019—that took place in Porto, Portugal, from 11 to 12 April 2019 The different chapters present diverse perspectives on the existing effective connections between mathematical methods and procedures and other knowledge areas. The intrinsic multidisciplinary character is visible throughout the whole book as a result of the applicability of the scope and the applications considered. The reader will find this book to be a useful resource for identifying problems of interest in different engineering and science areas, and in the development of mathematical models and procedures used in the context of prediction or verification computational tools as well as in the aided-learning/teaching context. This book is a must-read for anyone interested in the recent developments and applications of symbolic and numerical computation for a number of multidisciplinary engineering and science problems.

Associative and Non-Associative Algebras and Applications

Author : Mercedes Siles Molina
Publisher : Springer Nature
ISBN 13 : 3030352560
Total Pages : 338 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Associative and Non-Associative Algebras and Applications by : Mercedes Siles Molina

Download or read book Associative and Non-Associative Algebras and Applications written by Mercedes Siles Molina and published by Springer Nature. This book was released on 2020-01-02 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.

Non-Associative Algebra and Its Applications

Author : Lev Sabinin
Publisher : CRC Press
ISBN 13 : 1420003453
Total Pages : 553 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Non-Associative Algebra and Its Applications by : Lev Sabinin

Download or read book Non-Associative Algebra and Its Applications written by Lev Sabinin and published by CRC Press. This book was released on 2006-01-13 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.

Non-Associative Algebra and Its Applications

Author : Santos González
Publisher : Springer Science & Business Media
ISBN 13 : 9401109907
Total Pages : 429 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Non-Associative Algebra and Its Applications by : Santos González

Download or read book Non-Associative Algebra and Its Applications written by Santos González and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12--17, 1993. The conference brought together specialists from all over the world who work in this interesting and active field, which is currently enjoying much attention. All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection will point the way for further research for many years to come. The volume is of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics.

The Realm of Sedenions

Author : David R Ely
Publisher : David R Ely
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4./5 ( download)

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Book Synopsis The Realm of Sedenions by : David R Ely

Download or read book The Realm of Sedenions written by David R Ely and published by David R Ely. This book was released on 2024-05-22 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Realm of Sedenions: A Look Into Higher-Complex Numbers" dives into the fascinating world of sedenions, a 16-dimensional number system with unique properties. The book explores the motivation behind studying sedenions, their formal definition with addition and non-commutative, non-associative multiplication, and how they differ from familiar number systems like real and complex numbers. While sedenions lack widespread practical applications yet, the book delves into potential areas of exploration in physics and computer science. It also highlights the challenges mathematicians face due to the complex multiplication rules and the lack of a straightforward geometric interpretation for these high-dimensional numbers. The book provides historical context by mentioning James Joseph Sylvester, who introduced sedenions. While directly visualizing 16 dimensions is difficult, the book discusses potential approaches like subspace projections and geometric analogies to gain a better understanding. Exercises tailored to the audience's level and a resource section for further exploration round out the book, making it a valuable resource for anyone curious about venturing beyond the realm of familiar numbers.

Leibniz Algebras

Author : Shavkat Ayupov
Publisher : CRC Press
ISBN 13 : 1000740404
Total Pages : 157 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Leibniz Algebras by : Shavkat Ayupov

Download or read book Leibniz Algebras written by Shavkat Ayupov and published by CRC Press. This book was released on 2019-11-11 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory. Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well. Features: Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts

Non-associative Structures and Other Related Structures

Author : Florin Felix Nichita
Publisher : MDPI
ISBN 13 : 3039362542
Total Pages : 106 pages
Book Rating : 4.0/5 (393 download)

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Book Synopsis Non-associative Structures and Other Related Structures by : Florin Felix Nichita

Download or read book Non-associative Structures and Other Related Structures written by Florin Felix Nichita and published by MDPI. This book was released on 2020-06-16 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler (1707–1783) was born in Basel, Switzerland. Euler's formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. When its variable is the number pi, Euler's formula evaluates to Euler's identity. On the other hand, the Yang–Baxter equation is considered the most beautiful equation by many scholars. In this book, we study connections between Euler’s formulas and the Yang–Baxter equation. Other interesting sections include: non-associative algebras with metagroup relations; branching functions for admissible representations of affine Lie Algebras; super-Virasoro algebras; dual numbers; UJLA structures; etc.

On The Role Of Division, Jordan And Related Algebras In Particle Physics

Author : Feza Gursey
Publisher : World Scientific
ISBN 13 : 981449822X
Total Pages : 483 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis On The Role Of Division, Jordan And Related Algebras In Particle Physics by : Feza Gursey

Download or read book On The Role Of Division, Jordan And Related Algebras In Particle Physics written by Feza Gursey and published by World Scientific. This book was released on 1996-11-22 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics, particularly in particle physics. It concerns the interplay between division algebras, specifically quaternions and octonions, between Jordan and related algebras on the one hand, and unified theories of the basic interactions on the other. Selected applications of these algebraic structures are discussed: quaternion analyticity of Yang-Mills instantons, octonionic aspects of exceptional broken gauge, supergravity theories, division algebras in anyonic phenomena and in theories of extended objects in critical dimensions. The topics presented deal primarily with original contributions by the authors.

Algebraic Structure from Basic to Advanced Concepts

Author : Dr.Manish Kumar
Publisher : SK Research Group of Companies
ISBN 13 : 811998093X
Total Pages : 108 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Algebraic Structure from Basic to Advanced Concepts by : Dr.Manish Kumar

Download or read book Algebraic Structure from Basic to Advanced Concepts written by Dr.Manish Kumar and published by SK Research Group of Companies. This book was released on 2024-03-04 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr.Manish Kumar, Officer, Ministry of Science & Technology, Department of Science & Technology, New Delhi, India.

Encyclopaedia of Mathematics (set)

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9781556080104
Total Pages : 982 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Encyclopaedia of Mathematics (set) by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics (set) written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1994-02-28 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.