Non Associative Algebraic Structures Using Finite Complex Numbers
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Non Associative Algebraic Structures Using Finite Complex Numbers
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Author : W.B. Vasantha Kandasamy, Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2012
Non Associative Algebraic Structures Using Finite Complex Numbers written by W.B. Vasantha Kandasamy, Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Exploring The Extension Of Natural Operations On Intervals Matrices And Complex Numbers
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Author : W. B. Vasantha Kandasamy, Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2012
Exploring The Extension Of Natural Operations On Intervals Matrices And Complex Numbers written by W. B. Vasantha Kandasamy, Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Algebra categories.
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
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date :
Smarandache Special Elements In Multiset Semigroups written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
The Encyclopedia Of Neutrosophic Researchers 1st Volume
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2016-11-12
The Encyclopedia Of Neutrosophic Researchers 1st Volume written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-12 with Mathematics categories.
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.
Non Associative Algebra And Its Applications
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Author : Lev Sabinin
language : en
Publisher: CRC Press
Release Date : 2006-01-13
Non Associative Algebra And Its Applications written by Lev Sabinin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-13 with Mathematics categories.
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. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.
Algebra Ii
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Author : A.I. Kostrikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebra Ii written by A.I. Kostrikin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra • Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le.
Leibniz Algebras
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Author : Shavkat Ayupov
language : en
Publisher: CRC Press
Release Date : 2019-11-11
Leibniz Algebras written by Shavkat Ayupov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
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
Numerical And Symbolic Computation
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Author : Maria Amélia Ramos Loja
language : en
Publisher: MDPI
Release Date : 2020-12-29
Numerical And Symbolic Computation written by Maria Amélia Ramos Loja and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-29 with Technology & Engineering categories.
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.
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences
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Author : Ivor Grattan-Guiness
language : en
Publisher: Routledge
Release Date : 2004-11-11
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences written by Ivor Grattan-Guiness and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-11 with History categories.
First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
A Century Of Advancing Mathematics
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Author : Paul Zorn
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-08-23
A Century Of Advancing Mathematics written by Paul Zorn and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-23 with Mathematics categories.
The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott. This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.