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...ry has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised...

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...ute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Departmen... ... HEXIS Church Rock 2004 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Inf... ... ISBN: 1-931233-87-X Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS P r e f a c e ... ...d neutrosophic matrices. So we for the first time introduce and study these concepts. As our analysis in this book is application of neutrosophic al... ...is devoted for this purpose. Chapter Three introduces many new neutrosophic concepts in graphs and applies it to the case of neutrosophic cognitive ... ...at is when we are not in a position to associate a relation between any two concepts then we denote it as an indeterminacy or when a concept cannot ... ... by psychologists L. Festinger and D. Cartwright. The world of Theoretical physics discovered graph theory for its own purposes more than once. In ... ...wo points are adjacent whenever both spaces are occupied. Another aspect of physics employs graph theory rather as pictorial device. Feynmann propos...

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...e prezentate chiar la congrese si conferinse nasionale cat si internasionale [vezi "Lista publicasiilor autorului pe tema tezei"). Ea se structureazs in patru capitole: - in primele trei capi tole se introduc noi funsii in teoria numerelor, se studiazs proprietssile lor, probleme nerezol vate legate de ele, implicasii in lumea stiinsific! internasional! (ce alsi matematici...

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...stitute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Depar... ... HEXIS Church Rock 2004 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest... ... ISBN: 1-931233-86-1 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS D e d i c a t i o... ... P r e f a c e 7 Chapter One FUZZY RELATIONAL EQUATIONS: BASIC CONCEPTS AND PROPERTIES 1.1 Fuzzy Relational Equations and their ... ...ts 230 5 3.3 On neutrosophic lattices 235 3.4 Neutrosophic notions: Basic concepts 239 3.5 Neutrosophic matrices and fuzzy neutrosophic mat... ...borers etc. Chapter three for the first time defines several new neutrosophic concepts starting from the notion of neutrosophic fuzzy set, neutros... ...terminacy, and falsity may overlap, and n_sup = 30+51+28 > 100 in this case. Physics Examples a) For example the Schrodinger’s Theory says that ... ...one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosophic set. After...

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...Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduc...

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...itute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Departm... ...@gmail.com HEXIS Phoenix, Arizona 2005 2 This book can be ordered in a paper bound reprint from: Books on Deman... ...s.htm ISBN: 1931233-98-5 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ...rica 3 CONTENTS Preface 5 Chapter One BASIC CONCEPTS ON BIMATRICES 1.1 Definition and Basic Operation on Bimatr... ... bigraphs, trigraphs and n-graphs and describe some of its properties. These concepts are also extended neutrosophically in this book. Using th... ...his book is organized into four chapters. The first chapter recalls the basic concepts of bimatrices and neutrosophic bimatrices. Second chapter int... ...roughout this book will be denoted by dotted lines. The world of theoretical physics discovered graph theory for its own purposes. In the study of ... ...n USA. He published over 75 books and 100 articles and notes in mathematics, physics, philosophy, psychology, literature, rebus. In mathematics hi... ...nd imprecise probability). Also, small contributions to nuclear and particle physics, information fusion, neutrosophy (a generalization of dialecti...

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...A complete understanding of what something is must include an understanding of what it is not. In his paper, “Paradoxist Mathematics” [19], Florentin Smarandache proposed a number of ways in which we could explore “new math concepts and theories, especially if they run counter to the classical ones.” In a manner consis...

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...is a representation of an s-manifold illustrating some of the behavior of lines in an s-manifold. This book has been peer reviewed and recommen... ...erine D’Ortona, Mansfield University of Pennsylvania This book can be ordered in microfilm format from: Books on Demand ProQuest Information & ... ...nfo/fabz54. ISBN: 1-931233-44-6 Standard Address Number: 297-5092 Printed in the United States of America 3 Table of Contents Introducti... ...entin Smarandache proposed a number of ways in which we could explore “new math concepts and theories, especially if they run counter to the classic... ...e the axioms of Hilbert in an s-manifold context. These cover most of the basic concepts of 2-dimensional geometry, and of course, all of the theorem... ... the discussions that generated the basic idea of an s-manifold and many of the concepts explored in this book. These include mikeantholy (Mike Anth... ... collection of all s-segments with endpoints A and B. The “q” refers to quantum physics, which inspires this definition, although fuzzy logic would b...

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...equalities for the remarkable elements of triangles or tetrahedrons. Other themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2 includes various diophantine equations, some of which are treatable by elementary methods; others are partial solutions of certain unsolved problems. An important method is based on the famous Euler-Bel...

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... American Research Press Rehoboth 2002 This book can be ordered in microfilm format from: Books on Demand ... ... ISBN: 1-931233-51-9 Standard Address Number 297-5092 Printed in the United States of America "...It is just this, which gives the hi... ...themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2 includes various diophantine equations, some of whic... ...nd important particular case a = b = c = 1 (with applications in geometry, physics, nomo- grams, etc.). We shall use the Euler-Bell-Kalm ar lemma. Al... ...uation is very important, since occurs in geometry, number-theory, optics, physics, etc. For three distinct solutions, see [1]. Let now,n 3. Let us n... ... 1. K. Alladi, On generalized Euler functions and related totients, in New Concepts in Arithmetic Functions, Mat. Sc. Report, no.83, Madras 1975. 2. S...

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...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a b...

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...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Math... ...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics PROGRESSINPHYSICS A quar... ...h the Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathS... .../ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Edito... ... Mexico, 200 College Road, Gallup, NM 87301, USA Copyright c Progress in Physics, 2005 All rights reserved. Any part of Progress in Physics howsoeve... ...ate citation of this journal. Authors of articles published in Progress in Physics retain their rights to use their own articles in any other publicat... ... by the building of new tools that implement Einstein’s general relativity concepts in the new context (in particular, covariant derivative and geodes... ..., and subsequently by Hermann Weyl [4] by a different method. The orthodox concepts of gravitational collapse and the black hole owe their existence t... ...h the source. Time stops at the Schwarzschild point-mass. The conventional concepts of the Schwarzschild sphere and its interior are meaningless. Doug...

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...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a b...

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...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Math... ...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics PROGRESSINPHYSICS A quar... ...h the Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathS... .../ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Edito... ... Mexico, 200 College Road, Gallup, NM 87301, USA Copyright c Progress in Physics, 2005 All rights reserved. Any part of Progress in Physics howsoeve... ...ate citation of this journal. Authors of articles published in Progress in Physics retain their rights to use their own articles in any other publicat... ... the measured time fow [49, 50, 51, 52]. † According to today’s mainstream concepts, the gravitational radiusr g of an object is that minimal distance... ...explanation of the mechanism(s) of the assumed interactions but resorts to concepts such as forces acting across an intervening void (“action-at-a- di...

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...This work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. It reviews some of the classical notions of Benthamite utility and the normative utility paradigm offered by the von Neumann-Morgenstern expected utility the...

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... HEXIS Phoenix 2005 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Informat... ... ISBN: 1-931233-85-3 Standard Address Number: 297-5092 Printed in the United States of America 3 Acknowledgements The author gr... ... from his supervisor Dr. Kuldeep Kumar, Associate Professor of Statistics in the School of Information Technology, Bond University. Dr. Kumar has i... ... 5 I. Summary This work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. It rev... ...th in the presence as well as absence of downside risk and postulates the concepts of resolvable and irresolvable risk. A formal theorem of consiste... ...amics in so far as that both neoclassical economics and classical thermal physics seek to model natural systems in terms of solutions to constrained... ...ences do show that thermodynamic entropy and economic utility are related concepts sharing the same formal framework. Utility is said to arise from ... ...Entropy and Bayesian Methods in Inverse Problems: Fundamental Theories of Physics, D. Reidel Publishing Company, Holland, 1985. Hull, J. C. Optio...

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...ich is also a very powerful algebraic tool that can yield itself to applications. With the recent introduction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialgebra and also give the applications of these algebraic structures....

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...In this section we give the definition of linear algebra and just state the few important theorems like Cayley Hamilton theorem, Cyclic Decomposition Theorem, Generalized Cayley Hamilton Theorem and give some properties about...

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...te of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department... ... HEXIS Phoenix, Arizona 2005 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Info... ... ISBN: 1931233-97-7 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ...TRODUCTORY COCEPTS OF BASIC BISTRUCTURES AND S-BISTRUCTURES 2.1 Basic concepts of bigroups and bivector spaces 37 2.2 Introduction of S-bigr... ...uction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialg... ...e study of these properties in case of complex fields. Here we recall the concepts of linear functionals, adjoint, unitary operators and normal ope... ...hich we will be defining as neutrosophic graphs. The world of theoretical physics discovered graph theory for its own purposes. In the study of sta...

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...otality, limited view on a system because of its complexity) or the acquisition errors (intrinsically imperfect observations, the quantitative errors in measures).”...

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... (second printed edition) 2002 This book can be ordered in microfilm format from: Books on Demand ProQuest Informati... ... ISBN: 1-931233-67-5 Standard Address Number: 297-5092 Printed in the United States of America First International Confe... ...unm.edu/~smarandache/FirstNeutConf.htm. A selection of them is being published in these Proceedings of the Conference. Abstracts of papers were... ...t=time, s=space, etc., that's why the neutrosophic logic can be used in quantum physics. The Dynamic Neutrosophic Calculus can be used in psychology... ... - interprets the uninterpretable; - regards, from many different angles, old concepts, systems: showing that an idea, which is true in a given ref... ...acy, and falsity may overlap, and n_sup = 30+51+28 > 100 in this case. 3.3 Physics Examples: a) For example the Schrodinger’s Cat Theory says t... ...c and Their Applications in Neural Networks, Computer Programming, and Quantum Physics, Institute of Physics, editors: Kenneth Holmlund, Mikko Kartt... ...ikulich Eds, Vol. 9, pp. 149 194, 1979. Dynamic Fuzzy Sets and Neutrosophic Concepts Andrzej Buller ATR Human Information Science Laboratories... ... - interprets the uninterpretable; - regards, from many different angles, old concepts, systems: showing that an idea, which is true in a given ref...

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...It was known to me his setting up in 1980’s of a new literary and artistic avant-garde movement that he called “paradoxism”, because I received some books and papers dealing with it in order to review them for the German journal “Zentralblatt fár Mathematik”....

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...Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive used of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations....

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...FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC... ...ress Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC... ... a new branch of philosophy: 13 2. Neutrosophic Logic - a unifying field in logics: 87 3. Neutrosophic Set - a unifying field in sets: 112 4. Neut... ... and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dia... ..., s=space, etc., that's why the neutrosophic logic can be used in quantum physics. The Dynamic Neutrosophic Calculus can be used in psychology. N... ...nterprets the uninterpretable; - regards, from many different angles, old concepts, systems: showing that an idea, which is true in a given referent... ...ill be classified as neutrality. K) Delimitation from Other Philosophical Concepts and Theories: 1. Neutrosophy is based not only on analysis of opp... ...ee negativity. Not com-plementarity (used by Bohr and Heisenberg in physics philosophy), but tri­ plementarity (negativity, positivity, and neu... ... expression displayed on the page... A poem is a philosophical system. A physics law, a chemical formula, a mathematical equation too. For example...

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...In this book for the first time we have ventured into the total analysis of migrant labourers in rural Tamil Nadu who are victims of HIV/AIDS using FCM, BAM and Neutrosophic Cognitive Maps. As in our study and analysis we fel...

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...Migration acquires great significance in the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has enormous impact on livelihood, life-styles, employment, socioeconomic and pol...

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...EUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India XIQUAN Phoenix 2004 ANALYSIS OF SOCIAL ASPECTS OF M... ...NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India W. B. Vasantha Kandasamy Department of Mathematics Indian Ins... ...e of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department ... ... Factors For Migration and Vulnerability To HIV/AIDS 3.1 Some basic concepts of BAM 98 3.2 Use of BAM model to study the cause of vulnerab... ...heterosexual men and has sought to downplay and distinguish/segregate the concepts of masculinity and risk- taking (that includes multiple sex partne... ...ulation, Crime, Economic condition, Poverty and Unemployment as nodes or concepts. Here the simple trivalent directed graph is given by the foll... ...ich we will be defining as neutrosophic graphs. The world of theoretical physics discovered graph theory for its own purposes. In the study of stat... ...o, B., “Differential Hebbian Learning,” Proceedings American Institute of Physics: Neural Networks for Computing, 277-282 (1986). 56. Kosko, B., “F...

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...This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it ...

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...ion to Multi- Valued Algebra 2.1 Introduction to trivalent logic and plurivalent logic We all have heard of typical binary logic, Yes or No. Or in a famous phrase by Shakespeare: “To be or not to be.” In the same way all computer hardwares from early sixties up to this year are built upon the same binary logic. It is known that the Classical Logic, also called Bi...

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... Non-Standard Logic 93 Appendix 3: List of some known paradoxes 95 Appendix 4: A few basic notations 103 Appendix 5: A few historical achievements in foundation of set theory 105...

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...Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

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...x1. Introduction The study of Smarandache loops was initiated by W.B. Vasantha Kandasamy in 2002. In her book [19], she defined a Smarandache loop (S-loop) as a loop with at least a subloop which forms a subgroup under the binary operation of the loop. For more on loops and their properties, readers should check ...

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...T. Jayeo. la : An holomorphic study of the Smarandache concept in loops 1 Z. Xu : Some arithmetical properties of primitive numbers of power p 9 A. Muktibodh : Smarandache Quasigroups 13 M. Le : Two Classes of Smarandache Determinants 20 Y. Shao, X. Zhao and X. Pan : On a Subvariety ...