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...Abstract. The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the apparently unscientific ideas in...

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...matics, NonMathematics, or even Anti-Mathematics: not in a nihilistic way, but in positive one. The truly innovative researchers will banish the old concepts in oder of check, by heuristic processes, some new ones: their opposites. Don't simply follow the crowd, and don't accept to be manipulated by any (political, economical, social, even scientific, or artistic, cultur...

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...n the Number Theory .82 -- Contributii la Studiul unor Functii §i Conjecturi in Teoria Numerelor .85 -- "The Function that You Bear its Name" .112 -- Smarandache Type Functions Obtained by Duality .113 -- Func!;ii Analitice .129 -- Funct;ii Prime §i Coprime .137 -- Asupra unor Conjecturi §i Probleme Nerezolvate Referitoare la 0 Funct;ie in Teoria l'\umerelor 138 -- K-Divis...

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...Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it ...

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...36, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexic... ... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup,... ...ity, Atlanta, GA 30302, USA Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy.... ...ta, GA 30302, USA Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy. Cover de... ...an be downloaded from this E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-95-0 HEXIS Pu... ... 5 Preface Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equation... ...a, bigroupoids, bisemigroups, etc. But most of these are abstract algebraic concepts except, the bisemigroup being used in the construction of biau... ... and Kama Kandasamy for formatting this book. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K. ILANTHENRAL 7 Chapter One BIMATRI... ...e reader to supply proofs for our main motivation is introduce several new concepts and the proofs which are left for the reader is more a matter o...

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...ly invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe some of its properties. These concepts are also extended neutrosophically in this book....

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...0036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mex... ...a e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallu... ..., Alaska, USA. Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K.Ilanthenral Layout by Kama Kandas... ...SA. Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K.Ilanthenral Layout by Kama Kandasamy. Cover... ...wnloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-98-5 Stand... ...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... ...rt Kosko, the father of Fuzzy Cognitive Maps. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K.ILANTHENRAL 7 Chapter One ...

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...gebraic 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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...6, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico... ...e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, ... ...sore, Karnataka, India. Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy. ... ...ataka, India. Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy. Cover des... ...andasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-97-7 ... ...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... ...ent in every manner made this book possible. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K. ILANTHENRAL 7 Chapter One I... ...e study of these properties in case of complex fields. Here we recall the concepts of linear functionals, adjoint, unitary operators and normal ope...

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This book contains a collection of Haiku poems compiled by Florentin Smarandache.

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...SILENCE'S BELL by Florentin Smarandache (non-standard haiku poems, translated from Romanian by Stefan B... ...fa of dreams. - Do not wait for me, I'll linger a little among the stars. Florentin Smarandache, a Poet with the Dot under the I ... ...ams. - Do not wait for me, I'll linger a little among the stars. Florentin Smarandache, a Poet with the Dot under the I ... ...or of these lines is confronted with two assertions. The first one: who is Florentin Smarandache? The second: the poet has no biography; his poetry is... ...e lines is confronted with two assertions. The first one: who is Florentin Smarandache? The second: the poet has no biography; his poetry is his biogr... ...book at the Romanian publishing houses. But this "happy regime" is not for Florentin Smarandache, who from 15 titles could see only two books publish... ...finitely led by Florentin Smarandache ­ they have, as an ideational basis, concepts and theses identical or close to those promoted by the modern lite... ...Popa reconfirms the possibility to enlarge the literature through negative concepts. "Paradoxism does not intend to destroy literature. It is interest... ...aning temporary / everlasting, ephemeral / eternal. They are contradictory concepts which must be present within the poem, balancing one part of the h...

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...allup 1-3 December 2001 (second printed edition) FLORENTIN SMARANDACHE editor PROCEEDINGS OF THE FIRST INTERNATIO... ... 1-3 December 2001 (second printed edition) FLORENTIN SMARANDACHE editor PROCEEDINGS OF THE FIRST INTERNATIONAL CONFE... ...co Contributed papers were sent, by November 30, 2001, to the organizer: Florentin Smarandache, University of New Mexico, 200 College Road, Ga... ...ntributed papers were sent, by November 30, 2001, to the organizer: Florentin Smarandache, University of New Mexico, 200 College Road, Gallup, NM 8... ...Neutrosophic Conference). E-mail: smarand@unm.edu, http://www.gallup.unm.edu/~smarandache/FirstNeutConf.htm. A selection of them is being published... ...ophic Logic, Neutrosophic Set, and Neutrosophic Probability and Statistics) Florentin Smarandache Department of Mathematics University of New Me... ... - interprets the uninterpretable; - regards, from many different angles, old concepts, systems: showing that an idea, which is true in a given ref... ...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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...N 1-879585-76-6 American Research Press Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEU... ...-76-6 American Research Press Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, ... ...script from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philo... ...m the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - re... ... and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dia... ...ables, odds, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement ... ...s, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement of the art... ...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...

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... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC... ... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATION... ...600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New M... ...dia e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gal... ...Mysore, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by... ...rnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kan... ... 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...

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...Thanks to Dr. Smarandache for his interest in Chinese culture. I cannot decline his warm request to write the preface, even with my fragments of knowledge – no insight nor wisdom, and therefore can be misleading. I have been extremely regr...

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...ownloaded from the following Digital Library: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm Peer Reviewers: Dr. M. Khoshn... ... Xi'an, Shaanxi, 710061, P. R. China 1. Introduction Thanks to Dr. Smarandache for his interest in Chinese culture. I cannot decline his warm ... ...c.). Is there a component of philosophism in neutrosophy? However, Dr. Smarandache is blending A with Non-A all the time For example, he blends Go... ...ntal structure. They invoke the re-recognition and restructuring of basic concepts in philosophy, logics, sets, cognitive science, information scien... ...trinsic structure of science and infrastructure implied in the scientific concepts and principles (the infrastructure inside infrastructures), and i... ... to be extended and opened to a general level. Quantum dynamics, semantic concepts, logic and knowledge are not exact in nature, but we are seeking ... ..., also by Octogon, Brasov, Romania, Vol. 10, No. 1, pp. 194-203. F. Liu, Florentin Smarandache: “Logic: a Misleading Concept － A Contradiction Study... ...ook series, Vol. 13), American Research Press 2002 (ISBN 1-931233-56-X). Florentin Smarandache, A Unifying Field in Logics: Neutrosophic Logic: Neut... ... in the Chinese Translation of Neutrosophics Liu Feng (bold sentences) Florentin Smarandache (regular sentences) Does Dr. Smarandache’s emigr...

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... Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Editors Prof. Florentin Smarandache smarand@unm.edu Dr. Larissa Borissova lborissova@yaho... ...tor Dmitri Rabounski rabounski@yahoo.com Associate Editors Prof. Florentin Smarandache smarand@unm.edu Dr. Larissa Borissova lborissova@yahoo.com Step... ...downloaded free from the E-library of Science: http://www.gallup.unm.edu/ smarandache ISSN: 1555-5534 (print) ISSN: 1555-5615 (online) Standard Addre... ...New Method to Measure the Speed of Gravitation. . . . . . . . . . . . 3 F. Smarandache Quantum Quasi-Paradoxes and Quantum Sorites Paradoxes. . . 7 F.... ... IN PHYSICS Volume 1 Quantum Quasi-Paradoxes and Quantum Sorites Paradoxes Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C... ... A New Form of Matter — Unmatter, Composed of Particles and Anti-Particles Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C... ... 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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... Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Editors Prof. Florentin Smarandache smarand@unm.edu Dr. Larissa Borissova lborissova@yaho... ...tor Dmitri Rabounski rabounski@yahoo.com Associate Editors Prof. Florentin Smarandache smarand@unm.edu Dr. Larissa Borissova lborissova@yahoo.com Step... ...downloaded free from the E-library of Science: http://www.gallup.unm.edu/ smarandache ISSN: 1555-5534 (print) ISSN: 1555-5615 (online) Standard Addre... ...s. . . . . . . . . . . . . . . . . . . . 92 D. Rabounski, L. Borissova, F. Smarandache Quantum Causality Threshold in the General Theory of Relativity... ... 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... ...d in the General Theory of Relativity Dmitri Rabounski, Larissa Borissova, Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C... ... Experiments, More Types of Unmatter, and a Quantum Chromodynamics Formula Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C...

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...ssays, drama. Collection and heard expressions of folklore. The books emphasize scientific and write it down on edge about possible generalization of concepts or theorems found that later I will guide you towards writing an article or a book....

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...ms. Further, this book gives lots of references so that the interested reader can make use of them. This book has two chapters. In Chapter One, basic concepts about fuzzy matrices are introduced. Basic notions of matrices are given in section one in order to make the book self contained. Section two gives the properties of fuzzy matrices. Since the data need to be transfor...

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...Preface 4 Dedication 6 Chapter One BASIC MATRIX THEORY AND FUZZY MATRIX THEORY 7 1.1 Basic Matrix Theory 7 1.2 Basic Concepts on Fuzzy Matrices 33 1.3 Basic Concepts on Graphs 47 Chapter Two DESCRIPTION OF SIMPLE FUZZY MODELS AND THEIR APPLICATIONS TO REAL WORLD PROBLEMS 71 2.1 Description of Simple Fuzzy Matrix Model 72 2.2 Definitio...

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...În perioada 24-25 aprilie 2010 s-a desfăşurat A Şasea Conferinţă Internaţională în Teoria Numerelor şi Noţiuni Smarandache la Universitatea Normală din Tianshui, China. Organizatorii conferinţei au fost prof. univ. dr. Zhang Wenpeng de la Universitatea Nordvest din Xi’an şi prof. univ. dr. Wangsheng He de la Universitatea Normală din ...

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...19 Chapter 3 - Knowledge about student’s personality .............20 The phases of intellectual under‐development......................20 The miss‐concepts of individual, person and personality..................21 The psychological miss‐concept of personality ......................22 Chapter 4 – Programs of study and characterization ............ 26 The main characte...

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...9 The ceremony of the oath non-deposition......................60 Country’s anti-defense ............................61 The sources of the party’s concepts disregarding the country’s anti-defense .........61 Component elements of the anti-defense systemless. .................62 The necessity of not knowing the country’s law in relation to its military. ..........63 K...

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...simple and an effective one as it can analyse the data by directed graphs and connection matrices. DEFINITION 1.2.1: An FCM is a directed graph with concepts like policies, events etc. as nodes and causalities as edges. It represents causal relationship between concepts. Example 1.2.1: In Tamil Nadu (a southern state in India) in the last decade several new engineering c...

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...Dedication 5 Preface 6 Chapter One BASIC CONCEPTS 1.1 Definition of Interval Matrices and Examples 8 1.2 Definition of Fuzzy Cognitive Maps 9 1.3 An Introduction to Neutrosophy 13 1.4 Some Basic Neutrosophic Structures 16 1.5 Some Basic Notions about Neutrosoph...

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...in the analysis of the problem of school dropout and their life after are described briefly in this chapter. We provide also the references for these concepts. Bart Kosko introduced the Fuzzy Cognitive Maps (FCMs) in the year 1986. Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mat...

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...Preface 5 Chapter One INTRODUCTION 7 Chapter Two BASIC CONCEPTS 21 Chapter Three CAUSES OF SCHOOL DROPOUTS – A MATHEMATICAL ANALYSIS 35 Chapter Four SCHOOL DROPOUTS AS CHILD LABOURERS 59 Chapter Five SCHOOL DROPOUTS AS RAG PICKERS USING FUZZY MODELS 79 Chapter Six PERFOR...

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...Dedication 5 Preface 7 Chapter One INTRODUCTION TO BASIC CONCEPTS 9 1.1 Introduction to Bilinear Algebras and their Generalizations 9 1.2 Introduction to Neutrosophic Algebraic Structures 11 Chapter Two NEUTROSOPHIC LINEAR ALGEBRA 15 2.1 Neutrosophic Bivector Spaces 15 2.2 S...

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...Preface 5 Chapter One INTRODUCTION TO SOME BASIC CONCEPTS 7 1.1 Properties of Rooted Trees 7 1.2 Basic Concepts 9 Chapter Two GROUPS AS GRAPHS 17 Chapter Three IDENTITY GRAPHS OF SOME ALGEBRAIC STRUCTURES 89 3.1 Identity Graphs of Semigroups 89 3.2 Special Identity ...

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...ill be helpful in working independently. Also work can be used for extra school work because the reader will find in it important formulas, theorems, concepts, and basic definitions which are not always included in school textbooks....

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...hic bigroup linear algebras, neutrosophic semigroup (bisemigroup) linear algebras and neutrosophic biset bivector spaces. The fuzzy analogue of these concepts are given in chapter six. An interesting feature of this book is it contains nearly 424 examples of these new notions. The final chapter suggests over 160 problems which is another interesting feature of this book....

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... neutrosophic group though has a group structure is not a neutrosophic group and a neutrosophic group cannot be a pseudo neutrosophic group. Both the concepts are different. Now we see a neutrosophic group can have substructures which are pseudo neutrosophic groups which is evident. ...

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...roups or neutrosophic biinterval semigroups. We derive results pertaining to them. The new notion of quasi bisubsemigroups and ideals are introduced. Smarandache interval neutrosophic bisemigroups are also introduced and analysed. Also notions like neutrosophic interval bigroups and their substructures are studied in section two of this chapter. Neutrosophic interval bigro...

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...Preface 5 Chapter One BASIC CONCEPTS 7 1.1 Neutrosophic Interval Bisemigroups 8 1.2 Neutrosophic Interval Bigroups 32 1.3 Neutrosophic Biinterval Groupoids 41 1.4 Neutrosophic Interval Biloops 57 Chapter Two NEUTROSOPHIC INTERVAL BIRINGS AND NEU...

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... WITH ILLUSTRATIONS 1.1 Fuzzy matrices and their applications 9 1.2 Definition and illustration of Fuzzy Relational Maps (FRMs) 16 1.3 Some basic concepts of BAM with illustration 20 1.3.1 Some basic concepts of BAM 22 1.3.2 Use of BAM Model to study the cause of vulnerability to HIV/AIDS and factors for migration 28 1.4 Introduction to Fuzzy Associative Memories (F...

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...poids and quasi loops. This new notion is well illustrated by 140 examples. These can find applications only in due course of time, when these new concepts become familiar. The final chapter suggests over 300 problems some of which are research problems....

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...THEOREM 2.1: Let G = {C(Zn), *, (t, u); t, u ∈ Zn} be a complex modulo integer groupoid. If H ⊆ G is such that H is a Smarandache modulo integer subgroupoid, then G is a Smarandache complex modulo integer groupoid. But every subgroupoid of G need not be a Smarandache complex modulo interger subgroupoid even if G is a Smarandache groupoid. ...

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...In this chapter we only indicate as reference of those the concepts we are using in this book. However the interested reader should refer them for a complete understanding of this book. In this book we define the notion of natural product in matrices so that we have a nice natural pr...

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...e form [a, b] where a b or a and b not comparable. In the final chapter we have defined the new notion of bimatrices and n-matrices. Using these new concepts we have constructed linear algebra of type I and linear algebra of type II. Using these matrices we can build n-eigen values and n-eigen vectors....

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two NON ASSOCIATIVE SEMILINEAR ALGEBRAS 13 Chapter Three NON ASSOCIATIVE LINEAR ALGEBRAS 83 Chapter Four GROUPOID VECTOR SPACES 111 Chapter Five APPLICATION OF NON ASSOCIATIVE VECTOR SPACES / LIN...

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...In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein’s four dimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), ...

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two ALGEBRAIC LINEAR CODES AND THEIR PROPERTIES 29 Chapter Three ERASURE DECODING OF MAXIMUM RANK DISTANCE CODES 49 3.1 Introduction 49 3.2 Maximum Rank Distance Codes 51 3.3 Erasure Decoding of MRD...

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES 13 Chapter Three APPLICATIONS OF n-LINEAR ALGEBRA OF TYPE I 81 Chapter Four SUGGESTED PROBLEMS 103 FURTHER READING 111 INDEX 116 ABOUT THE AUTHOR...

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... neutrosophic group though has a group structure is not a neutrosophic group and a neutrosophic group cannot be a pseudo neutrosophic group. Both the concepts are different. Now we see a neutrosophic group can have substructures which are pseudo neutrosophic groups which is evident from the following example....

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...; therefore he introduced new terms ‘contingency’ and ‘possibility’ into his modal logic [5]. And then American logician Lewis first formulated these concepts of logical modality. ...

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...Preface 6 Chapter One INTRODUCTION TO BASIC CONCEPTS 11 Chapter Two ANALYSIS OF THE COLLECTED DATA OF THE PWDS FROM MELMALAYANUR AND KURINJI PADI BLOCKS IN TAMIL NADU 13 Chapter Three THE NEW FUZZY COGNITIVE RELATIONAL MAPS (FCRMS) BIMODEL 29 Chapter Four ANALY...

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...onclusions derived on Vedic Mathematics and the Calculations of Guru Tirthaji - Secrets of Ancient Maths 61 Chapter Three INTRODUCTION TO BASIC CONCEPTS AND A NEW FUZZY MODEL 65 3.1 Introduction to FCM and the Working of this Model 65 3.2 Definition and Illustration of Fuzzy Relational Maps (FRMS) 72 3.3 Definition of the New Fuzzy Dynamical System 77 3.4 Neutros...

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...Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Ge...

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...This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly any n-dimensional space of refined labels...

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...gebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and study these concepts. As our analysis in this book is application of neutrosophic algebraic structure we found it deem fit to first introduce and study neutrosophic graphs and their applications to neutrosophic models....

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...36, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexic... ... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup,... ...re, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Mee... ...aka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kandasa... ...Kandasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-87-X ... ...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 ... ...standing of Periyar's ideology and approach. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 7 Chapter One Introduction to So... ...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 ...

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...origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mode of thinking are [90-94]: It proposes new philosophical theses, principles, laws, methods, formulas and movements; it reveals that the world is full ...

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...W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY COGNITIVE MAPS AND NEUTROSOPHIC COGNITIV... ...W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY COGNITIVE MAPS AND NEUTROSOPHIC COGNITIVE MAPS ... ...ology, Madras Chennai – 600036, India E-mail: vasantha@iitm.ac.in Florentin Smarandache Department of Mathematics University of New Mexico ... ...ras Chennai – 600036, India E-mail: vasantha@iitm.ac.in Florentin Smarandache Department of Mathematics University of New Mexico Gallup, N... ...h of the Neutrosophic Relational Map exhibiting the relations between the concepts of Women Empowerment and Community Mobilization and the HIV/AIDS ... ...ersity, Australia. Copyright 2003 by W. B. Vasantha Kandasamy, Florentin Smarandache, and Xiquan, 510 E. Townley Ave., Phoenix, AZ 85020,... ...stralia. Copyright 2003 by W. B. Vasantha Kandasamy, Florentin Smarandache, and Xiquan, 510 E. Townley Ave., Phoenix, AZ 85020, USA ... ...erica 3 CONTENTS Dedication 4 Preface 5 Chapter One BASIC CONCEPTS ABOUT FUZZY COGNITIVE MAPS AND FUZZY RELATIONAL MAPS 1.1 Defi... ... interprets the uninterpretable; regards, from many different angles, old concepts, systems and proves that an idea which is true in a given referen...

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...36, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mex... ... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallu... ...Sciences, Sofia, Bulgaria. Copyright 2005 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by ... ...ofia, Bulgaria. Copyright 2005 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kanda... ... can be downloaded from this E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-96-9 ... ...AM is the only fuzzy tool that can give the gradations of each of the nodes/ concepts. In Chapter 4 for the first time we use neutrosophic theory i... ...e world who are bravely battling the AIDS epidemic. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 7 Chapter One INTRODUCTION ... ...the cumulative or the over-all effect. The second method will interrelate two concepts, which 14 cannot be interrelated directly, but has an indir... ...ecause this model alone can give the gradations of each of the attributes or concepts relative to the other concepts. So we have chosen this model,...

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...a Kandasamy e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache e-mail: smarand@unm.edu K. Kandasamy e-... ...y e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache e-mail: smarand@unm.edu K. Kandasamy e-mail: dr.... ...Karnataka, India Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K. Kandasamy Cover Design and Lay... ...India Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K. Kandasamy Cover Design and Layout by Kama... ...wnloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-00-4 S... ...to working for the rights of the subjugated people. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K.KANDASAMY 26-11-2005 9 Chapter On... ...make the book a self contained one. In this chapter we just recall the basic concepts of the fuzzy tools and the neutrosophic tools used in this bo... ... the notion of Fuzzy Relational Maps (FRMs). In section four we introduce the concepts neutrosophy. Section five gives the definition of Neutrosophi... ... very high mathematics. DEFINITION 1.1.1: An FCM is a directed graph with concepts like policies, events etc. as nodes and causalities 10 as e...

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... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC... ... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATION... ...600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New M... ...dia e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gal... ...Mysore, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by... ...rnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kan... ... 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...

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...W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE ANALYSIS OF SOCIAL ASPECTS OF MIGRANT LABOURERS... ...W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE ANALYSIS OF SOCIAL ASPECTS OF MIGRANT LABOURERS LIVING W... ..., India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico ... ...-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, N... ...ad, Andhra Pradesh, India Copyright 2004 by W. B. Vasantha Kandasamy, Florentin Smarandache, and Xiquan, 510 E. Townley Ave., Phoenix, AZ 85020 ... ... Pradesh, India Copyright 2004 by W. B. Vasantha Kandasamy, Florentin Smarandache, and Xiquan, 510 E. Townley Ave., Phoenix, AZ 85020 USA L... ... 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...