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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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...phic dynamic system. A neutrosophic system is a quasi- or (t,i,f)–classical system, in the sense that the neutrosophic system deals with quasi-terms/concepts/attributes, etc. [or (t,i,f)-terms/concepts/attributes], which are approximations of the classical terms/concepts/attributes, i.e. they are partially true/membership/probable (t%), partially indeterminate (i%), and p...

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...The author introduces for the first time the concept of plithogeny in philosophy and, as a derivative, the concepts of plithogenic set / logic / probability / statistics in mathematics and engineering – and the degrees of contradiction (dissimilarity) between the attributes’ values that contribute to a more accurate construction o...

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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...