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Florentin Smarandache, a lliathematician from Eastern Europe, escaped fran his country because the communist authorities had prohibited the publication of his resea~ch papers and his participation in international congresses. After two years of waiting in a political ~efugee camp in Turkey, he emigrated to the united states. As research workers, receiving our co-worker, we decided to publish a selection of his papers....

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In this paper we defme a function L with will allowus to generalize (separately or simultaneously) some theorems from Numbers Theory obtained by Wilson, Fermat, Euler, Gauss, Lagrange, Leibnitz, Moser, Sierpinski. (Some papers not included in the volume were confiscated by the Secret Police in September 1988, when the author left Romania. He spent 19 months in a Turkish political refugee camp, and emigrated to the United Stales in March 1990. Despite efforts by his fric; is, the papers were not rcncvcred ...)...

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K.R.Narayanan was a lauded hero and a distinguished victim of his Dalit background. Even in an international platform when he was on an official visit to Paris, the media headlines blazed, ‘An Untouchable at Elysee’. He was visibly upset and it proved that a Dalit who rose up to such heights was never spared from the pangs of outcaste-ness and untouchability, which is based on birth. Thus, if the erstwhile first citizen of India faces such humiliation, what will be the plight of the last man who is a Dalit? As one of the world’s largest socio-economically oppressed, culturally subjugated and politically marginalized group of people, the 138 million Dalits in India suffer not only from the excesses of the traditional oppressor castes, but also from State Oppression— which includes, but is not limited to, authoritarianism, police brutality, economic embargo, criminalization of activists, electoral violence, repressive laws that aim to curb fundamental rights, and the non-implementation of laws that safeguard Dalit rights. The Dalits were considered untouchable for thousands of years by the Hindu society until the Constitution of India...

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In this book authors study and analyze the problem of school dropouts and their life after. The problems can by no means be analyzed by collecting the numerical data. For such data can only serve as information beyond that the data can be of no use, for the school dropouts suffer an environment change after becoming a school dropout. Thus the emotions of the school dropout; is technically involved....

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The basic tools used 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 mathematical tool for modeling complex systems. FCM was a fuzzy extension of the cognitive map pioneered in 1976 by political scientist Robert Axelord, who used it to represent knowledge as an interconnected, directed, bilevel-logic graph....

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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 PERFORMANCE ASPECTS OF SCHOOL STUDENTS USING RULE BASED CONTROL SYSTEM 89 Chapter Seven MIGRATION OF PARENTS AND THE SCHOOL DROPOUTS A STUDY USING THE FUZZY RELATIONAL MAPS MODEL 99 Chapter Eight THE IMPACT OF MISSIONARY INTERVENTIONS ON THE EDUCATION AND REHABILITATION OF DEPRIVED CHILDREN – A FUZZY ANALYSIS 117 Chapter Nine CONCLUSIONS AND SUGGESTIONS 129 FURTHER READING 139 INDEX 143 ABOUT THE AUTHORS 145...

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Over the years many researchers have analyzed the political aspects of the air war in Southeast Asia. Their studies range from the original Pentagon Papers to those published more recently. Very little, however, focuses on the economic and operational aspects of the war. The purpose of this book is to fill that void by presenting a set of case studies that subject selected air campaigns during the Southeast Asia era to rigid economic analysis....

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This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central Government-run institutions in India. The experts we consulted were divided into 19 groups depending on their profession. These groups of experts gave their opinion and comments on the news-items that appeared about reservations in dailies and weekly magazines, and the gist of these lengthy discussions form the third chapter of this book. The fourth chapter gives the conclusions based on our study....

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Dedication 5 Preface 6 Chapter One INTRODUCTION TO NEW SUPER FUZZY MODELS 7 1.1 Supermatrices and Fuzzy Supermatrices 7 1.2 Super Fuzzy Relational Maps 45 Chapter Two ANALYSIS OF THE ROLE OF MEDIA ON RESERVATION FOR OBC USING SUPER FUZZY MODELS 57 2.1 Brief Description of the Attributes Given by the Experts 58 2.2 Super Row FRM Model to Study the Role of Media on OBC Reservation 77 2.3 Super Fuzzy Mixed FRM Model to Study the Role of Media in Falsely Blaming the Government and Supporting Dr. Venugopal 88 2.4 Use of Super Column FRM Model to Study the Interrelation between the Government and Public 102 2.5 Analysis of Role of Media on Reservation for OBC using Fuzzy Cognitive Map 117 2.6 Observations based on this Analysis by Students and Experts through Seminars and Discussions 121 Chapter Three EXCERPT OF NEWS FROM PRINT MEDIA AND SUGGESTIONS AND COMMENTS BY THE EXPERTS 145 Chapter Four ANALYSIS SUGGESTIONS AND CONCLUSIONS BASED ON DISCUSSIONS, QUESTIONNAIRE, INTERVIEWS AND MATHEMATICAL MODELS 357 4.1 A View and Analysis by Group of Educationalists about Role of Media on OBC Reservation 357 4.1.1 Students Pro...

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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 into scientific ones, and to develop their study (The Theory of Imperfections). And finally, to interconnect opposite (and not only) human fields of knowledge into a.s-heterogeneous-as-possible another fields. The author welcomes any co=ents, notes, articles on this paper and/or the 120 open questions bothering him, which will be published in a collective monograph about the paradoxist mathematics....

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The "Paradoxist Mathematics" may be understood as Experimental Mathematics, 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, cultural, etc.) media! Learn to conradict everuthing and everybody!! "Duibito, ergo cogito; cogito, ergo sum", said Rene Descartes, "I doubt, therefore I think; I think, therefore I exist" (metaphysical doubt). See what happens if you deny the classics' theory?...

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Paradoxist Mathematics [Anti-Mathematics, Multi-Structure and Multi-Space, Space of Non-Integer or Negative Dimention, Inconsistent Sysytem ofAxiomas or Contradictory Theory, Non-Euclidean Geometries: Paradoxist Geometry, Non-Geometry, CounterProjective Geometry and Counter-Axioms, Anti-Geometry and Anti-Axioms, Model of an Anti-Geometry, Discontinuous Geometries] 5 -- Logica sau iogica Matematica? .29 -- Mathematics and Alcohol and God . 30 -- Subjective Questions and Answers for a MathInstructor of Higher Education .32 -- o Geometrie Paradoxista .49 -- Geometric Conjecture .50 -- A Function in the ~umber Theory . 51 -- An Infinity of Unsolved Problems Concerning a Function in the :'-lumber Theory . 57 -- Solving Problems by Using a Function in the Number Theory .79 -- Some Linear Equations Involving a Function in 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 ...

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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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Smarandache inversion sequence Abstract We study the Smarandache inversion sequence which is a new concept, related sequences, conjectures, properties, and problems. This study was conducted by using (Maple 8){a computer Algebra System. Keywords Smarandache inversion, Smarandache reverse sequence. Introduction In [1], C.Ashbacher, studied the Smarandache reverse sequence: 1; 21; 321; 4321; 54321; 654321; 7654321; 87654321; 987654321; 10987654321; 1110987654321; (1) and he checked the _rst 35 elements and no prime were found. I will study sequence (1), from different point of view than C. Ashbacher. The importance of this sequence is to consider the place value of digits for example the number 1110987654321, to be considered with its digits like this : 11; 10; 9; 8; 7; 6; 5; 4; 3; 2; 1, and so on. (This consideration is the soul of this study because our aim is to study all relations like this (without loss of generality). Definition. The value of the Smarandache Inversions (SI) of a positive integers, is the number of the relations i > j ( i and j are the digits of the positive integer that we concern with it), where i alw...

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M. Karama : Smarandache inversion sequence 1 W. He, D. Cui, Z. Zhao and X. Yan : Global attractivity of a recursive sequence 15 J. Earls : Smarandache reversed slightly excessive numbers 22 X. Ren and H. Zhou : A new structure of super R¤-unipotent semigroups 24 J. Li : An equation involving the Smarandache-type function 31 P. Zhang : An equation involving the function ±k(n) 35 Y. B. Jun : Smarandache fantastic ideals of Smarandache BCI-algebras 40 T. Jayeo. la : On the Universality of some Smarandache loops of Bol-Moufang type 45 W. Kandasamy, M. Khoshnevisan and K. Ilanthenral : Smarandache representation and its applications 59 Y. Wang, X. Ren and S. Ma : The translational hull of superabundant semigroups with semilattice of idempotents 75 M. Bencze : Neutrosophic applications in ¯nance, economics and politics|a continuing bequest of knowledge by an exemplarily innovative mind 81 J. Fu : An equation involving the Smarandache function 83 W. Zhu : The relationship between Sp(n) and Sp(kn) 87 X. Du : On the integer part of the M-th root and the largest M-th power not exceeding N 91 J. Earls : On the ten's complement fa...

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The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors...

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This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

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Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen................................

Description Details
The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors...

Excerpt Details
This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

Table of Contents Details
Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen................................