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The creation of a book is an act that requires several preconditions. I) An interesting and worthwhile subject; 2) A fair, yet demanding editor.; 3) Someone willing to put the words on paper. Given the existence of these three items, the leap to making the book a good one becomes the responsibility of the author. The Smarandache function is simultaneously a logical extension to earlier functions in number theory as well as a key to many future paths of exploration. As such, it is hoped that you get as much out of this book as the author did in writing it. While all books are a collective work, the responsibility for any errors ultimately falls to the author, and this is no exception....

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As one of the oldest of mathematical disciplines, the roots of number theory extend back into antiquity. Problems are often easy to state, but extremely difficult to solve. Which is the origin of much of their charm. All mathematicians, amateurs and professionals alike, have a soft spot in their hearts for the "purity" of the integers. When "Fermat's Last Theorem" was finally proven after centuries of effort, the result was discussed on many major news shows in the US. Brief comments also appeared in the major weekly news magazines....

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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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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 theory; exploring its major pitfalls before moving into what is postulated as an entropic notion of utility. Extrinsic utility is proposed as a cardinally measurable quantity; measurable in terms of the expected information content of a set of alternative choices. The entropic notion of utility is subsequently used to model the financial behavior of individual investors based on their governing risk-return preferences involving financial structured products manufactured out of complex, multi-asset options. Evolutionary superiority of the Black-Scholes function in dynamic hedging scenarios is computationally demonstrated using a haploid genetic algorithm model programmed in Borland C. The work explores, both theoretically and computationally, the psycho-cognitive factors governing the financial behavior of individual investors both in the presence as well as absence o...

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This book contains 23 papers, most of which were written by participants to the fifth International Conference on Number Theory and Smarandache Notions held in Shangluo University, China, in March, 2009. In this Conference, several professors gave a talk on Smarandache Notions and many participants lectured on them both extensively and intensively. All these papers are original and have been refereed. The themes of these papers range from the mean value or hybrid mean value of Smarandache type functions, the mean value of some famous number theroretic functions acting on the Smarandache sequences, to the convergence property of some infinite series involving the Smarandache type sequences. ...

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3. Remarks Sandor [2] has considered the problem of finding the S-perfect and completely S-perfect numbers, but his proof is not complete. He has proved that the only S-perfect of the form n = p q is n = 6 and there is no S-perfect number of the form n = 2kq where k ¸ 2 is an integer and q is an odd prime. On the other hand, Theorem 2.1 gives all the S-perfect numbers. Again, Sandor only proved that, the only completely S-perfect number of the form n = p2q is n = 28, and all completely S-perfect numbers are given by Theorem 2.2. Theorem 2.1 and Theorem 2.2 ¯nd respectively the S-perfect and completely S-perfect numbers when S(1) = 1. The situation is quite different if one adopts the convention that S(0) = 1. In the latter case, as has been proved by Gronas [3], all completely S-perfect numbers are n = p(prime), 9, 16, 24. All that is known about the S-perfect numbers is that, among the ¯rst 106 numbers, n = 12 is the only S-perfect number (see Ashbacher [4]). In exactly the same way, the Z-perfect and completely Z-perfect numbers may be defined. Thus, given an integer n, 1. ...

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J. Wang : An equation related to the Smarandache power function 1 X. Lu and J. Hu : On the F.Smarandache 3n-digital sequence 5 B. Cheng : An equation involving the Smarandache double factorial function and Euler function 8 A. A. K. Majumdar : S-perfect and completely S-perfect numbers 12 B. Zhao and S. Wang: Cyclic dualizing elements in Girard quantales 21 P. Chun and Y. Zhao : On an equation involving the Smarandache function and the Dirichlet divisor function 27 F. Li and Y. Wang : An equation involving the Euler function and the Smarandache m-th power residues function 31 H. Gunarto and A. Majumdar : On numerical values of Z(n) 34 K. Nagarajan, etc.: M-graphoidal path covers of a graph 58 H. Liu : On the cubic Gauss sums and its fourth power mean 68 A. A. K. Majumdar : On the dual functions Z¤(n) and S¤(n) 74 S. S. Gupta : Smarandache sequence of Ulam numbers 78 L. Li : A new Smarandache multiplicative function and its arithmetical properties 83 Y. Yang and X. Kang : A predator-prey epidemic model with infected predator 86 R. Fu and H. Yang : An equation involving the Lucas numbers 90 W. Yang : Two rings in IS-a...

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A book on Smarandache's achievements throughout his life time with a short history on his personal life.

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In the beginning, this international avant-garde was a mutism: to make literature by not writing literature at all!! (any mathematical/chemical/physical etc. abstract sign, any drawing, draft, picture, graffito (having no words, no letters) could mean a poem; the non-literature created became, paradoxically, a new kind of literature; later the paradoxism has generalized the old term of for the n-dimensional and other scientific (Lobacevsky, Riemann, Banach, etc.) spaces, thus a poem can be; an object, a being, a phenomenon, a status ... understandable in a universal language. And further, using mathematics and literature, he got to the Paradoxist Philosophy with the thesis that "Nothing is noncontradictorial" ....

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Abstract................................... 3 Biography Smarandache's wrong life........................ 4 As a mathematician............................ 6 Political reason to leave his native country............. 10 Smarandache Function......................... 20 Mathematical poems........................... 22 What is the paradoxism?........................ 23 Funny stories.............................. 25 Scientific activity Affiliations............................... 27 Mathematical books published.................... 27 Mathematical articles published................... 28 Contributions to many journals................... 32 Collective collections of mathematical problems books..... 33 Manuscripts............................... 33 International congresses of mathematics.............. 34 National seminars/colloquiums................... 34 Student mathematical competitions................. 35 Paintings................................... 37 Literary activity Affiliations............................... 38 The Paradoxist Literary Movement................. 39 Books written in English language................. 39...

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These ideas were either collected or inspired from author's various lectures of books, journals, newspapers, tv and radio shows, personal conversations. I started to write down such ideas since I was a high school student and continue even today - I always bear with me a small pen and small notebook where I write in the plane, or driving my car, or even in class room. Despite three decades of postponement, I hope this booklet will keep on inspiring the reader, as good ideas will always be worth to ponder....

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• Be competitive; • Don’t be panic, when under pressure; • Use probabilities (how much % you’re expected to produce); • Infiltrate in certain organizations; • To have power of influence; • Charm those who interact with you; • Be firm and fast in decisions; • To make a plan for a long period of time and subdivide it in smaller sub-plans for short periods of time...

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PREFACE ........................................ 3 CONTENTS......................................... 5 LIFE STRATEGIES 1. Best Tips for Life ...................................................... 6 2. Life Strategies in General Science..........................8 3. Life Strategies in Mathematics..............................11 4. Life Strategies in Medical Science .......................23 5. Life Strategies in Workplace & Social Life........28 6. Life Strategies in Personal Life .............................34 7. Life Strategies in General Arts .............................41 Appendix: Miscellaneous App.1. FS........................................ 54 App.2.American writing..............................................55 App3.The International Phonetic Alphabet.............67...

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Chapter 1 first introduces the interval neutrosophic sets which is an instance of neutrosophic sets. In this chapter, the definition of interval neutrosophic sets and set-theoretic operators are given and various properties of interval neutrosophic set are proved. Chapter 2 defines the interval neutrosophic logic based on interval neutrosophic sets including the syntax and semantics of first order interval neutrosophic propositional logic and first order interval neutrosophic predicate logic. The interval neutrosophic logic can reason and model fuzzy, incomplete and inconsistent information. In this chapter, we also design an interval neutrosophic inference system based on first order interval neutrosophic predicate logic. The interval neutrosophic inference system can be applied to decision making. Chapter 3 gives one application of interval neutrosophic sets and logic in the field of relational databases. Neutrosophic data model is the generalization of fuzzy data model and paraconsistent data model. Here, we generalize various set-theoretic and relation-theoretic operations of fuzzy data model to neutrosophic data model. Chapter ...

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The neutrosophic set generalizes the above mentioned sets from philosophical point of view. From scientific or engineering point of view, the neutrosophic set and set-theoretic operators need to be specified. Otherwise, it will be difficult to apply in the real applications. In this chapter, we de_ne the set theoretic operators on an instance of neutrosophic set called Interval Neutrosophic Set (INS). We call it as “interval" because it is subclass of neutrosophic set, that is we only consider the subunitary interval of [0; 1]....

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Preface iii 1 Interval Neutrosophic Sets 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Neutrosophic Set . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Interval Neutrosophic Set . . . . . . . . . . . . . . . . . . . . . 6 1.4 Properties of Set-theoretic Operators . . . . . . . . . . . . . . . . . . 14 1.5 Convexity of Interval Neutrosophic Set . . . . . . . . . . . . . . . . . . 15 1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Interval Neutrosophic Logic 21 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Interval Neutrosophic Propositional Calculus . . . . . . . . . . . . . . . 23 2.2.1 Syntax of Interval Neutrosophic Propositional Calculus . . . . . . . . . 23 2.2.2 Semantics of Interval Neutrosophic Propositional Calculus . . . . . . . . . 24 2.2.3 Proof Theory of Interval Neutrosophic Propositional Calculus . . . . . . . . 25 2.3 Interval Neutrosophic Predicate Calculus . . . . . . . . . . . . . . . . 27 2.3.1 Syntax of Interval Neutrosophic Predicate Cal...

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This book is organized into seven chapters. The first one is introductory in nature. In the second chapter authors give the unique and new way of analyzing the data which is time dependent. In chapter three the authors for the first time define the new concept of matrices with linguistic variables. In chapter four authors have used super matrices in super fuzzy models like super FCMs, super FRMs super FAMs etc. In chapter five we define interval matrix and matrix interval using the natural class of intervals, that is intervals of the 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 INTRODUCTION 7 Chapter Two AVERAGE TIME DEPENDENT (ATD) DATA MATRIX 9 Chapter Three FUZZY LINGUISTIC MATRICES AND THEIR APPLICATIONS 43 Chapter Four SUPERMATRICES AND THEIR APPLICATIONS 65 Chapter Five INTERVAL MATRICES AND NATURAL CLASS OF INTERVALS 149 Chapter Six DSM MATRIX OF REFINED LABELS 203 Chapter Seven N-MATRICES AND THEIR APPLICATIONS 205 FURTHER READING 217 INDEX 222 ABOUT THE AUTHORS 226...

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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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This book has five chapters. First chapter is introductory in nature. Here we just study chemical pollution caused by garment industries in chapter two of this book using fuzzy associative memories. In chapter three we give ways to control pollution by improving the system performance using hierarchical genetic fuzzy control algorithm. This study is carried out using the past data reported by Shimada et al (1995). Health hazards suffered by the agriculture labourers; caused by the chemicals used as fertilizers and pesticides is analysed in chapter four using RTD matrices. Chapter five gives a method of minimization of SOx and NOx using fuzzy control theory in cement industries to reduce pollution....

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In this chapter, we have used the fuzzy control method to find the correct measure of pressure and speed of kiln. Using data from Alathur cement industry, we have used mean of maximum method of fuzzy control with the data and we found the pressure and speed of kiln. Here the speed and pressure of kiln are important parameters in the kiln, because the SOx and N0X concentration is dependent on the kiln feed, coal feed and the kiln feed, coal feed are dependent on speed and pressure of kiln. That means if we increase the kiln feed and coal feed we must increase the kiln pressure and speed. By this way the mixing of SOx and NOx with kiln feed is maintained properly or otherwise the SOx and NOx will not mix fully with the kiln feed. The remaining unmixed gases of SOx and NOx are the wastage polluting the environment. For this, we convert all this kiln feed and coal feed level and pressure of kiln and speed of kiln into fuzzy control. By using fuzzy control we identify a correct pressure and speed of the kiln for a given kiln feed and coal feed. When we choose a correct pressure of kiln and speed of kiln through fuzzy control, the SO...

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Preface 5 Chapter One INTRODUCTION 7 Chapter Two USE OF FAM MODELS TO ANALYSE THE POLLUTION CAUSED BY THE GARMENT INDUSTRIES 11 Chapter Three HIERARCHICAL GENETIC ALGORITHM TO IMPROVE THE SYSTEM PERFORMANCE AND REDUCE POLLUTION BY CHEMICAL PLANTS 51 3.1 Introduction 51 3.2 Description of the Problem 53 3.3 Application of Hierarchical Genetic Fuzzy Control Algorithm to Control Process Variables of Decision Tables in Chemical Plants 56 3.4 Use of Hierarchical Genetic Fuzzy Control Algorithm in the Real Data 58 3.5 Conclusions 73 Chapter Four IDENTIFICATION OF THE MAXIMUM AGE GROUP IN WHICH THE AGRICULTURAL LABOURERS SUFFER HEALTH HAZARDS DUE TO CHEMICAL POLLUTION USING RTD MATRIX 75 4.1 Introduction 75 4.2 Estimation of the Maximum Age Group of the Agricultural Labourers having Cardio Vascular Problem due to Chemical Pollution using RTD Matrices 77 4.3 Conclusion 93 Chapter Five MINIMIZATION OF SOX AND NOX USING FUZZY CONTROL THEORY IN CEMENT INDUSTRIES TO REDUCE POLLUTION 95 5.1 Introduction 95 5.2 Description of the Problem 97 5.3 Process Fates of Sulfur in Cement Kiln 98 5.4 Process Fates of Ni...

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Technology Horizons is our vision for key Air Force science and technology investments over the next decade that will provide us with truly game-changing capabilities to meet our strategic and joint force responsibilities. The coming decades hold high promise for amazing new capabilities across the air, space, and cyber domains. Yet the Air Force and our nation will also be confronted with substantial strategic, technology, and budget challenges. Our greatest advances will come with a focused investment of resources in the most promising technologies. The vision in Technology Horizons provides the shared awareness of the challenges and opportunities that will enable us to achieve this focus....

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LIST OF ILLUSTRATIONS . . . . . vii FOREWORD BY THE SECRETARY OF THE AIR FORCE AND CHIEF OF STAFF OF THE AIR FORCE . . . . ix PREFACE BY THE CHIEF SCIENTIST OF THE AIR FORCE . . . . xi ACKNOWLEDGMENTS . . . . xv EXECUTIVE SUMMARY . . . . . xvii 1 INTRODUCTION . . . . 1 A Vision for Air Force Science and Technology 2010–30 . . . . 1 Lessons Learned from Prior Air Force Science and Technology Visions . . . . 5 Organization and Conduct of Technology Horizons . . . . . 8 Organization of Results from Technology Horizons . . . . . 14 Caveats . . . . 16 2 STRATEGIC CONTEXT FOR AIR FORCE S&T 2010–30 . . . . . 19 Relation to National Security Objectives . . . . . 21 Technology-Derived Challenges to Air Force Capabilities . . . . . 22 Strategic Implications of S&T Globalization . . . . 38 Federal Budget Implications for Air Force S&T Strategy . . . . . 41 3 ENDURING REALITIES FOR THE AIR FORCE 2010–30 . . . . . 43 Ensuring Interoperability with Legacy Systems . . . . 43 Sustainment Costs for Legacy Systems . . . . . 43 Importance of Low-Observable Systems . . . . 44 Energy Costs and Availability . . . . . 44 Growing Role ...

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Do you think "math = awesome" is a true statement? After reading this book, you might change your answer to a yes. With "jargon avoidance" in mind, this recreational math book gives you the lowdown on why math is fun, interesting and relevant in today's society. Intended for anyone who is curious about math and where it is circa 2010. This book is less concerned with exploring the mathematical details than it is with exploring the overall impact of various discoveries and insights, and aims to be insightful, cutting edge-y and mathematically rigorous....

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Book Directory: 1. Introduction 2. Picking a Winner is as Easy as 1, 2, 3. 3. That's my Birthday! 4. Sizing up Infinity 5. I am a Liar 6. Gratuitous Mathematical Hype 7. LOL Math, Math LOL 8. In Addition to High School Geometry 9. Abstraction is for the Birds 10. NKS: Anti-Establishment as Establishment 11. 42% of Statistics are Made up 12. Undercover Mathematicians 13. I Will Never Use This 14. Gaussian Copula: $ Implications 15. A Proven Savant 16. History of the TOE and E8 17. One Heck of a Ratio 18. A Real Mathematical Hero 19. Casinos Heart Math 20. The Man who was Sure About Uncertainty 21. We Eat This Stuff Up 22. Do I Have a Question for you! 23. When Nothing is Something 24. Think Binary 25. Your Order Will Take Forever 26. When you Need Randomness in Life 27. e=mc^2 Redux 28. Quipu to Mathematica 29. Through the Eyes of Escher 30. Origami is Realized Geometry 31. Quantifying the Physical 32. Geometric Progression Sure Adds up 33. Nature = a + bi and Other Infinite Details 34. Mundane Implications of Tim...

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A collection of papers concerning Smarandache type functions, numbers, sequences, integer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc. is published this year....

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This document will describe the current status on the search for factors of Smaranda.che consecutive numbers and their reverse. A complete list up to index 200 will be given, with all known factors. Smarandache numbers are the concatenation of the natural numbers from one up to the given index, and reverse Smaranda.che numbers are the concatenation of the natural numbers from the given index dO\vIJ. to 1....

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A collection of papers concerning smarandache type functions, numbers, sequences, integer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc. is published this year....

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A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the combinatorial properties of maps. The main trend is the enumeration of maps, particularly the rooted maps, pioneered by W. Tutte, and today, this kind of papers are still appeared on the journals frequently today. All of those is surveyed in Liu’s book [33]. To determine the embedding of a graph on surfaces, including coloring a map on surfaces is another trend in map theory. Its object is combinatorialization of surfaces, see Gross and Tucker [22], Mohar and Thomassen [53] and White [70], especially the [53] for detail. The construction of regular maps on surfaces, related maps with groups and geometry is a glimmer of the map theory with other mathematics....

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Why after thirty years, should Beckwith’s Hawaiian Mythology be reprinted? Why, for the last twenty-five years, have scholars and amateurs alike sought for either new or used copies of this book which has become a rarity? To begin with, it was the first, and is still the only, scholarly work which charts a pathway through the hundreds of books and articles, many of them obscure and scarce, and through the little-known manuscripts that record the orally transmitted myths, legends, traditions, folktales, and romances of the Hawaiian people. Beckwith herself saw it as a “guide to the native mythology of Hawaii” (p. xxxi), and by mythology she meant “the whole range of story-telling” (p.2). Secondly, from the vantage point of Hawaiian oral narrative the book directs the reader into similar material from peoples elsewhere in Polynesia who are closely related to the Hawaiians, reminding him of relevant narratives from areas west of Polynesia and occasionally even east of Hawaii. The southern Pacific comparison Beckwith offers as “an important link in tracing routes of intercourse during the period of migration of related Polynesian groups...

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This guide to the native mythology of Hawaii has grown out of a childhood and youth spent within sound of the hula drum at the foot of the domelike House of the Sun on the windy island of Maui. There, wandering along its rocky coast and sandy beaches, exploring its windward gorges, riding above the cliffs by moonlight when the surf was high or into the deep forests at midday, we were aware always of a life just out of reach of us latecomers but lived intensely by the kindly, generous race who had chanced so many centuries ago upon its shores. Not before 1914 did the actual shaping of the work begin. The study covers, as any old Hawaiian will discover, less than half the story, but it may serve to start specific answers to the problems here raised and to distinguish the molding forces which have entered into the recasting of such traditional story-telling as has survived the first hundred years of foreign contact. To the general student of mythology the number and length of proper names in an unfamiliar tongue may seem confusing. Hawaiian proper names are rarely made up of a single word but rather form a series of words recalling s...

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Introduction. vii -- Preface. xxxi -- Coming of the Gods. 1 -- Ku Gods. 12 -- The God Lono. 31 -- The Kane Worship. 42 -- Kane and Kanaloa. 60 -- Mythical Lands of the Gods. 67 -- Lesser Gods. 81 -- Sorcery Gods. 105 -- Guardian Gods. 122 -- The Soul after Death. 144 -- The Pele Myth. 167 -- The Pele Sisters. 180 -- Pele Legends. 190 -- Kamapua?a. 201 -- Hina Myths. 214 -- Maui the Trickster. 226 -- Aikanaka-Kaha?i Cycle. 238 -- Wahieloa-Laka Cycle. 259 -- Haumea. 276 -- . Papa and Wakea. 293 -- Genealogies. 307 -- Era of Overturning . 314 -- Mu and Menehune People. 321 -- Runners, Man-Eaters, Dog-Men. 337 -- Hawaiian Mythology - The Moikeha-La?a Migration. 352 -- Hawaiiloa and Paao Migrations. 363 -- Ruling Chiefs. 376 -- Usurping Chiefs. 387 -- Kupua Stories. 403 -- Trickster Stories. 430 -- Voyage to the Land of the Gods. 448 -- Riddling Contests. 455 -- The Kana Legend. 464 -- The Stretching-Tree Kupua. 478 -- Romance of the Swimmer. 489 -- Romance of the Island of Virgins. 498 -- Romances of Match-Making. 506 -- Romances of the Dance. 519 -- Wooing Romances. 526 -- References. 545 -- Index. 555 --...

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The question is, will we ever know if there are objects outside of the detectable universe radiating in wave length longer than CBR? We only measure the universe with visual radiations. Doesn't it seem that the age of the universe is determined by the size of our telescope? Nevertheless, there are activities of elementary particles which can not be detected by us? Isn't' it impossible to picture how far some active objects, say neutrinos, can be other than infinite. ...

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Suppose we have perfect telescope that is limitless in range; And, we don't see anything when we look pass all objects; Can we say we have reached the edge of the Space or Universe? Or, there is infinity beyond Space? ...

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1 Introduction 1 2 Probability Function of Doppler Effect 3 NED’s Redshift Survey Database 4 Estimate Age of The Universe Based On NED Database 5 Cosmic Background Radiation 6 Can We Really Tell The Size & Age of The Universe? 7 Appendix II: Accumulated Probability Distribution References...

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Proves mathematically that the Doppler blueshift is terminal event and Doppler redshift is dominating by natural. However, radiation redshift is not only the result of Doppler effect but also the quality loss of radiation over vast distance. An observer is surrounded by radiations of all frequencies, much like a background noise of light, sound and smell of a city. CBR will show redshift as visible radiations. Nevertheless, not the indication of growing universe....

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The dominating and exponential natures of radiation redshift do not suggest the acceleratingly physical departure of all astronomical objects; and, neither inflation nor a common origin. Universe will continue as is, no extra matter and energy needed. Otherwise, besides the demand of run-away energy; the interactions among energy, matter, run-away energy, run-away matter, and acceleratingly expanding the space to carry objects away can only lead to run-away interpretations....

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1 Introduction 2 Creation of Doppler Effect 2.1 Limited Range of Doppler Blueshift 2.2 Mathematical Model of Blueshift Detection in Space 2.3 Probability Function of Blueshift Detection 2.4 Probability Distribution of Blueshift Detection 2.5 Underlying Conditions 2.6 Cross-Check with Redshift Survey 2.7 Probability Function in Surface Observation 2.8 Probability Function in Linear Observation 2.9 Probability Function Comparison 2.10 Properties of Doppler Effect 2.10.1 Properties of Doppler Blueshift 2.10.2 Properties of Doppler Redshift 3 Observer and the Environment 3.1 Doppler Effect of Rotating Observer 3.2 Environment Conditions 3.3 Heliosphere of The Solar System 3.4 Cross Radiations in Space 3.5 Sky In A Box 4 Lost in Translation 5 Cosmic Background Radiation 6 Conclusion 7 Appendixes 7.1 Paradox of Space Expansion 7.2 Real Life Analogy of Inertia in Expanding Space 7.3 Paradox of Redshift and Expanding Space 7.3.1 Real Life Analogy of Radiation Trap 7.4 Paradox of Constant Pulsating Quasars in Expanding Space 7.5 Mind-Bending Questions 7.6 Can We Really Tell The Size & Age of The Universe? 7.7 A...

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Proves mathematically that the Doppler blueshift is terminal event and Doppler redshift is dominating by natural. However, radiation redshift is not only the result of Doppler effect but also the quality loss of radiation over vast distance. An observer is surrounded by radiations of all frequencies, much like a background noise of light, sound and smell of a city. CBR will show redshift as visible radiations. Nevertheless, not the indication of growing universe. ...

Excerpt Details
The dominating and exponential natures of radiation redshift do not suggest the acceleratingly physical departure of all astronomical objects; and, neither inflation nor a common origin. Universe will continue as is, no extra matter and energy needed. Otherwise, besides the demand of run-away energy; the interactions among energy, matter, run-away energy, run-away matter, and acceleratingly expanding the space to carry objects away can only lead to run-away interpretations....

Table of Contents Details
1 Introduction 1 2 Creation of Doppler Effect 2.1 Limited Range of Doppler Blueshift 2.2 Mathematical Model of Blueshift Detection in Space 2.3 Probability Function of Blueshift Detection 2.4 Probability Distribution of Blueshift Detection 2.5 Underlying Conditions 2.6 Cross-Check with Redshift Survey 2.7 Probability Function in Surface Observation 2.8 Probability Function in Linear Observation 2.9 Probability Function Comparison 2.10 Properties of Doppler Effect 2.10.1 Properties of Doppler Blueshift 2.10.2 Properties of Doppler Redshift 3 Observer and the Environment 3.1 Doppler Effect of Rotating Observer 3.2 Environment Conditions 3.3 Heliosphere of The Solar System 3.4 Cross Radiations in Space 3.5 Sky In A Box 4 Lost in Translation 5 Cosmic Background Radiation 55 6 Conclusion 58 7 Appendixes 7.1 Paradox of Space Expansion 7.2 Real Life Analogy of Inertia in Expanding Space 7.3 Paradox of Redshift and Expanding Space 7.3.1 Real Life Analogy of Radiation Trap 7.4 Paradox of Constant Pulsating Quasars in Expanding Space 7.5 Mind-Bending Questions 7.6 Can We Really Tell The Size & Age of The Univ...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

Excerpt Details
Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming Abstract: This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn-Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated together with weak; strong and converse duality theorems are proved. Key Words: Generalized multiobjective fractional programming; Disjunctive programming; Convexity; Concavity; fuzzy parameters Duality. ...

Table of Contents Details
Contents Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming BY E.E.AMMAR . . . . . . . . . . . . . . . . . . . . 01 Surface Embeddability of Graphs via Joint Trees BY YANPEI LIU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Plick Graphs with Crossing Number 1 BY B.BASAVANAGOUD AND V.R.KULLI . . . . . . . . . . . . . . . . . . . . . . 21 Effects of Foldings on Free Product of Fundamental Groups BY M.El-GHOUL, A. E.El-AHMADY, H.RAFAT AND M.ABU-SALEEM. . . . . . . 29 Absolutely Harmonious Labeling of Graphs BY M.SEENIVASAN AND A.LOURDUSAMY . . . . . . . . . . . . . . . . . . . . 40 The Toroidal Crossing Number of K4n BY SHENGXIANG LV, TANG LING AND YUANGQIU HUANG . . . . . . . . . . 52 On Pathos Semitotal and Total Block Graph of a Tree BY MUDDEBIHAL M. H. AND SYED BABAJAN. . . . . . . . . . . . . . . . . . 64 Varieties of Groupoids and Quasigroups Generated by Linear-Bivariate Polynomials Over Ring Zn BY E.ILOJIDE, T.G.JAIYEOLA AND O.O.OWOJORI . . . . . 79 New Characterizations for Bertrand Curves in Minkowski 3-Space BY BAHADDIN BUKCU, MURAT K...