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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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This study investigates Europe’s motives to develop the independent satellite navigation system known as Galileo despite the existence of America’s successful global positioning system (GPS). The study begins by analyzing both systems to familiarize the reader with global navigation satellite systems (GNSS) and to provide an understanding of the strengths and weaknesses of GPS and Galileo, as well as the systems’ similarities and differences. Although the two systems have different founding principles, they employ similar infrastructures and operational concepts. In the short term, Galileo will provide better accuracy for civilian users until GPS upgrades take effect. But performance is only part of the rationale. The author contends that Europe’s pursuit of Galileo is driven by a combination of reasons, including performance, independence, and economic incentive. With Galileo, Europe hopes to achieve political, security, and technological independence from the United States....

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DISCLAIMER . . . . . . . . . . . . . . . . . . . . . . .ii FOREWORD . . . . . . . . . . . . . . . . . . . . . . .vii ABOUT THE AUTHOR . . . . . . . . . . . . . . . . .ix ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . .xi 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . 1 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 GPS VERSUS GALILEO . . . . . . . . . . . . . . .11 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . .27 3 WHY GALILEO? . . . . . . . . . . . . . . . . . . .31 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . .45 4 IMPLICATIONS AND RECOMMENDATIONS . .51 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 66 ABBREVIATIONS . . . . . . . . . . . . . . . . . . . .69 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . 71 Illustrations 1 Satellite geometry 9 2 Global positioning system (GPS) satellite 14 3 Galileo satellite 16 Table 1 Number of visible satellites for various masking angles . . . . . . . . . . . . . . . . . . . .13...

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Per caso, a Rio de Janeiro, si ritrovano le tracce di uno degli oggetti più ricercati della storia. E' fatto di metallo e ha la forma di una testa, può dare indicazioni sul futuro generando un esagramma, che deve poi essere interpretato con l'aritmetica binaria. Ha iniziato il suo viaggio circa duemila anni fa in Tibet, facendo tappa in Palestina. Arrivato nel Nuovo Mondo è stato preso in consegna dagli uomini-pipistrello, una Specie di Indios che comunica con ultrasuoni e vede nel buio. E' stato chiamato in passato il Baphomet dei Templari. Un etnologo fai-da-te, aiutato da una funzionaria del Jardim Botanico di Rio, un latinista d'esportazione, un narco-trafficante internazionale e una ambiziosa Mae de Santo, leader della Macumba, si trovano coinvolti nello strano affare nella città carioca. L'etnologo è alla ricerca di uno scoop sul VoooDoo mentre il latinista viene semplicemente chiamato in causa senza averlo desiderato; il narco-trafficante cerca unicamente di incrementare il suo business e invece la Mae de Santo è alla ricerca del Potere Esoterico. A loro insaputa sono tutti sulle tracce di qualcosa di importante, che interess...

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La Cidade Maravillhosa - Jardim Botanico - Zangbeto - Traficantes - Rocinha - Tijuca - Algebra Esoterica - The Secret Power - L'Oracolo - Ultimo capitolo - Qumran - Baia di Guanabara - The Fetish - Palma Mater...

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Per caso, a Rio de Janeiro, si ritrovano le tracce di uno degli oggetti più ricercati della storia. E' fatto di metallo e ha la forma di una testa, può dare indicazioni sul futuro generando un esagramma, che deve poi essere interpretato con l'aritmetica binaria. Ha iniziato il suo viaggio circa duemila anni fa in Tibet, facendo tappa in Palestina. Arrivato nel Nuovo Mondo è stato preso in consegna dagli uomini-pipistrello, una Specie di Indios che comunica con ultrasuoni e vede nel buio. E' stato chiamato in passato il Baphomet dei Templari. Un etnologo fai-da-te, aiutato da una funzionaria del Jardim Botanico di Rio, un latinista d'esportazione, un narco-trafficante internazionale e una ambiziosa Mae de Santo, leader della Macumba, si trovano coinvolti nello strano affare nella città carioca. L'etnologo è alla ricerca di uno scoop sul VoooDoo mentre il latinista viene semplicemente chiamato in causa senza averlo desiderato; il narco-trafficante cerca unicamente di incrementare il suo business e invece la Mae de Santo è alla ricerca del Potere Esoterico. A loro insaputa sono tutti sulle tracce di qualcosa di importante, c...

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Hacking - Così è perfetto. - Dumbo pensava che uno script, per essere veramente efficace, doveva avere anche una sua bellezza intrinseca. Dopo aver digitato l'ultimo byte lo aveva girato e rigirato come un guanto, disponendo le istruzioni nel modo migliore per l'esecuzione del compito loro affidato. - Quello script ha una sua bellezza intrinseca – commentò Isis che lo osservava lavorare da dietro le spalle. - Grazie – rispose Dumbo provando una genuina simpatia per Isis e decidendo di condividere con lei il piacere che quel lavoro gli dava. - E oltretutto sarà anche piuttosto efficace. Questo Spider percorrerà in lungo e in largo il cyberspazio alla ricerca dei siti nel cui contenuto profondo si nascondono le keywords che mi avete dato, ma non solo, creerà per voi una mappa geografica con l'ubicazione dei siti e l'elenco di tutti i documenti che contengono una o più parole chiave. E se lo volete farà il download dei documenti interessanti e li salverà proprio su questo computer, a vostra completa disposizione. - Dumbo sorrideva radioso a Isis e cominciava a notare, ora che la concentrazione per il la...

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- La Cidade Maravillhosa - Jardim Botanico - Zangbeto - Traficantes - Rocinha - Tijuca - Algebra Esoterica - The Secret Power - L'Oracolo - Ultimo capitolo - Qumran - Baia di Guanabara - The Fetish - Palma Mater ...

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The Theory Of Interpretive Relativity: A Unified Map Of Literary Theory is a comprehensive study organizing and mapping all literary interpretive theory, from classical philosophy to postmodern theory, into one formulaic model. Interpretive Relativity uses, for its method of organizational strategy, the philosophy of relativism to explain how all theoretical interpretation compliment one another rather than contradict one another. This thesis uses extensive graphs and illustrations to aid in the visualization of how mapping theoretical interpretations is possible. The piece of literature, work of art, that is used through out the study is Shakespeare’s Hamlet. In other words, this thesis show how the philosophy of Einstein’s general theory of relativity could be applied to Hamlet....

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“The long concatenations of simple and easy reasoning which geometricians use in achieving their most difficult demonstrations gave me occasion to imagine that all matters which may enter the human mind were interrelated in the same fashion.” -- René Descartes ...

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I. INTRODUCTION: MATHEMATICAL CONSTRUCT STRATEGIES FOR GRAPHING LITERARY INTERPRETATION THEORIES INTO A VISUAL FIGURE, DEFINING TERMS 1 II. MAPPING LITERARY THEORY: DEFINING THE BODY OF LITERATURE, Ln, AND MESSAGE, EMBODIED IN ART, Ln 10 III. FORMING THE X AXIS: SETTING VALUES FOR X AS SIGN, SIGNIFICATION, AND SIGNAL (X1, X2, X3) 18 X1: Sign, Encoding Meaning 21 X2: Signification: The Three Aspects to the Value X2, Concept in a Medium, X21, X22, X23 23 X3: Signal, Decoding Meaning Plotting the 2s OF B’s X31, X32, X33 30 IV. FORMING THE Y AXIS: THE AUDIENCE’S INFINITE MULTIFARIOUS “REALIZATION” 36 The Search for 1: The Messenger and the Author 38 Y 1: The Author’s text 45 Y 2: The Text 50 Y 3: The World 54 Y 4: The Reader 57 V. FORMING THE Z AXIS: VALUES FOR Z, APPLIED RHETORICAL IDEOLOGY 65 Z 1: Marxist Literary Criticism 67 Z 2: Deconstruction Criticism 71 Z 3: Multicultural Literary Criticism 77 Z 4: Psychoanalytic Literary Criticism 80 Z 5: Liberation Literary Criticism 84 VI. CONCLUSION 87...

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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 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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As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for the actual system. The sources of uncertainty can be stochasticity (the case of intrinsic imperfection where a typical and single value does not exist), incomplete knowledge (ignorance of the totality, limited view on a system because of its complexity) or the acquisition errors (intrinsically imperfect observations, the quantitative errors in measures).”...

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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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The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications. With the recent introduction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialgebra and also give the applications of these algebraic structures....

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

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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...

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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. ...

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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...

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Describing a novel way of drawing the ground plan of Stonehenge with the peg and string method, revealing previously unknown relationships.

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Stonehenge is a supposedly Neolithic monument located on Salisbury plain in Southern England. A study of the monument ground-plan raises a number of questions that are not answered by existing science. Questions such as: - ‘How could primitive men subdivide a circle into 56 equal parts?’ The questions are not answered with the keys provided by science. We need a ‘dumb-key’ to resolve the problems and answer the questions. The dumb-key is found by asking ourselves what geometric drawing implements did the builders have? They must have marked the ground with some kind of plan or they would not have known where to dig the holes to place the stones. The only geometric implements they would have had access to would be the basic ones that men living in the wild might find in the environment. They would no doubt have a long straight pole or stick to use as a measure, and sharpened pegs to scratch lines in the turf, or to drive into the ground to mark places. They would have rope, or the ancient equivalent, made out of twisted fibres or knotted hide thongs. Pulled tight these would provide a straight line, which could be marked on the...

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Acknowledgements………………………………………..…..4 Introduction………………………………………………..……..5 Drawing the Ground-Plan………………………….…………6 Outer Monument…………………………………………………7 Inner Monument……………………………………………….19 Astro-Archaeology…………………………………………….26 Summary of Astronomy…………………….………………29 Graphs ………………………..……………….27 & 28, 31& 34 Tables 1,2,3…………………………………………….37,38,39 Exercise with Px……………………………………….………40 Printable Graphs………………………………………..42 & 43 ...

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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...

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x4: Radio labeling of P3n for n is less than or equal to 5 or n = 7 In this section we determine radio numbers of cube path of small order as a special case....

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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...

Table of Contents Details
Contents Tangent Space and Derivative Mapping on Time Scale BY EMIN ¨OZYILMAZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Basic Properties Of Second Smarandache Bol Loops BY T.G.JA´IY´E O. L´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Smarandachely Precontinuous maps and Preopen Sets in Topological Vector Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Path Double Covering Number of Product Graphs BY A. NAGARAJAN, V. MAHESWARI, S. NAVANEETHAKRISHNAN. . . . . . 27 Some Remarks on Fuzzy N-Normed Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 σ-Coloring of the Monohedral Tiling BY M. E. BASHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 The Forcing Domination Number of Hamiltonian Cubic Graphs BY H.ABDOLLAHZADEH AHANGAR AND PUSHPALATHA L. . . . . . . . . . 53 Permutation Polynomials modulo n, n 6= 2w and Latin Squares BY VADIRAJA BHATTA G. R. and SHANKAR B. R. . . . . . . . . . . . . . . . . 58 Graphoidal Tree d - Cover BY S.SOMASUNDARAM, A.NAGARAJAN AND G.MA...