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The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b. In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is a mathematical constant, approximately 1.6180339887.... At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. (From Wikipedia)...

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Science

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A recording of the first 2000 prime numbers (2-17389). Recommended listening for all math geeks and insomniacs!

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Science

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Lecture delivered before the International Congress of Mathematicians at Paris in 1900 and subsequently published in the Bulletin of the American Mathematical Society Vol. 8 (1902), 479-481....

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Essay/Short nonfiction, Science

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The Monadology ( La Monadologie , 1714) is one of Gottfried Leibniz’s best known works representing his later philosophy. It is a short text which sketches in some 90 paragraphs a metaphysics of simple substances, or monads. What he proposed can be seen as a modification of occasionalism developed by latter-day Cartesians. Leibniz surmised that there are indefinitely many substances individually 'programmed' to act in a predetermined way, each program being coordinated with all the others. This is the pre-established harmony which solved the mind body problem at the cost of declaring any interaction between substances a mere appearance, something which Leibniz accepted. Indeed it was space itself which became an appearance as in his system there was no need for distinguishing inside from outside. True substances were explained as metaphysical points which, Leibniz asserted, are both real and exact — mathematical points being exact but not real and physical ones being real but not exact. (Summary from Wikipedia)...

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Philosophy, Science

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Henry Gray's classic anatomy textbook was first published in 1858 and has been in continuous publication ever since, revised and expanded through many successive editions. This recording is of the public-domain 1918 US edition (some information may be outdated). For the recording, we have divided the book into five parts. Part 2 includes Syndesmology and Myology. The mathematical formulas (section 25) and the illustrations can be found in the online text at bartleby.com. (Summary by Laurie Anne Walden)...

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Science, Instruction, Nature

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Sidelights on Relativity contains ETHER AND THE THEORY OF RELATIVITY, an address delivered on May 5th, 1920, in the University of Leyden; and GEOMETRY AND EXPERIENCE, an expanded form of an address to the Prussian Academy of Sciences in Berlin on January 27th, 1921. (Intro from Project Gutenberg)...

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Nature, Science

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Flatland: A Romance of Many Dimensions is an 1884 science fiction novella by the English schoolmaster Edwin Abbott Abbott. As a satire, Flatland offered pointed observations on the social hierarchy of Victorian culture. However, the novella's more enduring contribution is its examination of dimensions; in a foreword to one of the many publications of the novella, noted science writer Isaac Asimov described Flatland as The best introduction one can find into the manner of perceiving dimensions. As such, the novella is still popular amongst mathematics, physics and computer science students....

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Fiction, Science fiction, Satire

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Jules Henri Poincaré (1854 – 1912) was one of France's greatest mathematicians and theoretical physicists, and a philosopher of science. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is considered to be one of the founders of the field of topology. Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form. He discovered the remaining relativistic velocity transformations and recorded them in a letter to Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. (Summary from Wikipedia)...

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Science

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This is an introduction to Einstein’s space-bending, time-stretching theory of Relativity, written by the master himself. Special and General relativity explain the structure of space time and provide a theory of gravitation, respectively. Einstein’s theories shocked the world with their counterintuitive results, including the dissolution of absolute time. In this book he brings a simplified form of his profound understanding of the subject to the layperson. In the words of Einstein: “The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics.” The book is challenging at times but, when approached patiently, proves itself one of the most lucid explanations of Relativity to be found anywhere. [Due to transcription or optical character recognition errors in creating online texts, and because of less-than-clear fonts in some printed texts, the variables as read in some of the equations here are not as...

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Science

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In contrast to Scott's South Pole expedition, Amundsen's expedition benefited from good equipment, appropriate clothing, and a fundamentally different primary task (Amundsen did no surveying on his route south and is known to have taken only two photographs) Amundsen had a better understanding of dogs and their handling, and he used of skis more effectively. He pioneered an entirely new route to the Pole and they returned. In Amundsen's own words: Victory awaits him who has everything in order -- luck, people call it. Defeat is certain for him who has neglected to take the necessary precautions in time; this is called bad luck. Short accounts by other members of the party are appended. (Summary adapted from Wikipedia by Karen Merline.)...

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Travel, Science, History

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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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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 present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of low energy reaction (coldfusion) phenomena. While some of these discussions may be found a bit too theoretical, our view is that once these phenomena can be put into rigorous theoretical framework, thereafter more 'openminded' physicists may be more ready to consider these New Energy methods more seriously. Our basic proposition in the present book is that considering these new theoretical insights, one can expect there are new methods to generate New Energy technologies which are clearly within reach of human knowledge in the coming years....

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In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has numerical solution with sinusoidal form, which differs appreciably from conventional Yukawa potential. In the present article we interpret and compare this result from the viewpoint of EQPET/TSC model described by Takahashi. Further observation is of course recommended in order to refute or verify this proposition....

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Peer-reviewers ii Abstract iii Preface by D. Rapoport iv Contents vi Foreword viii Prologue: Socio-economic impact of New Energy technologies xi Contributors to this volume xiv Short biography of Contributors xv Free energy and Topological Geometrodynamics 1. Nuclear string hypothesis – M. Pitkanen 1 2. The notion of free-energy and many-sheeted Space-Time concept – M. Pitkanen 44 3. Prediction and calculation of New Energy development – Fu Yuhua 111 4. Some unsolved problems in the physics of elementary particle – V. Christianto & F. Smarandache (PiP, vol. 3 no. 4, 2007) 127 5. About some unsolved problems in physics – M. Pitkanen 132 Beyond Standard Model, Unmatter and Yang-Mills Field 6. Bifurcations and pattern formation in particle physics: an introductory study – E. Goldfain (submitted to APS conference, 2008) 151 7. Dynamics of Neutrino oscillations and the Cosmological constant problem – E. Goldfain 168 8. Fractional dynamics and the Standard Model of Elementary particles – E. Goldfain (Comm. In Nonlin. Science and Numerical. Simulation, 2007) 176 9. A new possible form of Matter, Unmatter – formed by parti...

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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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A structure theorem of right C-rpp semigroups1 Abstract A new method of construction for right C-rpp semigroups is given by using a right cross product of a right regular band and a strong semilattice of left cancellative monoids. Keywords Right C-rpp semigroups, right cross products, right regular bands, left cancellative monoids. x1. Introduction Recall that a semigroup S is called an rpp semigroup if all its principal right ideals aS1, regarded as right S1-systems, are projective. According to J.B. Fountain[5], a semigroup S is rpp if and only if, for any a 2 S, the set Ma=fe 2 E j S1a µ Se and for all x; y 2 S1, ax = ay ) ex = eyg is a non-empty set, where E is the set of all idempotents of S. An rpp semigroup S is called strongly rpp if for every a 2 S, there exists a unique idempotent e in Ma such that ea=a. It is easy to see that regular semigroups are rpp semigroups and completely regular semigroups are strongly rpp semigroups. Thus, rpp semigroups are generalizations of regular semigroups. A strongly rpp semigroups S is said to be a right C-rpp semigroup if L. _ R is a congruence on S and Se µ eS for all e 2 E(...

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X. Pan and B. Liu : On the irrational root sieve sequence 1 H. Liu : Sub-self-conformal sets 4 K. Liu : On mean values of an arithmetic function 12 L. Wang and Y. Liu : On an infinite series related to Hexagon-numbers 16 X. Ren, etc. : A structure theorem of right C-rpp semigroups 21 A. R. Gilani and B. N. Waphare : Fuzzy extension in BCI-algebras 26 A. S. Shabani : The Pell's equation x2 ¡ Dy2 = §a 33 L. Cheng : On the mean value of the Smarandache LCM function 41 W. Guan : Four problems related to the Pseudo-Smarandache-Squarefree function 45 Y. Lou : On the pseudo Smarandache function 48 J. L. Gonzalez : A miscellaneous remark on problems involving Mersenne primes 51 Y. Liu and J. Li : On the F.Smarandache LCM function and its mean value 52 N. T. Quang and P. D. Tuan : A generalized abc-theorem for functions of several variables 56 W. Liu, etc. : An assessment method for weight of experts at interval judgment 61 Y. Xue : On the F.Smarandache LCM function SL(n) 69 Y. Zheng : On the Pseudo Smarandache function and its two conjectures 74 Z. Ding : Diophantine equations and their positive integer solutions 77 S. Gou ...

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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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Abstract In this paper, we use 4-cyclotomic cosets of modulo n and generator polynomials to describe quaternary simple-root cyclic codes of length n = 85. We discuss the conditions under which a quaternary cyclic codes contain its dual, and obtain some quantum error-correcting codes of length n = 85, three of these codes are better than previous known codes. Keywords Quaternary cyclic code, self-orthogonal code, quantum error-correcting code. x1. Introduction Since the initial discovery of quantum error-correcting codes, researchers have made great progress in developing quantum error-correcting codes. Many code construction are given. Reference [1] gives a thorough discussion of the principles of quantum coding theory. Many good quantum error-correcting codes were constructed from BCH codes, Reed-Muller codes, Reed-Solomon codes and algebraic geometric codes, see [2-6]. So it is natural to construct quantum error-correcting codes from quaternary cyclic codes. It is known that there is a close relation between cyclotomic coset and cyclic codes. Suggested by this relation, we use 4-cyclotomic coset modulo n and generator polyn...

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S. M. Khairnar and M. More : Subclass of analytic and univalent functions in the unit disk 1 Y. Ma, etc. : Large quaternary cyclic codes of length 85 and related quantum error-correcting 9 J. Chen : Value distribution of the F.Smarandache LCM function 15 M. Bencze : About a chain of inequalities 19 C. Tian and N. Yuan : On the Smarandache LCM dual function 25 J. Caltenco, etc. : Riemannian 4-spaces of class two 29 Y. Xue : On a conjecture involving the function SL¤(n) 41 Y. Wang : Some identities involving the near pseudo Smarandache function 44 A. Gilani and B. Waphare : On pseudo a-ideal of pseudo-BCI algebras 50 J. Chen : An equation involving the F.Smarandache multiplicative function 60 M. Enciso-Aguilar, etc. : Matrix elements for the morse and coulomb interactions 66 Y. Xu and S. Li : On s¤¡Supplemented Subgroups of Finite Groups 73 C. Tian : Two equations involving the Smarandache LCM dual function 80 W. Zheng and J. Dou : Periodic solutions of impulsive periodic Competitor- Competitor-Mutualist system 86 X. Zhang : On the fourth power mean value of B(Â) 93 Z. Lv : On the F.Smarandache function and its mean val...

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The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu....

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The main objective of this was to understand the basic psychological and social problems faced by the PWDs and their caretakers. To interpret the collected data, tabulations and analysis were made. Efforts were made to highlight the inferences in each table and in few places comments were made in order to use it for fuzzy analysis. Following is the list of organizations and the total population from 5 blocks is listed below....

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Preface 6 Chapter One INTRODUCTION TO BASIC CONCEPTS 11 Chapter Two ANALYSIS OF THE COLLECTED DATA OF THE PWDS FROM MELMALAYANUR AND KURINJI PADI BLOCKS IN TAMIL NADU 13 Chapter Three THE NEW FUZZY COGNITIVE RELATIONAL MAPS (FCRMS) BIMODEL 29 Chapter Four ANALYSIS OF THE SOCIO ECONOMIC PROBLEMS FACED BY THE PWDS USING (SFCMS) 47 4.1 Application of FCMs Models to Social and Psychological Problems 48 4.2 Expert Opinion of PWDs using Special FCMs to Analyse the Problem of PWDs 50 4.3 The Expert Opinion of the caretakers of the PWDs using SFCM 59 4.4 The Expert Opinion of the NGOs working with the PWDs using Special FCM Model 62 Chapter Five THE STUDY OF INTERRELATED PROBLEMS FACED BY THE PWDS AND THE CARE TAKERS 73 5.1 Introduction 73 5.2 Experts Opinion from a Public Person Living in Melmalayanur Block 77 5.3 Expert Opinion of PWDs using FRMs 84 5.4 Expert Opinion of Caretakers of the PWDs using FRM 87 5.5 Expert Opinion of the NGOs working with the PWDs using the FRM model 93 Chapter Six ANALYSIS OF PROBLEMS OF RURAL PWDs USING THE NEW FCRM BIMODEL 99 6.1 Expert Opinion of the Caretaker and a PWD using the ...

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Arguably a top tier concern for American foreign policy for more than a few years, Iran gets the meticulous attention of two distinguished Air Force scholars. Lt Cols Charles A. Douglass and Michael D. Hays are critical of the current American policy toward Iran and tell us why. More importantly, they point to elements necessary for an effective Iranian strategy. Their aim: “to change the fundamental calculus of the Iranian problem” to one beneficial for both Americans and Iranians....

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1 SOLVING IRAN . . . . . . . . . . . . . . . . . . . .1 Note . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 IRAN’S PERCEPTIONS AND PATTERNS: HISTORIC ROOTS . . . . . . . . . . . . . . . . . . .5 Ancient Persian Greatness and Cultural Pride . . . . . . . . . . . . . . . . . . . . . . 5 Resentment of Foreign Interference . . . . . . 7 Persian-Shiite Strategic Loneliness . . . . . 10 Pragmatic National Interest Replaces Revolutionary Ideology . . . . . . . . . . . . . .13 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3 ANALYSIS OF IRAN . . . . . . . . . . . . . . . . .23 Demographics, Politics, and Economics . . . .24 Internal Dynamics, Personalities, Power Centers, and Factions . . . . . . . . . . . . . . . 32 Nuclear Desire . . . . . . . . . . . . . . . . . . . . .40 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . .43 4 US PERCEPTIONS . . . . . . . . . . . . . . . . . .49 US Perceptions of Iran Internally . . . . . . . .49 US Perceptions of Iran Externally . . . . . . . 51 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5 REVIEW OF RECENT US POLICY . . . . . . . ....

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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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An identity involving the function ep(n) Abstract The main purpose of this paper is to study the relationship between the Riemann zeta-function and an in¯nite series involving the Smarandache function ep(n) by using the elementary method, and give an interesting identity. Keywords Riemann zeta-function, in¯nite series, identity. x1. Introduction and Results Let p be any fixed prime, n be any positive integer, ep(n) denotes the largest exponent of power p in n. That is, ep(n) = m, if pm j n and pm+1 - n. In problem 68 of [1], Professor F.Smarandache asked us to study the properties of the sequence fep(n)g. About the elementary properties of this function, many scholars have studied it (see reference [2]-[7]), and got some useful results. For examples, Liu Yanni [2] studied the mean value properties of ep(bk(n)), where bk(n) denotes the k-th free part of n, and obtained an interesting mean value formula for it. That is, let p be a prime, k be any fixed positive integer, then for any real number x ¸ 1, we have the asymptotic formula....

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F. Ayatollah, etc. : Some faces of Smarandache semigroups' concept in transformation semigroups' approach 1 G. Feng : On the F.Smarandache LCM function 5 N. Quang and P. Tuan : An extension of Davenport's theorem 9 M. Zhu : On the hybrid power mean of the character sums and the general Kloosterman sums 14 H. Yang and R. Fu : An equation involving the square sum of natural numbers and Smarandache primitive function 18 X. Pan and P. Zhang : An identity involving the Smarandache function ep(n) 26 A.A.K. Majumdar : A note on the Smarandache inversion sequence 30 F. Li : Some Dirichlet series involving special sequences 36 Y. Wang : An asymptotic formula of Sk(n!) 40 S. Gao and Z. Shao : A fuzzy relaxed approach for multi-objective transportation problem 44 J. Li : An infinity series involving the Smarandache-type function 52 B.E. Carvajal-Gamez, etc. : On the Lorentz matrix in terms of Infeld-van der Waerden symbols 56 X. Li : On the mean value of the Smarandache LCM function 58 K. Ran and S. Gao : Ishikawa iterative approximation of fixed points for multi-valued Ástrongly pseudo-contract mappings 63 X. Fan : On the divisi...

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This issue of the journal is devoted to the proceedings of the third International Conference on Number Theory and Smarandache Problems. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache problems in particular. In this volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems or other mathematical problems. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will get familiar with the beautiful identities and sharp asymptotic formulas obtained in the volume....

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Abstract : Let k be any ¯xed positive integer, n be any positive integer, Sk(n) denotes the smallest positive integer m such that m! is divisible by kn: In this paper, we use the elementary methods to study the asymptotic properties of Sk(n), and give an interesting asymptotic formula for it. Keywords : F. Smarandache problem, primitive numbers, asymptotic formula. ...

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J. Wang : Cube-free integers as sums of two squares 1 G. Liu and H. Li : Recurrences for generalized Euler numbers 9 H. Li and Q. Yang : Some properties of the LCM sequence 14 M. Liu : On the generalization of the primitive number function 18 Z. Lv : On the F. Smarandache LCM function and its mean value 22 Q. Wu : A conjecture involving the F. Smarandache LCM function 26 S. Xue : On the Smarandache dual function 29 N. Yuan : A new arithmetical function and its asymptotic formula 33 A. Muktibodh, etc. : Sequences of pyramidal numbers 39 R. Zhang and S. Ma : An e±cient hybrid genetic algorithm for continuous optimization problems 46 L. Mao : An introduction to Smarandache multi-spaces and mathematical combinatorics 54 M. Selariu : Smarandache stepped functions 81 X. Zhang and Y. Zhang : Sequences of numbers with alternate common di®erences 93 Y. Zhang : On the near pseudo Smarandache function 98 A. Muktibodh : Smarandache mukti-squares 102...