Description Details
This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially with geometric inequalities for the remarkable elements of triangles or tetrahedrons. Other themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2 includes various diophantine equations, some of which are treatable by elementary methods; others are partial solutions of certain unsolved problems. An important method is based on the famous Euler-Bell-Kalm ar lemma, with many applications. Article 20 may be considered also as an introduction to Chapter 3 on Arithmetic functions. Here many papers study the famous Smarandache function, the source of inspiration of so many mathematicians or scientists working in other elds. The author has discovered various generalizations, extensions, or analogues functions. Other topics are connected to the composition of arithmetic funct...

Description Details
A complete understanding of what something is must include an understanding of what it is not. In his paper, “Paradoxist Mathematics” [19], Florentin Smarandache proposed a number of ways in which we could explore “new math concepts and theories, especially if they run counter to the classical ones.” In a manner consistent with his unique point of view, he defined several types of geometry that are purposefully not Euclidean and that focus on structures that the rest of us can use to enhance our understanding of geometry in general....

Description Details
Taking an unusual approach to its topic, “Principles of Anarchism” applies classical logic and deductive reasoning to the subject of human interactions and rights. Beginning with the assumption that all human beings are equal, a concept which is termed the human equality axiom, the author goes on to draw a number of conclusions from this postulate in the manner of a Euclidean proof. These include the surprising contention that no such thing as human rights can exist, the assertion that anarchism is essentially intellectual rather than activist, and the uncomfortable suggestion that historical developments such as cities and industries are harmful to the human race rather than helpful. More centrally, though, the pamphlet argues very simply that any form of authority or government is logically incompatible with the existence of humanity. And it is the implications of this theory, rejection of which requires rejection of the equality axiom as well, which make the argument offered both novel and exceptionally relevant....

Description Details
Taking an unusual approach to its topic, “Principles of Anarchism” applies classical logic and deductive reasoning to the subject of human interactions and rights. Beginning with the assumption that all human beings are equal, a concept which is termed the human equality axiom, the author goes on to draw a number of conclusions from this postulate in the manner of a Euclidean proof. These include the surprising contention that no such thing as human rights can exist, the assertion that anarchism is essentially intellectual rather than activist, and the uncomfortable suggestion that historical developments such as cities and industries are harmful to the human race rather than helpful. More centrally, though, the pamphlet argues very simply that any form of authority or government is logically incompatible with the existence of humanity. And it is the implications of this theory, rejection of which requires rejection of the equality axiom as well, which make the argument offered both novel and exceptionally relevant....

Description Details
This book includes part of the research results about the Smarandache problems written by Chinese scholars at present, and its main purpose is to introduce various results about the Smarandache problems, such as Smarandache function and its asymptotic properties, series convergence, solutions about special equations. At the same time, we put forward to some new interesting problems either in order to research further. We hope this booklet will guide and inspire readers to these fields....

Excerpt Details
前言 数论这门学科最初是从研究整数开始的, 所以叫整数数论. 后来整数 数论又进一步发展, 就叫做数论了. 确切地说, 数论就是一门研究整数性 质的学科. 数论和几何学一样, 是古老的数学分支. 数论在数学中的地位是特殊的, 高斯曾经说过:“数学是科学的皇后, 数论是数学中的皇冠”. 虽然数论中的许多问题在很早就开始了研究, 并得到了丰硕的成果, 但是至今仍有许多被数学家称之为“皇冠上的明 珠”的悬而未解的问题等待人们去解决. 正因如此, 数论才能不断地充 实和发展, 才能既古老又年轻, 才能始终活跃在数学领域的前沿. Foreword Number theory, this discipline was originally started from the study integer, so called integer number theory. Later integer further development of number theory, number theory called up. Rather, number theory is an integer of study qualitative disciplines. Number theory and geometry, is an ancient branch of mathematics. Number theory in mathematics position is special, Gauss once said: "Mathematics is the queen of sciences, number theory is the mathematics of the crown. "Although many of the problems in number theory began very early in the research, And has been fruitful, but there are still many of the mathematicians call "crown Ming Pearl "of unsolved problems waiting to be solved for this reason, number theory can continue to charge Real and development in order to both old and young, can always active in the forefront of the field of mathematics....

Table of Contents Details
目录 第一章Smarandache 函数1 1.1 引言. . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 S(n) 函数和d(n) 函数的混合均值. . . . . . . . . . . . 4 1.3 关于F.Smarandache 函数S(mn) 的渐近性质. . . . . . . . 6 1.4 复合函数S(Z(n)) 的均值. . . . . . . . . . . . . . . . 7 1.5 是否为整数的问题. . . . . . . . . . . . . . . 10 1.6 关于函数S(n) 的一个方程. . . . . . . . . . . . . . . 13 1.7 关于函数S(nk) 的一个方程. . . . . . . . . . . . . . . 15 1.8 关于Smarandache 函数值的分布. . . . . . . . . . . . . 17 1.9 S(ak(n)) 函数的值分布. . . . . . . . . . . . . . . . . 21 1.10 两个包含Smarandache 函数的方程. . . . . . . . . . . . 25 1.11 S(n) 函数及其均值. . . . . . . . . . . . . . . . . . 27 第二章Smarandache 对偶函数 . . . . . . . . . . . . . . . . .30 2.1 引言. . . . . . . . . . . . . . . . . . . . . . . . 30 2.2 Smarandache 对偶函数的渐近公式. . . . . . . . . . . . 30 2.3 关于Smarandache 对偶函数的一个方程. . . . . . . . . . 33 2.4 关于Smarandache 对偶函数S¤¤(n) . . . . . . . . . . . 37 2.5 一个包含SM(n) 函数的方程. . . . . . . . . . . . . . 40 2.6 一个包含Smarandache 对偶函数的方程. . . . . . . . . . 44 第三章关于SL(n) 函数及其对偶函数的性质 . . . . . . . . . . . . . . . . .48 3.1 引言. . . . . . . . . . . . . . . . . . . . . . . . 48 3.2 SL(n) 函数的渐近公式. . . . . . . . . . . . . . ....

Description Details
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....

Table of Contents Details
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...

Description Details
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....

Table of Contents Details
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...

Description Details
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....

Description Details
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....

Excerpt Details
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...

Table of Contents Details
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...

Description Details
In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein’s four dimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed....

Excerpt Details
1.2 The basics of neutrosophy Neutrosophy studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. It considers that every idea tends to be neutralized, balanced by ideas; as a state of equilibrium. Neutrosophy is the basis of neutrosophic logic, neutrosophic set which generalizes the fuzzy set, and of neutrosphic probability and neutrosophic statistics, which generalize the classical and imprecise probability and statistics respectively. Neutrosophic Logic is a multiple-valued logic in which each proposition is estimated to have percentages of truth, indeterminacy, and falsity in T, I, and F respectively, where T, I, F are standard or non-standard subsets included in the non-standard unit interval ] −0, 1+[. It is an extension of fuzzy, intuitionistic, paraconsistent logics. ...

Table of Contents Details
Preface of the Editor 4 Chapter 1 PROBLEM STATEMENT . THE BASICS OF NEUTROSOPHY 1.1 Problem statement 5 1.2 The basics of neutrosophy 8 1.3 Neutrosophic subjects 13 1.4 Neutrosophic logic. The origin of neutrosophy 14 1.5 Definitions of neutrosophic 16 Chapter 2 TRAJECTORIES AND PARTICLES 2.1 Einstein’s basic space-time 18 2.2 Standard set of trajectories and particles. A way to expand the set 22 2.3 Introducing trajectories of mixed isotropic/non-isotropic kind 28 2.4 Particles moving along mixed isotropic/non-isotropic trajectories 31 2.5 S-denying the signature conditions. Classification of the expanded spaces 35 2.6 More on an expanded space-time of kind IV 45 2.7 A space-time of kind IV: a home space for virtual photons 52 2.8 A space-time of kind IV: non-quantum teleportation of photons 55 2.9 Conclusions 59 Chapter 3 ENTANGLED STATES AND QUANTUM CAUSALITY THRESHOLD 3.1 Disentangled and entangled particles in General Relativity. Problem statement 61 3.2 Incorporating entangled states into General Relativity 64 3.3 Quantum Causality Threshold in General Relativity 69 3.4 Conclusions 72 Biblio...

Description Details
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....

Excerpt Details
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....

Table of Contents Details
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...

Description Details
Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The Principia is "justly regarded as one of the most important works in the history of science". The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of mathematical Principles of natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton, spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses." A more recent assessment has been that while acceptance of Newton's theories was not immediate, by the end of a century after publication in 1687, "no one could deny...

Description Details
In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinatorialization, implicated in the foreword of Chapter 5 of my book Automorphism groups of Maps, Surfaces and Smarandache Geometries (USA, 2005). This conjecture is essentially a philosophic notion for developing mathematical sciences of 21st century, which means that we can combine different fields into a union one and then determines its behavior quantitatively. It is this notion that urges me to research mathematics and physics by combinatorics, i.e., mathematical combinatorics beginning in 2004 when I was a post-doctor of Chinese Academy of Mathematics and System Science. It finally brought about me one self-contained book, the first edition of this book, published by InfoQuest Publisher in 2009. This edition is a revisited edition, also includes the development of a few topics discussed in the first edition....

Excerpt Details
1.5 ENUMERATION TECHNIQUES 1.5.1 Enumeration Principle. The enumeration problem on a finite set is to count and find closed formula for elements in this set. A fundamental principle for solving this problem in general is on account of the enumeration principle: For finite sets X and Y , the equality |X| = |Y | holds if and only if there is a bijection f : X → Y . Certainly, if the set Y can be easily countable, then we can find a closed formula for elements in X....

Table of Contents Details
Contents Preface to the Second Edition . . . . . . . . . . . . . . . . . . . i Chapter 1. Combinatorial Principle with Graphs . . . . . . . . . . 1 1.1 Multi-sets with operations. . . . . . . . . . . . . . . . . . . . .2 1.1.1 Set . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Boolean algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Multi-Set . . . . . . . . . . . . . . . . . . . . . . . . . .8 1.2 Multi-posets . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.1 Partially ordered set . . . . . . . . . . . . . . . . . . . . .11 1.2.2 Multi-Poset . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Countable sets . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Countable set . . . . . . . . . . . . . . . . . . . . 16 1.4 Graphs . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . .18 1.4.2 Subgraph . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.3 Labeled graph. . . . . . ...