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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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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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x3. Some Observations Some observations about the Pseudo-Smarandache Function are given below : Remark 3.1. Kashihara raised the following questions (see Problem 7 in [1]) : (1) Is there any integer n such that Z(n) > Z(n + 1) > Z(n + 2) > Z(n + 3)? (2) Is there any integer n such that Z(n) < Z(n + 1) < Z(n + 2) < Z(n + 3)? The following examples answer the questions in the affirmative: ...

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A. Majumdar : A note on the Pseudo-Smarandache function 1 S. Gupta : Primes in the Smarandache deconstructive sequence 26 S. Zhang and C. Chen : Recursion formulae for Riemann zeta function and Dirichlet series 31 A. Muktibodh : Smarandache semiquasi near-rings 41 J. Sandor : On exponentially harmonic numbers 44 T. Jayeo. la : Parastrophic invariance of Smarandache quasigroups 48 M. Karama : Perfect powers in Smarandache n-expressions 54 T. Jayeo. la : Palindromic permutations and generalized Smarandache palindromic permutations 65 J. Sandor : On certain inequalities involving the Smarandache function 78 A. Muktibodh : Sequences of pentagonal numbers 81 J. Gao : On the additive analogues of the simple function 88 W. Zhu : On the primitive numbers of power p 92 A. Vyawahare : Smarandache sums of products 96 N. Yuan : On the solutions of an equation involving the Smarandache dual function 104 H. Zhou : An in¯nite series involving the Smarandache power function SP(n) 109...

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The present book, being a sequel to Dialectics of Force: Ontobia, is dedicated to the topics of progress and force of society - topics that may appear trivial at first sight, for a mountain of literature has been written on them. The author, however, having conscientiously presented the views on progress and force of all prominent thinkers over the past and the present, chose to follow a distinct path and formulated the criteria of progress based on entirely different scientific paradigms. Moreover, he dared to formulate the two Principles of Social Development, which are akin in their fundamental nature to the first and second laws of thermodynamics. The result is a book that is very complex in content. Nonetheless, the style of presentation used throughout most of the work makes it accessible even to those who have never read Hegel....

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This book is intended for instructors and students of philosophy and social sciences, and also for all those who are interested in problems of man and mankind....

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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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Set in a future in which humanity’s dream of total equality is fully realized and poverty in terms of material wealth has been eliminated, humanity has straight-jacketed itself into the only social system which could make this possible. Class differentiation is entirely horizontal rather than vertical and no matter what one’s chosen field, all advancement is based solely on seniority rather than ability. What is an intelligent and ambitious man to do when enslaved by a culture that forbids him from utilizing his God-given talents? If he’s a military officer in time of war, he might just decide to switch sides. If said officer is a true believer in the principles that enslave him and every bit as loyal as he is ambitious, that’s tantamount to breaking a universal law of physics, but Colonel Sebastian MacMaine has what it takes to meet the challenge. (Summary by Lee)...

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Science fiction

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In this theoretically sophisticated monograph Dr. Alex Battler formulates a new ontological interpretation of the category of force: - a definition of force as an ontological category; - the manifestation of force in the inorganic world within the framework of the idea of the Big Bang; - a definition of force in the organic world to determine the boundary between life and nonlife; - a solution to the mind–body problem (i.e., what consciousness and thought are), which has led me to a new formulation of the concept of Progress. ...

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PREFACE......................................................................................................9 INTRODUCTION: LEXICON AND METHOD....................................17 CHAPTER I. THE PHENOMENOLOGY OF FORCE.........................31 1. Foreword.............................................................................................32 2 . Ancient Greek Philosophers On Force............................................35 3. The Philosophy of Force in the Works of European Philosophers of the 15th–19th Centuries.................................................................41 Nicholas of Cusa..........................................................................41 Leonardo da Vinci.......................................................................42 Bernardino Telesio and Francis Bacon.......................................44 René Descartes and Isaac Newton..............................................47 Benedict de Spinoza....................................................................50 John Locke...................................................................................51 ...

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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...

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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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0. In 1999, the second author of this remarks published a book over 30 of Smarandache's problems in area of elementary number theory (see [1, 2]). After this, we worked over new 20 problems that we collected in our book [28]. These books contain Smarandache's problems, described in [10, 16]. The present paper contains some of the results from [28]. In [16] Florentin Smarandache formulated 105 unsolved problems, while in [10] C.Dumitresu and V. Seleacu formulated 140 unsolved problems of his. The second book contains almost all the problems from [16], but now each problem has unique number and by this reason in [1, 28] and here the authors use the numeration of the problems from [10]. In the text below the following notations are used....

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V. Mladen and T. Krassimir : Remarks on some of the Smarandache's problem. Part 2 1 W. Kandasamy : Smarandache groupoids 27 L. Ding : On the primitive numbers of power P and its mean value properties 36 D. Torres and V. Teca : Consecutive, reversed, mirror, and symmetric Smarandache sequence of triangular numbers 39 D. Ren : On the square-free number sequence 46 T. Ramaraj and N. Kannappa : On ¯nite Smarandache near-rings 49 X. Kang : Some interesting properties of the Smarandache function 52 L. Mao : On Automorphism Groups of Maps, Surfaces and Smarandache Geometries 55 L. Ding : On the mean value of Smarandache ceil function 74 M. Le : An equation concerning the Smarandache function 78 M. Bayat, H. Teimoori and M. Hassani : An extension of ABC-theorem 81 J. Ma : An equation involving the Smarandache function 89 C. Chen : Inequalities for the polygamma functions with application 91 W. Vasantha and M. Chetry : On the number of Smarandache zero-divisors and Smarandache weak zero-divisors in loop rings 96 M. Le : The function equation S(n) = Z(n) 109 Z. Li : On the Smarandache Pseudo-number Sequences 111 D. Mehendale :...

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This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigations while, Part 2 presents several applications of this new theory. Some ideas in this book are still under current development or improvements, but we think it is important to propose them in order to share ideas and motivate new debates with people interested in new reasoning methods and information fusion. So, we hope that this second volume on DSmT will continue to stir up some interests to researchers and engineers working in data fusion and in artificial intelligence....

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Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . 6 1.2.2 The conjunctive rule . . . . . . . . . 6 1.2.3 The disjunctive rule . . . . . . . . . 8 1.2.4 Dempster’s rule of combination . . . . . . . 8 1.2.5 Smets’ rule of combination . . . . . . . 9 1.2.6 Yager’s rule of combination . . . . . . . 9 1.2.7 Dubois & Prade’s rule of combination . . . . . . 9 1.2.8 The hybrid DSm rule . . . . . . . . 10 1.3 The general weighted operator (WO) . . . . . . . 11 1.4 The weighted average operator (WAO) . . . . . . . 12 1.4.1 Definition . . . . . . . . . 12 1.4.2 Example for WAO . . . . . . . . . 13 1.4.3 Limitations of WAO . . . . . . . . . 13 1.5 Daniel’s minC rule of combination . . . . . . . 14 1.5.1 Principle of the minC rule . . . . . . . 14 1.5.2 Example for minC . . . . . . . . . 15 1.6 Principle of the PCR rules . . . . . . . . . 20 1.7 The...

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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....

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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....

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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. . . . . . ...

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The July-August-September, 2011 edition of Hinduism's flagship spiritual magazine, Hinduism Today, has been released in digital form and is now available for free on your desktop. This issue takes you on a wondrous adventure through time as well as culture showcasing nine historic sites of ancient India. Get ready for an awe inspiring and thought provoking journey! We start with true our feature article with a magnificence recognizable by all of humanity. These nine ancient Hindu related sites demonstrate craftsmanship and artwork so awe-inspiring that the United Nations’s body for education, science and culture, (UNESCO) has deemed them as worthy of protection and care for the benefit of all of humanity. Our writers and photographers explore these temples and caves, dating back as early as 200 bce, introducing us to a depth and breadth of the rich Hindu landscape. You will be charmed by the historical accounts from western explorers. On a heart warming note, the middle section of this issue introduces our newly published "Hindu Children's Modern Stories, Books One and Two." These books bring the wisdom of the traditional yama...

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The first issue of the Kamehameha Journal of Education was published in January 1990 to share ideas, strategies, and research about the education of Hawaii's children. The Journal grew from 1,000 copies to 3,500 copies per issue over a period of six years. Hana Hou is a collection of articles from all twelve issues that represents the breadth of topics the Journal explored. We saw this journal as a chance to improve education and bring important information, strategies, views, and data to educators. We saw it as a vehicle for change: a chance to inform the education of Hawaii's children through research, successful practice, and curriculum and instruction that was relevant, interesting, and meaningful for students. Most of all, we wanted to make a difference for children. The Journal was more than a record of information or a vehicle for authors who were already writing for national journals. Rather, the editors, coming from a variety of disciplines including education, anthropology, clinical psychology, and the Kamehameha Elementary Education Program (KEEP) were able to identify methods and research that were effective and...

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Teaching and learning can—and does—go on in strange places. For so long, parents and teachers delegated learning to a formal setting with four walls, books, and a teacher teaching. Yet, those same parents and teachers taught children many unplanned—and often unintended—attitudes, language, and knowledge outside those walls. We learn from everything we do and the keys are our models and the richness of the learning environment. The three articles in this section describe how experiential, hands-on learning in widely varied contexts beyond the formal classroom may be more exciting, meaningful, memorable, and useful than the traditional style of education that students are largely accustomed to. Editors Gisela Speidel and Kristina Inn describe an unforgettable learning experience with master navigator Nainoa Thompson in “The Ocean Is My Classroom. ” Nainoa describes his path of learning from those who loved and cared for him through what felt like irrelevant school experiences, to his education aboard the Hokulea. In “A Hitchhiker's Guide to Technology,” Ian Jamieson shows us how to make a subject—as abstract and difficult...

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Introduction. 3 -- The Ocean Is My Classroom-Gisela E. Speidel & Kristina Inn Fall 1994. 7 -- A Hitchhiker's Guide To Technology-Ian Jamieson Summer 1995. 19 -- Home Schooling: A Way Of Life L.-Sierra Knight Fall 1994. 31 -- Learning And Teaching The Hula-Mele Ah Ho Fall 1994. 41 -- Information Literacy: A Challenge For Critical Thinking-Elaine Blitman Summer 1995. 49 -- An ?ohana Of Writing Teachers-Joy Marsella Fall 1993. 55 -- Eric Chock: Poet In The Schools-Wendie Yumori Spring 1993. 71 -- Whole Language: Some Thoughts-Ramona Newton Hao March 1991. 83 -- Methods: Teaching And Learning Principles-Anthony J. Picard & Donald B. Young September 1990. 93 -- Encouraging Voluntary Reading-Alice J. Kawakami January 1990 -- 109 -- Cultural Aspects Of Learning And Teaching The Child As A Member Of A Culture-Ginger Fink May 1990. 117 -- Becoming A Teacher In A Multicultural Classroom-Virgie Chattergy Fall 1993. 123 -- The Role Of Culture In Minority School Achievement-Cathie Jordan Fall 1992. 135 -- Kula Kaiapuni: Hawaiian Immersion Schools-Lilikala Kame?eleihiwa Fall 1992. 151 -- When Children Don't Speak The Language Of Instruction-Gisel...

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Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

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

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

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The Incunabula Papers are arguably the first immersive online legend complex that introduced readers to a host of content, including what religious historian Robert Ellwood has called the “alternative reality tradition. – Legend-Tripping Online: Supernatural Folklore and the Search for Ong’s Hat...

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INCUNABULA A Catalog of Rare Books, Manuscripts & Curiosa Conspiracy Theory, Frontier Science & Alternative Worlds Emory Cranston, Prop.Incunabulum: cocoon; swaddling clothes; cradle; in-cunae, in the cradle; koiman, put to sleep, winding- sheet; koimetarium (cemetery); printed books before 1501, hence by extension any rare & hermetic book… Introduction This catalog is a reproduction. This is not a commercial advertisement. ECommerce links to the available books are offered a as courtesy to researchers. Consider this first file an unusually complete bibliography to the story that unravels in the companion files. No book for sale here was actually printed before 1501, but they all answer to the description ” rare and hermetic” – even the mass market paperbacks, not to mention the xeroxes of unpublished manuscripts, which cannot be obtained from any other source! The symbol INCUNABULA was chosen for our company for it’s shape – cocoon, egg-like, gourd-like, the shape of Chaos according to Chaung Tzu. Cradle: beginnings. Sleep: dreams. Silken white sheets of birth and death; books, white pages, the cemetery of ideas. Thi...

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. Incunabula A Catalogue of Rare Books, Manuscripts & Curiosa. 2. Ong's Hat: Gateway to the Dimensions! A full color brochure for the Institute of Chaos Studies and the Moorish Science Ashram in Ong's Hat, New Jersey. 4. Joseph Matheny's Journal 3. Advances in Skin Science: Quantum Tantra...

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In the 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. There are a few papers which are not directly related to but should fall within the scope of Smarandache type problems. They are 1. L. Liu and W. Zhou, On conjectures about the class number of binary quadratic forms; 2. W. Liang, An identity for Stirling numbers of the second kind; 3. Y. Wang and Z. Sheng, Two formulas for x^n in terms of Chebyshev polynomials. 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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On Algebraic Multi-Vector Spaces Abstract A Smarandache multi-space is a union of n spaces A1;A2;An with some additional conditions hold. Combining these Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. Some characteristics of multi-vector spaces are obtained in this paper. Keywords Vector, multi-space, multi-vector space, dimension of a space. x1. Introduction These multi-spaces was introduced by Smarandache in under his idea of hybrid mathematics: combining different fields into a unifying field, which can be formally defined with mathematical words by the next definition. ...

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L. Mao : On Algebraic Multi-Vector Spaces 1 L. Liu and W. Zhou : On conjectures concerning class number of binary quadratic forms 7 W. Zhai and H. Liu : On square-free primitive roots mod p 15 X. Pan : A new limit theorem involving the Smarandache LCM sequence 20 M. Le : The Smarandache Perfect Numbers 24 N. Yuan : On the solutions of an equation involving the Smarandache dual function 27 J. Wang : Mean value of a Smarandache-Type Function 31 H. Yang and R. Fu : On the mean value of the Near Pseudo Smarandache Function 35 W. Liang : An Identity of Stirling Numbers of the Second Kind 40 R. Ma : On the F.Smarandache LCM Ratio Sequence 44 L. Mao : On Algebraic Multi-Ring Spaces 48 Y. Han : On the Product of the Square-free Divisor of a Natural Number 55 P. Zhang : Some identities on k-power complement 60 Y. Wang and Z. Sheng : Two Formulas for xn being Represented by Chebyshev Polynomials 64 X. Chen : Two Problems About 2-Power Free Numbers 70 X. Ma : The Asymptotic Formula of P n·x log Pad(n) 72 Q. Tian : On the K-power free number sequence 77 C. Lv : On a generalized equation of Smarandache and its integer sol...

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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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x1. Introduction The study of Smarandache loops was initiated by W.B. Vasantha Kandasamy in 2002. In her book [19], she defined a Smarandache loop (S-loop) as a loop with at least a subloop which forms a subgroup under the binary operation of the loop. For more on loops and their properties, readers should check [16], [3], [5], [8], [9] and [19]. In her book, she introduced over 75 Smarandache concepts on loops. In her ¯rst paper [20], she introduced Smarandache : left(right) alternative loops, Bol loops, Moufang loops, and Bruck loops. But in this paper, Smarandache : inverse property loops (IPL), weak inverse property loops (WIPL), G-loops, conjugacy closed loops (CC-loop), central loops, extra loops, A-loops, K-loops, Bruck loops, Kikkawa loops, Burn loops and homogeneous loops will be introduced and studied relative to the holomorphs of loops. Interestingly, Adeniran [1] and Robinson [17], Oyebo [15], Chiboka and Solarin [6], Bruck [2], Bruck and Paige [4], Robinson [18], Huthnance [11] and Adeniran [1] have respectively studied the holomorphs of Bol loops, central loops, conjugacy closed loops, inverse property loops, A-loops,...

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T. Jayeo. la : An holomorphic study of the Smarandache concept in loops 1 Z. Xu : Some arithmetical properties of primitive numbers of power p 9 A. Muktibodh : Smarandache Quasigroups 13 M. Le : Two Classes of Smarandache Determinants 20 Y. Shao, X. Zhao and X. Pan : On a Subvariety of + S` 26 T. Kim, C. Adiga and J. Han : A note on q-nanlogue of Sandor's functions 30 Q. Yang : On the mean value of the F. Smarandache simple divisor function 35 Q. Tian : A discussion on a number theoretic function 38 X. Wang : On the mean value of the Smarandache ceil function 42 Y. Wang : Some identities involving the Smarandache ceil function 45 J. Yan, X. Ren and S. Ma : The Structure of principal lters on po-semigroups 50 Y. Lu : F. Smarandache additive k-th power complements 55 M. Le : The Smarandache reverse auto correlated sequences of natural numbers 58 M. Karama : Smarandache partitions 60 L. Mao : On Algebraic Multi-Group Spaces 64 F. Russo : The Smarandache P and S persistence of a prime 71 Y. Lu : On the solutions of an equation involving the Smarandache function 76 H. Ibstedt : A Random Distribution Experiment 80 L. Mao...

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“I like the idea of mental synthesis very much ... I quite agree that language evolved in a way that facilitates synthesis and transmission of the synthesized mental image. ... I don't think there can be much doubt, purely conceptually, that language was a late arrival. Whatever mutation provided the key to it would have had no selectional advantage at all, and would have just been a useless “organ,” if it could not have linked up to pre-existing thought systems.” —NOAM CHOMSKY, Professor Emeritus of Linguistics, MIT “Boston University’s Andrey Vyshedskiy brings a neuroscientist’s perspective to the discussion of human mental history in On the Origin of the Human Mind.” —Scientific American Mind (July 2009) “I found the Mental Synthesis theory stimulating and provocative. The author puts forward an explanation for the evolution of the human mind based on predator detection that led to increased visual mental analysis which set the stage for visual mental syntheses. The author presents an impressive array of recent research on the brain with up to date references that are highly relevant to his case and the origin of mi...

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Introduction While studying the neuroscience of consciousness, I was struck with certain facts about mental imagery that seemed to shed some light on the process of the evolution of the human mind. The origin of the human mind remains one of the greatest mysteries of all times. The last 150 years, since Charles Darwin proposed that species evolve under the influence of natural selection (Darwin C, 1859), have been marked by great discoveries. Molecular biology described the genetic principles underlying species evolution and identified specific changes in the human genome since our lineage split off from the chimpanzee line about six million years ago (Somel M, 2013). Great paleontological discoveries have filled that span of six million years of human evolution with a number of intermediate species that display both human- and ape-like characteristics. However, the discussion of the evolution of the human intellect and specific forces that shaped the underlying brain evolution is as vigorous today as it was in Darwin’s times. At the center of the predicament about the origin of the human mind lies the question of human uniqu...

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Introduction 1 Part 1. Neuroscience of imagination 5 Chapter 1. Object encoding in the brain 6 Chapter 2. Neuronal synchronization 26 Chapter 3. Imagining new objects 32 Chapter 4. External manifestations of mental synthesis 39 Chapter 5. Humans versus animals 80 Chapter 6: Overall Discussion of Part 1 108 Part 2. Evolution of the Human Mind 135 Chapter 7. Introduction: a quick guide to paleoanthropology 136 Chapter 8. Cognitive evolution through the prism of paleontological evidence 160 Chapter 9. Evolutionary pressure drives better predator detection 191 Chapter 10. Overall Discussion of Part 2 219 Part 3. The “last” mutation 254 Chapter 11. The role of the prefrontal cortex in the process of mental synthesis 256 Chapter 12. Evolution of the prefrontal cortex 277 Conclusions 327 A wish list of experiments 339 Appendix 367 Acknowledgments 400 Bibliography 401 Illustrations credits 428 About the author 430 ...

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The Rise of Peace is an English version Of Urdu Novel“ Tuloo e Amn ” Dedicated to all victims of terrorist attacks (Muslims, Non Muslims) The Scenario… The Central Theme This Novel has been written in the context of present day fast changing political scenario of the world. Most important international burning issues have been touched in this novel in the most skilful and careful manner. Shall this peace seeking world ever reach the lasting peace..? There is destruction of all anti peace world forces in attempt to convert this world into peaceful world. All nations live peacefully in the long run. People respect each other’s religious, territorial limits and social taboo. This Novel is an action and adventure based fiction and an attempt to make this world as joint peaceful global village free of discriminations of caste and racial and Islamic and non Islamic likes and dislikes. Author seems to stress upon the fact that discriminations of this sort are very fatal for the restoration of world peace. Unless this discrimination is not completely finished it is almost impossible to convert this world into one peaceful ...

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Bismillah Hirrahmaan Nirraheem In the name of Allah Almighty, The Most Gracious and The Most Merciful….The Most Beloved Prophet of Allah Almighty, Holy Prophet Muhammad (Peace Be Upon Him) ************************************* A Novel in English and Urdu An English Version Of Urdu Novel“ Tuloo e Amn ” Author of Both Versions; Dr. Hafiz Muhammad Shahid Amin Sheikh (MBBS, DLO) Pakistan. Copy Rights are Reserved Copyright © 2011 Dr. Hafiz Shahid Amin All rights reserved. Neither this publication nor any part of it may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of The Dr. Hafiz Shahid Amin. The Rise of Peace 3 Table of Contents Title Of Novel About The Author The Scenario The Preface Chapter-1….Meeting Of World Leaders Chapter-2….Dr Jabran and Robot Sunny Chapter-3….The Chief of ZSCIA Chapter-4… Killing of EX PM Chapter-5….The Naval Fleet of Zulimistan Chapter-6….Deaths of Muslim Leaders Chapter-7…. Zulimistan Thinkers Association Chapter-8…. President David of Zulimis...

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Table of Contents Title of Novel About The Author The Scenario The Preface Chapter-1 Meeting Of World Leaders Chapter-2 Dr. Jabran and Robot Sunny Chapter-3…. The Chief of ZSCIA Chapter-4 Killing of EX PM Chapter-5 The Naval Fleet of Zulimistan Chapter-6 Deaths of Muslim Leaders Chapter-7 Zulimistan Thinkers Association Chapter-8 President David of Zulimistan Chapter- 9 Chief of MFP Dr. Jabran Chapter- 10 Operation Tariq Bin Ziyad Chapter- 11 Missile Attacks on Zamaril Chapter -12 ZTA in Zulimistan Court Chapter -13 President’s Plans against ZTA Chapter -14 MFP Attacks Green House Chapter -15 MFP Attacks on Zulimistan Chapter -16 MFP Addresses to Zulimistan Chapter -17 President David in MFP Chapter -18 The Destructions in Zulimistan Chapter -19 Supreme Court Verdict Chapter -20 World Peace Formula ...

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The concept of science and the sciences. Fundamental and historical development in the sciences. Great ideas that revolutionize our scientific world. The story of the cell and Biology. The birth of modern Biology. The rise of the modern University and experimental stations. The cell as the basic building block of life. The origin of life. The development of microbiology and microscopy. The germ theory of diseases, vaccines, and antibiotics. The vector insects and infectious diseases. The virus, viral diseases, and vaccines. The principle of vegetation and the basic requirements of plants. William Harvey, the heart and the circulatory system. Carl Linneaus and the development of modern taxonomy in biology. Charles Darwin and the development of evolution in biology. Gregor Mendel and the development of genetics and the laws of heredity....

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THE GREATEST FUNDAMENTAL INVENTIONS CREATED BY MOTHER NATURE THE ATOM AND ITS CAPACITY TO STORE AND RELEASE UNIVERSAL ENERGY BY MEANS OF PHYSICAL AND CHEMICAL PROCESSES THE CELL AND ITS CAPACITY TO SUSTAIN INDEPENDENT LIFE BY MEANS OF UNIQUE BIOLOGICAL PROCESSES THE PROCESS OF PHOTOSYNTHESIS AND ITS CAPACITY TO TRANSFORM SOLAR (LIGHT) ENERGY INTO CHEMICAL AND FOOD ENERGY BY MEANS OF BIOCHEMICAL PROCESSES LIGHT AND ITS CAPACITY TO TRANSPORT ENERGY AND CHANGE OUR UNIVERSE BY TRANSFORMING DARKNESS INTO LIGHTNESS BY THE MIRACLE OF ILLUMINATION THE PHENOMENON OF ELECTROMAGNETISM AND ITS CAPACITY TO PRODUCE THE DYNAMIC ELECTRIC CURRENT THAT ENERGIZES AND POWERS OUR UNIVERSE AND THE MOST FUNDAMENTAL OF ALL OF NATURE’S INTUITIVE CREATIONS IS THE PROCESS OF UNIVERSAL TRANSFORMATION, WHERE PHYSICAL, CHEMICAL AND BIOLOGICAL EVOLUTION TRANSFORM MATTER, ENERGY, SPACE, TIME AND LIFE ITSELF ...

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INTRODUCTION 1 ABSTRACT ON THE CONCEPT OF PERSPECTIVE AND SENSE OF DUTY 4 THE CONCEPT OF SCIENCE 5 FUNDAMENTAL AND HISTORIC DEVELOPMENTS IN THE SCIENCES 7 ABSTRACT ON THE ATOM AND ITS ENERGY 11 GREAT IDEAS THAT REVOLUTIONIZED OUR SCIENTIFIC WORLD 16 DEMOCRITUS (470 - 380 BC) Greek Philosopher 16 NICHOLAS COPERNICUS (1473 - 1543) Polish Astronomer 17 GALILEO GALILEI (1564 - 1642) Italian Mathematician and Astronomer 18 RENE DESCARTES (1596 - 1650) French Mathematician and Philosopher. 19 ISAAC NEWTON (1642 - 1727) English Scientist and Mathematician 20 ANTOINE LAVOISIER (1743 - 1794) French Chemist 23 JOHN DALTON (1766 - 1844) English Chemist 24 JONS J. BERZELIUS (1779 - 1848) Swedish Chemist 25 HUMPHRY DAVY (1778 - 1829) English Chemist 25 AMEDEO AVOGADRO (1776 - 1856) Italian Physicist 26 DMITRI MENDELEEV (1834 - 1907) Russian Chemist 26 FRIEDRICH A. KEKULE (1829 - 1896) German Organic Chemist 27 JACOBUS VAN’T HOFF (1852 - 1911) Dutch Physical Chemist 28 WILLIAM H. WOLLASTON (1766 - 1828) English Chemist and Physicist 28 EDWARD FRANKLAND (1825 - 1899) English Chemist 29 SVANTE A. ARRHENIUS (1859 -...

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The 2000 year history of the atom and chemistry, from the Classic Greek Era to the present, is described in 800 pages, depicted with some 300 pictures and illustrations. This history of the atom and chemistry discusses the lives of about 180 chemists and physicists, through the evolution of several stages of development, representing the most important scientific accomplishments. The most significant discoveries in chemistry and physics are presented chronologically to illustrate their contributions to the creation of the chemical sciences during the last 21 centuries....

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INTRODUCTION It is a genuine pleasure and challenge for me to try to express the full extent of my emotions and reasons for writing this book on the STORY OF THE ATOM AND THE SCIENCES, with special reference to the CHEMICAL SCIENCES. In one sentence, I can distill the essence of the purpose for this study by simply stating that it has been a labor of love that transcended the written word because sentiments and ideas belong in the realm of the ethereal and the philosophical as well as in the domain of LITERATURE and SCIENCE. Ever since a young and impressionable student attending a country school in a community of a few hundred people, began to be introduced to the world of knowledge over 65 years ago, the sciences became to me what water is to fish, air is to birds and earth is to humanity. The introduction to the mathematical, physical, chemical and biological sciences felt like reading a beautiful poem or listening to a romantic melody. In essence, it was truly a joyful experience, full of the enigmatic, the mysterious and the fantastic, beyond my wildest imagination. The words used in the title of this book, were car...

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TABLE OF CONTENTS INTRODUCTION 1 THE STORY OF THE ATOM AND CHEMISTRY 7 THE CAVE MAN 7 ABSTRACT ON THE CONCEPT OF PERSPECTIVE AND SENSE OF DUTY 8 THE MIGRATORY AND THE SEDENTARY MAN 9 ABSTRACT ON THE ATOM AND ITS ENERGY 11 THE CLASSIC GREEK AND ROMAN PHILOSOPHERS 17 EMPEDOCLES (492-432 BC) Greek Philosopher 20 Proposed the four basic elements: earth, water, air and fire. DEMOCRITUS (470-380 BC) Greek Philosopher 22 The founder of the atomic theory of antiquity. CLAUDIUS PTOLEMY (100-170) Greek Astronomer 24 Proponent of the geocentric theory of our solar system with the Earth and not the Sun at its center. ABSTRACT ON THE GENESIS OF AN ORDERLY AND SYSTEMATIC UNIVERSE 25 THE ALCHEMY OF ANTIQUITY AND THE MIDDLE AGES 32 THE METAL INDUSTRY OF ANTIQUITY 33 Mercury, Copper, Bronze, Iron and Steel. GEBER (721-815) Arabian Alchemist 38 One of the first scholars and alchemists of the Islamic world. OMAR KHAYYAM (12th Century). Persian Scientist and Astronomer 38 Brilliant astronomer and alchemist of the 12th Century. BERNARDO TREVISAN (1406 -1490) Italian Alchemist 39 One of the most famous alchemists of th...

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The whole paradoxist distich should be as a geometric unitary parabola, hyperbola, ellipse at the borders between art, philosophy, rebus, and mathematics – which exist in complementariness. The School of Paradoxist Literature, which evolved around 1980s, continues through these bi-verses closed in a new lyric exact formula, but with an opening to essence. For this kind of procedural poems one can elaborate mathematical algorithms and implement them in a computer: but, it is preferable a machine with … soul!...

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I M M O D E S T With the shame Shamelessness U N D E C I D E D Fighting Himself J A Z Z ( I ) Melodious Anarchy J A Z Z ( I I ) Anarchic Melody...

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Fore/word and Back/word _________ 3 The making of the distich : _____ 3 Characteristics: ______________ 3 Historical considerations: _____ 5 Types of Paradoxist distiches ___ 8 1. Clichés paraphrased: ___ 8 2. Parodies: _____________ 8 3. Reversed formulae: ____ 8 4. Double negation _______ 8 5. Double affirmation, ____ 8 6. Turn around on false tracks: _________________ 8 7. Hyperboles (exaggerated): __________________ 8 8. With nuance changeable from the title: ________ 8 9. Epigrammatic: ________ 8 10. Pseudo-paradoxes: ___ 8 11. Tautologies: ________ 9 12. Redundant: _________ 9 13. Based on pleonasms: _ 9 14. or on anti-pleonasms: 9 15. Substitution of the attribute in collocations ___ 9 16. Substitution of the complement in collocations 9 17. Permutation of various parts of the whole: ___ 9 18. The negation of the clichés ______________ 10 19. Antonymization (substantively, adjectively, etc.) ________________ 10 20. Fable against the grain: _________________ 10 21. Change in grammatical category (preserving substitutions’ homonymy): ________________ 10 22. Epistolary or colloquia style: _________...

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

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

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

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

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

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