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"Essayist Performance" This book demonstrates that artistic movement paradox lies founded by Romanian Smarandache far from reflecting a crisis of literature, it reconstructs, in an original and attractive. In this sense - appreciate Titu Popescu - movement is "an extension and formal doctrinal orientation destructionist that decade 70 - 80, has dominated American criticism", its source being in antimetaphyisics Nietzsche and Heidegger, in his critique of Freudian psychological identity....

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Titu Popescu reuşeşte să deosebească, în concertul policrom şi polifon al literaturii române, apariţia unei noi mişcări: mişcarea paradoxistă. Şi nu numai că o descoperă, dar o şi explică, analizându- i originile şi caracteristicile. Titu Popescu fails to distinguish the multicolored and polyphonic concert of Romanian literature, a new movement: movement paradoxist. And not only reveals, but also explains, analyzing its origins and characteristics....

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This play does not represent time in suspension or a snapshot cartoon, but rather a living entity in never ending motion. As with two people reading the same book but not imagining the same things, the actors and producers will be the true creators of new models and ideas due to the existing framework. Consider the theater as a painting with ideas made out of a malleable material. Time stamps its features upon it and producers remodel its structure. Actors, as factors from the literary system, influence the "personality" of the characters through their own personalities. ...

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In some places, some speeches may be adapted or the actors may improvise for a better connection between the moduli and the integrity of the play. In order to test the reaction of the audience, to measure the flair of the critics for the illogicality of the play, and to determine the force of electricity in the thinking and power of adaptability to the environment to the unpropitious conditions of living (Darwin's theory) of the spectators in a hostile and constraining world, the producer may create other variants to break the above conditions to realize totally illogical plays. I hope there will be an exact distinction between "the absurd" and "the illogical." The "absurd" has its absurd logical while the "illogical" has none. We can afford this illogicality because the world depicted in this play is an illogical one. It is an upside-down DRAMA. So the variants: IBAF H CG ED HGB DIF ACE GCE B AHI DF, are distinct illogical plays, even with the permutations done into the moduli G or G. Let's be serious even in... the unreliableness. ...

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Mathematician and author of over fifteen books published in Romania, Morocco, France, and USA, and winner of the poet contest literature from Bergerac, initiator of Curenlului Paradoxist now that the Corporate, holder of Honeywell computers (Phoenix · Arizona), Florentin Smarandache, in the 38 years old, consciousness is the magic word, and the fragility ~ and Flint. Putting their lives in the text, it gives us an exciting diary emigrant radiography in an area ecruţătoa unusual in that penetrates beyond the experience and you notice you expressed a rudimentary language, the desire to define the orientation and strategy self multiplied daily surface. 500 years after Columbus's first step into the world No AU a Romanian rediscovering America....

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The scholastic psychunlogy is the part of psychunlogy that studies the multiple aspects of the influence of the disorganized education practiced in schools, of the misprocesses resulted from the educational intervention with the psychological laws of the children’s education and instruction, of unlearning, of lifestyle deformation, and students’ personalities in the misprocess of educational instruction. Along with the child psychunlogy, the scholastic psychunlogy constitutes the principal source of misinformation and fundament of the science of parapedagogy. With this booklet, this unauthor introduces a new literary-scientific genre called psychological science fiction as part of the PARADOXISM movement in literature and science....

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The separation of psychunlogy from philosophy and its deformation as an autonomous science takes place, especially as a result of the great regresses registered in some of the unnatural sciences such as biology (the anatomy and biology of the nervous system, the neuronvegetative and endocrine systems, senses organs), and physics (the science that proved the possibility of mess-experimentations and non-objective and relative exact measurements)....

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Psychological Science Fiction (Unpreface) ................. 3 Table of Contents .................................. 4 Chapter 1 – The non-object and the psychunlogy’s problems .......... 7 The science of psychunlogy .............................. 7 The psychic, brain’s malfunction, non‐objective reflection of the non‐objective world ....... 7 The psychic misprocess of cognition .......................... 11 The psychic characteristics .............................. 12 The object of the scholastic psychunlogy ........................ 12 Chapter 2 – The unconscious psychic activity ............... 14 The conscienceless notion .............................. 14 The principal malfunctions of the conscienceless ..................... 15 The conscienceless dimensions ............................ 15 Self‐conscienceless (self‐awarenessless) ....................... 16 The collective self‐conscienceless (self‐awarenessless) .................. 16 The levels of disorganization of the psychic inhuman activities ................ 16 The psychic development in autogenesis ........................ 17 The factors of psychic’s non‐develop...

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The basic thesis of the paradoxism: Every thing/ phenomenon/ idea has a meaning and a non-meaning in a contradictory harmony. The essence of the paradoxism: a) The NonSense has a Sense: (and reciprocally) b) The Sense has a NonSense. The subsequent development of the paradoxism: To generalize the literature in scientific spaces ( Lobacevski, Riemann, Banach etc.), n-dimensional and infinite-dimensional spaces too. Paradoxism’s delimitation from other avant-gardes: ♦ paradoxism has a significance while dadaism, lettrism, the absurd movement do not; ♦ paradoxism especially reveals the contradictions, the antinomies, the anti- theses, antagonism, nonconformism, the paradoxes in other words of anything ( in literature, art, science), while futurism, cubism, abstractism and all other avant-gardes do not. The motto of the paradoxism: All is possible, the impossible too! The symbol of the paradoxism: A spiral - optic illusion or vicious circle. ...

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Intelligent creator, Florentin Smarandache has accumulated in the while enough self conviction in matters of paradoxism and enough (non)life ( literary and publishing inclusive) experience in order to create a coherent volume, where nothing ( or almost) is put/let at random. After Introduction in the empire of error ( a manifesto of the paradoxism too, but covered with another... linguistic packing), the volume continues with a “short resume” about the ... terror/theory’s features of Smarandache’s (non)existence/existentialism. Then in the shape of prose texts or verses (it is risky to name them prose or poetry!) we learn essential data and information about the “becoming” of this (almost) exile in his own country...Palillula. As another Villon, in full postmodernism he lets his testament of a man who lives, confessing his ideological and literary “crimes”, but, especially giving nonliterary declarations about his murderers, which ground their existence on his nonexistence! Also among his memories we met -true nightmares of the author- the caricatural portraits of the previous leaders, lampoons worthy of an Arghezi....

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A book of poems written by Florentin Smarandache whilst he was experiencing a dark time in life.

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EPILOGUE I leave you with my poems. Feel through me! I have achieves this volume in three years, but read it in T E N! It is a hut from the outside, and maybe a castle inside. (this volume holds connections with the earth!) The book has me between its covers - but now it is in its agony: ...

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Motto - 6 SHORT (AUTO)BIOGRAPHY - 7 THE MANIFESTO – PROGRAM - 9 =INAPPROPRIATE WORDS MADE APPROPRIATE= - 17 PEOPLE ARE FLYING THROUGH PEOPLE - 18 THE PHILOSOPHY OF PSYCHOLOGY - 19 OLD AGE WITHOUT YOUTH - 20 SCIENCE AND ART - 21 THIS OTHER WORLD - 22 VIVE LA PAIX! - 23 A NEEDED DRUG - 24 WESTERN POETRY - 25 PAZVANTE THE BLIND - 26 PHYSICAL EDUCATION / OF THE NERVES - 27 GEORGE DEVIL - 28 AT WORK: / WOMEN WITHOUT WORK - 29 ANTI-POEM OF LOVE - 30 ON WIMBLEY, IN BĂNIE - 31 COURSE OF GERMAN LANGUAGE - 33 FUSS WITH FISH – 34 PORTRAIT OF A GIRL - 35 SHE AND HE - 36 VIBRATIONS ON A SENSITIVE STRING - 37 A POSITIVE MINUS - 38 FRAGMENT OF FRAGMENT - 39 THE UNREAL IS REALITY - 40 BUREAUCRACY - 41 I LIVED MY LIFE / THE DYING WAY - 42 THE FIGHT OF OPPOSITES - 43 GO AHEAD, PLEASE! - 44 THEATER IN ABSURD - 45 HEARING AT GOD - 46 CITIZEN EDUCATION - 47 SCENE OF SCENERY - 48 DIALOGUE AT LONG DISTANCE - 49 THEATER ACTING - 50 DEMETER HAS DIED - 51 I EXIST AGAINST MYSELF - 52 ALLOW ME TO BE MYSELF - 53 CRIME WITHOUT PUNISHMENT - 54 LESSON OF PHILOSOPHY - 55 FLYING MANUAL - 56 PEACE TO YOU, LOVE - 57 LONG COUR...

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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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Parapedagogy is the science which studies the techniques of instruction and destruction and the deconfiguration of personality. It is concerned with non goals, discontents, anti principles, methods and disorganization forms of the education. In the misseducation research other disciplines are involved, such as the inhuman anatomy and psychology (especially the mass brain washing), the anti sociology of education which studies the psycho-asocial-anti-cultural medium and its sad influence over the personality. ...

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The parapedagogy definition The parapedagogy is the science which studies the techniques of instruction and destruction and the deconfiguration of personality. It is concerned with non goals, discontents, principles, methods and disorganization forms of the instruction and misseducation. The fundamental research in parapedagogy has the main goal to discover the laws and principles of parapedagogy, to establish an idealistic philosophy of the misseducation guideline in the misprocess of reconfiguration of the inhuman personality. The applicative research is preoccupied with student’s individuality, to detect and develop the inaptitude, anti talents, and the discovery of methods and procedures, which would decrease the school efficiency in its misprocess. In the parapedagogy research other disciplines are involved, such as the inhuman anatomy and psychology (especially the brain washing in mass), the sociology of misseducation which studies the psycho-asocial-anti-cultural medium and its influence over the personality. The historic and dialectic immaterialism constitutes the theoretical and methodological base of the parapedagogy res...

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Table of Discontents .................................5 Chapter 1 – Misseducation and Parapedagogy............... 10 Misseducation and parapedagogy...........................10 The miss concept of misseducation..........................13 Chapter 2 - The parapedagogic research.................. 14 The parapedagogy definition.............................14 The non‐objectives of parapedagogy research......................14 Research methods in parapedagogy..........................14 The biological bases of the psychological under development...............18 The role of the environment in personality disconfiguration................19 The rapport between maturity, learning, under‐development...............19 Chapter 3 - Knowledge about student’s personality .............20 The phases of intellectual under‐development......................20 The miss‐concepts of individual, person and personality..................21 The psychological miss‐concept of personality ......................22 Chapter 4 – Programs of study and characterization ............ 26 The main characteristics ...............................29 CHOLERIC...

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We have used the 2-adaptive fuzzy model having the two fuzzy models, fuzzy matrices model and BAMs viz. model to analyze the views of public about HIV/ AIDS disease, patient and the awareness program. This book has five chapters and 6 appendices. The first chapter just recalls the definition of four fuzzy models used in this book and gives illustration of some of them. Chapter two introduces the new n-adaptive fuzzy models. Chapter three uses for the first time 2 adaptive fuzzy models to study psychological and sociological problems about HIV/AIDS. Chapter four gives an outline of the interviews. Chapter five gives the suggestions and conclusion based on our study. Of the 6 appendices four of them are C-program made to make the working of the fuzzy model simple....

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In this chapter for the first time we introduce the new class of n-adaptive fuzzy models (n a positive integer and n ≥ 2) and illustrate it. These n-adaptive fuzzy models can analyze a problem using different models so one can get in one case the hidden pattern, in one case the maximum time period in some case output state vector for a given input vector and so on. So this new model has the capacity to analyze the problem in different angles, which can give multiple suggestions and solutions about the problem. This chapter has two sections. Section one defines the new model gives illustrations and section two defines some special n-adaptive models and proposes some problems....

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Chapter One SOME BASIC FUZZY MODELS WITH ILLUSTRATIONS 1.1 Fuzzy matrices and their applications 9 1.2 Definition and illustration of Fuzzy Relational Maps (FRMs) 16 1.3 Some basic concepts of BAM with illustration 20 1.3.1 Some basic concepts of BAM 22 1.3.2 Use of BAM Model to study the cause of vulnerability to HIV/AIDS and factors for migration 28 1.4 Introduction to Fuzzy Associative Memories (FAM) 35 Chapter Two ON A NEW CLASS OF N-ADAPTIVE FUZZY MODELS WITH ILLUSTRATIONS 2.1 On a new class of n-adaptive fuzzy models with illustrations 39 2.2 Some special n-adaptive models 49 Chapter Three USE OF 2-ADAPTIVE FUZZY MODEL TO ANALYZE THE PUBLIC AWARENESS OF HIV/AIDS 3.1 Study of the psychological and social problems the public have about HIV/AIDS patients using CETD matrix 52 3.2 Use of 2 adaptive fuzzy model to analyze the problem 72 Chapter Four PUBLIC ATTITUDE AND AWARENESS ABOUT HIV/AIDS 4.1 Introduction 77 4.2 Interviews 81 Chapter Five CONCLUSIONS 167 Appendix 1. Questionnaire 177 2. Table of Statistics 191 3. C-program for CETD and RTD Matrix 198 4. C-program for FRM 202 5. C-program for CFRM 2...

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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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The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem....

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1.2 Definition of Fuzzy Cognitive Maps In this section we recall the notion of Fuzzy Cognitive Maps (FCMs), which was introduced by Bart Kosko in the year 1986. We also give several of its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices. DEFINITION 1.2.1: An FCM is a directed graph with concepts like policies, events etc. as nodes and causalities as edges. It represents causal relationship between concepts. Example 1.2.1: In Tamil Nadu (a southern state in India) in the last decade several new engineering colleges have been approved and started. The resultant increase in the production of engineering graduates in these years is disproportionate with the need of engineering graduates. ...

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Dedication 5 Preface 6 Chapter One BASIC CONCEPTS 1.1 Definition of Interval Matrices and Examples 8 1.2 Definition of Fuzzy Cognitive Maps 9 1.3 An Introduction to Neutrosophy 13 1.4 Some Basic Neutrosophic Structures 16 1.5 Some Basic Notions about Neutrosophic Graphs 22 1.6 On Neutrosophic Cognitive Maps with Examples 28 1.7 Definition and Illustration of Fuzzy Relational Maps (FRMs) 33 1.8 Introduction to Fuzzy Associative Memories 40 1.9 Some Basic Concepts of BAM 43 1.10 Properties of Fuzzy Relations and FREs 49 1.11 Binary Neutrosophic Relations and their Properties 56 Chapter Two INTRODUCTION TO FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES AND THEIR GENERALIZATIONS 2.1 Fuzzy Interval Matrices 68 2.2 Interval Bimatrices and their Generalizations 76 2.3 Neutrosophic Interval Matrices and their Generalizations 92 Chapter Three FUZZY MODELS AND NEUTROSOPHIC MODELS USING FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES 3.1 Description of FCIMs Model 118 3.2 Description and Illustration of FRIM Model 129 3.3 Description of FCIBM model and its Generalization 139 3.4 FRIBM model and i...

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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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Neutrosophic Physics. Let be a physical entity (i.e. concept, notion, object, space, field, idea, law, property, state, attribute, theorem, theory, etc.), be the opposite of , and be their neutral (i.e. neither nor but in between). Neutrosophic Physics is a mixture of two or three of these entities , , and that hold together. Therefore, we can have neutrosophic fields, and neutrosophic objects, neutrosophic states, etc. Neutrosophic Physics is an extension of Paradoxist Physics, since Paradoxist Physics is a combination of physical contradictories and only that hold together, without referring to their neutrality . Paradoxist Physics describes collections of objects or states that are individually characterized by contradictory properties, or are characterized neither by a property nor by the opposite of that property, or are composed of contradictory sub-elements. Such objects or states are called paradoxist entities. ...

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2. The Gist of the Present Epistemology: The Surjective Qualon “Mere eruditic logic often turns – as has been generically said – philosophy into folly, science into superstition, and art into pedantry. How far away from creation and solitude, from play and imagination, from day and night, from noon and silhouette it is! How Genius is precisely everything other than being merely situational, alone as the Universe.” Herein we present a four-fold asymmetric theory of Reality whose essence – especially when properly, spontaneously understood – goes beyond the internal constitutions and extensive limitations of continental and analytic philosophies, including classical philosophy in its entirety (most notably: Platonism, neo-Platonism, atomism, dualism, and peripatetic traditions), monism (Spinoza-like and others), sophistic relativism and solipsism (which, as we know, has nothing to do with the actuality of the Einsteinian physical theory of relativity), dogmatic empiricism and materialism, Kantianism and neo-Kantianism, Hegelianism and non-Hegelian dialectics (existentialism), Gestalt psychologism, symbolic logic, hermeneutics, an...

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Preface: Neutrosophic Physics – as a new research field, by the Editor … 4 Neutrosophic Cosmologies, by Larissa Borissova and Dmitri Rabounski … 11 The Surjective Monad Theory of Reality: A Qualified Generalization of Reflexive Monism, by Indranu Suhendro … 29 A New Possible Form of Matter, Unmatter – Formed by Particles and Anti-Particles, by Florentin Smarandache … 58 Verifying Unmatter by Experiments, More Types of Unmatter, and A Quantum Chromodynamics Formula, by Florentin Smarandache … 63 Causality in Kaon Oscillations and Decay, by Thomas R. Love … 72 Examples of Unmatter, by Thomas R. Love … 80 Photon-Neutrino Symmetry and the OPERA Anomaly: a Neutrosophic Viewpoint, by Ervin Goldfain … 82...

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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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Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. Revealing the secrets of Nature, so that we truly see ‘the sunlit plains extended, and at night the wondrous glory of the everlasting stars’*, requires far more than mere technical ability and mechanical dexterity learnt from books and consensus. The dustbin of scientific history is replete with discredited consensus and the grand reputations of erudite reactionaries. Only by boldly asking questions, fearlessly, despite opposition, and searching for answers where most have not looked for want of courage and independence of thought, can one hope to discover for one’s self. From nothing else can creativity blossom and grow, and without which the garden of science can o...

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After the experiments were completed, the life span of such “atoms” was calculated theoretically in Chapiro’s works [61,62,63]. His main idea was that nuclear forces, acting between nucleon and anti-nucleon, can keep them far away from each other, hindering their annihilation. For instance, a proton and anti-proton are located at the opposite side of the same orbit and move around the orbit’s centre. If the diameter of their orbit is much larger than the diameter of the “annihilation area”, they can be kept from annihilation (see fig. 3). But because the orbit, according to Quantum Mechanics, is an actual cloud spreading far around the average radius, at any radius between the proton and the anti-proton there is a probability that they can meet one another at the annihilation distance. Therefore the nucleon---anti-nucleon system annihilates in any case, as this system is unstable by definition having a life span no more than 10-20 sec....

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Contents Preface 5 Foreword 6 1 Unsolved Problems in Theoretical Physics 8 1.1. Problems related to elementary particles 8 1.2. Problems related to Unmatter 11 1.3 Some unresolved problems, questions and applications of the Brightsen nucleon cluster model 21 2 Unsolved Problems in Mathematics 24 2.1. Maximum number of circles 25 2.2. Consecutive sequence 25 2.3. Diophantine equation 25 2.4. Van Der Waerden Theorem 26 2.5. Differential equation with fractional power 26 2.6. Representation of odd number with prime 26 2.7. Magic square problem 27 2.8. Palindromic number and iteration 27 2.9. Non-Euclidean geometry by giving up its fifth postulate 28 2.10. Smarandache Geometry and Degree of Negation in Geometries 28 2.11. Non-Archimedean triangle theorem 33 2.12. The cubic Diophantine equation 33 2.13. Multispaces and applications in physics 34 3 Unsolved Problems in Astrophysics 35 3.1. Unsolved problems in Celestial Mechanics 35 3.2. Unsolved problems in Astrophysics 37 4 Unsolved Problems in Geophysics 45 4.1. Introduction 45 4.2. Some new questions 45 5 Unsolved Problems in Sorites Quantum Paradox and Sm...

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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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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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NonNovel is indeed a novel of drawer, carried year after year in the bottomless sack of the exile. This fierce parabola about totalitarianism, about alienation, guilty obedience and lie, opportunism, cruelty, violence, monstrosity, written in a strong tensioned and lacking bashfulness style, situates Florentin Smarandache closer by Orwell, Konwicki, Koestler, Baconsky, and marks a new dimension of the Paradoxism....

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Mybreathin gstops Mybrea thingstops Myb reath ings tops Mybreathingstops Mybreat hin gsto ps M ybreath ingstops My breathing stops

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WARNING!: 5 Mister Editor (a letter arrived at the editorial office): 6 I: 7 Dedication: 10 The Adventures of Hon Hyn: 11 Happenings from Wodania: 23 II: 26 About patriotism: 28 The royal feast: 29 The press: 30 Post Office: 31 The State control: 32 Non-values’ Epoch: 36 Pluralism: 43 A leader not like anyone else: 45 Invisible barriers: 46 The graduates’ allocation: 49 The lunatic asylum: 50 The abolishing of the difference between man and animal: 56 III: 59 The Earthquake: 60 Modern gallinacean: 62 The crop of pea: 63 The peasantry: 64 The intellectuality: 66 A little meditation does not hurt: 67 The Fonfoist Party: 69 An unsafe life was provided to us: 70 A certain kind of speech: 72 The Fonfoist Society: 83 “We will live here in abundance”: 87 The multilateral development of personality: 93 The Police and the Revolution: 95 Imposing buildings of prisons: 97 Football: 99 Public genuflection: 100 The contemporary history: 102 Hon Hyn’s visit to Paris: 103 The National Museum: 104 The Management of the Economical Systems: 105 A few notions of psychology: 106 (editor’s note): 109 The wise po...

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Etymologically, aphorism + floral = aph(L)orism, which is a short reflection written on a floral design, or a short poetry accompanied by an artistic background. They are colorful contemplations. Maximus in minimis (Lat.) means very much in very little [max in min], or condensed thought, or ideating essence. They are actually maxims, adages, sayings mostly in one line (uni-stich) with a title, as a metaphoric statement, a breathing momentum that oils our soul....

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Nonchalantly : The wind with its mantle steps lightly. Skin Condition : The Sun has spots too. At what time? When it rains, God cries. Atmosphere : Blue, as the sky dirtied by clouds. Bright : A balcony full of Sun. Natural disaster : The swans look drunk on the fetid lake. Surprisingly : The crow is a beautiful black. Elegant woman : A bird high on her legs. Most powerful chess piece : You are a queen but only in the dark. Medicinal plant : You’re a flower but amongst weeds. Force that attracts food : The stomach’s gravitation pulls me to food....

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Passion.......................................................................23 Worthless.....................................................................23 Tired of you....................................................................23 Tittle-tattle....................................................................23 Talk is cheep...................................................................24 Give the man what he doesn’t have.................................................24 Novel for (non) writers...........................................................24 Desolate......................................................................24 Did I have the pleasure...........................................................24 Sloppy work....................................................................25 Despicable.....................................................................25 Wanted.......................................................................25 Talking in vain..................................................................25 Use caplets.....................................................

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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....

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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................................