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...This book consists of a selection of papers most of which were produced during the period 1999-2002. They have been inspired by questions raised in recent articles in current Mathematics journals and in Florentin Smarandache’s wellknown publication Only Problems, Not Solutions. All topics are independent of one an...

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... 1 =a 2 =1, a 2k+1 =a k+1 -1, a 2k+2 =a k+1 +1 This book can be ordered in paperbound form from: Books on Demand ProQuest Information & Learn... ...ts.htm ISBN: 1-931233-73-X Standard Address Number: 297-5092 Printed in the United States of America 3 Preface This... ...sts of a selection of papers most of which were produced during the period 1999-2002. They have been inspired by questions raised in recent article... ...d during the period 1999-2002. They have been inspired by questions raised in recent articles in current Mathematics journals and in Florentin Smar... ...asy to formulate but hard to solve – if ever, and if one finds a solution, new questions present themselves and one may end up having more new ques... ... from this iteration. Interesting results are found but the results produce new and very intriguing questions. Chapter IV. An interesting iterati... ... decimal fraction. This is the only article which is based on work prior to 1999. Chapter V. In the previous chapters iterations have lead to loop... ...→48→124 n=26 C 3 42 ↔ 20 … n=381 C 5 1023 ↔ 1536 The search for new cycles was continued up to n=552,000. No new ones were found. This l... ...eger. References: 1. R.K. Guy, Unsolved Problems in Number Theory. New York: Springer- Verlag, 1981, p. 120. 2. H. Ibstedt. Some Sequences of L...

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...Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an...

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...Matrices provide a very powerful tool for dealing with linear models. Bimatrices which we are going to define in this chapter are still a powerful and an advanced tool which can handle over one linear model at a time. Bimatrices will be useful when time bound comparisons are needed in the analysis of the model....

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...ute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Departmen... ...in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@unm.edu K. Ilanth... ... 2005 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Inf... ...ubl. Hse., Phoenix, Arizona Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ...f each other. The study of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear b... ...chapter gives some problems, which will make the reader to understand these new notions. We have given a possible list of books for the reader to u... ...7. 170 8. GEL'FAND, I.M., Lectures on linear algebra, Interscience, New York, 1961. 9. GREUB, W.H., Linear Algebra, Fourth Edition, Springer-Ve... ...eutrosophic probability, second edition, American Research Press, Rehoboth, 1999. 31. SMARANDACHE, Florentin, An Introduction to Neutrosophy, htt... ...56. 41. VASANTHA KANDASAMY, W.B., Bivector spaces, U. Sci. Phy. Sci., 11 (1999) 186-190. 42. VASANTHA KANDASAMY, W.B., On a new class of semivec...

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...e prezentate chiar la congrese si conferinse nasionale cat si internasionale [vezi "Lista publicasiilor autorului pe tema tezei"). Ea se structureazs in patru capitole: - in primele trei capi tole se introduc noi funsii in teoria numerelor, se studiazs proprietssile lor, probleme nerezol vate legate de ele, implicasii in lumea stiinsific! internasional! (ce alsi matematici...

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...stitute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Depar... ....ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu ... ... HEXIS Church Rock 2004 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest... ... ISBN: 1-931233-86-1 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS D e d i c a t i o... ...elation equation constraints 57 1.9 Neural fuzzy relational system with a new learning algorithm 63 1.10 Unattainable Solution of FRE 67 ... ... 1.13 Solvability and Unique solvability of max-min fuzzy equations 81 1.14 New algorithms for solving fuzzy relation equations 85 1.15 Novel ... ...or FRE X. Li and D. Ruan [53, 54, 55] have given 3 papers in the years 1997, 1999 and 2000 as three parts on the same title. Their work is a comm... ... method in Theorem 1.15.6. 1.16 Novel neural network part I In the year 1999 [53, 54, 55] have presented an extended fuzzy neuron and fuzzy ... ...ation Equations with a Linear Objective Function, Fuzzy Sets and Systems, 103 (1999) 107-113. [33, 49, 117-18, 122, 268] 25. Fang, S.C., and Puthen...

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...ry has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised...

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...ute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Departmen... ...in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu ... ... HEXIS Church Rock 2004 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Inf... ... ISBN: 1-931233-87-X Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS P r e f a c e ... ...n entire section is devoted for this purpose. Chapter Three introduces many new neutrosophic concepts in graphs and applies it to the case of neutro... ...roblems 6 about neutrosophic graphs which will make one understand this new subject. The authors are grateful to Ilanthenral for formatting t... ...al analysis we name the structure as Neutrosophic structure. Very recently (1999-2000) the notion of Fuzzy Relational Maps (FRM) was introduced. FRM... ...ert Reasoning, Fuzzy Logic and Complex Statutes, Vanderbilt Law Review, 52 (1999), 1243-1340. http://law.vanderbilt.edu/lawreview/vol525/adams.pdf ... ...Balakrishnan, R., and K. Ranganathan, A textbook of Graph Theory, Springer, 1999. 4. Balakrishnan, R., and Paulraja, P., Line graphs of subdivision...

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...Excerpt: Welcome to the seventh volume of Best of ?. For the past half dozen years we were Best of Four, publishing the best writing in English 004 classes, primarily on the Hazleton campus. Two years ago we began accepting submissions from some of the other Commonwealth College campuses, and this year we made the big plunge into accepting submissions from...

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............... 6 Adam Shaffer ?And Unknown Leader? .................................................................... 7 Khyati Valand ?A Neighborhood in India?............................................................... 9 Katie Aughenbaugh ?My Grandfather? ................................................................. 11 Devon Bowlin ?Almost Famous?.....................

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...of Four Volume 7 Student Voices A Commonwealth College Publication Editor in Chief Jim Manis Editor Lucy Morrison Associate Editors Liz Wright Suzann... ...the student essays contained herein were produced by students regis- tered in English 004, within the Commonwealth College of the Pensylvania Univer- ... ...en permission. No portion of Best of Freshman Writing may be repro- duced in any fashion without the express written permission of the authors. Best ... ...of all it’s hard to say, and that means it’s hard to re- member. We need a new name, something catchy that also tells folks something about what we’re... ...h the kids who camped regularly at the campground. They came from Florida, New Jersey, Maine, and many other states. We would ride our bikes, play in ... ...om Moyer’s Grove Campground allowed me to expand my imagi- nation and make new friends. I learned about many different people and places while living ... ... by Gibbs 42). Works Cited Cohen, Adam. “A Curse of Cliques.” Time (May 3, 1999): 44-45. Drummond, Tammerlin. “Battling the Columbine Copycats.” Time ... ...-45. Drummond, Tammerlin. “Battling the Columbine Copycats.” Time (May 10, 1999): 29. Gibbs, Nancy. “Special “Report the Littleton Massacre.” Time (Ma... ...: 29. Gibbs, Nancy. “Special “Report the Littleton Massacre.” Time (May 3, 1999): 25-35. Gibbs, Nancy and Timothy Roche. “The Columbine Tapes.” Time (...

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...al with mathematical ideas derived from the work of Florentin Smarandache, a man who seems to have no end of ideas. Most of the papers were published in Smarandache Notions Journal and there was a great deal of overlap. My intent in transforming the papers into a coherent book was to remove the duplications, organize the material based on topic and clean up some of the mos...

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...Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences Editor’s ... ... man who seems to have no end of ideas. Most of the papers were published in Smarandache Notions Journal and there was a great deal of overlap. My i... ...randache Notions Journal and there was a great deal of overlap. My intent in transforming the papers into a coherent book was to remove the duplicat... ... NE CEDAR RAPIDS, IOWA 42402 USA GENERALIZED PARTITIONS AND SOME NEW IDEAS ON NUMBER THEORY AND SMARANDACHE SEQUENCES ... ... Hexis Phoenix 2005 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Informat... ...andache Friendly Numbers and A Few More Sequences ………………… 86 2.6 Some New Smarandache Sequences, Functions and Partitions ………………… 89 6 2.... ... References 1. “Smarandache Notion Journal” Vol. 10 ,No. 1-2-3, Spring 1999. Number Theory Association of the University of Craiova. 2. " The ... ... York, NY. 8. "Smarandache Notion Journal" Vol. 10, No. 1-2-3, Spring 1999. Number Theory Association of the University Of Craiova. 9. V.Kri... ...marnath Murthy, "A General Result On The Smarandache Star Function", SNJ,.1999. 12. Amarnath Murthy, "More Results And Applications Of The General...

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...any simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new problems implicated and are still promoting the development of number theory and mathematics....

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...RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collected papers) Edited by ZHANG ... ... Hexis 200 4 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collect ed papers) Edited b... ...ty Xi’an, P. R. China Hexis 2004 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Informat... ... book is dedicated to the memory of Florentin Smarandache, who listed many new and unsolved problems in number theory. Contents Dedication v Preface ... ...marandache pseudo-number 111 Lou Yuanbing Several asymptotic formulae on a new arithmetical function 115 Guo Jinbao and He Yanfeng On the Smarandache ... ...g On the -th power free sieve sequence 155 Guo Jinbao and Zhao Xiqing On a new Smarandache sequence 159 Zhao Xiaopeng and Yang Mingshun On some asympt... ... an generalization of the Smarandache function, Note Numb.Th.Diser.Math. 5(1999),41-51 [2] Tom M A. Introduction to Analytic Number Theory. New York, ... ... an generalization of the Smarandache function, Note Numb.Th.Diser.Math. 5(1999),41-51 [2] Tom M A. Introduction to Analytic Number Theory. New York, ... ...ational Aspects of Number Sequences. USA Lupton : American Research Press, 1999. [4] S. Tabirca and T. Tabirca. Smarandache Notions Journal, 2002, 13:...

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...As if it wanted to be in accordance with the paradoxism and even to confirm it, the way the mathematician writer Florentin Smarandache is received is ... paradoxical. Tens of books, studies and articles have already been written about both, scient...

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... 2 Ion Soare PARADOXISM AND POSTMODERNISM IN FLORENTIN SMARANDACHE’S WORK ... ...ican Research Press Rehoboth 2001 3 This book can be ordered in microfilm format from: Bell and Howell Co. (University of Mi... ...er-art.htm ISBN: 1-931233-32-2 Standard Address Number 297-5092 Printed in the United States of America 4 Ion Soare PARADOXISM... ...by any of the two contradictory tendencies, the Oltenian- Romanian settled in New Mexico creates further on important works in the two large fields- ... ...f a prolonged shock: the Romanian- American “neovanguard” is the creator of a new practical and theoretical system, well fixed in its main joints an... ...of subjectivism or exaltation in front of the unwonted - real, anyway- of the new literary movement. But same reactions have had before me a series o... ... the devil’s paradise (1 st ed.-1992, 2 nd ed.1992, 3 rd ed.1994, 4 th ed.1999). The book is not a journal proper, the information being undated... ...sophy, puzzle and mathematics” (Romania Libera, Bucharest, nr.2725/march, 15, 1999, pag.2). Noticing the concision and, at the same time, the abunda... ...sk me to ask you( Intreaba-ma sa te intreb)- the interviews book published in 1999 at Macarie Publishing House, Targoviste, reproduces the texts fro...

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...equalities for the remarkable elements of triangles or tetrahedrons. Other themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2 includes various diophantine equations, some of which are treatable by elementary methods; others are partial solutions of certain unsolved problems. An important method is based on the famous Euler-Bel...

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... American Research Press Rehoboth 2002 This book can be ordered in microfilm format from: Books on Demand ... ... ISBN: 1-931233-51-9 Standard Address Number 297-5092 Printed in the United States of America "...It is just this, which gives the hi... ...themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2 includes various diophantine equations, some of whic... ...ties involving the Smarandache function . . . . . . . . . 124 3 On certain new inequalities and limits for the Smarandache function . . . . 129 4 On t... ...hmetic Functions . . . . . . . . . . . . . . . . . . . . . . . 167 15 On a new Smarandache type function . . . . . . . . . . . . . . . . . . . . . 169... ... for primes . . . . . . . . . . . . . . . . . . . . . . . 241 8 On certain new conjectures in prime number theory . . . . . . . . . . . . . 243 9 On c... ...A note on the Diophantine equation a x + b y = c z , Acta Arithmetica, XCI(1999), No.1, pp.85-93. 4. W. Sierpinski, A selection of problems in the the... ...ao, A note on the diophantine equationa x +b y =c z , Acta arithmetica XCI(1999), 85-93. 2. J. S andor, On the diophantine equation 3 x + 3 y = 6 z ,... ...raphy 1. M. Bencze, A new inequality for the Smarandache function, SNJ, 10(1999), no.1-2-3, p.139. 2. M. Bencze, An inequality for the Smarandache fun...

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...Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduc...

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...itute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Departm... ...c.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@unm.edu K. ... ...@gmail.com HEXIS Phoenix, Arizona 2005 2 This book can be ordered in a paper bound reprint from: Books on Deman... ...s.htm ISBN: 1931233-98-5 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ...ication to Bimatrices 23 Chapter Three APPLICATION OF BIMATRICES TO NEW FUZZY MODELS 3.1. Definition of Fuzzy Cognitive Maps 71 3.2. Fu... ...ese concepts are also extended neutrosophically in this book. Using these new tools we define fuzzy cognitive bimaps, fuzzy cognitive trimaps, f... ...ning, Fuzzy Logic and Complex Statutes, Vanderbilt Law Review, 52, 1243-1340, 1999. http://law.vanderbilt.edu/lawreview/vol525/adams.pdf 3. Albert... ...ional Intelligence Modelling, Control and Automaton, Edited by M.Mohammadian, 1999. http://digitais.ist.utl.pt/uke/papers/cimca99rbfcm.pdf 25. Car... ...he North American Fuzzy Information Processing Society, by NAFIPS, New York, (1999) 115- 119. http://digitais.ist.utl.pt/uke/papers/NAFIPS99rbfcm- ...

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...Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several imp...

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... . This is a major difference between a ring and a Smarandache ring. For, in a ring the lattice representation of ideals is always a modular lattice... ...e lattice representation of ideals is always a modular lattice but we see in case of S-rings the lattice representation of S-ideal need not in gener... ...ion of S-ideal need not in general be modular. This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Informat... ...gs 71 3.10 Special properties about S-rings 78 4 4. Some new notions on Smarandache rings 4.1 Smarandache mixed direct product r... ...t product rings 115 4.2 Smarandache rings of level II 119 4.3 Some new Smarandache elements and their properties 121 4.4 New Smarandache subs... ...RTIES This is the main chapter of this book. Here we introduce several new concepts in Smarandache rings and recall the definition of Smarandache... ...oups with systems of local units, Fundam. Prikl. Math., Vol. 5, 539-555, (1999). 59. Northcott.D.G, Ideal theory, Cambridge Univ. Press, (1953). ... ...rings which have trivial subrings, The Math. Edu., Vol. XXXIII, 180-181, (1999). 147. Vasantha Kandasamy W.B., On E-semi group rings, Caribbean J.... ...E-semi group rings, Caribbean J. of Math. and Comp. Sci., Vol. 9, 52-54, (1999). 148. Vasantha Kandasamy W.B., On demi- modules over rings, J. of ...

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...In this book, we study the subject of Smarandache Fuzzy Algebra. Originally, the revolutionary theory of Smarandache notions was born as a paradoxist movement that challenged the status quo of existing mathematics. The genesi...

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...e of Technology Madras Chennai – 600 036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv AMERICAN RESEA... ...th their liberal intersections, describe Smarandache algebraic structures. In fact, Smarandache Algebra, like its predecessor, Fuzzy Algebra, arose f... ... which is an amalgamation of alternatives. This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Informat... ... used in these sections are extensive and we have succeeded in presenting new concepts defined by several researchers. In the second chapter we intr... ...zzy Sets, Lofti. A. Zadeh. Emphasizing about the long time it takes for a new subject to secure its place in the spotlight, he says, "Now: Probabili... ...cepted. Previous to that it was not accepted. There was an article in the New York Times about Bayesian things. It says this technology is 276 years... ...Sandeep Kumar, (∈∨ q)-level subset, Fuzzy Sets and Systems, 103, 529-533 (1999). 25. BHAKAT, Sandeep Kumar, (∈, ∈∨ q)-fuzzy normal, quasi-normal an... ...quasi-normal and maximal subgroups, Fuzzy Sets and Systems, 112, 299-312 (1999). 26. BHUTANI, Kiran R., Fuzzy sets, fuzzy relations and fuzzy group... ...da, Fuzzy multiplication semigroup, Fuzzy Sets and Systems, 105, 171-176 (1999). 35. DIB, K.A., and GALHUM, N., Fuzzy ideals and fuzzy bi-ideals in...

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...I have met the Smarandache's world for the first time about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research Press web site dedicated to the Smarandache notions and held by Dr. Perez (address: http://www.gallup.unm.edu/~smarandach...

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...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICAN RESEARCH PRESS Lupton USA 2000 Wrong... ...first time about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the i... ... unsolved problems, notions and other proposed by Professor F. Smarandache in "The Florentin Smarandache papers" special collections at: the Arizona S... ...ous and interesting. This book, following the Smarandache spirit, presents new Smarandache functions, new conjectures, solved/unsolved problems, new S... ... conjectures, solved/unsolved problems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter (IV) is dedic... ...arandache's universe. So let's start our observation. 4 Chapter I On some new Smarandache functions in Number Theory. A number-theoretic function is ... ...1996 [3] E. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 1999 [4] F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ. [5] ... ...r Smarandache U-product sequences, Smarandache Notions Journal, Nov. 1999 [5] E. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, ... ... 111, 1221, 13331, 144441, 1555551, 16666661, 177777771, 1888888881, 19999999991, 1101010101010101010101,..... Starting with n repeat it n ti...

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...gueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a...

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...c Probability and Statistics University of New Mexico - Gallup 1-3 December 2001 (second... ... (second printed edition) 2002 This book can be ordered in microfilm format from: Books on Demand ProQuest Informati... ... ISBN: 1-931233-67-5 Standard Address Number: 297-5092 Printed in the United States of America First International Confe... ... Logic, Set, Probability and Statistics December 1-3, 2001 University of New Mexico Contributed papers were sent, by November 30, 2001, to... ... by November 30, 2001, to the organizer: Florentin Smarandache, University of New Mexico, 200 College Road, Gallup, NM 87301, USA. Tel.: (505) 863... ...unm.edu/~smarandache/FirstNeutConf.htm. A selection of them is being published in these Proceedings of the Conference. Abstracts of papers were... ...onsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due... ...don’t preserve monotonicity. In bio-mathematics Heitkoetter and Beasley (1993-1999) present the evolutionary algorithms which are used “to describe... ... Imprecision, Uncertainty & Vagueness: a reply (from his Ph. D. Dissertation), 1999, http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail99/0819.html. ...

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...It was known to me his setting up in 1980’s of a new literary and artistic avant-garde movement that he called “paradoxism”, because I received some books and papers dealing with it in order to review them for the German journal “Zentralblatt fár Mathematik”....

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...Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive used of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations....

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...FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC... ...F 1 ? F 2 ) ). ISBN 1-879585-76-6 American Research Press Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTR... ...ress Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC... ...F 1 ? F 2 ) ). ISBN 1-879585-76-6 American Research Press Rehoboth 1999, 2000, 2003 1 Contents: Preface by Charles T. Le: 3 0. Introducti... ...ents: Preface by Charles T. Le: 3 0. Introduction: 9 1. Neutrosophy - a new branch of philosophy: 13 2. Neutrosophic Logic - a unifying field in ... ... a new branch of philosophy: 13 2. Neutrosophic Logic - a unifying field in logics: 87 3. Neutrosophic Set - a unifying field in sets: 112 4. Neut... ...es - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of... ...“neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and p... ...Set, and Logic", Florentin Smarandache, American Research Press, 1998]. (1999-07-29) 3.2. Neutrosophic Logic: <logic> (Or "Smarandache logic") A g...

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...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a b...

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...As shown, experiments registered unmatter: a new kind of matter whose atoms include both nucleons and anti-nucleons, while their life span was very short, no more than 10-20sec. Stable states of unmatter can be built on quarks and anti-quarks: applying the unmatter prin...

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...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Math... ...h the Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathS... .../ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Edito... ...n J. Crothers thenarmis@yahoo.com Department of Mathematics, University of New Mexico, 200 College Road, Gallup, NM 87301, USA Copyright c Progress ... ...ssible Fluid. . . . . . 76 E. Harokopos Power as the Cause of Motion and a New Foundation of Clas- sical Mechanics. . . . . . . . . . . . . . . . . . ... ..., take the form μF α∙ ∙σ j σ =0. (60) The numerical coeffcient μ here is a new fundamental constant. This new constant having the dimension[ gramme /s... ...16. Weber J. General Relativity and gravitational waves. R. Mar- shak, New York, 1961 (referred with the 2nd edition, Foreign Literature, Moscow, 1962... ...fram.com/GeometricProbability.html 22. Frampton P., Kephart T. Phys. Rev., 1999, v. D60, 08790. 23. Nottale L. Fractal spacetime and microphysics, tow... ... 43–66. 12. Barbour J. The end of time. Oxford University Press, New York, 1999. 13. Baker D. Spacetime substantivalism and Einstein’s cosmological co...

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...ation theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications. With the recent introduction of bimatrices (2005) we have ventured in this book to introduc...

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

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...te of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department... ...n/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu K. I... ... HEXIS Phoenix, Arizona 2005 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Info... ... ISBN: 1931233-97-7 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ...economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very pow... ...troduction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear b... ...spaces and S-bivector spaces. The study of bivector spaces started only in 1999 [106]. Here we recall these definitions and extend it to the Smarand... ...utrosophic probability, second edition, American Research Press, Rehoboth, 1999. 35. SMARANDACHE, Florentin, An Introduction to Neutrosophy, 22... ...VASANTHA KANDASAMY, W.B., Bivector spaces, U. Sci. Phy. Sci., 11 , 186-190 1999. 48. VASANTHA KANDASAMY, W.B., Linear Algebra and Smarandache Line...

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...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a b...

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...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Math... ...h the Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathS... .../ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Edito... ...n J. Crothers thenarmis@yahoo.com Department of Mathematics, University of New Mexico, 200 College Road, Gallup, NM 87301, USA Copyright c Progress ... ...n the United States of America APRIL 2005 VOLUME 1 CONTENTS D. Rabounski A New Method to Measure the Speed of Gravitation. . . . . . . . . . . . 3 F. ... ...ntum Quasi-Paradoxes and Quantum Sorites Paradoxes. . . 7 F. Smarandache A New Form of Matter — Unmatter, Composed of Particles and Anti-Particles. . ... ...actals, v. 16, 2003, 565. 6. Nottale L. Chaos, Solitons & Fractals, v. 10, 1999, 459. 7. Pissondes J. C. Chaos, Solitons & Fractals, v. 10, 1999, 513.... ...ctals, v. 10, 1999, 513. 8. Pissondes J. C. J. Phys. A: Math. Gen., v. 32, 1999, 2871. 9. Nottale L. Chaos, Solitons & Fractals, v. 9, 1998, 1051. 10.... ...127. 2. Nottale L. La relativite dans tous ses etats. Hachette Lit., Paris 1999. Nottale L. Fractal spacetime and microphysics, towards scale relativi...

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...In this book for the first time we have ventured into the total analysis of migrant labourers in rural Tamil Nadu who are victims of HIV/AIDS using FCM, BAM and Neutrosophic Cognitive Maps. As in our study and analysis we fel...

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...Migration acquires great significance in the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has enormous impact on livelihood, life-styles, employment, socioeconomic and pol...

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...EUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India XIQUAN Phoenix 2004 ANALYSIS OF SOCIAL ASPECTS OF M... ...NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India W. B. Vasantha Kandasamy Department of Mathematics Indian Ins... ...e of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department ... .../~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu ... ...e system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept of indeterminacy to play a role ... ...r IV. In chapter V we use Neutrosophic Relational Maps and we define some new neutrosophic tools like Combined Disjoint Block FRM, Combined Overlap... ...d not tested his children for AIDS as he had the disease only in the year 1999 but the children were born much before that. He came to know about sa... ...ently the child’s health condition is very serious. His wife also died in 1999 in the General Hospital of HIV/AIDS. He got married in 1996. He has... ...Gray N. Powell, Handbook of Gender and Work. Sage Publication, New Delhi (1999). 35. Guest, C. C., and Tekolste, R., “Designs and Devices for Optic...

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...A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians tod...

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...iences American Research Press Rehoboth, NM 2005 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learn... ...erformats.htm ISBN:1-931233-92-6 Standard Address Number: 297-5092 Printed in the United States of America Preface A combinatorial map is a connected... ...e A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical... ...lems, in fact, any solution for one of these problems needs to establish a new mathematical system first. But as soon as the system has been establishe... ...e.,aglobalquestion,theideausedinthereferences[40]−[41] are not applicable. New approach should be used. 2.1 Combinatorial conditions for an automorphi... ...sultant M ∗ is a triangulation of the same surface and the valency of each new vertex is 6. Fig. 4.5 Then we get the following result. Theorem 4.4.2 F... ...s which underlie regular maps on closed surfaces, J.London Math. Soc.(2)59(1999),100- 108. [21] G.Gromadzki, Abelian Groups of automorphisms of compac... ...e Theory of Maps, Kluwer Academic Publishers , Dor- drecht/ Boston/ London,1999. [34] Y.P.Liu, Advances in Combinatorial Maps, Northern Jiaotong Unive... ... 2-cell imbeddings of complete bipartite graphs, J.Graph Theory, vol 30, 2(1999),77-90. [56] R.Nedela and M ˇ Skoviera, Regular embeddings of canonica...

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...ts speed is the same no matter who measures it." "That's true." I would respond; "That's just the second postulate of special relativity which is not in doubt; but that postulate applies to light, and we're talking about rocketships here." However it seemed that no one understood what I was saying. By referring to the universal constant c= 299.792 458 megameters per secon...

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...tauri with a round-trip manned and womanned mission as the proposed overarching goal under a clear plan of exploration - a grand experiment described in later chapters. Whether or not we succeed in grasping the goal under this or under any plan is not as important as it is to set a definite plan and work towards its goal. The plan outlined here is in two phases: Phase on...

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... Phase Two Experiment: Alpha Centauri or Bust!. 45 -- Ch.9. Voyage to the Center of the Galaxy. 50 -- Ch.10. An Hypothesis: There is no Speed Barrier in the Universe. 52 --...

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...ntemporary of Albert Einstein (1879-1955) This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Informat... ... ISBN: 1-931233-84-5 Standard Address Number: 297-5092 Printed in the United States of America 3 BEGIN THE ADVENTURE Ho... ...tin Smarandache Department of Mathematics and Sciences The University of New Mexico at Gallup, USA Pima... ...tes through the velocity of light; note that there is no longer a barrier in evidence; Bottom - The pattern corresponding to a particle moving ... ... engineer and the radio amateur, the term "resonance" can lead to a whole new vista of mental images, a healthy vista in the present context. To rad... ... Dr. Florentin Smarandache Associate Professor The University of New Mexico at Gallup February 2004 9 Guest Preface The ... ...n Paul J. Nahin's 600+page book, Time Machines, 2nd ed., Springer-Verlag, 1999, ISBN 0-387-98571-9. An impressive chronicle. Don't look for answers... ...sing the Atlantic Ocean around the turn of the century from London to New York and back in the same day on the Concorde. ... And, on the westbound l... ...996 finding of Roll Landauer of the IBM Thomas J.Watson Research Center in Yorktown Heights, New York, in which he concluded that there is no minimum...

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...ge of any kind. Any person using this document file, for any purpose, and in any way does so at his or her own risk. Neither the Pennsylvania State U... ...ained within the docu ment or for the file as an electronic transmission, in any way. What Is Man and Other Essays by Mark T wain (Samuel L. Clemens... ...ngoing student publication project to bring classical works of literature, in English, to free and easy access of those wishing to make use of them, a... ... Caricature of Mark T wain appearing in Life: 31 January 1907 Copyright © 1999 The Pennsylvania State University The Pennsylvania State University is... ...d, “I am told that you are a coward!” It was not he that turned over the new leaf—she did it for him. He must not strut around in the merit of it—i... ...es of outside influences—we originate nothing within. Whenever we take a new line of thought and drift into a new line of belief and action, the imp... ...inally he found himself examining it. From that moment his progress in his new trend was steady and rapid. He became a believ ing Christian. And now ... ...haracter and deeply religious. An earnest and practical laborer in the New York slums comes up there on vacation—he is leader of a section of the Univ... ...ll. But it could be that he argued that if he saved a hundred souls in New York— O.M. The sacrifice of the family would be justified by that great pr...