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...W. B. VASANTHA KANDASAMY SMARANDACHE LOOPS AMERIC... ...RCH PRESS REHOBOTH 2002 A 1 L 15 (8) {e} A 15 B 1 B 5 1 Smarandache Loops W. B. Vasantha Kandasamy Department of Mathematic... ... 2 The picture on the cover represents the lattice of subgroups of the Smarandache loop L 15 (8). The lattice of subgroups of the commutative loo... ...tative loop L 15 (8) is a non-modular lattice with 22 elements. This is a Smarandache loop which satisfies the Smarandache Lagrange criteria. But fo... ...dache loop which satisfies the Smarandache Lagrange criteria. But for the Smarandache concepts one wouldn't have studied the collection of subgroups ...

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... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATION... ...dia e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gal... ...rnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kan... ...ena Kandasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-86-1 ... ...re Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (http://gallup.unm.edu/~smarandache/NCMs.pdf) and Analysis of Social Aspects of Migrant Labo... ...olution. Let U and V be nonempty sets, and let L(U), L(V), and L(U × V) be the collections of fuzzy sets of U, V and U × V, respectively. Then an e...

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...In 1996 the author wrote reviews for "Zentralblatt fUr Mathematik" for books [11 and [21 and this was him first contact of with the Smarandache's problems. In [1] Florentin Smarandache formulated 105 unsolved problems, while in [21 C. Dumitrescu and V. Seleacu formulated 140 unsolved problems. The second book contains almost all problems from [11, but...

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...Preface 5 -- 1. On The 4-Th Smarandache's Problem 7 -- 2. On The 16-Th Smarandache's Problem 12 -- 3. On The 22-Nd, The 23-Rd, And The 24th -- Smarandache's Problems 16 -- 4. On The 37-Th And The 38th -- Smarandache's Problems 22 -- 5. On The 39-Th, The...

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...in the number theory" (to appear this year) . "Collection of Problems on Smarandache Notions", by Charles Ashbacher Copyright 1996 by Charles Ashb... ...rica Preface The previous volume in this series, An Introduction to the Smarandache Function, also by Erhus Cniversity Press, dealt almost exclusi... ...ity Press, dealt almost exclusively with some "basic" consequences of the Smarandache function. In this one, the universe of discourse has been expan... ...se of discourse has been expanded to include a great many other things A Smarandache notion is an element of an ill-defined set, sometimes being alm... ...m in the text, I will now extend my gratitude to all those who combed the Smarandache archives for much of the material explored here. Charles T Le ... ...unt' column in Personal Computer World Definition 33: A magic square is a collections of numbers a], a2, ., ak such that k = n*n is a perfect square...

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...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 another and can be read separately. Findings are illustrated with diagrams and tables. The latter have been kept to a minimum...

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... Mainly Natural Numbers - a few elementary studies on Smarandache sequences and other number problems Henry Ibstedt ... ... Mainly Natural Numbers - a few elementary studies on Smarandache sequences and other number problems Henry Ibstedt ... ...n Research Press The diagram on the cover illustrates the Smarandache partial perfect additive sequence. It has an amusing oscilla... ...esearch Press, Rehoboth, Box 141, NM 87322, USA. http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-73-X Standard A... ... raised in recent articles in current Mathematics journals and in Florentin Smarandache’s wellknown publication Only Problems, Not Solutions. All...

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...A Smarandache notion is an element of an ill-defined set, sometimes being almost an accident oflabeling. However, that takes nothing away from the interest and excitement that can be generated by exploring the consequences of ...

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...W.B.VASANTHA KANDASAMY BIALGEBRAIC STRUCTURES AND SMARANDACHE BIALGEBRAIC STRUCTURES ... ...tructures S-bistructures 5 4 2 3 0 1 1 Bialgebraic Structures and Smarandache Bialgebraic Structures W. B. Vasantha Kandasamy Departmen... ... USA Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-71-3 ... ... 43 1.7 Vector spaces and S-vector spaces 62 Chapter Two: BIGROUPS AND SMARANDACHE BIGROUPS 2.1 Bigroups and its properties 67 2.2 S-bigroups... ... 2.2 S-bigroups and its properties 78 Chapter Three: BISEMIGROUPS AND SMARANDACHE BISEMIGROUPS 3.1 Bisemigroups and its applications 87 3....

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... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup,... ...aka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kandasa... ...Kandasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-87-X ... ...f Periyar's ideology and approach. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 7 Chapter One Introduction to Some Neutr... ...cept of indeterminacy till the year 1995. Only in the year 1995 Florentine Smarandache introduced and studied the notion of indeterminacy, creating...

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...Smarandache notions, which can be undoubtedly characterized as interesting mathematics, has the capacity of being utilized to analyse, study and introduce, naturally, the concepts of several structures by means of extension o...

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... w. b. vasantha kandasamy smarandache semirings, semifields, and semivector spaces ... ...c,d} {a,b} {a,c} {a,d} {b,c} {b,d} {d,c} {a,b,d} {a,d,c} {b,d,c} 1 Smarandache Semirings, Semifields, and Semivector spaces W. B. V... ... constructed using the power set P(X) where X = {a, b, c} which is a finite Smarandache semiring of order 16. This book can be ordered in a pape... ...322, USA Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-62-4 ... ...NTS Preface 5 1. Preliminary notions 1.1 Semigroups, groups and Smarandache semigroups 7 1.2 Lattices 11 1.3 Rings and fields 19 1.... ...are not in general S-anti semifields. Proof: By an example. Consider the collections of prime fields of characteristic p. p a prime. None of them...

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This book contains a collection of poems compiled by the author Florentin Smarandache.

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...This book contains a group of Smarandache's theories and lessons on mathematics. It includes his famous "Smarandache Function" and how it is executed through with math....

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... Sebastián Martín Ruiz Applications of Smarandache Function, and Prime and Coprime Functions    = o... ...Smaranda@teleline.es www.terra.es/personal/smaranda Applications of Smarandache Function, and Prime and Coprime Functions ... ...141 NM 87322, USA E-mail: M_L_Perez@yahoo.com http://www.gallup.unm.edu/~smarandache/math.htm ISBN: 1-931233-30-6 Stand... ...92 Printed in the United States of America 4 Contents: Chapter 1: Smarandache Function applied to perfect numbers Chapter 2: A result obt... ...Function applied to perfect numbers Chapter 2: A result obtained using the Smarandache Function Chapter 3: A Congruence with the Smarandache Functi...

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...During the five years since publishing, we have obtained many new results related to the Smarandache problems. We are happy to have the opportunity to present them in this book for the enjoyment of a wider audience of readers. The problems in Chapter two have also been solved and published separately by the autho...

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... 1 1 a b a 1 1 a 1 1 . . . SOME... ... . . SOME SMARANDACHE PROBLEMS HEXIS Phoenix, 2004 Mladen Vassilev-Missana Krassimir Atanassov SOM... ...demy of Sciences Bulgaria, So¯a-1113, P.O.Box 12 e-mail: krat@bas.bg HEXIS Phoenix, USA 2004 Mladen V. Vassilev{Missana and Krassimir T. Atanassov SOM... ...r 297-5092 Printed in the United States of America Preface During the ¯ve years since publishing [2], we have obtained many new results related to th... ...aticians, particularly both professional and amateur number theorists. MladenV.Vassilev-Missana Krassimir T. Atanassov 3 4 Contents Chapter 1. On Som...

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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 genesis of Smarandache Notions, a field foun...

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...w. b. vasantha kandasamy SMARANDACHE FUZZY ALGEBRA AMERI... ... group semigroup semi group groupoid group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Depar... ...he classical algebraic structures with single binary operations and their Smarandache analogues. The pictures on the left, composed of concentric ci... ...and the pictures of the right, with their liberal intersections, describe Smarandache algebraic structures. In fact, Smarandache Algebra, like its p... ... USA Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-74-8 St...

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...w. b. vasantha kandasamy SMARANDACHE NON-ASSOCIATIVE RINGS AMERICAN RESEARCH PRESS... ...INGS AMERICAN RESEARCH PRESS REHOBOTH, NM 2002 1 Smarandache Non-associative rings W. B. Vasantha Kandasamy Departme... ... USA Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-69-1... ... 1. BASIC CONCEPTS 1.1 Basics of vector space and bilinear forms 7 1.2 Smarandache vector spaces 8 1.3 Basic definitions of other algebraic struc... ... Basic definitions of other algebraic structures 11 2. LOOP-RINGS AND SMARANDACHE LOOP-RINGS 2.1 Introduction of loops and Smarandache loops ...