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 Book Id: WPLBN0002096589 Subjects: Non Fiction, Education, Algebra Collections: Math, Literature, Education, Algebra, Authors Community, Mathematics ► Abstract Description Details...roup and a semigroup simultaneously. This book is a piece of work on Smarandache semigroups and assumes the reader to have a good background on group theory; we give some recollection about groups and some of its properties just for quick reference.... Full Text Search Details...an be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) ... ...liminary results 14 2.4 Subgroups 15 3. Some Classical Theorems in Group Theory 3.1 Lagrange's Theorem 21 3.2 Cauchy's Theorems 22 3.3 ... ...marandache semigroups and assumes the reader to have a good background on group theory; we give some recollection about groups and some of its proper... ...e used in this book. Chapters 2 and 3 gives most of the basic concepts on group theory and results in group theory which have been used in this text... ...rch on Smarandache notions. Smarandache notions are revolutionary because group theory does not make one think of the unthinkable that can naturally... ...see that the chapters two and three give most of the relevant concepts in group theory for which we have studied the Smarandache notions. In these t... ... for every b ∈ G, we must have for e ∈ G, e  f = e. Piecing these two bits of information together we get f = e  f = e and so e = f. THEOREM 2.... ... G ( o p , for every a ∈ G where a ∉ Z(G). Look at the class equation with this information. Since p α /o(G) we have that p/o(G), also ∑ ∉Z a )) a (... ...t be divisible by p, so we can write as kp, where k is an integer. Feeding this information back into our equation above, we have . kp 1 )) P ( N ...
 Book Id: WPLBN0002097038 Subjects: Non Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Authors Community, Mathematics ► Abstract Full Text Search Details...scu, V. Seleacu, "About the behaviour of some new functions in the number theory" (to appear this year) . "Collection of Problems on Smarandache No... ...tension ofan element of set (a). See Some Notions and Questions in Number Theory, edited by C Dumitrescu and V Seleacu, Erhus University Press, Glen... ...oblem (126) of [5] can easily be proven using well-known results of number theory 126) Smarandache Divisibility Theorem If a and m are integers, and... ...m - a)(m - I)' is divisible by m. Proof: The following theorem in number theory is well-known, Ifp is prime and a is a positive integer, then a P ... ... to Ifx E SPN then x f/: SPN which is a contradiction of the laws of set theory if x is indeed an element of SPN A statement equivalent to this wou... ...w York Springer-Verlag. 7. P Castini, Personal Correspondence Related to Information in the Smarandache Archives at Arizona State Lniversity 8 A S... ...Arizona State Lniversity 8 A Srinivas, Personal Correspondence Related to Information in the Smarandache Archives at Arizona State Lniversity 9. H ...
 Book Id: WPLBN0002097644 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Algebra, Authors Community, Mathematics ► Abstract Full Text Search Details...e ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 30... ... to prove the result). Supplementary Reading 1. Birkhoff, G. Lattice Theory. American Mathematical Society, Providence, R.I., 1967. 2. Bi... ...n Applied Algebra. Mc-Graw Hill, New York, 1970. 3. Gratzer, G. Lattice Theory. Freeman, San Francisco, 1971. 4. Hall, Marshall. Theory of Gr... ..., 1975. 6. Lang, S. Algebra. Addison-Wesley, 1967. 7. Nagata, M. Field Theory. Marcel Dekker, NewYork-Basel, 1977. 8. Passman, D.S. Infinite ... ... Justify your answer? Supplementary Reading 1. Birkhoff, G. Lattice Theory. American Mathematical Society, Providence, R.I., 1967. 2. Bi... ...n Applied Algebra. Mc-Graw Hill, New York, 1970. 3. Gratzer, G. Lattice Theory. Freeman, San Francisco, 1971. 4. Hall, Marshall. Theory of Gr...
 Book Id: WPLBN0002097651 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Description Details...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 founded by Florentine Smarandache, is alike to that of Fuzzy ... Full Text Search Details...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... .... In its trajectory of stupendous growth, it has also come to include the theory of fuzzy algebra and for the past five decades, several researchers... ...y the subject of Smarandache Fuzzy Algebra. Originally, the revolutionary theory of Smarandache notions was born as a paradoxist movement that chall... ...ns, a field founded by Florentine Smarandache, is alike to that of Fuzzy Theory: both the fields imperatively questioned the dogmas of classical ma... ...eing assigned a value between 0 and 1 by a membership function. Fuzzy set theory was guided by the assumption that classical sets were not natural, ... ...eld [112] introduced the notion of fuzzy group and showed that many group theory results can be extended in an elementary manner to develop the theor... ...y proved by any reader. The reader is also advised to refer [75] for more information . THEOREM 1.6.7: If F is a finite field, then every fuzzy su... ... we stop at this stage and request the reader to refer [123] for complete information regarding S-semigroup. Fuzzy semigroups are dealt in chapte... ...dache non associative ring which for short we denote as SNA-rings. Lot of information about SNA-rings can be had from [131]. Throughout this book...
 Book Id: WPLBN0002097647 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Description Details...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 important and innovative properties about S-rings. Writi... Full Text Search Details...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...ine.com Peer reviewers: Ion Goian, Department of Algebra and Number Theory, University of Kishinev, Moldova. Sebastian Martin Ruiz, Avda. De ... ...I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (S- rings) spe... ...etter if we thrust importance on results given in research papers on ring theory rather than detail the basic properties or classical results that t... ...gs are given. As we expect the reader to have a strong background in ring theory and algebra we have recollected for ready reference only the basic ... ...s a collection of suggested problems and it contains 200 problems in ring theory and Smarandache ring theory. It is pertinent to mention here that so...
 Book Id: WPLBN0002097643 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Description Details...y. This book assumes that the reader should have a good background of algebraic structures like semigroup, group etc. and a good foundation in number theory.... Full Text Search Details... be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) ... ...lgebraic structures like semigroup, group etc. and a good foundation in number theory. In Chapter 1 we just recall the basic notations and some imp... ...nger Verlag, (1958). 2. Ivan Nivan and H.S.Zukerman, Introduction to number theory, Wiley Eastern Limited, (1989). 3. W.B. Vasantha Kandasamy, ... ...d Kama. Her current interests include Smarandache algebraic structures, fuzzy theory, coding/ communication theory. In the past decade she has guide... ...cholars in the different fields of non-associative algebras, algebraic coding theory, transportation theory, fuzzy groups, and applications of fuzzy...
 Book Id: WPLBN0002097093 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Description Details...This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially ... Full Text Search Details... Books on Demand ProQuest Information and Learning (University of Microfilm International) 30... ...s or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric the- orems; Di... .... . . . . . . . . . . . . 241 8 On certain new conjectures in prime number theory . . . . . . . . . . . . . 243 9 On certain conjectures by Russo . . ... ...ve made it clear that there exists a very intimate correlation between the Theory of numbers and other departments of Mathematics, not excluding geome... ...or simply, H-triangle) if its area = Area(ABC) is an integer number. The theory of H-triangles has a long history and certain results are many times... ...scovered. On the other hand there appear always some new questions in this theory, or even there are famous unsolved problems. It is enough (see e.g. ... ... p 2; 3 p 3; 4 p 5, etc. are irrationals. 271 The next corollary gives an information on certain irrational values of a trigonometric function. Corol...
 Book Id: WPLBN0002097649 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...se two algebras heavily exploits the concepts of vector spaces and matrix theory we do not venture to approach Smarandache Lie algebras or Smarandac... ... way. This book is distinct and different from other non-associative ring theory books as the properties of associative rings are incorporated and s... ...of orthogonal ideals. This notion will find its place in algebraic coding theory. Now we proceed on to define the concept of Smarandache orthogonal ... ...tive and new concepts and notions which can be developed into a very good theory. 5.1 Basic properties of Jordan Algebras In this section w... ... it as a matrix structure. For the main reason is that Smarandache matrix theory and Smarandache vector spaces and Smarandache linear algebras are y...
 Book Id: WPLBN0002097036 Subjects: Non Fiction, Education, Mathematics ► Abstract Full Text Search Details...ook can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb ... ... on the rights was 2k. This is not divisible by 4 if k is odd. Additional information concerning the Concatenated Even Sequence can be gleaned by exa... ...e Fibonacci and Lucas sequences. References 1. Unsolved Problems in Number Theory, edited by Richard K. Guy, Springer, 2004, ISBN 0387208607. 70 Chap... ...hat kind of stereograms can be created by iterating combinations of number theory functions and plotting the number of iterations? 3.2 Altering the Ba...
 Book Id: WPLBN0002097083 Subjects: Non Fiction, Education, Mathematics ► Abstract Description Details... (Romania), and Archives of State (Rm. Valcea, Romania). The Smarandache's universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this universe has a very simple structure from number theory standpoint, it doesn't cease to be deeply mysterious and interesting. This book, following the Smarand... Full Text Search Details...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICAN RESEARCH PRESS Lupton USA 2000 Wrongness of n ... ...universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this univers... ...Even though sometime this universe has a very simple structure from number theory standpoint, it doesn't cease to be deeply mysterious and interesting... ...lems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter (IV) is dedicated to the analysis of Smarandach... ...the analysis of Smarandache Double factorial function introduced in number theory by F. Smarandache ("The Florentin Smarandache papers" special colle... ...of integers out of infinite number of them. Anyway we can get some further information from experimental data about the validity of this conjeture. In...
 Book Id: WPLBN0002097118 Subjects: Non Fiction, Education, Smarandache Collection ► Abstract Description Details...Physics template. This template can be downloaded from Progress in Physics home page http://www.geocities.com/ptep_online. Abstract and the necessary information about author(s) should be included into the papers. To submit a paper, mail the file(s) to Chief Editor. All submitted papers should be as brief as possible. Short articles are preferable. All that has been accept... Full Text Search Details.... . . . . . . . . . . . . . . . . . . 9 L. Nottale Fractality Field in the Theory of Scale Relativity. . . . . . . . . . . . . . . . . . 12 L. Borisso... ... . . . . . . . . . . . 20 C. Castro, M. Pavˇ siˇ c The Extended Relativity Theory in Clifford Spaces.. . . . .31 K. Dombrowski Rational Numbers Distri... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Information for Authors and Subscribers Progress in Physics has been create... ...home page http://www.geocities.com/ptep_online. Abstract and the necessary information about author(s) should be included into the papers. To submit a... ...nal, the detec- tor reacts to a wave of the metric in accordance with this theory. Therefore it is concluded that quadrupole mass detectors would be t... ... of chronometric invariants (physical observable quantities in the General Theory of Relativity) defnes gravitational inertial force F i without the R... ...ned invariant under acceleration- boosts. This could reveal very important information about Black-holes Entropy and Holography. C. Castro. On Dual Ph... ...ned invariant under acceleration- boosts. This could reveal very important information about Black-holes Entropy and Holography. The logarithmic cor- ... ...ons see [86], [128]. It was advocated long ago by Wheeler and others, that information theory [106], set theory and number theory, may be the ultimate...
 Book Id: WPLBN0002097103 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...ook can be ordered in microfilm format from: Books on Demand ProQuest Information & Learning (University of Microfilm International) ... ...s: J. Dezert (France), Charles Le (US), I. Stojmenovic (Canada). For more information on neutrosophics see the below links: • 0. Introduction: ... ... and instability of stable systems. Let's note by an idea, or proposition, theory, event, concept, entity, by what is not , and by
 Date: 2013, Volume 1 Book Id: WPLBN0002828224 ► Abstract Description Details...This book is devoted to an emerging branch of Information Fusion based on new approach for modeling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for De... Table of Contents Details...on the enumeration of isotone Boolean functions . . . 51 3.2.2 Ordering based on the DSm cardinality . . . 52 3.2.3 Ordering based on the intrinsic informational content . . . 56 3.3 Conclusion . . . . . 59 3.4 References . . . . . 60 4 Combination of beliefs on hybrid DSm models 61 4.1 Introduction . . . . . 61 4.2 On the independence of the sources of evidences ....
 Date: 2013, Volume 2 Book Id: WPLBN0002828226 ► Abstract Description Details...This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigations while, Par... Table of Contents Details...Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . ...
 Date: 2013, Volume 3 Book Id: WPLBN0002828228 ► Abstract Description Details...Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and info... Table of Contents Details...nality . . . . . . 46 1.6.3 The Generalized Pignistic Transformation . . . 47 1.7 The DSmP transformation . . . . . . . 48 1.7.1 The Probabilistic Information Content (PIC) . . . 49 1.7.2 The DSmP formula . . . . . . . 50 1.7.3 Examples for DSmP and BetP . . . . . . 51 1.8 Fusion of qualitative beliefs . . . . . . . 54 1.8.1 QualitativeOperators . . . . . . . 54 1....
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