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...The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absen...

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...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ... n c e s 113 I n d e x 119 5 PREFACE The theory of loops (groups without associativity), though researched by severa... ...the properties of loops are absent. This is in marked contrast with group theory where books are abundantly available for all levels: as graduate te... ...d as advanced research books. The only three books available where the theory of loops are dealt with are: R. H. Bruck, A Survey of Binary System... ...ein, H. O. Pflugfelder and J.D.H. Smith (editors), Quasigroups and Loops: Theory and Applications, Heldermann Verlag, 1990. But none of them are com... ...s. However, for the sake of readers who are involved in the study of loop theory we have provided a wide-ranging list of papers in the reference. We... ...s. The proof of the theorem is left for the reader. Refer [6] for more information. THEOREM 2.4.2: A diassociative Hamiltonian loop G is eithe... ...on the loop L. Now we go on to give the definition of isotopes for more information please refer Bruck [6]. DEFINITION 2.5.1: Let (L, •) be a l...

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..., LIU DUANSEN (EDITORS) RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMB... ...ORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMBER THEORY Hexis Phoenix, AZ 2005 EDITORS: ZHANG WEN... ...UO, SHAANXI, P.R.CHINA RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMB... ...ORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMBER THEORY Hexis Phoenix, AZ 2005 ... ...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...Florentin Smarandache, who listed many new and unsolved problems in number theory. Preface Arithmetic is where numbers run across your mind lookin...

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The Chinese edition of Advances and Applications of DSmT for Information Fusion (Collected Works) that explains the Dezert-Smarandache Theory.

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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 applicat...

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...rdered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 30... ... INDEX 175 ABOUT THE AUTHORS 181 5 Preface Matrix theory has been one of the most utilised concepts in fuzzy models and ne... ...eral real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable compo... ...the study of bimatrices for a while in order to develop some aspects of the theory of determinants which will be needed in our further investigatio... ...presented by a diagonal bimatrix D = D 1 ∪ D 2 we would gain considerable information about T = T 1 ∪ T 2 . For instance simple number associated... ... SUGGESTED PROBLEMS Now as such this book only views bimatrix as a theory. In fact several more results about bimatrices can also be devel... .... Cambridge Philos. Soc., 31 (1935) 433-435. 6. BURROW, M., Representation Theory of Finite Groups, Dover Publications, 1993. 7. DUBREIL, P., and ... ...lutions to the Student Mathematical Competitions. His latest interest is in information fusion were he works with Dr.Jean Dezert from ONERA (French ...

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...introduction of neutrosophic theory 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 f...

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...rdered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 30... ...d and recommended for publication by: Dr. Sukanto Bhattacharya, School of Information Technology, Bond University, Queensland, Australia. Dr. Ius... ...eutrosophic Vector spaces 8 Chapter Two SOME BASIC RESULTS ON GRAPH THEORY AND THEIR APPLICATION TO FUZZY MODELS 2.1 Some basics on Gr... ...ophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept by giving representation to i... ...n almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Mo... ... further development of the other chapters. Chapter Two recalls basic graph theory definitions and results which has interested us and for which we ... ...cking of e- mail by students. One of the major problems of today’s world of information technology that is faced by one and all is; How safe are the... ...phic Cognitive State maps of users web behavior is described. Searching for information in general is complex, with lot of indeterminacies and it is... ...ications of intimate technologies, owing to their ability to FIGURE: 3.7.11 INFORMATION CONSTRAINT SUCCESS RELEVANCE FAILURE SEARCH BROWSE TIM...

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...roduced in the year 2002. The concept of bialgebraic structures which we define and study are slightly different from the bistructures using category theory of Girard's classical linear logic. We do not approach the bialgebraic structures using category theory or linear logic....

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...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...ine and study are slightly different from the bistructures using category theory of Girard's classical linear logic. We do not approach the bialgebr... ...inear logic. We do not approach the bialgebraic structures using category theory or linear logic. We can broadly classify the study under four he... ... o(G), then G has an element of order p. For more results about group theory please refer [23 & 27]. Now we proceed on to recall some basic conc... ...n be found in the book [121], the reader is expected to refer it for more information. 1.3 Groupoids and S-groupoids In this section we give... ...X or y ∈ X. Several other notions can be had from any textbook on ring theory. We just define two types of special rings viz group rings and semi... ...r spaces. We recall basic properties. The reader can refer [122] for more information. DEFINITION 1.5.13: The Smarandache semiring S which will be... ...generates (N, +) is called a distributively generated near-ring. In the theory of near-rings a major role is played by the notion called N-groups. ...

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...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....

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...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 ...

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...is book can be ordered in paperbound form from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N.... ...sting iteration question was posed in the book Unsolved Questions in Number Theory (first edition) by R.K. Guy. Why does the repetitive application ... ...tions That Alternate the Pseudo-Smarandache and Classic Functions of Number Theory, Smarandache Notions Journal, Vol. 11, No 1-2-3. 26 ... ...tions That Alternate the Pseudo-Smarandache and Classic Functions of Number Theory, Smarandache Notions Journal, Vol. 11, No 1-2-3. 4. G.H. Hardy ... ... Vol. 11, No 1-2-3. 4. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, 1938. ... ...Some Sequences of Large Integers Abstract: In Unsolved Problems in Number Theory [1] the question why iteration of the sequence n / ) x ... x x 1 ... ...h we do not have a general formula for a n we may extract very interesting information in particular cases. Successive application of (2) to a case...

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...be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) ... ...iewed and recommended for publication by: Dr. Sukanto Bhattacharya, School of Information Technology, Bond University, Queensland, Australia. Dr.... ...S patients 211 Chapter Three SOME NEW AND BASIC DEFINITIONS ON NEUTROSOPHIC THEORY 3.1 Neutrosophic sets and neutrosophic logic 222 3.2 Fuzzy... ...nalysis of Social Aspects of Migrant Labourers Living With HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps: With Specific Reference to R... ... of the natural evolution of genetics. GAs emulate the biological evolutionary theory to solve optimization problems. In general, 50 GAs start... ...upervised by a superpoint and supervised by another parent. Since the existing theory of genetic algorithms cannot provide measurement for the perf... ...ch is not trivial at all. Here, f k is no longer required to be linear and the information of minimal solutions may be absent. A genetic algorithm ... ...oblems and proposed a new model, more expressive for representing the available information, and where the intended meaning of the membership degree... ...ons. This model is not capable of capturing the most general kind of incomplete information. 127 Reasoning in diagnosis problems: the com...

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...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 ...

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...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...

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...The author's motivating interest the past few years has been the development and dissemination of G-dimensional theory (GDT). K. Toshihara, from Japan, proposed the concept of a paper defining G-Dimensional theory in relation to the Smarandache quantum paradoxes. After reviewing a draft, Dr. M. L. Perez, Editor of the SNJ, suggested th...

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... L. Stephen Young G-DIMENSIONAL THEORY & THE SMARANDACHE QUANTUM PARADOXES: Comparative Logic and Mod... ...& THE SMARANDACHE QUANTUM PARADOXES: Comparative Logic and Modern Quantum Theory Table 1A. Elliptic Pa... ...Research Press Rehoboth 2001 2 L. Stephen Young G-DIMENSIONAL THEORY & THE SMARANDACHE QUANTUM PARADOXES: Comparative Logic and Mod... ...& THE SMARANDACHE QUANTUM PARADOXES: Comparative Logic and Modern Quantum Theory T a b l e o f C o n t e n t s Pa... ...g theoretical systems. Thus, the scientific paradox is a valuable source of information in comparing physical theories or in demonstrating the need ... ...cal, "marbles in a bag" geometry assumed in modern theory, which has little information to offer on intranuclear nucleon structure. 14. Assuming th... ...ing in an equal reflection angle with respect to the normal of the surface. Information transmitted concerning the matter field is limited to surfac... ... Snell's Law: (n i / n r = sinϕ r / sinϕ i ). [12] Atomic structural information of the through matter field is absent in VLS transmission. "... ...curs without transfer of momentum or energy, without transfer of structural information of the matter particles and occurs across the electromagneti...

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...Number theory is an ancient subject, but we still cannot answer many 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 impl...

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...RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collected papers) Edited by ZHANG WENPENG D... ... Hexis 200 4 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collect ed papers) Edited by ZHANG W... ...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (Univers ity of Microfilm International) 300... ...Florentin Smarandache, who listed many new and unsolved problems in number theory. Contents Dedication v Preface xi An arithmetic function and the pr... ...its mean value 49 Gao Nan viii RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY On the generalized constructive set 53 Gou su On the inferior and su... ...new problems implicated and are still promoting the development of number theory and mathematics. American - Romanian number theorist Florentin Sm...

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...Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences Editor’s Note This book ar... ...OWA 42402 USA GENERALIZED PARTITIONS AND SOME NEW IDEAS ON NUMBER THEORY AND SMARANDACHE SEQUENCES Hexis P... ...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...e On Maohua Le’s Proof of Murthy’s Conjecture On Reciprocal Partition Theory ………………. 18 1.4 Generalization of Partition Functions, Introducti... ...9 1.5 Open Problems and Conjectures On the Factor/Reciprocal Partition Theory ………………. 28 1.6 A General Result on the Smarandache Star Function... ...rs to the above questions leads to the need for the generalization of the theory of the partition function. Section 2 A Program to Determine t... ...papers, most of which appeared in “Smarandache Notions Journal”, and more information about SNJ is available at http://www.gallup.unm.edu/~smarandac...

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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 founded by Florentine Smarandache, is alike to that of Fuzzy ...

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...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...

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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 important and innovative properties about S-rings. Writi...

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...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...

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...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....

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... 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...

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...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 ...

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... 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...

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...ples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter beta is available in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficienc...

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... 2002 3 This book can be ordered in microfilm format from: ProQuest Information & Learning (University of Microfilm International) ... ...ssed interval containing the parameter beta is available in addition to sample information and analyses their properties. Some estimators are genera... ...lasses of estimators for population median M Y of the study character Y using information on two auxiliary characters X and Z in double sampling. I... ...ement errors on a family of estimators of population mean using multiauxiliary information. This error minimization is vital in financial modeling w... ...uessed interval containing the parameter β is available in addition to sample information and analyses their properties. Some estimators are genera... ...rresponding true values are termed as measurement errors. In general, standard theory of survey sampling assumes that data collected through surveys... ...ans. Jour. Ind. Soc.Agri. Statist., 36, 110-118. Murthy, M.N. (1967): Sampling Theory and Methods, Statistical Publishing Society, Calcutta. Olkin, ... ...3. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S. and Ashok, C. (1984): Sampling theory of surveys with applications. Iowa State University Press, USA...

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...be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) ... ...iewed and recommended for publication by: Dr. Sukanto Bhattacharya, School of Information Technology, Bond University, Queensland, Australia. Dr.... ...S patients 211 Chapter Three SOME NEW AND BASIC DEFINITIONS ON NEUTROSOPHIC THEORY 3.1 Neutrosophic sets and neutrosophic logic 222 3.2 Fuzzy... ...nalysis of Social Aspects of Migrant Labourers Living With HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps: With Specific Reference to R... ... of the natural evolution of genetics. GAs emulate the biological evolutionary theory to solve optimization problems. In general, 50 GAs start... ...upervised by a superpoint and supervised by another parent. Since the existing theory of genetic algorithms cannot provide measurement for the perf... ...ch is not trivial at all. Here, f k is no longer required to be linear and the information of minimal solutions may be absent. A genetic algorithm ... ...oblems and proposed a new model, more expressive for representing the available information, and where the intended meaning of the membership degree... ...ons. This model is not capable of capturing the most general kind of incomplete information. 127 Reasoning in diagnosis problems: the com...

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...om: Books on Demand ProQuest Information & Learning (University of Microfilm... ...bigraph will prove a major role in the applications of bimodels both in fuzzy theory and neutrosophic theory. Finally we give the matrix represen... ...that gives the hidden pattern of the situation. As we have a very well known theory, which states that the strength of the data 76 depends on, th... ...ps will also be directed neutrosophic graphs. It is no coincidence that graph theory has been independently discovered many times since it may quite... ...bject finds its place in the work of Euler. Subsequent rediscoveries of graph theory were by Kirchhoff and Cayley. Euler (1707-1782) became the fath... ... In Proc. of the 19 th International Conference of the North American Fuzzy Information Processing Society, NAFIPS2000, Atlanta, 2000. http://di... .... In Proc. of the 18 th International Conference of the North American Fuzzy Information Processing Society, by NAFIPS, New York, (1999) 115- 119. ... ...aras, D., and B. Karakostas. The Use of Fuzzy Cognitive maps to Stimulate the Information Systems Strategic Planning Process, Information and Softwa... ...tml 95. Montazemi, A.R., and D. W. Conrath. The Use of Cognitive Mapping for Information Requirements Analysis, MIS Quarterly, 10, 45-55, 1986. 9...

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...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...

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...ri Associate Professor of Mathematics Department of Mathematics and Computer Information Science Mansfield University Mansfield, PA 16933 hiser... ... This book can be ordered in microfilm format from: Books on Demand ProQuest Information & Learning (University Microfilm International) 300 N... ...s probably most active in the area of computational geometry. There is a lot of information available on the internet, and a good place to start a s... ...ifolds share with s-manifolds a focus on singularities. The Geometry Center has information on orbifolds at the websites [7, 6]. The focus of thi... ...ications, Inc. (Original work published 1912.) 4. Born, M. (1962). Einstein’s Theory of Relativity (Revised ed.). New York: Dover Publications, In... ...tion3.1.html. 8. Einstein, A. (1961). Relativity: the special and the general theory (R.W. Lawson, Trans.). New York: Three Rivers Press. 9. Eu... ... Press. 20. Stillwell, J. (1993). Classical Topology and Combinatorial Group Theory. New York: Springer-Verlag. 21. Weeks, J.R. (1985). The Sh...

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...om: Books on Demand ProQuest Information & Learning (University of Microfilm... ... untouchability and the caste-system of Hinduism using Fuzzy and Neutrosophic theory. In studying untouchability, we have chosen to view it throug... ...te is based on the 8 mind, it is appropriate to use Fuzzy and Neutrosophic theory. In Chapter Two we use the opinion of several experts to anal... ...that gives the hidden pattern of the situation. As we have a very well known theory, which states that the strength of the data depends on, the num... ...ons will be illustrated/ applied in the later sections of this chapter. Fuzzy theory only measures the grade of membership or the non-existence of a... ...I + F = 1. (B). But to refer to intuitionistic logic, which means incomplete information on a variable proposition or event one has T+ I+F <1. (C)... ...cally referring to Paraconsistent logic, which means contradictory sources of information about a same logical variable, proposition or event one ha... ... 1 Wendy Doniger, The Laws of Manu, Penguin, 1991. 2 For more biographical information refer p.103-113 of this book. 42 Respect Movement, was ... ...7-8-1930] Simon Commission By the polices of the Simon Commission and the information given by Chakravarthy, the cruelties of caste differences,...

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...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...

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...cs, together with Victor Vlădăreanu, Mihai Liviu Smarandache, Tudor Păroiu, and Ştefan Vlăduţescu, in 2D and 3D spaces in technology, philosophy, and information theory....

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...Romanian], by Florentin Smarandache, Tudor Păroiu: 79 7. Extension Communication for Solving the Ontological Contradiction between Communication and Information, by Florentin Smarandache, Ştefan Vlăduţescu: 99-112...

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... (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...

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...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...

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... logic and first order interval neutrosophic predicate logic. The interval neutrosophic logic can reason and model fuzzy, incomplete and inconsistent information. In this chapter, we also design an interval neutrosophic inference system based on first order interval neutrosophic predicate logic. The interval neutrosophic inference system can be applied to decision making. ...

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...sophic Propositional Calculus . . . . . . . . . 23 2.2.2 Semantics of Interval Neutrosophic Propositional Calculus . . . . . . . . . 24 2.2.3 Proof Theory of Interval Neutrosophic Propositional Calculus . . . . . . . . 25 2.3 Interval Neutrosophic Predicate Calculus . . . . . . . . . . . . . . . . 27 2.3.1 Syntax of Interval Neutrosophic Predicate Calculus . . . . . . ...

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...This work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. It reviews some of the classical notions of Benthamite utility and the normative utility paradigm offered by the von Neumann-Morgenstern expected utility theory; exploring its m...

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...YA Utility, Rationality and Beyond – From Behavioral Finance to Informational Finance 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 ... ... Utility, Rationality and Beyond – From Behavioral Finance to Informational Finance HEXIS ... ...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...umi.com/bod/search/basic Peer Reviewers: 1) Liu Feng, School of Information, Xi'an University of Finance and Economics, (Xi'an caijing xue... ...sor Dr. Kuldeep Kumar, Associate Professor of Statistics in the School of Information Technology, Bond University. Dr. Kumar has indeed been a remar... ...iness, Bond University for his thoughtful insights on some of the utility theory constructs. The author also feels indebted to a large extent to his ... ... This work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. It reviews some of the cla... ... utility paradigm offered by the von Neumann-Morgenstern expected utility theory; exploring its major pitfalls before moving into what is postulated ... ...nd not always explicable using the known rules of statistical probability theory. 10 Individuals often have very distorted perceptions of ...

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...those is surveyed in Liu’s book [33]. To determine the embedding of a graph on surfaces, including coloring a map on surfaces is another trend in map theory. Its object is combinatorialization of surfaces, see Gross and Tucker [22], Mohar and Thomassen [53] and White [70], especially the [53] for detail. The construction of regular maps on surfaces, related maps with group...

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...ook can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N.Zeeb Ro... ...acific University, AK, USA. H.Iseri, Department of Mathematics and Computer Information Science, Mansfield University, Mansfield, PA 16933, USA. Copyrigh... ... on surfaces, including coloring a map on surfaces is another trend in map theory. Its object is combinatorialization of surfaces, see Gross and Tucke... ...on surfaces, related maps with groups and geometry is a glimmer of the map theory with other mathematics. In fact, maps as a kind of the decomposition... ...sition of surfaces, should be given more attention to its role in surfaces theory, such as the Riemann surfaces, Klein surfaces and manifolds theory. ... ...s and toprofessor Yanpei Liu introduced meinto thefiled ofcombinatorial map theory. Thanks are also given to Professor Mingyao Xu, Professor Yanxun Cha... ...idean. It seems thattheSmarandachegeometriesareconnected withtheRelativity Theory(because they include the Riemann geometry in a subspace) and with th... ...c automorphism groups of some well-known graphs, which give us some useful information for the semi-arc automorphism groups, for example, Aut1 2 K n =...

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...ebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication 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 al...

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...dered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300... ...elds itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief econ... ...in this direction. 1.3.2 Smarandache Leontief economic models Matrix theory has been very successful in describing the interrelations between ... ...ween the industries in the economy 32 under considerations. Using matrix theory we evaluate certain parameters. The basic equations of the input-... ...entation existing between members of a set introduced, we have studied the theory of directed graphs to mathematically model the types of sets and r... ...or the first time we give the results of bimatrices in the field of coding theory. Very recently we have defined the notion of bicodes here we give ... ...utions to the Student Mathematical Competitions. His latest interest is in information fusion were he works with Dr.Jean Dezert from ONERA (French N...

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...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...

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.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 D. Rabounski A Theory of Gravity Like Electrodynamics. . . . . . . . . . . . . . . . . . .... ...sova Gravitational Waves and Gravitational Inertial Waves in the Gen- eral Theory of Relativity: A Theory and Experiments. . . . . . . . . . . . . . .... ...i, L. Borissova, F. Smarandache Quantum Causality Threshold in the General Theory of Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . . .... ...namics Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 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... ...d until it has been demonstrated that this is truly required by Einstein’s theory. Mere assumption is not permissible. 2 The basic geometry of the sim... ...ion of metric degrees of freedom into a part related to the true dynamical information and a part related only to the coordinate system. From this vie... ...xperimental statement on quan- tum teleportation has two channels in which information (the quantum state) transfers between two entangled particles: ... ...) transfers between two entangled particles: “teleportation channel” where information is transferred in- stantly, and “synchronization channel” — cla...

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...t XIX. Scavenger Economies, Predator Economies XX. Notes on the Economics of Game Theory XXI. Knowledge and Power XXII. Market Impeders and Mark... ... far better results. The outcome has been an embarrassing divorce between economic theory and its subjects. The economic actor is assumed to be con... ...f-interest" as the pursuit of the fulfillment of preferences is a tautology. The theory fails to predict important phenomena such as "strong reci... ...n accordance with the predictions of basic economic theories, such as the standard theory of utility and the theory of general equilibrium. Irritat... ...fects prevail). Thus, current economic thinking is woefully inadequate to deal with information monopolies (such as Microsoft), path dependence, and... ...e seems to have a clear answer. Advertising is concerned with the dissemination of information. Yet it is also a signal sent to consumers that a ce... ...graph, the telephone, electricity, the train, the car, the agricultural revolution, information technology and, now, biotechnology have all increase... ...to yield optimal results. Markets are supposed to regulate scarcity by storing information about our wants and needs. Markets harmonize supply ... ...upply and demand. They do so through the price mechanism. Money is, thus, a unit of information and a conveyor or conduit of the price signal - as w...

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...anctity of Human Life" by Baruch A. Brody). One form of calculus is the utilitarian theory. It calls for the maximization of utility (life, happines... ...es. Despite strong philosophical objections to some of the premises of utilitarian theory - I agree with its practical prescriptions. In this cont... ...tween aborting a fetus and destroying a sperm and an egg? These two contain all the information (=all the potential) and their destruction is philos... ...or falsified. Attaining an achievement involves the construction of an ad-hoc mini theory. Reality has to be thoroughly surveyed, models constructe... ...at the incentives are. That economists pretend otherwise - in "optimal contracting theory" - just serves to demonstrate how divorced economics is f... ...ve doubt. Markets are perceived as self-organizing, self-assembling, exchanges of information, goods, and services. Adam Smith's "invisible hand" ... ...gnore the future consequences of their actions. In other words, their attention and information processing faculties are distorted, skewed in favour... ...element of an idiosyncratic, non-communicable, language - we have no access to any information regarding it and, therefore, we are in no position t... ...about our health and imminent demise? Not likely. But why? What is the relevance of information about the future (our own looming death) when one is...

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...dered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...hingOnline.com Peer reviewers: Sukanto Bhattacharya, School of Information Technology, Bond University, Australia; Dr. Jean Dezert, ONERA... ...ntion here that the Neutrosophic logic is a further generalization of the theory of Fuzzy Logic. In this book we study the concepts of Fuzzy Cogn... ...Fuzzy Visions of Society and Science in the Digital Age writes that fuzzy theory can offer more choices and blur the hard lines of power that define... ...f our age. We have, in our effort at introducing indeterminacy into Fuzzy theory, and by our construction of neutrosophic structures of modeling, on... ...ting to these concepts. An almost exhaustive bibliography relating to the theory of FCMs completes the book. Some of the varied applications of F... ...functions and for feature selection. 4. Use of a decision engine to fuse information from different types of detection modules in order to make dec... ... Conditions = – 0.3 VIII: Competitor’s advertisements = +.5 32 This information can be organized into stimulus input vector: (0, 0, 0, 0, 0.3, ... ...wing theorem is suggested by Kim H.S. and Lee K.C. and for more elaborate information refer [50]. THEOREM [50]. When a concept C i is (Q i ∩ M ...

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...y listed companies, private equity firms are not legally bound to disclose information about their operations or those of the companies in which they ... ...oin hands to buy a target company, the significant flow of price sensitive information creates considerable potential for market abuse. The Boom and B... ...ment sectors have attracted more interest than traditional sectors such as information technology, information technology-enabled 41 Fixing Global Fi... ...,” CDSs are in effect bets on the credit-worthiness of a company. For more information, see Nicholas Hildyard, A (Crumbling) Wall of Money: Financial ... ... There is a paradox between the gains of capital account liberalization in theory and in practice. The arguments supportive of capital account liberal... ...much fewer in comparison with huge economic and social costs. Conventional theory suggests that if there are no restrictions on capital mobility, capi... ... witnessed in the ECA region during the financial crisis, the cross-border information sharing was squarely missing among the supervisory bodies of ho... ... the late 1970s. There is a paradox between the use of capital controls in theory and in practice. Although mainstream theory suggests that controls a... ...Great Crash 1929, Houghton-Mifflin, 1997. John Maynard Keynes, The General Theory of Employment, Interest and Money, Harcourt Brace Jovanovich, 1936/1...

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...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...

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...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 ....

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...This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigations while, Par...

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...Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . ...

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...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...

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...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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... An explanation of Beth experiment 66 6.4. Electrodynamics spin tensor 68 7 Other unsolved problems in various areas of science 72 7.1. Relativity theory 72 7.2. Questions related to Modified Bell’s theorem 73 7.3. Mind-matter interaction, hidden mystery of water 77 7.4. Quaternion wave interpretation of superconductor 80 7.5. Solar dynamics 83 7.6. Science of Ener...

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...ization of Venn Diagram, by Florentin Smarandache.........84 ECONOMICS, BUSINESS, AND POLITICS.................87 10. Introduction to Poly-Emporium Theory in Economics, by V. Christianto, F. Smarandache, in Authors’ book Cultural Advantage for Cities. An Alternative for Developing Countries, InfoLearnQuest, Ann Arbor, 61 p., 2008............88 11. Global Totalitarianism...

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...ization of Venn Diagram, by Florentin Smarandache.........84 ECONOMICS, BUSINESS, AND POLITICS.................87 10. Introduction to Poly-Emporium Theory in Economics, by V. Christianto, F. Smarandache, in Authors’ book Cultural Advantage for Cities. An Alternative for Developing Countries, InfoLearnQuest, Ann Arbor, 61 p., 2008............88 11. Global Totalitarianism...