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...o experiment.” B) Etymology: Paradoxism =paradox +ism, means the theory and school of using paradoxes in literary and artistic creation. ... ...Arizona) or in Gallup (New Mexico). I tried to answer each letter sending information on the paradoxism and also paradoxist diplomas where it was t... ...000000000100000000000000 0000000000000000000000000 referring to my number theory sequences that he found on the web. ... ...f the First International Conference on Smarandache Type Notions in Number Theory, Universitatea din Craiova, editori – C. Dumitrescu şi V. Seleacu,... ...0) A Set of New Smarandache Functions, Sequences and Conjectures in Number Theory, de Felice Russo, Lupton, 2000, 114 p. În afara acestor c ăr ţi,... ...f the First International Conference on Smarandache Type Notions in Number Theory, editori: C. Dumitrescu şi V. Seleacu, Lupton, 1997, 208 pag. 8. C...

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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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...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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...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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...tu Popescu synthesized that period with the inspired syntagma “From action to theory”. And back (for all the life long) to... practice, we should ad... ...the “postmodernization” with any price of the materialistic and old-fashioned theory concerning the “development in spiral”! All these things must... ...rganized the first international conference on the Smarandache notions in the theory of numbers; in 1997 (at the Chair in Algebra of the State Unive... ...ained the title of doctor in mathematics with the thesis New functions in the theory of numbers; about the Smarandache function have already been wr... ...erses (it is risky to name them prose or poetry!) we learn essential data and information about the “becoming” of this (almost) exile in his own coun... ... attentive and subtle observer that is Florentin Smarandache gives us so many information about Morrocco, about the civilization where he has lived ... ...ed.1992, 3 rd ed.1994, 4 th ed.1999). The book is not a journal proper, the information being undated; very seldom is mentioned some year, only wh... ...From the content’s point of view, its attractiveness is given by the unwonted information, a valid situation for those who do not know America. The ... ... our attention by itself. Author’s commentaries alternate everywhere with the information proper. Also, author’s common-sense and honestity are abso...

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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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...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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...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 <A> an idea, or proposition, theory, event, concept, entity, by <Non-A> what is not <A>, and by <A... ... to measure the truth, indeterminacy, and falsehood. My hypothesis is that no theory is exempted from paradoxes, because of the language imprecisio... ...ssible unlike myopic algorithms that look at each iteration only at very local information as with steepest descent method. As in non-monotonic logi... ...f this: what would happen if a non-p conclusion occurred? The inconsistence of information shows up in the result, if not eliminated from the beginn... ...eria and the complementarity of various sources. For example, the Possibility Theory (Zadeh 1978, Dubois, Prade) gives a better approach than the F... ... Theory (Zadeh 1978, Dubois, Prade) gives a better approach than the Fuzzy Set Theory (Yager) due to self-improving connectives. The Possibility Th... ..., The AI Magazine, 81-83, 1984. Combination of paradoxical sources of information within the neutrosophic framework Dr. Jean Dezert Abstrac...

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...science too! Let’s see an example from cybernetics, regarding the fusion of information. The robots dispose of multi-sensors which receive informat... ...f multi-sensors which receive informations that must be processed, but these informations are often contradictory in a smaller or higher degree. The... ...ry in a smaller or higher degree. The fusion of such conflicting, paradoxist informations in science is an old problem not entirely solved by the ex... ...ade, Smets, Yager, Zadeh (fuzzy sets), etc. The robot needs to process these informations and gets alone a decision. Here it is the paradoxism. Simi... ...lopment of computer science and technology in order to combine many types of information (fuzzy, uncertain, imprecise, paradoxist, incomplete etc.) ... ...n expertise, sensor measurements, AI expert systems, neural network, quantum theory, economics predictions). One such theory, that permits the comb... ...e combination of paradoxist information, has been called Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning for Data Fusion (2002). ... ...en nothing is impossible Except the possibility of everything. Haiku: SET THEORY If the Superset containing ALL sets Cannot be said to include...

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...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...rete, successive times of emission. Isochrons are spherical bubbles of information expanding at the speed of light with center at the position th... ...ts take you. The premise of this book is that the effects of the special theory of relativity are a kinematical perspective rather than being real;... ...an infinite speed. The basis for the hypothesis lies in the entanglement theory of quantum mechanics and deals with the transfer of information ove... ...e entanglement theory of quantum mechanics and deals with the transfer of information over large distances. Dr. Florentin Smarandache Associ... ...co at Gallup February 2004 9 Guest Preface The special theory of relativity (STR) is indeed a kinematical perspective. By that I ... ...ollier's). Recent trends in thinking view the distortions of the special theory of relativity as only appearances, unable to affect Human physiolog... ...ted from special relativity, did not materialize. You wonder if this new information will be enough to justify an attempt to break the light barrie... ...ication. Ship-to-shore communication has to do with sending and receiving information; and as Norbert Weiner said, "Information is not matter or ene...

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... ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...ache called Smarandache Notions Journal that is edited by Dr. Minh Perez. Information about it and other advances can be found on the web site devot... ...of Inference Section 7 Formal Reasoning Section 8 Quantification Theory Section 9 Uses of Logic In Computer Programming 7 13 14 1... ...o use truth tables to perform the computations. For that we need a formal theory. Definition 1.5.1: A formal theory is a system S constructed from... ...heorem in the system S. Example: The following is a formal axiomatic theory L a) The set of symbols in L are { ¬, →, (, ), T, F, p 1 , p 2 , ... ... . B Definition 1.5.2: The formal axiomatic theory L in the previous example is known as the propositional calculus. ... ... 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. ... ..., referring to paraconsistent logic, which means contradictory sources of information about a same logical variable, proposition, or event one has t ... ...hen it follows that t 2 = t 3 . However, if f 1 ≤ t 2 , then we have no information about t 3 , so we make no assumptions and set it equal to zero...