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...entin Smarandache, who seems to be a perpetual idea machine. Like classical logic, it can be used in many ways, everywhere from statistics to quantum mechanics. Neutrosophy is more than just a form of logic however. There are several different definitions, extending into many different fields. For our purposes here, we will concentrate almost exclusively on the logic, as t...

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...logic, it can be used in many ways, everywhere from statistics to quantum mechanics. Neutrosophy is more than just a form of logic however. There ... ...y, philosophy and mathematics among my collection. Yes, the plural can be applied to each category several times over. I would also like to thank... ...in formal proofs. The following is a list of additional rules that can be applied. • And – elimination From a conjunction, any of the propositio... ...hat uses the I has applications in the branch of physics known as quantum mechanics. Quantum mechanics is the physics of the very small, where even... ...of poison to be broken, which will kill the cat. According to quantum mechanics, the probability that the atom will decay during the interval of... ...live after the interval is ½. However, in the weird world of quantum mechanics, the atom can decay, but until the box is opened and examined, t... ... happen) and 0.0 (certain not to happen). This gradation of likelihood is applied to logic, creating degrees of truth. Fuzzy logic was originally de... ... snow tomorrow.” Fuzzy logic allows values between 0.0 and 1.0 to be applied to the variables. If the value is 0.0, then the variable is consid... ...ns satisfying the inductive assumptions. There are four rules that can be applied. Case 1: Rule iii) of the definition of a wff is applied to A. ...

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...oting and undershooting. This book has been designed for graduate students and researchers who are active in the area of estimation and data sampling applied in financial survey modeling and applied statistics. In our future research, we will address the computational aspects of the algorithms developed in this book....

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...nts and researchers who are active in the area of estimation and data sampling applied in financial survey modeling and applied statistics. In our f... ... (1951) : A Statistical distribution function of wide Applicability, Journal of Applied Mechanics, 18, 293-297. 25 WHITE, J. S. (1969) : The mome... ... A Statistical distribution function of wide Applicability, Journal of Applied Mechanics, 18, 293-297. 25 WHITE, J. S. (1969) : The moments of lo...

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...d the speed of light is best resolved by applying the rules of relativistic mechanics to the problem, determining the equations of motion of the roc... ...ent with equation (5) which gives 0.569 (The disagreement comes because we applied equation (5) to the 0.1c increment as one increment rather than ... ...Theory of Relativity is incomplete, since it is not compatible with Quantum Mechanics. At some future time relativity will be replaced by a more co... ...me relativity will be replaced by a more complete theory, just as Newtonian mechanics was replaced by relativity, but whatever replaces relativity m... ...e, their polarizations are opposite of each other; 37 - in quantum mechanics, objects such as subatomic particles do not have specific, fix... ...author): “It appears that the only things the Smarandache hypothesis can be applied to are entities that do not have real mass or energy or informat... ...orentin, "There Is No Speed Barrier In The Universe", <Bulletin of Pure and Applied Sciences>, Delhi, India, Vol. 17D (Physics), No. 1, p. 61, 1998;... ...Wright, Jason, “Superluminals and the Speed of Light”, Bulletin of Pure and Applied Sciences, Delhi, India, Vol. 20, Series D (Physics), No. 2, 107-... ...never realized. The ranking of physical theories by me: 1. Newtonian mechanics and Hamiltonian mechanics, good theories and essentially Galil...

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...reader progresses through the book. The test of reality to be ultimately applied is whether or not it is really impossible to make a round trip to A... ... The basis for the hypothesis lies in the entanglement theory of quantum mechanics and deals with the transfer of information over large distances.... ... Dr. Akhlesh Lakhtakia Distinguished Professor, Engineering Science and Mechanics Distinguished Professor, Graduate Program in Materials Pennsylv... ...le that question. Recent work with the entanglement theory under quantum mechanics also casts doubt on the impenetrability of the light barrier. F... ..." and an "annihilation operator" - serious mathematical tools for quantum mechanics. But, dear reader, mathematics is one thing and physics quite a... ...randache, There is no Speed Barrier in the Universe, Bulletin of Pure and Applied Sciences, Vol.17D (Physics), No. 1, p. 61, Jan-Jun, 1998. [4] R... ..., 2001: It appears that the only things the Smarandache hypothesis can be applied to are entities that do not have real mass or energy or informatio... ...entin, "There Is No Speed Barrier In The Universe", <Bulletin of Pure and Applied Sciences>, Vol. 17D (Physics), No. 1, p. 61, 1998; http://www.gall... ...right, Jason, “Superluminals and the Speed of Light”, Bulletin of Pure and Applied Sciences, Delhi, India, Vol. 20, Series D (Physics), No. 2, 107-11...

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...ual worlds”. There are general rules of combination, and ad hoc rules. For an applied logic to artificial intelligence, a better approach, the best ... ...roblems of small dimension. The DST is a powerful theoretical tool which can be applied for the representation of incomplete knowledge, belief updatin... ...so published in the Proceedings Volume, Maximum Entropy and Bayesian Methods in Applied Statistics, J.H. Editor, Cambridge University Press, pp. 1 25,... ...so published in the Proceedings Volume, Maximum Entropy and Bayesian Methods in Applied Statistics, P .F. Fougere Editor, Kluwer Academic Publishers, ... .... The first step is to classify our neural model. We have used 90 samples and applied Neutrosophic classification ( T,I,F) in three states ( T.I,F) ... ...veloped since the 17 th century completely and bodily. Also, from Aristotle’s mechanics to Einstein’s special theory of relativity and from classica... ...cial theory of relativity and from classical electrodynamics to modern quantum mechanics, the book has generalized the thoughts of unified field theo... ...s of temperature field, of existence and evolution of whirl vortex body), wave mechanics, electrodynamics, motion medium electrodynamics, trajectory ...

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...y authors) in what ”we can’t see the wood for the trees”! At an attentive and applied analysis of the theoretical (see ”the manifestoes”) and the pra... ...d an amazing work and a style- THE PARADOXISM, theorized and then brilliantly applied to every literary genres- lyrical, epic and dramatic. We will ... ...mentarity, finally resulting an exciting conception about poetry, brilliantly applied to a unique poetic work-” a second game more pure” of the obje... ...or universe, serving to its harmony and unity. The conception was marvelously applied in the famous Second game (“From time inferred”) (Joc secund, ... ... that his wish, that he couldn’t and hadn’t enough time to achieve, have been applied after almost half of a century by Florentin Smarandache. His l... ...funny: ”Ermizeu, the old synus / burning like a dual thought/ in the Hamilton mechanics/ with residual spectrum/ from the loxodromic siege/ had pull...

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...inclusive view of the various real-world problems to which FCMs have been applied. Though there are over a hundred research papers relating to FCMs, ... ...rn metropolitan public transportation. Now we just illustrate how we have applied FCM to the problem of determining the maximum utility of a route [1... ... neural networks were used to suggest business strategies, their approach applied FCM- based simulation analysis for environmental analysis. With thi... ...d as follows: ∀ i ≠ j: S i , ≠ S j . A markovian [71] modeling has been applied to look at the cognitive behavior of users on the Web in the graph... ...lications. It is pertinent to mention here that FCM model has also been applied in case of transportation problems like passengers preference, pea... ...discovered graph theory for its own purposes. In the study of statistical mechanics by Uhlenbeck the points stands for molecules and two adjacent po... ... 66. Lee, T.D., and C. N. Yang. Many Body Problems in Quantum Statistical Mechanics, Physical Review, 113 (1959) 1165-1177. 67. Lewin, K. Principles...

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...iscovered many times, since it may quite properly be regarded as an area of applied mathematics. Euler (1707-1782) became the father of graph theor... ...ph theory for its own purposes more than once. In the study of statistical mechanics by Uhlenbeck the points stand for molecules and two adjacent p... ... these five types of cases lot of indeterminacy is involved, so when NCM is applied certainly it will lead to better results. Example 3.7.9: Use o... ... the reader to model this problem using NCM and compare it when only FCM is applied; complete discussions using FCM is given in [65] as taken from [... ...th tools like the FCM and the NCM. Next we shall see how best NCM can be applied in medical diagnosis. FCMs have found applications in many medic... ...or nodes to be divided into two (or more) disjoint classes. FRMs cannot be applied when the nodes or attributes under consideration in a data canno...

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...s 199 2.11 Semantics of implication operators and fuzzy relational products applied to HIV/AIDS patients 211 Chapter Three SOME NEW AND BA... ...egular matrix multiplication. However the multiplication and addition that are applied to these combinations in the matrix multiplication are repla... ...ogramming methods, such as the simplex and interior-point algorithms, cannot be applied to this problem. [58] denote the solution set of problem (1... ... that dominates, z is a dominated criterion vector. The idea of dominance is applied to the criterion vectors whereas the idea of efficiency is a... ...nts can therefore be set aside from the problem. The genetic operators are then applied to this reduced problem. Without loss of generality, we assu... ...aradigm shifts are associated with the names of Copernicus (astronomy), Newton (mechanics), Lavoisier (chemistry) Darwin (biology), Maxwell (electr... ... Lavoisier (chemistry) Darwin (biology), Maxwell (electromagnetism), Einstein (mechanics) and Godel (mathematics). Although paradigm shifts vary f...

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...s 199 2.11 Semantics of implication operators and fuzzy relational products applied to HIV/AIDS patients 211 Chapter Three SOME NEW AND BA... ...egular matrix multiplication. However the multiplication and addition that are applied to these combinations in the matrix multiplication are repla... ...ogramming methods, such as the simplex and interior-point algorithms, cannot be applied to this problem. [58] denote the solution set of problem (1... ... that dominates, z is a dominated criterion vector. The idea of dominance is applied to the criterion vectors whereas the idea of efficiency is a... ...nts can therefore be set aside from the problem. The genetic operators are then applied to this reduced problem. Without loss of generality, we assu... ...aradigm shifts are associated with the names of Copernicus (astronomy), Newton (mechanics), Lavoisier (chemistry) Darwin (biology), Maxwell (electr... ... Lavoisier (chemistry) Darwin (biology), Maxwell (electromagnetism), Einstein (mechanics) and Godel (mathematics). Although paradigm shifts vary f...

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...of Sciences, Beijing 100080, P.R.China. Y.P.Liu and R.X.Hao, Department of Applied Mathematics, Beijing Jiaotong Uni- versity, Beijing 100044, P.R.Chi... ...erential geometry, Riemann geometry, Smarandache ge- ometries, ··· and the mechanics, theoretical physics, ···. For doing this, the most possible way ... ...S.ChimientiandM.Bencze, Smarandacheparadoxistgeometry,Bulletin of Pure and Applied Sciences, Delhi, India, Vol.17E, No.1(1998), 123-1124. [17] J.Edmon... ...ao and Y.P.Liu, Group action approach for enumerating maps on sur- faces,J.Applied Math. & Computing, vol.13, No.1-2,201-215. [47] L.F.Mao and Y.P.Liu... ...rationresearchinjournals. He was born in December 31,1962and got his BA in applied mathematics in Peking University in 1995 learnt by himself. In 2002... ...he automorphism groups of a Klein surface and a Smarandache manifold, also applied to the enumeration of unrooted mapsonorientableandnon-orientablesur...

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...y discovered many times since it may quite properly be regarded as an area of applied mathematics. The 152 subject finds its place in the work of ... ...cs discovered graph theory for its own purposes. In the study of statistical mechanics by Uhlenbeck the points stands for molecules and two adjacen... ...examples we make it clear that all unsupervised data need not have NCMs to be applied to it. Only data which have the relation between two nodes to ... ... 251 87. Lee, T.D., and C. N. Yang. Many Body Problems in Quantum Statistical Mechanics, Physical Review, 113, 1165-1177, 1959. 88. Lewin, K. Princ... ...Model, Proc. of the 9 th National Conf. of the Vijnana Parishad of India on Applied and Industrial Mathematics held at Netaji Subhas Inst. of Tech...

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...iscovered many times since it may quite properly be regarded as an area of applied mathematics. The subject finds its place in the work of Euler. Su... ...ered graph theory for its own purposes. In the study of statistical 139 mechanics by Uhlenbeck the points stands for molecules and two adjacent p... ...space or (bi subspace) of the domain space. Some amount of caution must be applied while studying bitransformations. We will define a pseudo subspa...

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...T, stocks and share etc. Use of neutrosophic notions will be illustrated/ applied in the later sections of this chapter. Fuzzy theory only measures ... ...scovered many times since it may quite properly be regarded as an area of applied mathematics. The subject finds its place in the work of Euler. Sub... ...discovered graph theory for its own purposes. In the study of statistical mechanics by Uhlenbeck the points stands for molecules and two adjacent p... ...ples we make it clear that all unsupervised data need not have NCMs to be applied to it. Only data which have the relation between two nodes to be a... ... on the eyelids, big boils on the body, some bandaged, some with medicine applied, some not properly taken care of with flies hovering on. (2) A... ...pecially migration from the rural areas. So we do not say the same can be applied to patients who have not acquired the disease due to migration—onc...