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... of the sky between the two horizons, and the distance to the objects, among other variables. Our APPARENT horizon (what we can actually see) and t... ...NEP.htm l Newton, Isaac Isaac Newton (1642-1727), the father of modern physics and mathematics, was an avowed and dedicated alchemist, mystic, theo... ...h increasing hours of daylight. It is not correlated with any other meteorological variable, such as rainfall or temperature. Suicide rates appeare... ...intellectuals, the lingua franca, akin to English today. Nor was he acquainted with mathematics until he was 30. Leonardo was born out of wedloc...

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...ral Tamil Nadu in India W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, ... ...n web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: s... ... varies from women to women we are forced to analyze the problem using fuzzy mathematics. This chapter has two sections. In the first section we in... ...roduction of learning as encoding. We avoid all types of high and complicated mathematics. As our study is a psychological one, we give more import... ...unction. We specify in advance the numerical universe of discourse for fuzzy variables X 1 , X 2 and Y. For each universe of discourse or fuzzy va... ...of the input space X. They represent the fuzzy set values assumed by a fuzzy variable. A different library of fuzzy sets similarly quantizes the ou... ...ymposium on Mathematical Methods and Applications, held at the Department of Mathematics, IIT Madras, December 22, 2003. 135. Vasantha Kandasamy...

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...ished independently (as is often the case in science) the basics of a new branch in Mathematics (and logic): computability or recursive functions (l... ... human population growth and that this barrier is related to the biotic and abiotic variables of the environment - is undisputed. Whatever debate th... ...ems do not respect man-made borders and by the stubborn refusal of many ecological variables to succumb to numbers. To complicate things further, d... ...possess the same sense organs that we do (eyes) and may not be acquainted with our mathematics and geometry. Reality can be successfully described ...

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...I have met the Smarandache's world for the first time about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research Press web site dedicated to the Smarandache notions and held by Dr. Perez (address: http://www.gallup.unm.edu/~smarandache/), the Smarandache Notions Jo...

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...eading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research P... ...tions at: the Arizona State University (Tempe, USA), Archives of American Mathematics (University of Texas at Austin, USA), University of Craiova Lib... ... fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this universe has a very simple structur... ...rhus Univ. Press, 1996 [3] E. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 1999 [4] F. Smarandache, "Only Problems, not Soluti... ...************************** 1040 ' 1050 ' The sub return the value of variable PASS. 1060 ' If pass is equal to 1 then N is a prime. 1070 '... ...e check the sum of p and q. If it is greater than n+r then we decrease the variable q to the largest prime smaller than the previous one. On the contr... ...evious one. On the contrary if the sum is smaller than n+r we increase the variable p to the next prime. This loop continues untill p is lower than q.... ...ues untill p is lower than q. If this is not the case then we increase the variable r to the next prime and we restart again the check on p and q. If ... ...**************************** 350 ' 360 ' The sub return the value of variable PASS. 370 ' If pass is equal to 1 then N is a prime. 380 ' ...

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...al model of utility that is independent of spatio-temporal and behavioral variables. The problem of utility is best illustrated by the proble... ... time t = T, Z 0 is the initial wealth at time t = 0, x is a random loss variable, I(x) is the indemnification function, C(x) is the cost of insura... ...ns to constrained optimization problems. Both economic and physical state variables come in intensive/extensive variable pairs and the one such pair... ...els, our approach is predominantly numerate and substantiated by rigorous mathematics rather than being merely normative or speculative. The... ...s in the options market are somewhat unique as the only non-deterministic variable in option pricing theory is volatility. Moreover, given the knowl... ... While countless research papers have been written and published on the mathematics of option pricing formulation, surprisingly little work has be... ...g fundamental assumptions: 84 (1). W 0 =0 (2). W t -W s is a random variable that is normally distributed with mean 0 and variance t-s (3). W ... .... Numerical Methods and Software. Prentice-Hall Series in Computational Mathematics, New Jersey: Prentice-Hall, 1989. Khoshnevisan, M., S. Bhatt... ...78. Lyuu, Yuh-Dauh. Financial Engineering and Computation – Principles, Mathematics, Algorithms. Cambridge University Press, U.K., 2002. Mark...

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...he. In addition, I have edited two others that also deal with the areas of mathematics under the Smarandache Notions umbrella. All of this is a credit... ...mmetric sequences for an arbitrary base, which is stored in the base1 variable. All elements will be sequentially constructed up to the eleme... ...er("3"); /* The elements will first be created as strings. The base1String variable will store the left side of the element and the base2String var... ...l create the elements of the Mirror Sequence for the base stored in the variable base1. It will then determine if the number is prime. Written by C... ...te the elements of the Natural Sequence for the base value assigned to the variable base1. Listing 4 /* This program will compute the elements of the ... ...new BigInteger(theInput.toString()); // The BigInteger theIncrement is the variable that will by multiplied with the // accumulator. // The process wi... ...arandache is truly a Renaissance man, having produced quality work in art, mathematics and literature. This is my fifth book where I expand on some o...

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...A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the combinatorial pro...

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...ress Rehoboth, NM 2005 Linfan MAO Institute of Systems Science Academy of Mathematics and Systems Chinese Academy of Sciences Beijing 100080, P.R.Chi... ...lib.umi.com/bod/search/basic Peer Reviewers: F.Tian and X.D.Hu, Academy of Mathematics and Systems, Chinese Academy of Sciences, Beijing 100080, P.R.C... ...ces, Beijing 100080, P.R.China. Y.P.Liu and R.X.Hao, Department of Applied Mathematics, Beijing Jiaotong Uni- versity, Beijing 100044, P.R.China. S.Bh... ... S.Bhattacharya, Alaska Pacific University, AK, USA. H.Iseri, Department of Mathematics and Computer Information Science, Mansfield University, Mansfield... ...n a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its f... ...ons among g[Γ](x), g[Γ](x) or G[Γ](x) are known, and vice via. Denote the variable vector (x 1 ,x 2 ,···) by x ¯ , r ¯ (Γ) =(···, r 2 (Γ), r 1 (Γ),r ...

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...AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036... ...ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail:... ...cademia Technica Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, I... ...m-dimensional vector where c i represents the weight (or cost) associated with variable x i , for i ∈ I. The optimization problem we are... ... (6) DEFINITION 1.4.1: For a solution x ∈X (A, b), we call 0 i x a binding variable if 0 i x . j i 0 a = b j for i 0 ∈ I and x i a ij ≤ b ... ...y relation equations. And, the set Λ represents all combinations of the binding variables such that every combination can satisfy every fuzzy relati... ...onsider a set of constraints, say B, which can be satisfied by a certain set of variables, say X B . If the decision to choose which variable in the... ...problem into k sub-problems. I (1) and J (1) correspond to sets of indices of variables and constraints, respectively, on which the B&B method is ... ...al, and thus one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosoph...

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... Fuzzy and Neutrosophic Models W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, In... ...n web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: sma... ...mia Technica Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, India... ...d many times, since it may quite properly be regarded as an area of applied mathematics. Euler (1707-1782) became the father of graph theory. In 18... ...ed the important class of graphs called trees by considering the changes of variables in the differential calculus. Later he was engaged in enumerat... ...al doctrine. The most famous problem in graph theory and perhaps in all of mathematics is the celebrated four color conjecture. The remarkable prob...

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...* r C r-k ]. 38 k=0 With the change of variables r – k = w, we get k = 0, w = r and k = r, w = 0. ... ...e Florentin Smarandache Special Collection”, Archives of American Mathematics, Centre for American History, University of Texas at Austin, US... ...sum of the products. As an example, the following is a chart for the four variables x 1 , x 2 , x 3 , x 4 . Elementry symmetric funcions (sum of t... ...andache Star Function", SNJ, Vol.11, No. 1-2-3, 2000. 6. Problem 2/31, Mathematics & Informatics Quarterly, 3/99 Volume 9, Sept' 99, Bulgaria. ... ...age 240. 12. Amarnath Murthy, “On The Infinitude of Prime Numbers”, The Mathematics Education, India, Vol. XXIX, No. 1, March, 1995. 13. Felice... ... 6. “The Florentine Smarandache Special Collection”, Archives of American Mathematics, Centre for American History, University of Texas at Austin, US... ...0. " The Florentine Smarandache Special Collection”, Archives of American Mathematics, Centre for American History, University of Texas at Austin, US...

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...e Light Barrier by A.D. 2070 Homer B. Tilton Department of Mathematics and Engineering Pima Community College, EC, USA Florentin... ... Pima Community College, EC, USA Florentin Smarandache Department of Mathematics and Sciences The University of New Mexico at Gallup, USA ... ...ed of light, the observer loses sight of it anyway, and even relativistic mathematics is unable to penetrate beyond that point. The application of ... ...to penetrate beyond that point. The application of sublight relativistic mathematics beyond that speed is clearly idealistic and virtual. It is si... ...rial objects is the speed of light. / The argument has been made that the mathematics are correct, but that the "apparent" velocities are just an ill... ...rnal to it in space. A rear-facing camera can present a view aft on that variable-transparency viewscreen. After familiarization training, the re...

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...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a brief review of a problem and obtained results. All submissions should be designed in LATEX format using Progress in Physics template. Th...

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...According to the Dictionary of Mathematics (Borowski and Borwein, 1991 [1]), the paradox is “an apparently absurd or self-contradictory statement for which there is prima facie support, or an explicit contradiction derived from apparently unexceptionable p...

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...ies in Theoretical and Experimental Physics, including Related Themes from Mathematics PROGRESSINPHYSICS A quarterly issue scientifc journal, register... ...lborissova@yahoo.com Stephen J. Crothers thenarmis@yahoo.com Department of Mathematics, University of New Mexico, 200 College Road, Gallup, NM 87301, ... ...ies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, ... ...asi-Paradoxes and Quantum Sorites Paradoxes Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 College Road, Gallup, NM 87301, ... ...n. We shall express the energy equation in terms of the various equivalent variables which we use in scale relativity, namely, the wave function ψ, th... ...ativistic factor in eq-(2.1) involves the ratios of two proper forces. One variable force is given bymg(τ) and the maximal proper force sustained by a... ...ers automatically the standard Lorentz transformations for the X,T and E,P variables separately, leaving invariant the intervals dT 2 −dX 2 =(dτ) 2 an... ...oisson brackets. Since the coordinates and momenta are no longer commuting variables the classical Newtonian dynamics is going to be modifed since the... ...tes, supersymmetry, holography, higher derivative gravity with torsion and variable dimensions/signatures. It permits to study the dynamics of all (cl...

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...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a brief review of a problem and obtained results. All submissions should be designed in LATEX format using Progress in Physics template. Th...

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...ies in Theoretical and Experimental Physics, including Related Themes from Mathematics PROGRESSINPHYSICS A quarterly issue scientifc journal, register... ...lborissova@yahoo.com Stephen J. Crothers thenarmis@yahoo.com Department of Mathematics, University of New Mexico, 200 College Road, Gallup, NM 87301, ... ...ies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, ... ...per radius and the curvature radius, both of which are functions of r. The variable r is actually a Euclidean parameter which is mapped to non-Euclide... ...ld, namely, the proper radius and the curvature radius. 1 Introduction The variabler has given rise to much confusion. In the con- ventional analysis,... ...e. This how- ever, does not follow in any rigorous way. In (M g ,g g ) the variable r is nothing more than a real-valued parameter, of no physical sig... ...Field of the Point-Mass 3 Volume 2 PROGRESS IN PHYSICS July, 2005 (a) The variable r is a radius and/or coordinate of some kind in the gravitational ... ...follows: (a) The coordinate radius isD=|r−r 0 |. (b) Ther-parameter is the variabler. (c) The radius of curvature isR c = p C(r). (d) The proper radiu... ...another name for the product of mass and acceleration, which occurs in the mathematics of solving a problem. Furthermore, the idea of force as a cause...

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...This dual will be studied in a separate paper (in preparation). 2. The additive analogues of the functions 5 and 5. are real variable functions, and have been defined and studied in paper [31. (See also one book [61, pp. 171-174). These functions have been recently further extended, by the use of Euler's gamma function, ill place of the factorial...

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...Introduction In survey sampling, the use of auxiliary information can increase the precision of an estimator when study variable y is highly correlated with the auxiliary variable x. but in several practical situations, instead of existence of auxiliary variables there exists some auxiliary attributes, which are highly correlated with study va...

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....................41 5.Almost Unbiased Ratio and Product Type Estimator of Finite Population Variance Using the Knowledge of Kurtosis of an Auxiliary Variable in Sample Surveys....................................54 6.A General Family of Estimators for Estimating Population Variance Using Known Value of Some Population Parameter(s).....................62-73...

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...zzy 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 Theory: both the fields imperatively questioned the dogmas of classical mathematics....

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...HE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology Madras Chennai – 600 036, Indi... ...tarted because of my perception at that time, that the world of classical mathematics – was a little too much of a black and white world, that the p... ...born as a paradoxist movement that challenged the status quo of existing mathematics. The genesis of Smarandache Notions, a field founded by Floren... ...y Theory: both the fields imperatively questioned the dogmas of classical mathematics. Despite the fact that Fuzzy Algebra has been studied for ov... ...r. We proceed on to define fuzzy polynomial near-rings when the number of variables is more than one x and y. DEFINITION 1.8.17: Let R be the rea... ...re than one x and y. DEFINITION 1.8.17: Let R be the reals x, y be two variables we first assume xy = yx. Define the fuzzy polynomial near-ring. ... ... {R [x [0, 1] , y [0, 1] ], ⊕, } be a fuzzy polynomial near-ring in the variable x and y. A fuzzy polynomial p(x, y) is said to be homogenous o... ...{x [0, 1] , y [0, 1] , ⊕, ‘ ’} be the fuzzy polynomial near-ring in the variables x and y. A symmetric fuzzy polynomial is a homogenous polynomial ... ...ke other polynomials we can extend the fuzzy polynomials to any number of variables say X 1 , X 2 , …, X n . under the assumption X i X j = X j X i...

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...s due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for the actual system. The sources of uncertainty can be stochasticity (the case of intrinsic imperfection where a typical and single value does not exist), incompl...

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...ir comments and recommendations on these papers: I. Balacenoiu, Department of Mathematics, University of Craiova, Romania; C. Corduneanu, Departmen... ...eutrosophic Probability and Statistics) Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA 0.1 In... ...n) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for the a... ..., and start again. We may add rules that don’t preserve monotonicity. In bio-mathematics Heitkoetter and Beasley (1993-1999) present the evolutiona... ...= 1 and i = 0, and 0 [ t, i, f [ 1); from "CRC Concise Concise Encyclopedia of Mathematics", by Eric W. Weisstein, 1998, the fuzzy logic is "an exte... ...n the set are equal to the number of monotonic increasing Boolean functions of variables, and also the number of free distributive lattices with gene... ...Hardcover 608 Pages, February 1994 [72] Zadeh L.A.,“The Concept of a Linguistic variable and its Application to Approximate Reasoning I,II,III” Inform... ...ty. Sengupta created a model of Shumpeterian Dynamics. In that model, two key variables were introduced through a two staged formulation using Schu... ...roach is to cast out undesirable clusters in our training data. The linguistic variables, terms, membership functions, rule blocks, rules and interf...

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...ractitioners sought to disguise its nature as a social science by applying complex mathematics where common sense and direct experimentation would ... ...either lack predictive powers or lapse into logical fallacies, such as the "omitted variable bias" or "reverse causality". The former is concerned w... ...tted variable bias" or "reverse causality". The former is concerned with important variables unaccounted for - the latter with reciprocal causation... ...conclusion was that markets overshoot in response to surprising changes in economic variables. A sudden increase in the money supply, for instance, ... ... reference. Other prices combine a fixed element (e.g., a subscription fee) with a variable element (e.g., payment per broadband usage). Volume dis... ...re and the machine tools used in the manufacturing process. The actual production ("variable" or "marginal") cost of each unit is a mere few cents -... ...ntists and mathematicians of the XX century. Apart from his great contributions to mathematics, computing and other fields, the minor fact that he ... ... three-dimensional extension of formal logic which is the set of RULES that govern mathematics. Then came the Macintosh and its emulation, the win... ...ependently (as is often the coincidence in science) the basics of a new branch in Mathematics (and logic): computability or recursive functions (l...

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...an give rise to many types of entirely unrelated products. There are too many free variables here. The origin exists as a "wave function": a series... ...ractitioners sought to disguise its nature as a social science by applying complex mathematics where common sense and direct experimentation would ... ...either lack predictive powers or lapse into logical fallacies, such as the "omitted variable bias" or "reverse causality". The former is concerned w... ...tted variable bias" or "reverse causality". The former is concerned with important variables unaccounted for - the latter with reciprocal causation... ...ifferently to the same transformation? Arithmetic, formal logic, and, by extension, mathematics and physics deal with proving identities in equation... ...ecognized as an important contribution and applied to problems in geometry, logic, mathematics, computation and physics. One of the first questions... ...t infinite sets are organized in a hierarchy. Russel and Whitehead concluded that mathematics was a branch of the logic of sets and that it is ana... ... human population growth and that this barrier is related to the biotic and abiotic variables of the environment - is undisputed. Whatever debate th... ...ems do not respect man-made borders and by the stubborn refusal of many ecological variables to succumb to numbers. To complicate things further, d...

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...ks heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by ...

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...3) Professor Emeritus C. Corduneanu Texas State University Department of Mathematics Arlington, Texas 76019, USA. ISBN: 1-931233-60-8 S... ...logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs a... ...are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes ... ...Chapter three describes the rules of fuzzy logic, where the values of the variables can be any value in the continuum from zero to one. Finally, cha... ...ooks, over twenty research papers and several problems that were posed in mathematics journals. He is truly a Renaissance man, I have books of his a... ...n 5 Rules of Inference in Fuzzy Logic Section 6 Modal Logic with Fuzzy Variables Section 7 Temporal Logic 37 37 39 40 40 46 48 5... ...assical Logic Section 1 Propositions In classical logic, a logical variable is restricted to the values of true(T) and false(F). The logical ... ...ome authors use the lowercase letters p, q and r and so forth to represent variables that can be either true or false. Others use the uppercase lette... ...ers A, B, C and so forth. In this book, both will be used. Since each variable in classical logic is restricted to these two values, if an expres...