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...p://www.gallup.unm.edu/~smarandache/), the Smarandache Notions Journal always published by American Research Press, and several books on conjectures, functions, unsolved problems, notions and other proposed by Professor F. Smarandache in "The Florentin Smarandache papers" special collections at: the Arizona State University (Tempe, USA), Archives of American Mathematics (U...

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...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICA... ...ys published by American Research Press, and several books on conjectures, functions, unsolved problems, notions and other proposed by Professor F. Sm... ...ing. This book, following the Smarandache spirit, presents new Smarandache functions, new conjectures, solved/unsolved problems, new Smarandache type ... ...) ( ) ( , ) 1 ( 1 k k a k a N c b where k Sz c b p 2) Smarandache sequence density Let a(n) be a Smarandache sequence strictly increasing and composed... ... composed of nonnegative integers. We can define the Smarandache sequence density as: n n A S n ) ( lim ¥ fi = d where A(n) is the number of terms (in... ...0 1 - £ £ - n d 77 The Prime Number Theorem [4] states (roughly) that the probability of a randomly chosen number of the size of n being prime is ab... ...me which is not a repunit must generate d distinct numbers by cycling. The probability that these are all primes is roughly d d d ł Ł ... ...th a good 2 R value (97%). Fig. 5.2 Assuming this function as empirical probability density function we can evaluate the probability that 1 0 > n ... ...2 R value (97%). Fig. 5.2 Assuming this function as empirical probability density function we can evaluate the probability that 1 0 > n B and then ...

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... as interpreted by modern quantum theory. Quantum theorists use statistical probability in the case for non-structural projection and would assume t... ... locus of zero potential energy for the mass of S'. Assuming a uniform mass density, the body's center of mass (c.o.m.) is thus located at the ellip... ...5 Hypothetical 20 8 64 48 132 5.6 Hypothetical 24 13 104 78 206 7.583 The functional relationships listed in Table 2 define the number of octet, fa... ...atomic number (A), increases, the ratio of the exterior to interior nucleon density must decrease. This assumption appears non-logical, given the nuc... ...del of minimal volume, (compression by -ϒ), so that one would assume nucleon density to be approximately uniform. Table 4. NOBLE GAS Nucleon Config... ...tio, as, Noble Nucleon: O/I = 2O / (2I + E) . (29) The noble functional relationship (29), corresponding to atomic number and listed i... ...ars safe to conclude the face-sites are filling up, with the extra neutrons functioning as mass counterbalances to the odd-numbered face-sites. Then... ...], where l is the average length between absorption- emission events and the probability of success of each event must be 100% for a successful event ... ...ity of success of each event must be 100% for a successful event set. The probability of this event-set differs markedly from that of reflection, w...

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...link their legs to form a living fabric on which the queen resides and performs her functions. http://www.lingolex.com/ants.htm http://ant.ed... ... system. The GALT disappears after age 60, though. The appendix has additional functions. Endocrine cells appear in the appendix of the human f... ...du/IHS/plague.html Black Holes Black holes are extremely dense bodies. Their density and gravitation are so enormous that it was thought noth... ... do not render the patient unconscious! Moreover, the cerebral cortex continues to function, though at a very depressed level, akin to that of barb... ...her. It was Francis Galton, a 19-century statistician, who pegged, in 1892, the probability that the prints of two individuals would match at 1:... ...n forensic practice, only 8-16 such points are used. No one knows to calculate the probability of matching fragments of two individual fingerprints... ...iluted in a solvent. As opposed to most solids, pure, non-commercial, glass has low density (i.e., large interstitial spaces between its atoms). Suc...

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...GICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY. (third edition) NL(A 1 I A 2 ) = ( T 1 ? ({1} 0T 2 ) /T 2 ?... ...GICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY. (third edition) NL(A 1 I A 2 ) = ( T 1 ? ({1} 0T 2 ) /T 2 ?... ...: 87 3. Neutrosophic Set - a unifying field in sets: 112 4. Neutrosophic Probability - a generalization of classical and imprecise probabilities - ... ...are subsets, but dynamically the components T, I, F are set-valued vector functions/operators depending on many parameters, such as: time, space, etc... ...es with respect to the observer (subjectivity is another parameter of the functions/operators T, I, F). For example: “John is smart” can be (.35, .... ...crete (Empirical)>). A self-regulating and self-unregulating mechanism is functioning in each system, moving from equilibrium to dis-equilibrium bac... ...g characteristics of an 41 idea: - novelty - quality - originality - density - continuity - brightness - quantity - analysis - synthesis ... ... A paradox within a Sorites paradox: a frontal bald man, with a hair high density on the remaining region of his head, may have more hairs on his he... ...another man who is not bald but the skin surface of his head and the hair density are smaller than the previous one. 2.9. Definition of Neutrosophic...

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...Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics Univer... ...NFERENCE ON NEUTROSOPHY, NEUTROSOPHIC LOGIC, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS ... ... First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and Statistics December 1-3, 2001 University of New ... ...ant on many parameters, and therefore they can be considered set-valued vector functions or even operators. The parameters can be: time, space, etc.... ...changes with respect to the observer (subjectivity is another parameter of the functions/operators T, I, F). For example: “John is smart” can be (.3... ...ent sequence, calculating more and more terms, or by calculating the limit of a function successively substituting the argument with values closer an... ...ody of different sizes… Therefore, the nearer to the center, the larger matter density and the faster rotation velocity, the whirl vortex bodies hav... ... bodies have. And, the whorl vortex bodies with small sizes have larger matter density and larger matter gains around with the rotating linear veloc... ...he maximum internal energy is congregated in electrons and atoms. In the super-density environment of electrons and atoms, the time-space scale stru...

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...n preferences involving financial structured products manufactured out of complex, multi-asset options. Evolutionary superiority of the Black-Scholes function in dynamic hedging scenarios is computationally demonstrated using a haploid genetic algorithm model programmed in Borland C. The work explores, both theoretically and computationally, the psycho-cognitive factors go...

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... ... 37 3. Exploring the Biological Basis of Utility Functions – Computational Implementation of a Genetic Algorithm ... ...ogical basis of the Black-Scholes -type expected utility functions ... ...mplex, multi-asset options. Evolutionary superiority of the Black-Scholes function in dynamic hedging scenarios is computationally demonstrated usin... ...ay-off at stake, f (X) is a pre-determined loss function and p (X) is the probability of receiving the total pay-off. If the individual decides to p... ...on could indeed have unfortunate cases where f(X) > X indicating a finite probability of complete financial ruin for the trader but no meaningful mat... ...the assumption of logarithmic utility! Additionally, a very small probability of “infinite loss” will not always deter enterprising profit-s... ...an analogy between utiltiy and probability through the notion of a utiltiy density function. The core idea was to define a utility density function a... ...tion, one should use that utiltiy curve (or utility vector) whose utiltiy density function (or utility increment vector) has maximum entropy subject... ...he differential form of entropy expression in continous form to a utility density function to get a value of U X . It is also intuitively obv...

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...amily of estimators of population mean using multiauxiliary information. This error minimization is vital in financial modeling whereby the objective function lies upon minimizing over-shooting 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 ...

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...nd recommended for publication by: Dr. V. Seleacu, Department of Mathematics / Probability and Statistics, University of Craiova, Romania; Dr. Sabi... .... This error minimization is vital in financial modeling whereby the objective function lies upon minimizing over-shooting and undershooting. Th... ..., x n be a random sample of size n from a two-parameter Weibull distribution, probability density function of which is given by : () () {} fx x x... ...random sample of size n from a two-parameter Weibull distribution, probability density function of which is given by : () () {} fx x x x ;, e x p ... ...ample of size n from a two-parameter Weibull distribution, probability density function of which is given by : () () {} fx x x x ;, e x p / ; , , ... ...the log-Weibull distribution [e.g. White(1969)], cumulative distribution function of which is given by : () Fy yu b yu b =− − −        ... ...ased estimator of β with Var() ) 4 ( 2 ˆ 2 − β = β h and th b g = ∧ having density () 0 ; 2 exp 2 2 / 1 ) ( 1 ) 2 / ( 2 / >       β −   ... ...venkataramana, T. and Tracy, D.S. (1989): Two-phase sampling for selection with probability proportional to size in sample surveys. Biometrika, 76, ...

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...ny plan is not as important as it is to set a definite plan and work towards its goal. The plan outlined here is in two phases: Phase one has a high probability of success, given the required propulsion system; the chances of phase two working will be indicated by results obtained from phase one. A fundamental problem is the one of propulsion. It is important to the wor...

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... its goal. The plan outlined here is in two phases: Phase one has a high probability of success, given the required propulsion system; the chances ... ...the mass-object which equals the intrinsic (proper) mass, and the average density of the graviton field. The source strength is constant, the other ... ...nus sixth. [One chance in a million.] Fermi: This is much too low. The probability is more like ten percent. The significance of that convers... ... The significance of that conversation is that neither gentleman put the probability at zero. Two directly opposing camps have developed: those wh... ...alog of rocketship acceleration. For such an analysis in terms of Bessel functions see for example R. W. Landee et al, Electronic Designers' Handb... ...er of intelligent species arising in the region because of the increased density of stars; (2) The relative closeness of the neighboring stars t...

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...Experiments. . . . . . . . . . . . . . . . . . . 30 C. Castro On Geometric Probability, Holography, Shilov Boundaries and the Four Physical Coupling C... ...ov Hydrodynamic Covariant Symp- lectic Structure from Bilinear Hamiltonian Functions. . . . . . . . . . . . . . . . . . . . 92 D. Rabounski, L. Boriss... ...nal feld are the proper radius and the curvature radius, both of which are functions of r. The variable r is actually a Euclidean parameter which is m... ...r)dr 2 −C(r) dθ 2 +sin 2 θdϕ 2 , (2a) A,B,C>0, whereA,B,C are analytic functions. I emphatically remark that the geometric relations between the c... ...o the conclusion that the components of the observer’s vector b α defne a “density” of physically observable time in his accompanying reference frame.... ...is accompanying reference frame. As it is easy to see, the observable time density depends on the gravitational potential and, in the general case, on... ...of observable time references. For this reason we will call it the feld of density of observable time. In the same way, a feld of the tensor h αβ =−g ... ...eory and Experiments July, 2005 PROGRESS IN PHYSICS Volume 2 On Geometric Probability, Holography, Shilov Boundaries and the Four Physical Coupling C... ...: czarlosromanov@yahoo.com; castro@ctsps.cau.edu By recurring to Geometric Probability methods, it is shown that the coupling constants, αEM ;α W ;α C...

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... A FRE in dynamic fuzzy systems 113 1.20 Solving FRE with a linear objective function 117 1.21 Some properties of minimal solution for a FRE 1... ...n algorithm for largest solution 268 4.9 Solving NRE with a linear objective function 269 4.10 Some properties of minimal solution for NRE 270 4... ...ies It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary relations R(X, ... ... each x i . P(Select the rth individual) = q 1 (1-q) (r-1) , where q is the probability of selecting the best individual, r is the rank of the i... ...in Y is (estimated as) some number from 0 to 1 inclusive. This may sound like a probability, but it is not. The quickest way to see this is from the... ...d labor. While studying this problem in practice researchers have has neglected density variations across each stream. The mass balance equations ac... ...an 0 or greater than 1. Thus: x (50, 20, 30) belongs to A (which means, with a probability of 50% x is in A, with a probability of 30% x is not in A... ... the new effect due to chemical reactions which may change due to change in the density/ viscosity of the fluid under study their by changing the fl... ...ich in many cases are not up to expectations, leakage of pipe, the viscosity or density after chemical reaction time factor, which is related with t...

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... A FRE in dynamic fuzzy systems 113 1.20 Solving FRE with a linear objective function 117 1.21 Some properties of minimal solution for a FRE 1... ...n algorithm for largest solution 268 4.9 Solving NRE with a linear objective function 269 4.10 Some properties of minimal solution for NRE 270 4... ...ies It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary relations R(X, ... ... each x i . P(Select the rth individual) = q 1 (1-q) (r-1) , where q is the probability of selecting the best individual, r is the rank of the i... ...in Y is (estimated as) some number from 0 to 1 inclusive. This may sound like a probability, but it is not. The quickest way to see this is from the... ...d labor. While studying this problem in practice researchers have has neglected density variations across each stream. The mass balance equations ac... ...an 0 or greater than 1. Thus: x (50, 20, 30) belongs to A (which means, with a probability of 50% x is in A, with a probability of 30% x is not in A... ... the new effect due to chemical reactions which may change due to change in the density/ viscosity of the fluid under study their by changing the fl... ...ich in many cases are not up to expectations, leakage of pipe, the viscosity or density after chemical reaction time factor, which is related with t...

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... role of chance in evolution has long been recognized and increasing structural and functional adaptability has been attributed to random-stochastic... ...se to the most order increasing event. If we were to construct and apply this wave function to our world we, humans, would probably have found ours... ... isotropy, lack of interaction with other forms of energy and matter, infinitesimal density, negative pressure) suggest that dark energy, the Cosmo... ...aracteristics as the sole vehicle of evolution) and Evolution Theory postulate that function determines form. Natural selection rewards those forms ... ...m a-priori structures embedded in the human mind. 2. It provides high information density, akin to stenography. Just a few symbols arranged in for... ... and be measured more often (the wave function collapses more frequently into high probability states). But this does not exclude the less probable... ...e (superposition) and their endpoints are interference patterns. D-branes are the probability fields of all possible vibrations. The Universe A ... ...ary (e.g., its gravitational horizon). As the universe's entropy grows (and energy density falls), it "decays" and its inflation stops. This event ... ...hods of observation, experimentation, and analysis (e.g., the use of statistics and probability in the studies conducted at the Parapsychology Labor...

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...d by c to preserve the ratio to c nature of the arguments of the hyperbolic functions. Then to get the time coordinate the 1/g term in the t equati... ...gically inconsistent language. Namely, one cannot introduce geometry into a probability theory, because a probability theory has the uncertainty pri... ...he neutrinos detected are not the type predicted, and the machinations of a probability based theory to explain this discrepancy are not believable.... ...ergy levels. But the whole theory is very inadequate, degenerating into the density functional method which is mostly an experimental method for fin... ...els. But the whole theory is very inadequate, degenerating into the density functional method which is mostly an experimental method for finding gro... ...ften stated that no known measurement has ever contradicted QM, but QM is a probability based theory, so this statement might be best compared to th... ...structure of space-forms give an alternative context with which to view the function spaces on which differential operators act, and from which solu...

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...a/caft-20). 6. Smarandache F. Invisible paradox. Neutrosophy, Neutrosophic Probability, Set, and Logic, American Research Press, Reho- both, 1998 (see... ...mber of antiprotons in the second type. If antimatter exists then a higher probability would be for the unmatter to exist, and reciprocally. Unmatter ... ...ble to test the production of unmatter. If antimatter exists then a higher probability would be for the unmatter to exist, and reciprocally. The 1998 ... ... is given byF =m(U.∇U+DΔU). Recall that, after one has introduced the wave function ψ from the complex actionS=S R +iS I , namely,ψ= exp (iS/2mD)= √ P... ...be known only after having solved the Schr ¨ odinger equation for the wave function. This is a situation somewhat different from that of general relat... ...ler-Newton representation. In the end, the particle is described by a wave function (which is constructed, in the scale relativity theory, from the ge... ...nck scale one reproduces precisely the observed value of the vacuum energy density! [25]: ρ L −2 Planck R −2 H =L −4 P (L Planck /R H ) 2 10 −122 ... ... energy-momentum (via Noether’s theorem) defned in terms of the Lagrangian density variation. We refer to [75] for further details. The gauge invarian... ... with m. Therefore, if we expand the number lattice infnitely, the average density of rational numbers in the plane (the ratio between the number of r...

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...d as murder. Phenomenology is deceiving: the acts look the same (cessation of life functions, the prevention of a future). But murder is the intent... ...ial to the one fetus created. The egg and sperm can be compared to the famous wave function (state vector) in quantum mechanics – the represent mil... ... (=millions of potential embryos and lives). The fetus is the collapse of the wave function: it represents a much more limited set of potentials. I... ...lan of action must be seen to be reasonable and pragmatic and leading – with great probability – to the achievement. In other words: the plan must ... ...able). It is neither true nor false. It is a probabilistic statement, but without a probability distribution. It is, in short, a meaningless stateme... ...echanics. For instance: strategies could have been described as wave functions with probability distributions. The same treatment could be accorded ... ...itative phase transition. Or this: Large populations lead to the emergence of high density urban centers. It is inefficient to cultivate ever small...

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...d as murder. Phenomenology is deceiving: the acts look the same (cessation of life functions, the prevention of a future). But murder is the intent... ...ial to the one fetus created. The egg and sperm can be compared to the famous wave function (state vector) in quantum mechanics – the represent mil... ... (=millions of potential embryos and lives). The fetus is the collapse of the wave function: it represents a much more limited set of potentials. I... ...lan of action must be seen to be reasonable and pragmatic and leading – with great probability – to the achievement. In other words: the plan must ... ...able). It is neither true nor false. It is a probabilistic statement, but without a probability distribution. It is, in short, a meaningless stateme... ...echanics. For instance: strategies could have been described as wave functions with probability distributions. The same treatment could be accorded ... ...itative phase transition. Or this: Large populations lead to the emergence of high density urban centers. It is inefficient to cultivate ever small...

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...vanish. They are going to metamorphose. This is because they fulfil a few functions and provide a few services whose importance is only enhanced by ... ...y do best: content creation, and reduce their overhead by outsourcing the functions of distribution and relationships management. The existence of c... ...a state of flux. Old maxims break down. New modes of operation emerge. Functions are amalgamated, outsourced, dispensed with, or created from scra... ...n authorities, many of them for both fixed and mobile numbers. Fixed line density is so low, mobile penetration, at 20 percent, so dismal, prices so... ...ystems and on their associated energies). The wave function describes the probability of a particle (originally, the electron) to be inside a small ... ...e a small volume of space defined by the aforementioned coordinates. This probability is proportional to the square of the wave function. This is a ...

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...as some disadvantages. The main advantage of this method it is simple. It functions on expert's opinion. When the data happens to be an unsupervised... ...concept C j measures how much C i causes C j . The time varying concept function C i (t) measures the non negative occurrence of some fuzzy event, ... ... 1 on the temporal associative memories recall process. Threshold signal functions synchronously update each concept after each pass, through the c... ...lyzed the FCMs using the following definitions: DEFINITION 1.2.1: The density of a cognitive map D is an index of connectivity. D = C / N(N –... ... D = C / N(N – 1) or alternatively D = C / N 2 . This is known as the density equation where in C represents the number of connections possible ... ... (A). To maintain consistency with the classical and fuzzy logics and with probability there is the special case where T + I + F = 1. (B). But to ... ...he chance of being in pending is 10% or 20% or 30%. Then the neutrosophic probability that Popescu emigrates to the Unites States is NP (Popescu)... ...,30}), closer to the life. This is a better approach than the classical probability, where 40 P(Popescu) 60, because from the pending chance – whi... ...ection matrix, 8 Cyclic FRM, 93 Cyclic NCM, 135 Cyclic NRM, 170 D Density equation, 25 Density of a cognitive map, 25 Directed cycle, 9 Di...

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...nebulous and remote (as far as I am concerned) field as a discoverer of a function that wears the poet’s name: Smarandache’s function. And there is... ...f meanings produces humour, the “sliding” of meanings assumes an ironical function, the unexpected passage from the figurative to the literal sense ... ... neutralizes the differences between literature and show (a very important function in dramaturgy, the lowering from the solemn level to the vulgar o... ... usually an increase of the vigor of the whole construction and a greater density of its meanings. In the Romanian literature, the formula of anti... ...st recognize, the text draws attention from the very beginning through the density and the ingenuity of suggestions and hints spread in a foamy, unpr... ..., read among the thematic intarsies, of a paradoxical and visionary 74 density, from the poetic theorems. The confirmation following from them is ... ...assical probabilities, as well as the indefinite one, to the neutrosophic probability, defining it as a tridimensional vector whose elements are rea...

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...d and Perfection Pg 527 Tool Principles vs. Human principles Pg 529 Linear Functionality Pg 540 Tool-functioning vs. Human Functioning Pg 541 ... ...5 Disease Pg 1388 Exploration of the Subconscious Pg 1393 Social Form and Function Pg 1395 The Power of Myth Pg 1397 History and Myth Pg 139... ...ea. Actual Infinity is not imaginary. It is not a possibility. It is not a probability. Infinity is not an abstract concept invented by humans. ... ...asses of Energy, while going through Infinite Permutations of Possibility and Probability. While Space is going Out. After the first Split of Time,... ...ged its characteristics and properties depending on its larger structures and density: not its intrinsic characteristics. The Conditions that the U... ...ince Actual Infinity contains within it all Infinite Possibility and Infinite Probability, the process of Infinite Splitting goes through an Infinit... ...in one unique niche of the original ecosystem we were genetically designed to function in…. That is; in Africa, where we originally came from, as n... ...d… and the sparseness of their numbers. As we spread out: our population density rose all over this planet because we used tools better. It too... ...ools better. It took at least 50-100 thousand years of increasing population density before it reached a critical mass for settled civilizations to...