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...F. Smarandache has defined many sequences of integers formed by concatenating the positive integers in specific ways. A question that is often asked about most of these sequences concerns the number of primes in the sequence. As Paul Erdos pointed out, d...

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...Using the bases from three through nine to form new sequences, we can then ask the same question regarding the number of primes in the sequence. That appears to be a question just as difficult as the one for base ten numbers, and is summarized in the following statement....

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...Preface.3 -- Table of Contents.4 -- Chapter 1 Sequences Formed by Concatenating All the Positive Integers.5 -- Chapter 2 Sequences Formed by Concatenating Selected Natural Numbers .44 -- Chapter 3 Smarandache Stereograms .70 3.1 -- The Stereogram.70 -- 3.2 Altering the B...

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...CHARLES ASHBACHER Smarandache Sequences, Stereograms and Series 1111111111111111111111111111111111111... ...Hexis Phoenix 2005 Charles Ashbacher Mount Mercy College Smarandache Sequences, Stereograms and Series Hexis Phoenix 2005 2 This book can be or... ... Preface ………………. …………………. 3 Table of Contents ………………. …………………. 4 Chapter 1 Sequences Formed by Concatenating All the Positive Integers …………………. 5 Chap... ...ces Formed by Concatenating All the Positive Integers …………………. 5 Chapter 2 Sequences Formed by Concatenating Selected Natural Numbers …………………. 44 Chap... ...Smarandache Function …………………... 95 Index …………………. ………………… 133 5 Chapter 1 Sequences Formed By Concatenating All the Positive Integers F. Smarandache... ...through n, so the probability that they are prime is higher than that of a randomly selected odd integer. The elements of the Permutation Sequence ar... ...ncatenation of the primes modulo numbers, prime or not prime, appear to be randomly distributed. Once the issue of the apparent appearance of random ... ...ent with the idea that the elements of the Concatenated Prime Sequence are randomly distributed around the prime numbers. 4) Smarandache Concatenated ...

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...ther necessitates the effect, or is a sufficient condition for its occurrence. The sequence is either inevitable, or possible. The meaninglessness ... ...tations, including those related to human life directly. We even issue patents for sequences of human DNA. And people do own forests and rivers and... ... beings. On the contrary, complexity usually points towards a natural source and a random origin. It is also true that complexity and artificiality...

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...n 1956 IBM invented the first computer disk storage system, the 305 RAMAC (Random Access Method of Accounting and Control). This system could store ... ... the process that moves the read/write heads to the correct cylinder on a random access on the hard disk. Therefore, at the time that the heads arri... ... that represents the composite of all the other specifications reflecting random performance positioning in the hard disk. As such, it is the best fi... ...lso depends on the access pattern of the particular program being run (the sequence of addresses being read and written). Caches rely on two properti...

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...n 1956 IBM invented the first computer disk storage system, the 305 RAMAC (Random Access Method of Accounting and Control). This system could store ... ... the process that moves the read/write heads to the correct cylinder on a random access on the hard disk. Therefore, at the time that the heads arri... ... that represents the composite of all the other specifications reflecting random performance positioning in the hard disk. As such, it is the best fi... ...lso depends on the access pattern of the particular program being run (the sequence of addresses being read and written). Caches rely on two properti...

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...ies: an even-number (α-particle) progression in nucleo protons and Fibonacci sequence in the outer proton, (octet and face) sites. The projection of ... ...of light in refractive transmission is attributed to an absorption-emission sequence of the light by atoms of the matter field; in which, successive... ...atter), (diffuse reflection), is defined as incident VLS being reflected at random angles due to uneven contours, (height: h 1 - h 2 > λ), in the m... ... in the matter field surface. The typically non-opalescent effect indicates randomness of angle reflection ≅ 100%. This indicates two modes of refle... ...0%. This indicates two modes of reflection having very different degrees of randomness in reflection angle affect. Specular: the light is reflected ... ...ble) scale. SQP-1 Conclusions in MT To summarize, the absorption-emissive sequence in refraction imparts no visible atomic field to the radiation,... ...ide molecular structural information from diffractive effects, but the high randomness in diffuse reflection angles precludes this possibility. Lumin...

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...e that kind of a thing. It is the other way around. It hits but it hits at random. That is the way nature operates, lightning hits you somewhere. It ... ...its and is helping the people by providing shade, etc. It just strikes at random. In exactly the same way, it happens to a particular individual. ... ...If this is so then where is the room for practices and volition? It comes randomly, not because you deserve it. If you are lucky enough to have th... ...single event. It is the logical, cause and effect thinking that imposes a sequence to events. The sudden evidence of light and the throwing of the l...

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...sionmark 200 2nd Ave. SE Cedar Rapids, IA 52401 Chapter 1 Smarandache Sequences In the time since it was first published[ 1], the Smarandache fu... ...order. In this first chapter, we will concentrate on notions that involve sequences, moving on to other, more specific points in the second. The fi... ...t problem we will deal with is number (6) in [5]. Smarandache permutation sequence: 12,1342.135642, 13578642, 1357910864~ 135791112108642,. Or as a... ...)(2n)(2n-2)(2n-4) 642 where SPS is an acronym for Smarandache Permutation Sequence. Note on notation: As a general principle, acronyms will be creat... ...ect of the next theorem. Theorem 10: If a positive integer n is chosen at random, the odds are overwhelming that n is a pseudo-odd number of the fir... ... 4 * 5'-[ k-digit numbers containing no odd number. The probability of a random k-digit number containing all even numbers is then 4*5"-: _ .f --... ... the digits is odd. Theorem 11: If a positive even integer n is chosen at random, the odds are overwhelming that n is a pseudo-odd number of the sec... ...e digits is an odd number. It should be clear that the probability that a randomly chosen positive integer is pseudo- odd of the third kind is also o... ...nition is the following. Theorem 12: If a positive integer n is chosen at random, the probability that n is both a pseudo-odd number of the first ki...

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...ing. This book, following the Smarandache spirit, presents new Smarandache functions, new conjectures, solved/unsolved problems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter (IV) is dedicated to the analysis of Smarandache Double factorial function introduced in number theory by F. Smarandache ("The Florentin Smarandache p...

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...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICAN RESEARCH P... ...functions, new conjectures, solved/unsolved problems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter ... ...respectively) values. For the first 1000 values of Zt(n) the largest found sequences have k=5 and k=4 respectively. Example: Z... ...repeated application of the Zt function. An n-cycle, instead, is a finite sequence of points 1 , 1 0 , - n Y Y Y K such that, under the function Zt,... ...Totient numbers. Problem 37. Is the number 0.1243549107585.... where the sequence of digits is Zt(n) for 1 ‡ n an irrational or trascendental number... ...77 The Prime Number Theorem [4] states (roughly) that the probability of a randomly chosen number of the size of n being prime is about: ... ...act this estimate has to be increased since such numbers are not chosen at random; they are specifically chosen not to be divisible by 2 or 5 so the ...

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...nt of power p in n. That is, ep(n) = m, if pm j n and pm+1 - n. In problem 68 of [1], Professor F.Smarandache asked us to study the properties of the sequence fep(n)g. About the elementary properties of this function, many scholars have studied it (see reference [2]-[7]), and got some useful results. For examples, Liu Yanni [2] studied the mean value properties of ep(bk(n)...

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...ive function 18 X. Pan and P. Zhang : An identity involving the Smarandache function ep(n) 26 A.A.K. Majumdar : A note on the Smarandache inversion sequence 30 F. Li : Some Dirichlet series involving special sequences 36 Y. Wang : An asymptotic formula of Sk(n!) 40 S. Gao and Z. Shao : A fuzzy relaxed approach for multi-objective transportation problem 44 J. Li : An ...

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...tems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Phy...

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...Sequences on Graphs with Symmetries Linfan Mao Chinese Academy of Mathematics and System Science, Beijing, 10080, P.R.China Beijing Institute of Civil Engineering and Architecture, Beijing, 100044, P.R.China E-mail: maoli...

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...Contents Lucas Graceful Labeling for Some Graphs BY M.A.PERUMAL, S.NAVANEETHAKRISHNAN AND A.NAGARAJAN . . . . . 01 Sequences on Graphs with Symmetries BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Supermagic Coverings of Some Simple Graphs BY P.JEYANTHI AND P.SELVAGOPAL . . . . . . . . . . . . . ....

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... it is being tragically eroded by our current copyright, patent, and trademark laws. In a series of fascinating case studies, Boyle explains why gene sequences, basic business ideas and pairs of musical notes are now owned, why jazz might be illegal if it were invented today, why most of 20th century culture is legally unavailable to us, and why today's policies would prob...

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... should be the farthest from the market. In stories about stem cell and gene sequence patents, critics have mused darkly about the way in which the st... ...y interfere with your plans to use it for growing crops. By contrast, a gene sequence, an MP3 file, or an image may be used by multiple parties; my The... ...t 49 ___-1 ___0 ___ 1 37278_u01.qxd 8/28/08 11:04 AM Page 49 layer; gene sequence patents come very close to being rights over a particular discov... ...hich simply means that you strike the notes of the chord individually and in sequence. It was, in fact, a pretty standard “deedly” sound, familiar fro... ... The original beats have a totemic significance—like the great standard chord sequences in jazz. One cannot substitute replicas for James Brown’s funki... ...hat these questions are fun to debate but ultimately irrelevant. 12 Assume a random distribution of incentive struc- tures in different people, a glob... ...effectively scattered U.S. approach to data privacy, for example, pro- duces random islands of privacy protection in a sea of potential vulnerability.... ...e Definitive History of the Most Important Artists and Their Music (New York: Random House, 1992), 130. Notes to pages 127–130 281 ___-1 ___0 ___ 1 372... ...e Future of Ideas: The Fate of the Com- mons in a Connected World (New York: Random House, 2001), and Lawrence Lessig, Free Culture (New York: Penguin...

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...re of principal lters on po-semigroups 50 Y. Lu : F. Smarandache additive k-th power complements 55 M. Le : The Smarandache reverse auto correlated sequences of natural numbers 58 M. Karama : Smarandache partitions 60 L. Mao : On Algebraic Multi-Group Spaces 64 F. Russo : The Smarandache P and S persistence of a prime 71 Y. Lu : On the solutions of an equation involv...

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...al wealth at 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 co... ...s that the generalized financial market cannot possibly be reduced to pure random walk if we do away with the assumption of normality, it does not ne... ...w information. Some inefficiency however may also be attributed to purely random white noise unrelated to any coherent market information. If the pr... ...al price-path meaning that all market information (as well as some of the random white noise) could become automatically anchored to this perceived ... ...lied volatility on short- term options with probability 0.99 or out of (C) random white noise with probability of 31 0.01. The other sees it as ei... ...etter j will be received. A code word of length n is defined as a sequence of n input letters, which are actually n integers chosen from 1, ... ...= 1, 2 … n. As per Shannon’s coding theorem, it is possible to encode all sequences of n message integers into sequences of binary digits in such a w... ....A., 1984. Gerard, H. B. Choice difficulty, dissonance and the decision sequence. Journal of Personality 35, 1967: 91-108. Goldberg, D. E. Gen...

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...Probability (called sometimes the objective probability) process uncertainty of random type (stochastic) introduced by the chance. Uncertainty of th... ...t result. This might be comparable to approximating the limit of a convergent sequence, calculating more and more terms, or by calculating the limit... ...be a finite discrete set of exhaustive and exclusive hypotheses or outcomes of a random experiment. The probability of has been defined and interpreted ... ...just know that the cardinality numbers of follow the integers of the Dedekind’s sequence minus one when Card increases. Examples 1. If we consider (em... ...ations in the mathematical community. Cardinality numbers follow the Dedekind’s sequence (minus one), i.e. when Card . 4.3 General basic assignment n... ...onmental Studies, Duke University, Durham, NC, 1986. [35] Li X.R.,“Probability, Random Signals, and Statistics”,CRC Press, 1999. [36] Mahler R., “Comb... ...Functions”, Comm. Pure Appl. Math., 23, pp. 299 312, 1970. [55] Sloane N.J.A., “Sequences A006826/M2469, A007153/M3551, and A014466”, in “An On Line V... ...imum Deviation=3% Average Deviation=.1 Neural network learning method: Batch Random Step width =.03 Winner Neuron=4 Winner Neuron=4 Winner N... ...best compromise is used in most control applications. The rule block is 1 with random Dos value generator. 5.Conclusions: 5.Conclusions: 5.Conclus...

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...nized and increasing structural and functional adaptability has been attributed to random-stochastic processes (such as environmentally-induced gen... ...eter) against Disorder. In this context, natural selection is no more "blind" or "random" than its subjects. It is discriminating, encourages stru... ...hance happening. We are the culmination of orderly processes - not the outcome of random events. The Universe enables us and our world because - a... ...nt. Therefore, we are forced to conclude that quantum events are guided by some non-random principle (such as the increase in order). This, exactly,... ... beings. On the contrary, complexity usually points towards a natural source and a random origin. Complexity and artificiality are often incompatib... ...re carefully "selected" for some purpose, within a certain pattern and in a certain sequence. What could that purpose be? Probably, the extension an... ...ecause a minimum number of axioms and hypotheses yield, in an inexorable deductive sequence, everything else known in the field the theory pertains... ..."meaning". Both Donald Davidson and Alfred Tarski suggested that truth exists where sequences of objects satisfy parts of sentences. The meanings of... ...ecause a minimum number of axioms and hypotheses yield, in an inexorable deductive sequence, everything else known in the field the theory pertains...

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... working years at the Gazette and in retirement, curiosity prompted notes randomly taken and linked to history trails recalled from high school and ... ... Europe. Expanded Access To Wasted Intellect Feeding my curiosity with random research convinced me of the following: • Earlier Inf... ...eyond geometry— fixes the zero as the starting linchpin in plus and minus sequences. History of the missing number hazy Mathematicians find the ... ...rint shop helpers were still known before the advent of union apprentices—randomly and appropriately tossed it into a ―hell box.‖ Later, the prin... ...third digits and then by a decimal point and more numbers. (Note that the sequence recognizes the proper placement of zero by starting with 000 rath... ...or ETAOIN SHRDLU to be listed in the Oxford English Dictionary and in the Random House Webster's Unabridged Dictionary. CHAPTER 21 ―Einstein wasn’... ...imon and Schuster, 2001. Boorstin, Daniel J. The Discoverers. New York: Random House, 1983. Broder, David. Behind the Front Page: A Candid Look ...

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... working years at the Gazette and in retirement, curiosity prompted notes randomly taken and linked to history trails recalled from high school and ... ... Europe. Expanded access to wasted intellect Feeding my curiosity with random research convinced me of the following: • Earlier Inf... ...eyond geometry— fixes the zero as the starting linchpin in plus and minus sequences. History of the missing number hazy Mathematicians find the ze... ...rint shop helpers were still known before the advent of union apprentices—randomly and appropriately tossed it into a ―hell box.‖ Later, the print... ...third digits and then by a decimal point and more numbers. (Note that the sequence recognizes the proper placement of zero by starting with 000 rath... ...or ETAOIN SHRDLU to be listed in the Oxford English Dictionary and in the Random House Webster's Unabridged Dictionary. CHAPTER 21 ―Einstein wasn’... ...imon and Schuster, 2001. Boorstin, Daniel J. The Discoverers. New York: Random House, 1983. Broder, David. Behind the Front Page: A Candid Look ...

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...are is closely correlated to its market price; 2. That price movements are mostly random, though somehow related to the aforementioned "value" of ... ... loss. The distribution of gains and losses in the long term is pretty even, i.e., random. The price level revolves around an anchor, supposedly th... ..., sought to rebuff technical analysis. Markets, they say, are efficient and "walk" randomly. Prices reflect all the information known to market pla... ...oo, alchemy, and astrology - for instance by Burton Malkiel in his seminal work, "A Random Walk Down Wall Street". The paradox is that technicians ... ...charts.com: "One way of viewing it is that markets may witness extended periods of random fluctuation, interspersed with shorter periods of nonrand... ... the Lessons of History" published by the Friedberg Mercantile Group, this was the sequence in London in 1720 (the infamous "South Sea Bubble"), an...

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............................................................................. 89 Randomness................................................................ ...idality in Human Values Pg 713 The Pyramidality of Values Pg 715 Chaos and Randomness Pg 716 Values Pg 717 The Values of Ease and Hardship Pg... ...emerged. Actual Causality The Dynamic of Actual Causality is a connected sequence of events. Every cause is an effect, and every effect is a c... ... cause. It is the Dynamic which actually causes things to happen in a strict sequence. Cause and Effect can also be defined by Newton’s Third Law ... ...use-effect-cause-effect-cause-effect-cause-effect-cause effect By tracing a sequence of events backwards: forensic experts can go into a burned ou... ...One: The Universe 2 make them tip over in one direction in a strict causal sequence of events. You can also tip them over in the opposite direct... ... as it actually is in any larger context is another question altogether. Randomness 13 billion years ago, the Universe was an amorphous mass ... ...ed, organic design out of an amorphous mass of disorganized mass of energy by random chance! Just because the Causal Process of the Universe is Act... ...infinite Causal complexity doesn’t mean that the Causality of the Universe is random. It is not. The apparent randomness of the Universe is only du...

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...ng rights to life of two people). One way to decide among equally potent claims is randomly (by flipping a coin, or casting dice). Alternatively, w... ...son has the intention to achieve a goal. He then engages in a series of absolutely random and unrelated actions, one of which yields the desired re... ... of action and by a declared intention. Otherwise, the effort will be judged to be random, devoid of meaning, haphazard, arbitrary, capricious, etc... ...ic resources. The market's great advantages over central planning are precisely its randomness and its lack of self-awareness. Market participants ... ...eter) against Disorder. In this context, natural selection is no more "blind" or "random" than its subjects. It is discriminating, encourages stru... ...ther necessitates the effect, or is a sufficient condition for its occurrence. The sequence is either inevitable, or possible. The meaninglessness ... ...e in the past, then eternity would have elapsed up to the present. Thus an infinite sequence would have been completed. Since this is impossible, th... ...ty traits, or behaviour patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is proven about the i... ...tations, including those related to human life directly. We even issue patents for sequences of human DNA. And people do own forests and rivers and...

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...ng rights to life of two people). One way to decide among equally potent claims is randomly (by flipping a coin, or casting dice). Alternatively, w... ...son has the intention to achieve a goal. He then engages in a series of absolutely random and unrelated actions, one of which yields the desired re... ... of action and by a declared intention. Otherwise, the effort will be judged to be random, devoid of meaning, haphazard, arbitrary, capricious, etc... ...ic resources. The market's great advantages over central planning are precisely its randomness and its lack of self-awareness. Market participants ... ...eter) against Disorder. In this context, natural selection is no more "blind" or "random" than its subjects. It is discriminating, encourages stru... ...ther necessitates the effect, or is a sufficient condition for its occurrence. The sequence is either inevitable, or possible. The meaninglessness ... ...e in the past, then eternity would have elapsed up to the present. Thus an infinite sequence would have been completed. Since this is impossible, th... ...ty traits, or behaviour patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is proven about the i... ...tations, including those related to human life directly. We even issue patents for sequences of human DNA. And people do own forests and rivers and...

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...l notions some of Romanian origin, among that: the function Smarandache , the sequences (41) Smarandache, the constants Smarandache, the paradox Sma... ...in order to create a coherent volume, where nothing ( or almost) is put/let at random. After Introduction in the empire of error ( a manifesto of th... ...ection, the unitary, rounded or closed work lacks, as a rule, at Smarandache. Sequences and rough copies of life (otherwise actual- objective or subj... ... given by the somehow film succession/ agglomeration of the contemporary life sequences- itself a strange and variegated show seeming escaped from t...

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...e asynchronous and stochastic behaviour. At each moment each neuron can randomly decide whether to change state or whether to emit a new signal gi... ...p subsets of the F Y neurons can decide to change state. Each neuron may randomly decide whether to check the threshold conditions in the equations... ...ns in the equations (3.5) and (3.6). At each moment each neuron defines a random variable that can assume the value ON(+1) or OFF(0 or -1). The netw... ...ch as possible we have given the interview verbatim not even altering the sequence of their expressions and talks. Secondly it is seen in some place... ... we, as interviewers, could gather. We have not tried even to change the sequences in which they spoke. This is mainly done for the sake of simpli... ...giving a very wrong view of life. Not only are some of the song and dance sequences the worst in vulgarity, but some of the messages that the movies... ...1 Parameter, 18-19 Peer group, 17 Pull factors, 7 Push factors, 7 Random variable, 9 Red light area, 9 Refined Time Dependent Data (RTD) m...

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...ary theory to solve optimization problems. In general, 50 GAs start with a randomly generated population and progress to improve solutions by u... ... proposed GAOFRC uses floating-point representation for individuals. Instead of randomly generating a population, the initialization process generat... ... process to a much smaller space. In general, a GA initializes the population randomly. It works well when dealing with unconstrained optimization... ...trained optimization problems. However, for a constrained optimization problem, randomly 51 generated solutions may not be feasible. Since GAOF... ...es) feasible, we present an initialization module to initialize a population by randomly generating the individuals inside the feasible domain. Sin... ... are allowed to reiterate before the first appearance of some others). The data sequence is described as (A (υ) , B (υ) ), ν∈N, where (A (υ) , B (... ...llowing theorem can be had from [53]. THEOREM 1.15.1. If {W (t)} is a weight sequence of the fuzzy δ rule, then it is a monotone decreasing seque... ...for the reader if need be refer [55]. THEOREM 1.17.1: If {W(t)} is a weight sequence of the fuzzy δ rule J, then it is a monotone decreasing seq... ...{x}) for x ∈ X. We note that α q ~ : ζ (X) → ζ(X). For α ∈ [0, 1] and x ∈ X, a sequence { } ,... 1 , 0 ) ( ~ = α k k x q is defined iteratively by ...

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...ary theory to solve optimization problems. In general, 50 GAs start with a randomly generated population and progress to improve solutions by u... ... proposed GAOFRC uses floating-point representation for individuals. Instead of randomly generating a population, the initialization process generat... ... process to a much smaller space. In general, a GA initializes the population randomly. It works well when dealing with unconstrained optimization... ...trained optimization problems. However, for a constrained optimization problem, randomly 51 generated solutions may not be feasible. Since GAOF... ...es) feasible, we present an initialization module to initialize a population by randomly generating the individuals inside the feasible domain. Sin... ... are allowed to reiterate before the first appearance of some others). The data sequence is described as (A (υ) , B (υ) ), ν∈N, where (A (υ) , B (... ...llowing theorem can be had from [53]. THEOREM 1.15.1. If {W (t)} is a weight sequence of the fuzzy δ rule, then it is a monotone decreasing seque... ...for the reader if need be refer [55]. THEOREM 1.17.1: If {W(t)} is a weight sequence of the fuzzy δ rule J, then it is a monotone decreasing seq... ...{x}) for x ∈ X. We note that α q ~ : ζ (X) → ζ(X). For α ∈ [0, 1] and x ∈ X, a sequence { } ,... 1 , 0 ) ( ~ = α k k x q is defined iteratively by ...

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...m a previous idea and determines another idea, like an infinite recurrent sequence. 82 d) Sophisticalism: the more unintelligible, ambiguous, uns... ...s, Boston, 1960. [24] McKeon, Richard P., "An Introduction to Aristotle", Random House, Inc., New York, 1947. [25] McNeil, Martin, F., Thro, Ellen,... ...bility (called sometimes the objective probability) process uncertainty of random type (stochastic) introduced by the chance. Uncertainty of the chan... ...robability and statistics, fuzzy sets, possibility, evidential reasoning, random sets, neural networks and neuro-mimetic approaches, and logics (Dez... ...e operational notation of logic, mathematics, or functional language to a sequence of modifications to the input data structure. Temporal Logic is ... ...ult. This might be comparable to approximating the limit of a convergent sequence, calculating more and more terms, or by calculating the limit of a... ...ic statistics. The function that models the neutrosophic probability of a random variable x is called neutrosophic distribution: NP(x) = ( T(x), I(x... ...c probability. The function that models the neutrosophic probability of a random variable x is called neutrosophic distribution: NP(x) = ( T(x), I(x...

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... useful fingers (especially the thumb and forefinger combination), first batting at random, then reaching accurately. The inflation of its body mus... ... big roulette of life. Growers - of anything from cereals to cattle - similarly use random culling to improve their stock. As mathematical models s... ...y traits, or behaviour patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is proven about the i...

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...markets and over different spans of time. As opposed to the received wisdom of the random walk model, most investment vehicles sport different vola... ...y is especially high when both supply and demand are inelastic and liable to large, random shocks. This is why the prices of industrial goods are le... ..., sought to rebuff technical analysis. Markets, they say, are efficient and "walk" randomly. Prices reflect all the information known to market pla... ...oo, alchemy, and astrology - for instance by Burton Malkiel in his seminal work, "A Random Walk Down Wall Street." The paradox is that technicia... ...rts.com, : "One way of viewing it is that markets may witness extended periods of random fluctuation, interspersed with shorter periods of nonrand... ..., to obtain any meaningful data, one has to observe behaviour in time, to obtain a sequence of reactions and actions. To isolate, observe and manip... ...mental variables and study human interactions. No snapshot can approximate a video sequence where humans are concerned. Return Financial Crises, ... ...nature itself. Every economic cycle invariably starts with inflation. The previous sequence having ended – and the new one just begun – the environ...

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...o obtain a means by which all particular solutions, in terms of an infnite sequence, may be con- structed, according to the general prescription of Ed... ...ed conditions (the Metric Conditions of Abrams [7]), from which an infnite sequence of particular solutions can be obtained [1] is, C n (D(r))= ... ...when r 0 =0 and r r 0 , and n is taken in integers, the following infnite sequence of particular solutions obtains, C 1 (r)=(r+α) 2 (Brillouin’s solu... ... When r 0 =α and r∈ + , and n is taken in integers, the following infnite sequence of particular solutions is obtained, C 1 (r)=r 2 (Droste/Weyl/(Hil... ... introduced the notion that reality has an information-theoretic intrinsic randomness. Since this pioneering paper the model of reality known as Proce... ...ocesses. These are normally associated with Brownian-type motions in which random processes are used in modelling many-body dynamical systems. We argu... ...processes are used in modelling many-body dynamical systems. We argue that random processes are a fundamental and necessary aspect of reality — that t... ...rithmic Informa- tion Theory (AIT). This shows that number systems contain randomness and unpredictability, and extends G¨ odel’s dis- covery, which r... ...hus self-referential, then the mathematical model must necessarily contain randomness. Here we consider one very simple such model and proceed to show...

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...uthors from sales of the electronic versions of their work (anywhere from Random House's 35% to 50% paid by smaller publishers). As this tectonic sh... ...200 sites, a minuscule number. Some recommendation services often produce random - at times, wrong - selections for their users. There are also conc... ...rst, there is the insatiable appetite big publishers (such as McGraw-Hill, Random House, and Harper Collins) have developed to converting their hithe... ...on Agency." It is backed by a few major publishers, such as McGraw-Hill, Random House, Pearson, and Wiley. This ostensibly modest agenda conceals ... ...u put up with packet sniffers or other eavesdropping technologies to take random samples of the copy traffic, as long as your identity was not record... ...friendliness (i.e., the interfaces require specific knowledge and specific sequences of specific commands). Even the most "user-friendly" interface ...

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... the Funny Side of the Street … (Our Blunders, Bloopers, Typos, One-liners and Jokes) Random Quotes Links and Resources Abbreviations U... ...? Both have about a one in 3 million chance of becoming a human being." Return Random Quotes Search Sam's Web site: http://samva... ...oughts whose violence cannot be harnessed. He develops ritualistic reactions to them: a sequence of motions, an act, or an obsessive counter-thought... ... "The typical narcissist has a short attention span and believes that the world is a random, menacing place. Catch as catch can. Carpe Diem (seiz...

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...s or questionnaire mailings. The laws of large numbers require that the random samples be independent identically distributed random variables wit... ... input path of υ if i. ν 1 has no input or has only an external input sequence; ii. ν i , 1 < i < r do not belong to any circle of υ; ν 1 is c... ...ome static after L inference interactions unless it has an external input sequence, where L is the length of the longest path of the FCM. The pro... ...ecome static after L inference iterations unless it has an external input sequence, where L is the length of the path. DEFINITION [136]: A vertex...

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...itwise operations. Data in computers is expressed in binary form, or as a sequence of zeros and ones. A bitwise operation matches the bit positions ... ...ample, if the set of discourse is all real numbers and the choice of x is random, we could argue that the value is (0.50,0.0,0.50). This could be i... ... = T. In the case of A ├ B, A is the hypothesis and B the conclusion. The sequence of steps that start with A and lead to B are known as a proof. ... ...g the steps that start at B and lead to C. The combination will then be a sequence of steps that will start at A and lead to C. Therefore, A can be ...

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...ses, personality traits, or behaviour patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is prove... ...vitable. They see a sign of hope in every fluctuation. They read meaning and patterns into every random occurrence, utterance, or slip of tongue. Th...

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...ics), hiIh directivity narrow beam communications (directional antennae and lasers), and hoppinl randomly and rapidly from one frequency to another. (... ... is knock the cryptographic transmitters and receivers out of sync or disrupt the initialization sequences that prefix • • • • • • • • • • • • • • • •... ...or altopther and be traDlmitted in the clear. Another - IDua1ly more insidious - is a failure in randomizer circuitry caIDiq prectictable or RPetitlve... ...five feet in bciabt, eiaht to ten feet wide, and extCDdiDI over 100 yards in Jenatb. He poked at random with a sharp stick, and tho_ diIcoDsoJately of...

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...ternal. After we die we eventually enter new bodies and the endless cyclic sequence of birth, life, and death continues on through all eternity. The w... ...m of “seeing” imaginary shapes, the traditional constellations, amidst the random pattern of stars in the night sky. Jung himself traced the developme... ...ually that the universe is not necessarily a cosmos (an ordered whole) but randomness which we assume to have a coordinated or coordinating center by ... ...ars to share some dreams with friends, and at one time I was a member of a sequence of small dream groups that met to share and discuss dreams over a ...

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... staggers us. The framework is briefly, yet adequately, con- structed. The sequence of events is rapid and Consistent. Only one jarring note is there,... ...ters oratorical to be ascribed to student indifference? Or is it a natural sequence to the gradual change of the times? — .3 J^ 11 IV— "~ ^- |i' ."_ s... ...taggers us. The frameworl: is briefly, yet adecjuately, con- structed. The sequence of eventi is rapid and consistent. Onh one jarring note is there, ... ...ters oratorical to be ascribed to student indifference? Or is it a natural sequence to the gradual change of the times? such as town meetings, sooinl ... ...ion to produce his results, and thus we have neither clear desoription nor sequence of events. "Arcades Anibo" is a capital piece of satire, a sort of... ... and and team work for them was im- possible The work of both teams was so random and ragged that more than a dozen fouls were called on each team, Ha...

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...t is not sufficient to barre us the libertie of contradicting him: yet at random to condemne all such like histories, seemeth to me a notable impude... ...r one charge which done, all the time of her conception she let him go at random, and that past, she gave him leave to begin againe: a notable and g... ...tions in her trouble and uncertaintie. We reason rashly, and discourse at random, saith Timeus in Plato: for even as we, so have our discourses grea... ...ificers; and that every man might, at his pleasure, dispute of it, and at random speake his mind of the same. And it should be a great shame for us,... ...at only to a quicknesse of the sense of hearing, without discourse or con sequence, is but a fond conceipt, and cannot enter into my imagination. Th... ...d with the right strikes it away with his racket; in a piece he shutes at randome; and is well pleased with what his men tell him, be it high or wid...