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...lting images are continuously posted on the Web and are available to anyone with a computer. The last decade witnessed a spate of films, all conce... ...turn The Matrix It is easy to confuse the concepts of "virtual reality" and a "computerized model of reality (simulation)". The former is a sel... ...the two concepts are often confused because they are both mediated by and reside on computers. The computer is a self-contained (though not closed) ... ... doing so. This is the ominous "what if" in artificial intelligence (AI). What if a computer were to refuse to correlate its internal (virtual) real... ...he privileged one? In the visually tantalizing movie, "The Matrix", a breed of AI computers takes over the world. It harvests human embryos in la... ...eorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true but unprovable ("not decidable") sente... ...he world (women) – or of living longer (children). Societal etiquette reflects the arithmetic of the species, in this (and in many another) case. ... ...eorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true but unprovable ("not decidable") sente...

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...is absent there is no circumference at all. That is pure and simple basic arithmetic. This point has no continuity. It comes into being in response t... ... its natural operation through the medium of thought. Your natural bodily computer is already programmed. You don't have to do a thing. Somehow, you... ... useful,helpful or meaningful. _______ The living organism is like a computer with an extraordinary intelligence. But here the energy is a sort... ...is already there but you are all the time asking questions. These are two computers talking but you want to introduce an element which is not part of...

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...ty, Jinan, Shandong, P. R. China. Guo Jinbao, College of Mathematics and Computer Science, Yanan University, Yanan, Shaanxi, P. R. China. ... ...e, who listed many new and unsolved problems in number theory. Preface Arithmetic is where numbers run across your mind looking for the answer. A... ...nsofthe equationφ(n) = am(n),andgiveallsolutionsforthisequation. Keywords: Arithmeticalfunction;Equation;Solutions. §1. Introduction For any positive ... ...nctionφ(n),andgiveaninteresting identity. Keywords: Multiplicativefunction;Arithmeticalproperty;Identity. §1. Introduction For any positive integern≥ ... ...fδ k (n)byϕ(n),andfindallthensuchthatϕ(n)| δ k (n). Keywords: Eulerfunction;Arithmeticalfunction;Divisibility. §1. Introductionandmainresults For a fixe... ...s For a fixed positive integer k and any positive integer n, we define a new arithmeticfunctionasfollowing: δ k (n) = max{d|d|n,(d,k) = 1} If n ≥ 1 the ...

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...As someone who works 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 f...

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...ica 3 Foreword As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern ... ...c from those courses. Logic is also a fundamental component of advanced computer classes. I am currently teaching advanced courses in assembly lan... ... currently teaching advanced courses in assembly language programming and computer organization. Reference is constantly being made to how the rules... ...ow the rules of logic are incorporated into the fundamental circuits of a computer. The logic used in these classes is known as classical or Boolean... ...oning Section 8 Quantification Theory Section 9 Uses of Logic In Computer Programming 7 13 14 15 16 17 19 19 22 Chapter 2 Three-... ...ic are not numeric, the definitions of the connectives cannot involve any arithmetic operations such as max and min. This can be a limitation in th...

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...ived both at that exact moment where my experiences could straddle working in print shops and in the current digital eBook era.. My degree in human-computer interfaces in 1973 led to my appointment as adjunct professor at Benedictine University, where I built the world‘s first electronic library in 1988. You could walk into that library, and the first thing you‘d see wa...

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...in print shops and in the current digital eBook era.. My degree in human-computer interfaces in 1973 led to my appointment as adjunct professor at ... .... You could walk into that library, and the first thing you‘d see was the computer asking if there were any books you wanted. You selected books fro... ... lost books. You could search books using the SEARCH function on your own computer, import quotations into paper e-mails, etc., and copy the book. ... ...OGY as ―the technology involving the development, maintenance, and use of computer systems, software, and networks for the processing and distributio... ... those two words was in 1978, the same year I bought the Apple II desktop computer that introduced me to modern Information Technology. Aware that ... ...ook twelve years of schooling just to learn to read, write, and do simple arithmetic. Pictographic culture‘s rigorous nature, moreover, left priest... ... the quadrivium’s Real Art—―the four ways‖— moved on to the studies of:  arithmetic—math applied to basic numbers  geometry—math applied to space ...

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...in print shops and in the current digital eBook era.. My degree in human-computer interfaces in 1973 led to my appointment as adjunct professor at ... .... You could walk into that library, and the first thing you‘d see was the computer asking if there were any books you wanted. You selected books fro... ... lost books. You could search books using the SEARCH function on your own computer, import quotations into paper e-mails, etc., and copy the book. ... ...OGY as ―the technology involving the development, maintenance, and use of computer systems, software, and networks for the processing and distributio... ... those two words was in 1978, the same year I bought the Apple II desktop computer that introduced me to modern Information Technology. Aware tha... ...ook twelve years of schooling just to learn to read, write, and do simple arithmetic. Pictographic culture‘s rigorous nature, moreover, left prie... ...the quadrivium’s Real Art—―the four ways‖— moved on to the studies of:  arithmetic—math applied to basic numbers  geometry—math applied to space ...

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...ions. In this book a number of problems are about iterations. In many cases computer simulation is followed by analysis leading to conclusions or co... ...k Surfing on the Ocean of Numbers with some applications in the second book Computer Analysis of Number Sequences. A brief summary will now be g... ...ives the answer to this question. In the study of R(n) it is found that the arithmetic function d(n), the number of divisors of n, plays an importan... ...st positive integer m such that 1+2+…+m is divisible by n. Adding up the arithmetical series results in an alternative and more useful formulati... ... values of this function are given in [1], which also contains an effective computer algorithm for calculation of Z(n). The following properties are... ...terval but as can be seen it is generally scarcely represented. Prohibitive computer execution times made it impossible to systematically examine a... ... authors book “Surfing on the ocean of numbers”. Even with for ever faster computers and better software for handling large numbers empirical studie... ... Clarendon Press, Oxford, Fifth edition 1979. 4. H. Davenport, The Higher Arithmetic, Reprint: Dover Publications, Inc., New York, 1983. 5. C. D... ...e integers used to create the sequence? After all 0 is indispensable in all arithmetics most of which can be done using 0 and 1 only. 2. The proces...

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...n particular. I was also inspired and informed by colleagues and students in computer science, English, history, and political science. But the work I... ...a colleague—helped in more ways than I can count. A number of scientists and computer scientists made me see things I other- wise would not have—Drew ... ...le of thought. Today, though, I am viewing his letter over the Internet on a computer screen. (You can too. The details are at the back of the book.) ... ...e there no free- speech limitations? When other forms of authorship, such as computer pro- grams, are brought into copyright’s domain, does the power ... ...llows for parody, commentary, and criticism, and also for “decompilation” of computer programs so that Microsoft’s competitors can reverse engineer Wo... ...net, working out the daily prices of a bundle of mutual funds through simple arithmetic, or buying something online with one click. 45 I would have as...

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...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...ctor can be constrained to collapse to the most order-enhancing event. If we had a computer the size of the Universe that could infallibly model it... ...have been compared to the latest technological innovation in every generation. The computer metaphor is now in vogue. Computer hardware metaphors w... ... "brain-children", the results of "brain-storming", conceived by "minds". What is a computer, a software application, a communications network if no... ... the developmental phases of the origin. Consider the software-mind metaphor. The computer is a "thinking machine" (however limited, simulated, re... ...o one another. This relation is by virtue of two facts: (1) Both the brain and the computer are "thinking machines" and (2) the latter is the produ... ...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...he world (women) – or of living longer (children). Societal etiquette reflects the arithmetic of the species, in this (and in many another) case. B... ... casting dice). Alternatively, we can add and subtract rights in a somewhat macabre arithmetic. Thus, if the continued life of an embryo or a fetus ...

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...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...ctor can be constrained to collapse to the most order-enhancing event. If we had a computer the size of the Universe that could infallibly model it... ...have been compared to the latest technological innovation in every generation. The computer metaphor is now in vogue. Computer hardware metaphors w... ... "brain-children", the results of "brain-storming", conceived by "minds". What is a computer, a software application, a communications network if no... ... the developmental phases of the origin. Consider the software-mind metaphor. The computer is a "thinking machine" (however limited, simulated, re... ...o one another. This relation is by virtue of two facts: (1) Both the brain and the computer are "thinking machines" and (2) the latter is the produ... ...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...he world (women) – or of living longer (children). Societal etiquette reflects the arithmetic of the species, in this (and in many another) case. B... ... casting dice). Alternatively, we can add and subtract rights in a somewhat macabre arithmetic. Thus, if the continued life of an embryo or a fetus ...

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...ey (1993-1999) present the evolutionary algorithms which are used “to describe computer-based problem solving systems which employ computational mo... ...e should be strict rules, and rules with exceptions. Recursivity is seen as a computer program that learns from itself. The statistical regression... ...ves/fuzzy-mail99/0819.html. [13] Girard, Jean-Yves, Linear logic, Theoretical Computer Science, 50:1-102, 1987. [14] Guinnessy, Paul; Gilbert, Joh... ...oceedings on the Neutrosophic Logic and Their Applications in Neural Networks, Computer Programming, and Quantum Physics, Institute of Physics, edit... ...definite sets - a new type of data for knowledge representation, Preprint 232, Computer Center of the USSR Academy of Sciences, Novosibirsk, 1980 (in... ...s, the overall result would evaluate as NL(0.01, 0.9, 0.09), assuming standard arithmetic connectives (summing over a simple diagonal matrix of trip...

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...athy and appreciation expressed about his name. From now, a record in the computer would be necessary to put them in full evidence. I believe that h... ... } to be loved and to be detested } in a same time Program the computers so that they write for yourselves! No free word in poetry, or b... ... style and of poems without verses, without words, the paralinguistic and computerized literature, the creation of literature from anything, also fro... ...? If we consider the recent playsome effects of the dexterity through the computer and the sum of the valuable resultsobtained in this way, we can a... ...uthor. The nonconformism is fore-shadowed through apprehension before the computer poetry (“following mechanical methods, spiritual states are manufa... ... Journal (Harwey Mudd College, Claremont, CA, USA, 12, 1995): POEM IN ARITHMETIC SPACE By Larry Seagull There exist sequences defined as “Sma... ...” amalgamate small but firm spaces and introduce the simple colored line; arithmetic, in palimpsest, is canceled, by color, with a ludic exposing dur... ...Larry Seagull publishes, in Humanistic Mathematics Network (USA), Poem in arithmetic space, on the base of Smarandache sequence of numbers, together ... ...s Network Journal”, Harvey Mudd College, no.12. Seagull, Larry, Poem in Arithmetic Space, in Humanistic Mathematics Network Journal”, Harvey Mudd ...

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...owe. A well-documented and large dictionary, dealing with terms needed in Computer Science, The Free Online Dictionary of Computing, is edited by D... ...ization, a theory loses its transcendental, myth, beauty, and becomes too arithmeticsized, technical, mechanical. Or, if a system of axioms is defin... .... Logicism: Frege's axioms for set theory, to derive the whole arithmetic, were inconsistent (see Bertrand Russell's Paradox). Look at t... ...anical Philosophy? Devices of producing presuppositions on running belt (computer programming) - futile philosophy. 47 A priori thought à l... ...zarre ideas. g) Futurist Philosophy: ideas created by machines, robots, computers using artificial intelligence; this is the philosophy of tomorr... ...ing to ! it is the case that A, and it is used in the verification of the computer programs. Combinatory Logic (Schoenfinkel, Haskell Curry, 1920s) ... ...ated reasoning (information processing) due to inconsistent data stored in computers, and by the fact that people impart opposite beliefs. There are... ...last or second one respectively. An intriguing idea would be to take the arithmetic average of the corresponding components of the truth-, indetermi...

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...l partition of unity and demonstrated some properties. In this section, a computer program written in the C language will be presented. /* This ... ...sed as the sum of the reciprocals of a set of natural numbers that are in Arithmetic Progression. 29 (8). Let Σ 1/r ≤ n ≤ ∑ 1/(r+1) ... ... Remarks: This algorithm would be quite helpful in the development of a computer program for the listing of SFPs. Section 14 A Program For D... ...with a comment about how the algorithm would be helpful in constructing a computer program to list the SFP’s. In this section, such a program in the ... ...n with be the Pascalisation of the Fibonacci sequence with the indexes in arithmetic progression. Consider the following sequence formed by the F... ...e following sequence formed by the Fibonacci numbers whose indexes are in arithmetic progression. F 1 , F d+1 , F 2d+1 , F 3d+1 , . . . on Pa... ... which can be proven by induction. Generalization: We can take any arithmetic progression with the first term a and the common difference b a... ...randache Dual Symmetric functions give us another way of generalizing the Arithmetic-Geometric Mean Inequality. One can easily prove that: (x 1 x... ...n SAS sequence. This is the sequence used to represent numbers in digital computers. In general, n = ∑ a k t k , where a k = 0 or 1 and t k is a p...

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...orced from corporeal reality. Our genetic baggage makes us resemble a personal computer. We are an all-purpose, universal, machine. Subject to ... ...lization, education, upbringing) - we can turn out to be anything and everything. A computer can imitate any other kind of discrete machine, given t... ..., thing. It has a single purpose and a unitary function. We, humans, are more like computers than like television sets. True, single genes rarel... ...aise and nurture their younger relatives more that straights do. Moreover, the arithmetic of genetics would rule out such a stratagem. If the a... ...in English. Business Experience 1980 to 1983 Founder and co-owner of a chain of computerized information kiosks in Tel- Aviv, Israel. 1982 to 19... ...vision – Manager of the Data Processing Division – Project Manager of the Nigerian Computerized Census – Vice President in charge of RND and Advanc...

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...d unsolved problems in number theory. Contents Dedication v Preface xi An arithmetic function and the primitive number of power 1 Zhang Wenpeng On t... ...hefeng On the Smarandache pseudo-multiples of sequence 17 Wang Xiaoying An arithmetic function and the divisor product sequences 21 Zhang Tianping The... ...tion and the number of prime factors 73 Xu Zhefeng On the mean value of an arithmetical function 77 Wang Xiaoying Two asymptotic formulae on the divis... ...en number Sequence 85 Zhang Xiaobeng, Lou Yuanbing On the mean value of an arithmetical function 89 Lv Chuan An arithmetical function and its cubic co... ...ndache pseudo-number 111 Lou Yuanbing Several asymptotic formulae on a new arithmetical function 115 Guo Jinbao and He Yanfeng On the Smarandache func... ...ARITHMETICAL FUNCTION Guo Jinbao and He Yanfeng College of Mathematics and Computer Science, Yanan University, Yanan, Shaanxi, P .R.China yadxyzb2391@... ...ANDACHE CEIL FUNCTION He Xiaolin and Guo Jinbao College of Mathematics and Computer Science, Yanan University, Yanan, Shaanxi, P .R.China yadxyzb2391@... ... FREE SIEVE SEQUENCE Guo Jinbao and Zhao Xiqing College of Mathematics and Computer Science, Yanan University, Yanan, Shaanxi, P .R.China yadxyzb2391@...

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...ional objectives Sometimes, there is simply no substitute for significant computer power. Others in my queue of those to thank include all who have ... ...he number of possibilities grows rapidly, so the search is best left to a computer. A simple program was written that allows for the examination of ... ... SCm) = p grows rapidly as p does. Sometimes it is advantageous to use a computer to compute the terms of a sequence. Then, by examining the terms,... ...in which several sequences are defined. The stated challenge was to write computer programs to compute the terms of the given sequences. Many of th... ...ts are not random, but repeat certain sequences according to the rules of arithmetic. With this in mind, the author makes the following conjectures ... ...of the general family of polygonal numbers. This is an infinite family of arithmetic sequences of the second order and the general formula for the f... ...al sequences could form the basis for further exploration using the given computer programs. Another sequence of numbers that can be investigated ar... ... above force the number of digits in nl and n2 to both be j. Gsing simple arithmetic, all values in the range nl = 100 000 to nl = 499 999 j-l O's ... ...j-I Therefore, 2*n I must vield a (j-l )-digit number Again, using simple arithmetic, all numbers in the range nl = 500 000 to nl = 999 999 j - I O...

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...ew are, of course, those like (n) j whose value depends in some way on the arithmetic nature of the argument, and not simply on its size. But the beh... ...or function [3], that by definition is the largest integer n £ . In many computer languages, the floor function is called the integer part function ... ...Unsolved question: Is it this true for all n? Examining the results of a computer search looks like that the following inequality hold: ) 2 ( ) 1 ( ... ...,r) the number of solutions of that equation for x n £ and fixed r. By a computer search the following result has been obtained: 0 ) 4 , 4 10 ( 0 ) ... ...,r) the number of solutions of this equation for x n £ and a fixed r. By a computer search we have found: 38 N(1000,2)=0 N(1000,3)=0 N(1000,4)... ...1 ( 1 c c c £ £ £ is said nonaveraging if it contains no three terms in arithmetic progression. That is, ) ( 2 ) ( ) ( k c j c i c „ + for any th... ...ture: An infinte number. 66 • Are there k (k>1) terms in this sequence in arithmetical progression? (for example in these first ones there are 2 ter... ...e maximum value of a(n) for the previous sequence? For n<=8000 via a computer program searching the maximum has been found at n=1025 with ...

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.... 30, 2000, 139. 95. Gottesman D. The Heisenberg representation of Quantum Computers. arXiv: quant-ph/9807006. 96. Baugh J., Finkelstein D., Galiautdi... ...r to fnd an analogous result that had been previously obtained by a purely arithmetical way. We will use the second option because it is easier (alt- ... ... the decay registered by the detector in 1-second intervals, are stored in computer archive. Depending on specifc targets, a time sequence of 1- secon... ...ils see in [8, 9]). Comparison of histograms was performed using auxiliary computer program by Edwin Pozharski [8]. A mechanical device designed by on... ..., 2000, v. 43(2), 205–209. 4. Shnoll S. E. Discrete distribution patterns: arithmetic and cosmophysical origins of their macroscopic fuctuations. Biop...

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...CM for Decision Support in an Intelligent Intrusion Detection System As computer technology advances and the threats of computer crime increase, th... ...ver the years, intrusion detection has become a major area of research in computer science. Intrusion detection systems are often characterized based... ...ed as part of an intrusion detection research effort in the Department of Computer Science at Mississippi State University. The following unique fea... ...he causal strength per one unit-time s * ij on an edge e ij , simply the arithmetic division might be considered (i.e. s * ij = s ij / t ij for a... ...es, S and T. This 62 entails an increased use of memory storage in the computer, but the computation for causal inferences is greatly facilitated... ...I recently designed a system that, had I implemented it using an FCM, the arithmetic-multiply operator would have been a necessary operator. "Arm... ...ganisation’s biggest asset: its collective brain-power. 6. The lack of computer based models affects the effectiveness of the SISP process. Th...

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... Alaska Pacific University, AK, USA. H.Iseri, Department of Mathematics and Computer Information Science, Mansfield University, Mansfield, PA 16933, USA.... ...automorphism Lemma 2.4.1 Let N = k i=1 p r i i ,p 1 <p 2 <···<p k be the arithmetic decomposition of the integer N and m i ≥1,m i |N for i=1,2,···,k... ... α,β ,P) with φ(M) faces and N = k i=1 p r i i ,p 1 < p 2 <···<p k , the arithmetic decomposition of the integer N, there exists a voltage assignmen... ...,β ,P) be a map and N = p r 1 1 ···p r k k ,p 1 < p 2 < ··· < p k , be the arithmetic decomposition of the integer N. Then for any voltage assignment ...

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...the firm, the attainment of its development plans and its investments. 9. To fully computerize all the above activities in a combined hardware-soft... ...premises, factories, etc.; 6. The planning and implementation of line connections, computer network connections, protocols, solving issues of compa... ...cal side of the business. 2. The planning and implementation of a fully operative computer system (hardware, software, communication, intranet) to... ...tainties and shifting fashions with mathematical formulae and elaborate econometric computerized models. So much is certain, though - that people o... ... and BEAR markets 22. Consolidation pattern - if underlying trends continues 23. Arithmetic versus logarithmic graphs 24. Seasaw - non breakthro... ...d in English. Business Experience 1980 to 1983 Founder and co-owner of a chain of computerised information kiosks in Tel-Aviv, Israel. 1982 to 19...