The continued fraction algorithm and Euclid’s
An Efficient Continued Fraction Algorithm for Nonlinear Optimization and Its Computer Implementation
... the continued fractions may be placed in the age of Euclid’s algorithm for the greatest common divisor [14], ...[15]. Continued fractions experience a revival nowadays thanks to their applications in ...
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On the continued fraction algorithm
... An account of the continued fraction algorithm (giving the regular continued fraction expansion of a real number) is also given in Hardy and Wright [2, Chs. This fraction is infinite if [r] ...
Clock Arithmetic and Euclid s Algorithm
... Clock Arithmetic and Euclid’s Algorithm Lecture notes for Access 2007 by Erin Chamberlain. Earlier we discussed Caesar Shifts and other substitution ciphers, and we saw how easy it was to break these ciphers by ...
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CiteSeerX — Continued Fraction Gems
... B.C., continued fractions have found their way into many corners of ...link continued fractions with an array of mathematical notions, and display some of these gems along the ...
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The Rogers–Ramanujan continued fraction
... Rogers–Ramanujan continued fraction possesses a rich and beautiful theory containing fasci- nating and surprising results, and so the purpose of this paper is to provide a survey of our present knowledge ...
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The random continued fraction transformation
... random continued fraction map ...convergent continued fraction expansions for all points in its domain and we explore some of the properties of these ...
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The Mixed Binary Euclid Algorithm
... Av. J.-B. Cl´ ement, 93430, Villetaneuse, France Email: [email protected] Abstract We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its ...
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Algorithm for Fast Calculation of Hirzebruch Jung Continued Fraction Expansions to Coding of Graph Manifolds
... This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, which we used to simulate the coupling constant hierarchy for the universe with five ...
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An Extension of Raney s Algorithm for Transducing Continued Fractions
... Raney’s algorithm to NICF, a solution needs to be found to either or both of these ...Euclidean algorithm such that M W = W 0 M 0 can always be solved with a matrix M ∈ DB n , if such a set of restrictions ...
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INTRODUCTION TO EUCLID S GEOMETRY
... But in civilisations like Greece, the emphasis was on the reasoning behind why certain constructions work. The Greeks were interested in establishing the truth of the statements they discovered using deductive reasoning ...
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Arithmetic of the Ramanujan–Göllnitz–Gordon continued fraction
... Further, by showing that v τ is a modular unit over Z we give a new proof of the fact that the singular values of v τ are units at all imaginary quadratic arguments and obtain that the[r] ...
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A recovery of Brouncker's proof for the quadrature continued fraction
... beautiful continued fraction for ...Brouncker’s continued fractions coincide up to a rotation with Wilson’s orthogonal polynomials corresponding to the parameters a = 0, b = 1/2, c = d = ...
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Parametric Evaluations of the Rogers Ramanujan Continued Fraction
... In this paper with the help of the inverse function of the singular moduli we evaluate the Rogers- Ranmanujan continued fraction and its first derivative.. 1..[r] ...
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Continued Fraction Evaluation of the Universal Y’s Functions
... Keywords Universal Kepler Equation, Continued Fraction Technique, Y-Universal Function 1. Introduction Today, one of the well-known facts of space dynamics is the desperate needs of the universal ...
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On some continued fraction expansions for the ratios of the function
... In section 2, we prove some key functional relations satisfied by ρ(a, b), which will be used in the development of continued fractions. In section 3, we prove our main results and in section 4 we obtain some ...
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A Gauss Kuzmin Lévy theorem for a certain continued fraction
... [15] M. Iosifescu and C. Kraaikamp, Metrical Theory of Continued Fractions, Mathematics and Its Applications, vol. 547, Kluwer Academic Publishers, Dordrecht, 2002. [16] A. Y. Khintchin, Continued ...
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A Wirsing type approach to some continued fraction expansion
... Actually, in Theorem 4.3 of Section 4 we obtain upper and lower bounds of the convergence rate which provide a near-optimal solution to the Gauss-Kuzmin-L´evy problem.. 2..[r] ...
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Modular Identities and Explicit Evaluations of a Continued Fraction of Ramanujan
... 1 · · · . 1.8 The continued fraction Rq has a very beautiful and extensive theory almost all of which was developed by Ramanujan. In particular, his lost notebook 2 contains several results on the ...
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A matrix continued fraction approach to multiserver retrial queues
... efficient algorithm to compute the joint stationary distribution of the M/M/c/c retrial queue, based on the backward algorithms presented in [8, ...an algorithm to compute the last row vectors efficiently in ...
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Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
... Academic Editor: Rui A. C. Ferreira Received: 1 November 2016; Accepted: 2 December 2016; Published: 9 December 2016 Abstract: The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in ...
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