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On Transfer Operators for Continued Fractions with Restricted Digits
, 2001
"... For I N, let I denote those numbers in the unit interval whose continued fraction digits all lie in I. Dene the corresponding transfer operator L I; f(z) = P n2I 1 n+z f 1 n+z for Re() > max(0; I ), where Re() = I is the abscissa of convergence of the series P n2I n . Wh ..."
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For I N, let I denote those numbers in the unit interval whose continued fraction digits all lie in I. Dene the corresponding transfer operator L I; f(z) = P n2I 1 n+z f 1 n+z for Re() > max(0; I ), where Re() = I is the abscissa of convergence of the series P n2I n
Continued Fraction Algorithms, Functional Operators, and Structure Constants
, 1996
"... Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2dimensional generalization. This paper surveys the main properties of functional operators,  transfer o ..."
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Cited by 31 (6 self)
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Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2dimensional generalization. This paper surveys the main properties of functional operators,  transfer
REVERSALS AND PALINDROMES IN CONTINUED FRACTIONS
"... Abstract. Several results on continued fractions expansions are direct on indirect consequences of the mirror formula. We survey occurrences of this formula for Sturmian real numbers, for (simultaneous) Diophantine approximation, and for formal power series. 1. ..."
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Cited by 8 (2 self)
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Abstract. Several results on continued fractions expansions are direct on indirect consequences of the mirror formula. We survey occurrences of this formula for Sturmian real numbers, for (simultaneous) Diophantine approximation, and for formal power series. 1.
The Hurwitz Complex Continued Fraction
, 2006
"... The Hurwitz complex continued fraction algorithm generates Gaussian rational approximations to an arbitrary complex number α by way of a sequence (a0, a1,...) of Gaussian integers determined by a0 = [α], z0 = α − a0, (where [u] denotes the Gaussian integer nearest u) and for j ≥ 1, aj = [1/zj−1], zj ..."
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], zj = 1/zj−1−aj. The rational approximations are the finite continued fractions [a0; a1,..., ar]. We establish a result for the Hurwitz algorithm analogous to the GaussKuz’min theorem, and we investigate a class of algebraic α of degree 4 for which the behavior of the resulting sequences 〈aj
Approximating Rational Numbers by Fractions
"... Abstract. In this paper we show a polynomialtime algorithm to find the best rational approximation of a given rational number within a given interval. As a special case, we show how to find the best rational number that after evaluating and rounding exactly matches the input number. In both results ..."
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Abstract. In this paper we show a polynomialtime algorithm to find the best rational approximation of a given rational number within a given interval. As a special case, we show how to find the best rational number that after evaluating and rounding exactly matches the input number. In both
Blazys Expansions and Continued Fractions
, 2013
"... A few years ago Don Blazys caused a ripple of excitation among numerologists by presenting a real number which, applying an iterative computation recipe, produced all prime numbers. The procedure is one of an infinity of possible mappings between subsets of real numbers and subsets of integer sequen ..."
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mapping bf(s) which, in addition, can be cast as a special type of generalized continued fractions. This article presents the definitions, the proofs of the bijection and the pertinent algorithms. It also analyses some simple properties of these mappings.
Analog and digital, continuous and discrete
 Philos. Stud
, 2010
"... Representation is central to contemporary theorizing about the mind/brain. But the nature of representation—both in the mind/brain and more generally—is a source of ongoing controversy. One way of categorizing representational types is to distinguish between the analog and the digital: the received ..."
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will defend and extend David Lewis’s account of analog and digital representation, distinguishing analog from continuous representation, as well as digital from discrete representation. I will argue that the distinctions available in this fourfold account accord with representational features of theoretical
Continued Fractions, Diophantine Approximations, and Design of Color Transforms
"... We study a problem of approximate computation of color transforms (with real and possibly irrational factors) using integer arithmetics. We show that precision of such computations can be significantly improved if we allow input or output variables to be scaled by some constant. The problem of findi ..."
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Cited by 1 (0 self)
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We study a problem of approximate computation of color transforms (with real and possibly irrational factors) using integer arithmetics. We show that precision of such computations can be significantly improved if we allow input or output variables to be scaled by some constant. The problem
• Continued Fraction Algorithm (CFRAC)
, 2011
"... This package for GAP 4 provides a generalpurpose integer factorization routine, which makes use of a combination of factoring methods. In particular it contains implementations of the following algorithms: • Pollard’s p − 1 • Williams ’ p + 1 ..."
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This package for GAP 4 provides a generalpurpose integer factorization routine, which makes use of a combination of factoring methods. In particular it contains implementations of the following algorithms: • Pollard’s p − 1 • Williams ’ p + 1
Results 1  10
of
167,960