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Complex networks applied to political analysis: Group voting behavior in the Brazilian congress. [PDF]
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METRIC THEORY OF PARTIAL QUOTIENTS OF N-CONTINUED FRACTIONS
Fractals, 2022On analogy of the regular continued fractions, for any fixed positive integer [Formula: see text], every [Formula: see text] can be expanded into an [Formula: see text]-continued fraction, denoted by [Formula: see text], where [Formula: see text] are called the partial quotients.
JINFENG WANG, YUAN ZHANG
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A Note on The Metrical Theory of Continued Fractions
The American Mathematical Monthly, 2000(2000). A Note on The Metrical Theory of Continued Fractions. The American Mathematical Monthly: Vol. 107, No. 9, pp. 834-837.
Glyn Harman, Kam C. Wong
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Monatshefte f�r Mathematik, 2003
The authors study the metric theory of fibred systems in the case of continued fraction mixing systems. They obtain the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to the theorems for the regular continued fractions, obtained
Nakada, Hitoshi, Natsui, Rie
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The authors study the metric theory of fibred systems in the case of continued fraction mixing systems. They obtain the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to the theorems for the regular continued fractions, obtained
Nakada, Hitoshi, Natsui, Rie
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Recent Advances in the Metric Theory of Continued Fractions
1978This is a survey of recent results in the metric theory of continued fractions concerning Gauss-Kuzmin-Levy theorem and extreme value theory.
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The Metrical Theory of Prime Divisibility via Continued Fractions
This paper explores the intricate relationship between the metrical properties of continued fractions and the distribution of prime divisors within the partial quotients. We investigate how the statistical behavior of continued fraction expansions, typically studied through ergodic theory and measure theory, can shed light on the occurrence and ...Revista, Zen, MATH, 10
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Lithuanian Mathematical Journal, 1987
Every irrational x in the interval [G-2, G], with \(G=(1+\sqrt{5})/2\), has a continued fraction expansion of the form \(x=\epsilon_ 1/(\alpha_ 1+\epsilon_ 2/(\alpha_ 2+...\), where \(\epsilon_ j\) is either -1 or \(+1\), and each digit \(\alpha_ j\) is an odd positive integer.
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Every irrational x in the interval [G-2, G], with \(G=(1+\sqrt{5})/2\), has a continued fraction expansion of the form \(x=\epsilon_ 1/(\alpha_ 1+\epsilon_ 2/(\alpha_ 2+...\), where \(\epsilon_ j\) is either -1 or \(+1\), and each digit \(\alpha_ j\) is an odd positive integer.
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Mathematische Nachrichten, 1987
This paper gives a method for proving of estimates of the difference between the distribution function (df) of a sum \(X_ 1+...+X_ n\) of \(\psi\)-mixing rv's (with \(\psi\) (s)\(\leq Ce^{-\alpha s})\) and a stable df with exponent less than 2. This method is based on the derivation and solution of a formal differential equation (in \(u\in [0,1])\) for
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This paper gives a method for proving of estimates of the difference between the distribution function (df) of a sum \(X_ 1+...+X_ n\) of \(\psi\)-mixing rv's (with \(\psi\) (s)\(\leq Ce^{-\alpha s})\) and a stable df with exponent less than 2. This method is based on the derivation and solution of a formal differential equation (in \(u\in [0,1])\) for
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