Results 1 to 10 of about 436,402 (269)
Continued fractions and the Thomson problem [PDF]
Scientific Reports, 2023 We introduce new analytical approximations of the minimum electrostatic energy configuration of n electrons, E(n), when they are constrained to be on the surface of a unit sphere.
Pablo Moscato +2 more
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Continued fractions for permutation statistics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We explore a bijection between permutations and colored Motzkin paths that has been used in different forms by Foata and Zeilberger, Biane, and Corteel.
Sergi Elizalde
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Extreme Value Theory for Hurwitz Complex Continued Fractions [PDF]
Entropy, 2021 The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and
Maxim Sølund Kirsebom
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Mathematics, 2021 We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964.
Dan Lascu, Gabriela Ileana Sebe
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Continued Fractions and Linear Fractional Transformations
, 2014 Rational approximations to a square root $\sqrt{k}$ can be produced by iterating the transformation $f(x) = (dx+k)/(x+d)$ starting from $\infty$ for any positive integer $d$.
O'Dorney, Evan
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Approximating the nuclear binding energy using analytic continued fractions [PDF]
Scientific ReportsUnderstanding nuclear behaviour is fundamental in nuclear physics. This paper introduces a data-driven approach, Continued Fraction Regression (cf-r), to analyze nuclear binding energy (B(A, Z)).
Pablo Moscato, Rafael Grebogi
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Transcendental Continued Fractions
Communications in Mathematics, 2022 In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$
Ahallal, Sarra, Kacha, Ali
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Polynomial continued fractions [PDF]
Acta Arithmetica, 2002 Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one.
Bowman, Douglas, McLaughlin, James
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Pell Equations and ℱpl-Continued Fractions
Journal of Mathematics, 2022 In this note, the solvability of the Pell equation, X2−DY2=1, is discussed over ℤ×plℤ. In particular, we show that this equation is solvable over ℤ×plℤ for each prime p and natural number l.
Seema Kushwaha
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International Journal of Number Theory, 2006 We use the method of generating functions to find the limit of a q-continued fraction, with 4 parameters, as a ratio of certain q-series. We then use this result to give new proofs of several known continued fraction identities, including Ramanujan's continued fraction expansions for (q2; q3)∞/(q; q3)∞and [Formula: see text]. In addition, we give a new
Bowman, Douglas +2 more
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