Results 1 to 10 of about 125,919 (262)
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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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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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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An unusual continued fraction [PDF]
Proceedings of the American Mathematical Society, 2015 We consider the real number σ \sigma ...
Badziahin, D., Shallit, J.
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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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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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A Specialised Continued Fraction [PDF]
Canadian Journal of Mathematics, 1993 AbstractWe display a number with a surprising continued fraction expansion and show that we may explain that expansion as a specialisation of the continued fraction expansion of a formal series: A series ΣchX-h has a continued fraction expansion with partial quotients polynomials in X of positive degree (other, perhaps than the 0-th partial quotient ...
van der Poorten, A. J., Shallit, J.
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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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Algorithms, 2023 In the field of Artificial Intelligence (AI) and Machine Learning (ML), a common objective is the approximation of unknown target functions y=f(x) using limited instances S=(x(i),y(i)), where x(i)∈D and D represents the domain of interest.
Pablo Moscato +4 more
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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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