Results 11 to 20 of about 92,586 (253)
The quantum chaos conjecture and generalized continued fractions [PDF]
Sbornik: Mathematics, 2003 Summary: The proof of the quantum chaos conjecture is given for a class of systems including as a special case the model of a rotating particle under the action of periodic impulse perturbations. (The distribution of the distances between adjacent energy levels is close to the Poisson distribution and differs from it by terms of the third order of ...
L. Pustyl'nikov
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Maximizing weighted sums of binomial coefficients using generalized continued fractions [PDF]
Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2023 Let $m,\,r\in {\mathbb {Z}}$ and $\omega \in {\mathbb {R}}$ satisfy $0\leqslant r\leqslant m$ and $\omega \geqslant 1$ .
S. Glasby, G. R. Paseman
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Generalized Notions of Continued Fractions
, 2023 Juan Fernández Sánchez +3 more
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Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution.
Pierre Arnoux +3 more
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Computational Triangulation in Mathematics Teacher Education
Computation, 2023 The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser
Sergei Abramovich
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Mathematics, 2022 The paper promotes the notion of computational experiment supported by a multi-tool digital environment as a means of the development of new mathematical knowledge in the context of education. The main study of the paper deals with the issues of teaching
Sergei Abramovich
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On the Generalized Rogers-Ramanujan Continued Fraction [PDF]
The Ramanujan Journal, 2003 The generalized Rogers-Ramanujan continued fraction is defined for \(| q|< 1\) and any complex \(a\) by \[ R(a,q)= {1\over 1}{\;\atop +} {aq\over 1}{\;\atop +} {aq^2\over 1}{\;\atop +} {aq^3\over 1}{\;\atop +}\cdots. \] The authors prove an asymptotic formula stated by Ramanujan for \(R(a,e^{-x})\) as \(x\to 0+\).
Berndt, Bruce C., Yee, Ae Ja
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Repdigits as Product of Terms of k-Bonacci Sequences
Mathematics, 2021 For any integer k≥2, the sequence of the k-generalized Fibonacci numbers (or k-bonacci numbers) is defined by the k initial values F−(k−2)(k)=⋯=F0(k)=0 and F1(k)=1 and such that each term afterwards is the sum of the k preceding ones.
Petr Coufal, Pavel Trojovský
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PLoS ONE, 2023 ObjectivesE-cigarettes pose significant risks to youth, but smokers may benefit from switching to e-cigarettes by reducing their exposure to toxicants, which creates a challenge for the Food and Drug Administration (FDA) in regulating e-cigarettes to ...
Yoo Jin Cho +8 more
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On irrationality exponents of generalized continued fractions [PDF]
, 2014 Text We study how the asymptotic irrationality exponent of a given generalized continued fraction K n = 1 ∞ a n b n , a n , b n ∈ Z + , behaves as a function of growth properties of partial coefficient sequences ( a n ) and ( b n ) .
J. Hančl +3 more
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