• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1049-1061
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• 2019

For ${\alpha}{\geq}1$, let $s_{\alpha}(n)={\lceil}{\alpha}n{\rceil}-{\lceil}{\alpha}(n-1){\rceil}$. A continued fraction $C({\alpha})=[0;s_{\alpha}(1),s_{\alpha}(2),{\ldots}]$ is considered and analyzed. Appealing to Diophantine approximation, we investigate the differentiability of $C({\alpha})$, and then show its singularity.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.857-870
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• 2000

In this paper, we estimate correlation dimensions of discrete quasi periodic ordits with frequencies, irrational numbers, which are called quasi Roth numbers. We specify the lower estimate valuse of the dimensions by using the parameters which are derived the rational approximable properties of the quasi Roth numbers.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.542-554
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• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.