arXiv subjects

Yuichi Kamiya

Publications and source records attributed to Yuichi Kamiya.

2 recordsLinked to original sources

arXiv2024

Non-self-intersective dragon curves

Let us fold a strip of paper many times in the same direction, and then unfold it to form a fixed angle $\theta$ at all creases. The resulting shape is called the Dragon curve with the unfolding angle $\theta$. When $0\le\theta<90^{\circ}$, the corresponding Dragon curve has a self-intersection. When $\theta=180^{\circ}$, the corresponding Dragon curve is a straight line, which has no self-intersection. In this paper, we will show that any Dragon curve whose unfolding angle is greater than $99.3438^{\circ}$ and less than $180^{\circ}$ has no self-intersection.

math.MG↗

arXiv2015

On a distribution function of a probability measure involving a permutation

In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums. [3,Theorem 4] states that the higher order derivatives of the distribution function with respect to a certain parameter are expressed by a generalization of the Takagi function. In [3], we only gave the sketch of the proof of Theorem 4, because the complete proof is very long. The purpose of this paper is to give the complete proof of [3,Theorem 4].

math.NT↗