Lai Jiang

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math.CA2025

Box dimension of the graphs of recurrent fractal interpolation functions

Lai Jiang, Xiao-Hui Li, Zhen Liang +1

Let $f$ be a generalized affine recurrent fractal interpolation function with vertical scaling functions. In this paper, by introducing underlying local iterated function systems o…

math.CA2025

Representations of rational numbers and Minkowski dimension

Haipeng Chen, Lai Jiang, Yufeng Wu

In this paper, we investigate the representations of rational numbers via continued fraction, Egyptian fraction, and Engel fraction expansions. Given $m \in N$ , denote by…

math.CA2025

Local level sets of the Takagi-van der Waerden function

Lai Jiang, Ting-Ting Ying, Yi-Yang Zhang

In this paper, we investigate the Takagi-van der Waerden function, $T_{r} (x) = n = 0 \sum \infty \frac{ϕ ( r ^{n} x )}{r ^{n}}, x \in [0, 1], r \in Z^{+},$ where $ϕ(x)=…

math.CA2025

Assouad dimension of the Takagi function

Lai Jiang

For any integer $b \geq 2$ and real series ${c_{n}}$ such that $\sum_{n = 0}^{\infty} ∣ c_{n} ∣ < \infty$ , the generalized Takagi function $f_{c, b} (x)$ is defined by $$ f_{{\mathbf c}…