Wenxia Li

activity

20112025

most citedHausdorff dimension of unique beta expansions

46 citations · 140 across the 27 of their papers we have counts for

collaborators

28 papers

math.CA2025

The generalized upper box dimension

Lipeng Wang, Wenxia Li

We introduce the generalized upper box dimension which is defined for any set, whether the set is bounded or unbounded. We study basic properties of the generalized upper box dimen…

math.DS2023

On the union of homogeneous symmetric Cantor set with its translations

Derong Kong, Wenxia Li, Zhiqiang Wang +2

Fix a positive integer $N$ and a real number $0 < β < 1/ (N + 1)$ . Let $Γ$ be the homogeneous symmetric Cantor set generated by the IFS $$ \Big\{ ϕ_i(x)=βx + i \frac{1-β}{N}: i=0,1,\cdo…

math.CA2022★ 3 cited

The Spectrality of Infinite Convolutions in $R^{d}$

Wenxia Li, Zhiqiang Wang

In this paper, we study the spectrality of infinite convolutions in $R^{d}$ , where the spectrality means the corresponding square integrable function space admits a family o…

math.CA2022★ 4 cited

Spectrality of Infinite Convolutions and Random Convolutions

Wenxia Li, Jun Jie Miao, Zhiqiang Wang

In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integ…

math.CA2022

Weak Convergence and Spectrality of Infinite Convolutions

Wenxia Li, Jun Jie Miao, Zhiqiang Wang

Let ${A_{k}}_{k = 1}^{\infty}$ be a sequence of finite subsets of $R^{d}$ satisfying that $# A_{k} \geq 2$ for all integers $k \geq 1$ . In this paper, we first give a sufficient a…

math.NT2022★ 4 cited

Rational Points in Translations of The Cantor Set

Kan Jiang, Derong Kong, Wenxia Li +1

Given two coprime integers $p \geq 2$ and $q \geq 3$ , let $D_{p} \subset [0, 1)$ consist of all rational numbers which have a finite $p$ -ary expansion, and let $$ K(q, \mathcal{A})=\bigg\{…

math.CA2022★ 16 cited

Spectrality of random convolutions generated by finitely many Hadamard triples

Wenxia Li, Jun Jie Miao, Zhiqiang Wang

Let ${(N_{j}, B_{j}, L_{j}) : 1 \leq j \leq m}$ be finitely many Hadamard triples in $R$ . Given a sequence of positive integers ${n_{k}}_{k = 1}^{\infty}$ and $ω=(ω_k)_{k=1}^\infty \…

math.DS2022

Random β-transformation on fat Sierpinski gasket

Tingyu Zhang, Karma Dajani, Wenxia Li

We consider the iterated function system (IFS) $f_{q} (z) = \frac{z + q}{β}, q \in {(0, 0), (1, 0), (0, 1)} .$ As is well known, for $β = 2$ the attractor, $S_{β}$ ,…

math.NT2022

Bases which admit exactly two expansions

Yi Cai, Wenxia Li

For a positive integer $m$ let $Ω_{m} = {0, 1, \dots, m}$ and \begin{align*} \mathcal B_2(m)=&\left \{q\in(1,m+1]: \text{ $\exists x \in [0, m / (q - 1)]$ has exactly }\right. \\ &\left…

math.DS2021

On a class of self-similar sets which contain finitely many common points

Kan Jiang, Derong Kong, Wenxia Li +1

For $λ \in (0, 1/2]$ let $K_{λ} \subset R$ be a self-similar set generated by the iterated function system ${λ x, λ x + 1 - λ}$ . Given $x \in (0, 1/2)$ , let $Λ (x)$ be the set of $λ\in(0…

math.DS2021★ 5 cited

How likely can a point be in different Cantor sets

Kan Jiang, Derong Kong, Wenxia Li

Let $m \in N_{\geq 2}$ , and let $K = {K_{λ} : λ \in (0, 1/ m]}$ be a class of Cantor sets, where $K_{λ} = {\sum_{i = 1}^{\infty} d_{i} λ^{i} : d_{i} \in {0, 1, \dots, m - 1}, i \geq 1}$ . We i…

math.DS2020★ 1 cited

Pointwise densities of homogeneous Cantor measure and critical values

Derong Kong, Wenxia Li, Yuanyuan Yao

Let $N \geq 2$ and $ρ \in (0, 1/ N^{2}]$ . The homogenous Cantor set $E$ is the self-similar set generated by the iterated function system \[ \left\{f_i(x)=ρx+\frac{i(1-ρ)}{N-1}: i=0,1,\ldo…

math.DS2020★ 3 cited

On the sum of squares of middle-third Cantor set

Zhiqiang Wang, Kan Jiang, Wenxia Li +1

Let $C$ be the middle-third Cantor set. In this paper, we show that for every $x \in [0, 4]$ , there exist $x_{1}, x_{2}, x_{3}, x_{4} \in C$ such that $x = x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2},$ which a…

math.NT2019★ 1 cited

Univoque bases of real numbers: local dimension, Devil's staircase and isolated points

Derong Kong, Wenxia Li, Fan Lv +2

Given a positive integer $M$ and a real number $x > 0$ , let $U (x)$ be the set of all bases $q \in (1, M + 1]$ for which there exists a unique sequence $(d_{i}) = d_{1} d_{2} \dots$ with…

math.NT2019

Intersections of Siepinski gasket with its translation

Yi Cai, Wenxia Li

Let $E$ be the Sierpinski gasket, i.e., the self-similar set generated by the IFS ${f_{a} (x) = \frac{x + a}{q} : a \in {(0, 0), (0, 1), (1, 0)}}$ . In paper, we provide a desc…

math.DS2019★ 3 cited

Visibility of Cartesian products of Cantor sets

Tingyu Zhang, Kan Jiang, Wenxia Li

Let $K_{λ}$ be the attractor of the following IFS \begin{equation*} \{f_1(x)=λx, f_2(x)=λx+1-λ\}, \;\;0<λ<1/2. \end{equation*} Given $α \geq 0$ , we say the line $y = α x$ is visible thro…

math.DS2018★ 2 cited

Critical base for the unique codings of fat Sierpinski gasket

Derong Kong, Wenxia Li

Given $β \in (1, 2)$ the fat Sierpinski gasket $S_{β}$ is the self-similar set in $R^{2}$ generated by the iterated function system (IFS) \[ f_{β,d}(x)=\frac{x+d}β,\quad…

math.DS2018

The $β$ -transformation with a hole at 0

Charlene Kalle, Derong Kong, Niels Langeveld +1

For $β \in (1, 2]$ the $β$ -transformation $T_{β} : [0, 1) \to [0, 1)$ is defined by $T_{β} (x) = β x (mod 1)$ . For $t \in [0, 1)$ let $K_{β} (t)$ be the survivor set of $T_{β}$ with hole $(0, t)$ giv…

math.DS2017

Algebraic sums and products of univoque bases

Karma Dajani, Vilmos Komornik, Derong Kong +1

Given $x \in (0, 1]$ , let $U (x)$ be the set of bases $q \in (1, 2]$ for which there exists a unique sequence $(d_{i})$ of zeros and ones such that $x = \sum_{i = 1}^{\infty} d_{i} / q^{i}$ .…

math.DS2017

Estimating the Hausdorff dimensions of univoque sets for self-similar sets

Xiu Chen, Kan Jiang, Wenxia Li

An approach is given for estimating the Hausdorff dimension of the univoque set of a self-similar set. This sometimes allows us to get the exact Hausdorff dimensions of the univoqu…

math.NT2016★ 2 cited

On the bifurcation set of unique expansions

Charlene Kalle, Derong Kong, Wenxia Li +1

Given a positive integer $M$ , for $q \in (1, M + 1]$ let $U_{q}$ be the set of $x \in [0, M / (q - 1)]$ having a unique $q$ -expansion with the digit set ${0, 1, \dots, M}$ , and l…

math.NT2016★ 3 cited

Univoque bases and Hausdorff dimension

Derong Kong, Wenxia Li, Fan Lü +1

Given a positive integer $M$ and a real number $q > 1$ , a \emph{ $q$ -expansion} of a real number $x$ is a sequence $(c_{i}) = c_{1} c_{2} \dots$ with $(c_{i}) \in {0, \dots, M}^{\infty}$ such th…

math.NT2015★ 7 cited

Multiple expansions of real numbers with digits set ${0, 1, q}$

Karma Dajani, Kan Jiang, Derong Kong +1

For $q > 1$ we consider expansions in base $q$ over the alphabet ${0, 1, q}$ . Let $U_{q}$ be the set of $x$ which have a unique $q$ -expansions. For $k = 2, 3, \dots, ℵ_{0}$ l…

math.NT2015

Smallest bases of expansions with multiple digits

Derong Kong, Wenxia Li, Yuru Zou

Given two positive integers $M$ and $k$ , let $\B_k$ be the set of bases $q > 1$ such that there exists a real number $x$ having exactly $k$ different $q$ -expansions over the alphabet…

The generalized upper box dimension

On the union of homogeneous symmetric Cantor set with its translations

The Spectrality of Infinite Convolutions in Rd

Spectrality of Infinite Convolutions and Random Convolutions

Weak Convergence and Spectrality of Infinite Convolutions

Rational Points in Translations of The Cantor Set

Spectrality of random convolutions generated by finitely many Hadamard triples

Random β-transformation on fat Sierpinski gasket

Bases which admit exactly two expansions

On a class of self-similar sets which contain finitely many common points

How likely can a point be in different Cantor sets

Pointwise densities of homogeneous Cantor measure and critical values

On the sum of squares of middle-third Cantor set

Univoque bases of real numbers: local dimension, Devil's staircase and isolated points

Intersections of Siepinski gasket with its translation

Visibility of Cartesian products of Cantor sets

Critical base for the unique codings of fat Sierpinski gasket

The β-transformation with a hole at 0

Algebraic sums and products of univoque bases

Estimating the Hausdorff dimensions of univoque sets for self-similar sets

On the bifurcation set of unique expansions

Univoque bases and Hausdorff dimension

Multiple expansions of real numbers with digits set {0,1,q}

Smallest bases of expansions with multiple digits

The Spectrality of Infinite Convolutions in $R^{d}$

The $β$ -transformation with a hole at 0

Multiple expansions of real numbers with digits set ${0, 1, q}$