贝西科维奇-埃格利斯顿类型的线性分形

良逼近数的维数

The dimension of well approximable numbers

本文综述了受Besicovitch结果启发的丢番图逼近核心主题，重点介绍了Mass Transference Principle、Ubiquity及流形与分形上的逼近进展，并揭示了数论与分形几何的联系及开放问题。

Singular probability distributions and fractal properties of sets of real numbers defined by the asymptotic frequencies of their s-adic digits

Properties of the set $T_s$ of "particularly non-normal numbers" of the unit interval are studied in details ($T_s$ consists of real numbers $x$, some of whose s-adic digits have the asymptotic frequencies in the nonterminating $s-$ adic expansion of $x$, and some do not). It is proven that the set $T_s$ is residual in the topological sense (i.e., it is of the first Baire category) and it is generic in the sense of fractal geometry ($T_s$ is a superfractal set, i.e., its Hausdorff-Besicovitch dimension is equal to~1). A topological and fractal classification of sets of real numbers via analysi…

4进制表示中给定渐近均值的实数集合的拓扑、度量和分形性质（当数字频率存在时）

Topological, metric and fractal properties of the set of real numbers with a given asymptotic mean of digits in their $4$-adic representation in the case when the digit frequencies exist

本文研究了4进制表示中实数的渐近均值集合的拓扑、度量和分形性质，探讨了其水平集的构造、连续性、稠密性以及测度和分形维度的估计。

非零冗余数制及其在局部复函数理论中的应用

Numeral systems with non-zero redundancy and their applications in the theory of locally complex functions

本文研究了具有非零冗余的数制在局部复函数理论中的几何与拓扑性质，探讨了函数的连续性、单调性和变分性质。

具有自然基和冗余字母表的数字系统中不同数字表示的集合

Sets of distinct representations of numbers in numeral systems with a natural base and a redundant alphabet

研究了具有自然基s≥2和冗余字母表A_r={0,1,…,r}的数字系统，分析了区间[0,r/(s-1)]中唯一表示的数集的拓扑、度量和分形性质，并证明了该集的Hausdorff-Besicovitch维数为ln(2s-r-1)/ln s。