5 citations · 9 across the 6 of their papers we have counts for
6 papers
On Constructions of full-dimensional absolutely normal sets of uniqueness
Chun-Kit Lai, Yu-Hao Xie
We construct a class of homogeneous Cantor-Moran measures with all contraction ratios being reciprocals of integers, and prove that they are pointwise absolutely normal. Our approa…
Dimensions of orthogonal projections of typical self-affine sets and measures
De-Jun Feng, Yu-Hao Xie
Let be a family of invertible real matrices with for . For , let $π^{\bf a}\c…
-spectrum of graph-directed self-similar measures that have overlaps and are essentially of finite type
Yuanyuan Xie
For self-similar measures with overlaps, closed formulas of the -spectrum have been obtained by Ngai and the author for measures that are essentially of finite type in [J. Aus…
Semilinear heat equations and parabolic variational inequalities on graphs
Yong Lin, Yuanyuan Xie
Let be a locally finite connected weighted graph, and be an unbounded subset of . Using Rothe's method, we study the existence of solutions for the semilinear heat…
Application of Rothe's method to a nonlinear wave equation on graphs
Yong Lin, Yuanyuan Xie
We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption…
The existence of the solution of the wave equation on graphs
Yong Lin, Yuanyuan Xie
Let be a finite weighted graph, and be a domain such that . In this paper, we study the following initial boundary problem for the n…