5 citations · 13 across the 15 of their papers we have counts for
16 papers
VIS-Ground: Video Interactive Storytelling with Contextual Grounding
Bingxuan Li, Yiwen Song, Xueqing Wu +10
Video interactive storytelling enables viewers to actively steer how a video unfolds. However, once we allow viewers to intervene during generation, a new challenge arises: The vie…
From Lipschitz embedding to Lipschitz equivalence between dust-like self-similar sets
Huo-Jun Ruan, Jian-Ci Xiao
Let be two dust-like self-similar sets sharing the same Hausdorff dimension. We consider when the mere existence of a Lipschitz embedding from to a…
Box dimension of generalized affine fractal interpolation functions (II)
Lai Jiang, Huo-Jun Ruan
Let be a generalized affine fractal interpolation function with vertical scaling functions. In this paper, we prove the monotonicity of spectral radii of vertical scaling matri…
Box dimension of generalized affine fractal interpolation functions
Lai Jiang, Huo-Jun Ruan
Let be a generalized affine fractal interpolation function with vertical scaling function . In this paper, we study , the box dimension of the graph of , under…
A separation property for iterated function systems of similitudes
De-Jun Feng, Huo-Jun Ruan, Ying Xiong
Let be the attractor of an iterated function system on , where , and are orthogonal transformations on $…
The connectedness of Sierpiński sponges with rotational and reflectional components and associated graph-directed systems
Huo-Jun Ruan, Jian-Ci Xiao
We provide two methods to characterize the connectedness of all -dimensional generalized Sierpiński sponges whose corresponding IFSs are allowed to have rotational and reflectio…
On the existence of cut points of connected generalized Sierpinski carpets
Huo-Jun Ruan, Yang Wang, Jian-Ci Xiao
In a previous work joint with Dai and Luo, we show that a connected generalized Sierpiński carpet (or shortly a GSC) has cut points if and only if the associated -th Hata graph…
Connectedness and local cut points of generalized Sierpinski carpets
Xin-Rong Dai, Jun Luo, Huo-Jun Ruan +2
We investigate a homeomorphism problem on a class of self-similar sets called generalized Sierpinski carpets (or shortly GSCs). It follows from two well-known results by Hata and W…
Gap sequences and Topological properties of Bedford-McMullen sets
Zhen Liang, Jun Jie Miao, Huo-Jun Ruan
In this paper, we study the topological properties and the gap sequences of Bedford-McMullen sets. First, we introduce a topological condition, the component separation condition (…
Construction and box dimension of recurrent fractal interpolation surfaces
Zhen Liang, Huo-Jun Ruan
In this paper, we present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on rectangular grids. Then we introduce bilinear RFISs, which are easy t…
Metrics on the Sierpinski carpet by weight functions
Qingsong Gu, Hua Qiu, Huo-Jun Ruan
We construct certain metrics on the Sierpinski carpet via a class of self-similar weight functions. Using these metrics and by applying known results, we obtain the two-sided sub-G…
Lipschitz equivalence of Cantor sets and irreducibility of polynomials
Jun Jason Luo, Huo-Jun Ruan, Yi-Ling Wang
In the paper, we provide an effective method for the Lipschitz equivalence of two-branch Cantor sets and three-branch Cantor sets by studying the irreducibility of polynomials. We…
Energy and Laplacian of Fractal Interpolation Functions
Xiao-Hui Li, Huo-Jun Ruan
In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with un…
Lipschitz Equivalence of Self-Similar Sets: Algebraic and Geometric Properties
Hui Rao, Huo-Jun Ruan, Yang Wang
In this paper we provide an up-to-date survey on the study of Lipschitz equivalence of self-similar sets. Lipschitz equivalence is an important property in fractal geometry because…
Lipschitz equivalence of self-similar sets with touching structures
Huo-Jun Ruan, Yang Wang, Li-Feng Xi
Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios…
The resolvent kernel for PCF self-similar fractals
Marius Ionescu, Erin P. J. Pearse, Luke G. Rogers +2
For the Laplacian defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet boundary conditions, and also w…