In this paper,the authors construct a class of fractal surfaces,Bush type surfaces,based on the Bush type functions.The Box dimension,Packing dimension and Hausdorff dimension of such surfaces are investigated.
Ⅰ. INTRODUCTION AND DEFINITIONLet r be a positive integer and p∈[1, +∞]. We consider the following Sobolev function classes over the real line R, W<sub>p</sub><sup>r</sup>（R）:={f∈L<sup...Ⅰ. INTRODUCTION AND DEFINITIONLet r be a positive integer and p∈[1, +∞]. We consider the following Sobolev function classes over the real line R, W<sub>p</sub><sup>r</sup>（R）:={f∈L<sup>p</sup>（R）: f<sup>r-1</sup> is locally absolutely continuous on展开更多
This paper presents a new and simple scheme to describe the convex hull in R^d,which only uses three kinds of the faces of the convex hull,i.e.,the d-1-faces,d-2-faces and 0-faces.Thus,we develop an efficient new algo...This paper presents a new and simple scheme to describe the convex hull in R^d,which only uses three kinds of the faces of the convex hull,i.e.,the d-1-faces,d-2-faces and 0-faces.Thus,we develop an efficient new algorithm for constructing the convex hull of a finite set of points incrementally. This algorithm employs much less storage and time than that of the previously-existing approaches.The analysis of the running time as well as the storage for the new algorithm is also theoretically made.The algorithm is optimal in the worst case for even d.展开更多
文摘In this paper,the authors construct a class of fractal surfaces,Bush type surfaces,based on the Bush type functions.The Box dimension,Packing dimension and Hausdorff dimension of such surfaces are investigated.
文摘Ⅰ. INTRODUCTION AND DEFINITIONLet r be a positive integer and p∈[1, +∞]. We consider the following Sobolev function classes over the real line R, W<sub>p</sub><sup>r</sup>（R）:={f∈L<sup>p</sup>（R）: f<sup>r-1</sup> is locally absolutely continuous on
基金This work is supported by the National Natural Science Foundation of China.
文摘This paper presents a new and simple scheme to describe the convex hull in R^d,which only uses three kinds of the faces of the convex hull,i.e.,the d-1-faces,d-2-faces and 0-faces.Thus,we develop an efficient new algorithm for constructing the convex hull of a finite set of points incrementally. This algorithm employs much less storage and time than that of the previously-existing approaches.The analysis of the running time as well as the storage for the new algorithm is also theoretically made.The algorithm is optimal in the worst case for even d.
