Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is ...Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.展开更多
Some atomic decomposition theorems for Banach-space-valued martingales are established. Using them, the embedding relationships between martingale spaces with small index are discussed. The results obtained here are c...Some atomic decomposition theorems for Banach-space-valued martingales are established. Using them, the embedding relationships between martingale spaces with small index are discussed. The results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of Banach space in which the martingales take values.展开更多
In this paper, the author establishes the embedding theorems for different metrics of inhomoge-neous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. As an application, the author obtainssome estimates...In this paper, the author establishes the embedding theorems for different metrics of inhomoge-neous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. As an application, the author obtainssome estimates for the entropy numbers of the embeddings in the limiting cases between some Besov spacesand some logarithmic Lebesgue spaces.展开更多
A space-filling curve in 2,3,or higher dimensions can be thought as a path of a continuously moving point.As its main goal is to preserve spatial proximity,this type of curves has been widely used in the design and im...A space-filling curve in 2,3,or higher dimensions can be thought as a path of a continuously moving point.As its main goal is to preserve spatial proximity,this type of curves has been widely used in the design and implementation of spatial data structures and nearest neighbor-finding techniques.This paper is essentially focused on the efficient representation of Digital Ele-vation Models(DEM) that entirely fit into the main memory.We propose a new hierarchical quadtree-like data structure to be built over domains of unrestricted size,and a representation of a quadtree and a binary triangles tree by means of the Hilbert and the Sierpinski space-filling curves,respectively,taking into account the hierarchical nature and the clustering properties of this kind of curves.Some triangulation schemes are described for the space-filling-curves-based approaches to efficiently visualize multiresolu-tion surfaces.展开更多
In the compactized Minkowski space, which is equivalent to the conformal spaceM 4, we introduced a Lorentz metric d σ2 and a Yang-Mills field θ. Later, we proved that dσ2 and θ together satisfy the EYM (Einstein-Y...In the compactized Minkowski space, which is equivalent to the conformal spaceM 4, we introduced a Lorentz metric d σ2 and a Yang-Mills field θ. Later, we proved that dσ2 and θ together satisfy the EYM (Einstein-Yang-Mills) equation. In this paper, it is proved that θ onM 4 (which is the boundary of the anti-de-Sitter space AdS5) can be extended to be a Yang-Mills field $\hat \theta $ on AdS5 such that Hua’s metric ds2 on AdS5, together with $\hat \theta $ satisfies the EYM equation on AdS5.展开更多
基金National Natural Science Foundations of China(No.10901033,No.10971023)Shanghai Pujiang Project,China(No.08PJ1400600)+1 种基金Shanghai Shuguang Project,China(No.07SG38)the Fundamental Research Funds for the Central Universities of China
文摘Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.
基金the National Natural Science Foundation of China (Grant No. 10071059) .
文摘Some atomic decomposition theorems for Banach-space-valued martingales are established. Using them, the embedding relationships between martingale spaces with small index are discussed. The results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of Banach space in which the martingales take values.
基金This work was supported by the Alexander von Humboldt Foundation of Germany and the State Education Department of China.
文摘In this paper, the author establishes the embedding theorems for different metrics of inhomoge-neous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. As an application, the author obtainssome estimates for the entropy numbers of the embeddings in the limiting cases between some Besov spacesand some logarithmic Lebesgue spaces.
基金Supported by the GeneSIG Project, University of Informatics Sciences (UCI), Havana, Cuba
文摘A space-filling curve in 2,3,or higher dimensions can be thought as a path of a continuously moving point.As its main goal is to preserve spatial proximity,this type of curves has been widely used in the design and implementation of spatial data structures and nearest neighbor-finding techniques.This paper is essentially focused on the efficient representation of Digital Ele-vation Models(DEM) that entirely fit into the main memory.We propose a new hierarchical quadtree-like data structure to be built over domains of unrestricted size,and a representation of a quadtree and a binary triangles tree by means of the Hilbert and the Sierpinski space-filling curves,respectively,taking into account the hierarchical nature and the clustering properties of this kind of curves.Some triangulation schemes are described for the space-filling-curves-based approaches to efficiently visualize multiresolu-tion surfaces.
基金This work was partially supported by the Ministry of Sci. and Tech. , FNS of China ( Grant No. 19631010) Fundamental Research Bureau of CAS respectively.
文摘In the compactized Minkowski space, which is equivalent to the conformal spaceM 4, we introduced a Lorentz metric d σ2 and a Yang-Mills field θ. Later, we proved that dσ2 and θ together satisfy the EYM (Einstein-Yang-Mills) equation. In this paper, it is proved that θ onM 4 (which is the boundary of the anti-de-Sitter space AdS5) can be extended to be a Yang-Mills field $\hat \theta $ on AdS5 such that Hua’s metric ds2 on AdS5, together with $\hat \theta $ satisfies the EYM equation on AdS5.
