A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some f...A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.展开更多
Currently,the cloud computing systems use simple key-value data processing,which cannot support similarity search efectively due to lack of efcient index structures,and with the increase of dimensionality,the existing...Currently,the cloud computing systems use simple key-value data processing,which cannot support similarity search efectively due to lack of efcient index structures,and with the increase of dimensionality,the existing tree-like index structures could lead to the problem of"the curse of dimensionality".In this paper,a novel VF-CAN indexing scheme is proposed.VF-CAN integrates content addressable network(CAN)based routing protocol and the improved vector approximation fle(VA-fle) index.There are two index levels in this scheme:global index and local index.The local index VAK-fle is built for the data in each storage node.VAK-fle is thek-means clustering result of VA-fle approximation vectors according to their degree of proximity.Each cluster forms a separate local index fle and each fle stores the approximate vectors that are contained in the cluster.The vector of each cluster center is stored in the cluster center information fle of corresponding storage node.In the global index,storage nodes are organized into an overlay network CAN,and in order to reduce the cost of calculation,only clustering information of local index is issued to the entire overlay network through the CAN interface.The experimental results show that VF-CAN reduces the index storage space and improves query performance efectively.展开更多
文摘A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.
基金supported by National Natural Science Foundation of China(No.61071093)Research and Innovation Projects for Graduates of Jiangsu Province(Nos.CXZZ12 0483 and CXLX12 0481)+1 种基金Science and Technology Support Program of Jiangsu Province(No.BE2012849)Priority Academic Program Development of Jiangsu Higher Education Institutions(No.yx002001)
文摘Currently,the cloud computing systems use simple key-value data processing,which cannot support similarity search efectively due to lack of efcient index structures,and with the increase of dimensionality,the existing tree-like index structures could lead to the problem of"the curse of dimensionality".In this paper,a novel VF-CAN indexing scheme is proposed.VF-CAN integrates content addressable network(CAN)based routing protocol and the improved vector approximation fle(VA-fle) index.There are two index levels in this scheme:global index and local index.The local index VAK-fle is built for the data in each storage node.VAK-fle is thek-means clustering result of VA-fle approximation vectors according to their degree of proximity.Each cluster forms a separate local index fle and each fle stores the approximate vectors that are contained in the cluster.The vector of each cluster center is stored in the cluster center information fle of corresponding storage node.In the global index,storage nodes are organized into an overlay network CAN,and in order to reduce the cost of calculation,only clustering information of local index is issued to the entire overlay network through the CAN interface.The experimental results show that VF-CAN reduces the index storage space and improves query performance efectively.
