dc.contributor.author 施慧华 dc.contributor.author 张皛晶 dc.date.accessioned 2017-11-14T02:50:51Z dc.date.available 2017-11-14T02:50:51Z dc.date.issued 2006-09-30 dc.identifier.citation 厦门大学学报(自然科学版),2006,(05):35-37 dc.identifier.issn 0438-0479 dc.identifier.other XDZK200605007 dc.identifier.uri https://dspace.xmu.edu.cn/handle/2288/154707 dc.description.abstract 考虑如下问题:对一个Banach空间X,已知其单位球面SX可以被n+1个不含原点为其内点的闭球所覆盖,则其最小覆盖半径是多少?本文针对一特殊空间Rn,首先证明了在Rn中,若有一点集{xi}im=1满足一定条件,则可给出一特殊的球覆盖,且此覆盖的半径即为最小半径.进一步本文还给出了在Rn中若任意给定r≥32,可找到一个以r为覆盖半径的球覆盖,且此覆盖的势为极小的. dc.description.abstract Considering the following problem: for a Banach space X with dimX=n,it has already known that the sphere of the unit ball of X can be covered by a ball-covering of n+1 closed balls not containing the origin in its interior,then what is its smallest radius? This article first proves that there exists a specific ball-covering with the smallest radius in R~n if a set {x_i}~m_(i=1) satisfying some given term,then presents a minimal ball-covering with arbitrary given r≥32 as its radius. dc.language.iso zh_CN dc.subject 球覆盖 dc.subject Rn dc.subject 覆盖半径 dc.subject 极小势 dc.subject ball-covering dc.subject R~n dc.subject radius dc.subject minimal dc.title R~n空间中单位球面的极小球覆盖 dc.title.alternative Minimal Ball-covering of the Unit Spheres in R~n dc.type Article
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