| p-截面体的性质与推广 |
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| 引用本文： | 沈亚军. p-截面体的性质与推广[J]. 浙江大学学报(理学版), 2010, 37(2): 144-147. DOI: 10.3785/j.issn.1008-9497.2010.02.005 |
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| 作者姓名： | 沈亚军 |
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| 作者单位： | 浙江林学院应用数学系,浙江,临安,311300 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 对p≥-1,GARDNER RJ和GIANNOPOULOS A A引进了p-截面体CpK,并就p的不同取值,对CpK的凸性作了探讨.首先证明了CpK的一些性质,诸如原点对称的n维椭球E的p-截面体是它的极体的一个伸缩、CpCqE=CqCpE,V(CnK)=V(IK)等.而后通过探讨混合径向平均体Rp(K,L)与混合p-截面体Cp(K,L)的相关性,将p-截面体的一些性质推广到了Cp(K,L),并证明了当K和L是En中的凸体且K■L时,C1(K,L)是一个凸体.
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| 关 键 词： | p-截面体 混合p-截面体 凸性 推广 |
Some properties of p-cross-section bodies and generalazation |
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| SHEN Ya-jun. Some properties of p-cross-section bodies and generalazation[J]. Journal of Zhejiang University(Sciences Edition), 2010, 37(2): 144-147. DOI: 10.3785/j.issn.1008-9497.2010.02.005 |
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| Authors: | SHEN Ya-jun |
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| Affiliation: | SHEN Ya-jun(Department of Applied Mathematics,College of Sciences,Zhejiang Forestry University,Lin＇an 311300,Zhejiang Province,China) |
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| Abstract: | For p≥-1,Gardner R J and Giannopoulos A A introduced p-cross-section bodies C_pK and went further into.the convexity of C_pK for different P.Some new properties of C_pK are proved,for example,the P-cross-section body of an origin symmetric ellipsoid is a dilatation of its polar,C_pC_qE=C_qC_pE,V(C_nK):V(IK)etc.,then some properties of C_pK to mixed p-cross-section bodies C_p(K,L)by approaching the relationship between R_p(K,L)and C_p(K,L)are generalized and it is proved that if K and L are convex bodies in E~n,K(∈)L,then C_1(K,L)is a convex body. |
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| Keywords: | p-cross-section body mixed p-cross-section body convexity generalazation |
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