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本文研究了文献[1]所引入的Orlicz投影体问题.利用Orlicz投影体在线性变换下的不变性,获得了椭球的Orlicz投影体仍是椭球的结果.作为例子,计算了当取两个特定的凸函数时单位球的Orlicz投影体的支持函数. 相似文献
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关于L_p-混合质心体的Busemann-Petty问题 总被引:1,自引:0,他引:1
对p≥1,Lutwak和Zhang引进了R~n中一个星体K的L_p-质心体Γ_pK的概念,Grinberg和Zhang研究了L_p-质心体算子Γ_p的Busemann-Petty问题;最近,马统一引进了星体K的L_p-混合质心体Γ_(p,i)K(i∈R)的概念,即L_p-质心体是它的特殊类.本文研究了Γ_(p,i)K(?)Γ_(p,i)L是否一定(?)的问题.其结果是Grinberg和Zhang关于L_p-质心体算子Γ_p的Busemann-Petty问题的推广形式. 相似文献
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L_p-混合质心体和对偶L_p-混合质心体 总被引:1,自引:0,他引:1
本文引进了L_p-混合质心体Γ_(p,i)K、对偶L_p-混合质心体Γ_(-p,i)K和R~n中星体K和L的L_p-混合调和Blaschke加K+_pL的概念,成功地解决了L_p-混合质心体和对偶L_p-混合质心体的Shephard型问题.并且结合星体的L_p-混合调和Blaschke加的概念,分别建立了L_p-混合质心体的均质积分和对偶均质积分的Brunn-Minkowski型不等式.所获结论推广了已有文献的结果. 相似文献
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《应用数学与计算数学学报》2018,(3)
广义质心体是关于概率测度的Orlicz质心体的多元情形.考虑广义质心体的非对称版本,即将关于概率测度的非对称Orlicz质心体推广到多元情形,并建立相应的质心不等式. 相似文献
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本文研究了新几何体Γ_(-p)K与L_p-质心体和L_p-John椭球有关的几个有趣不等式,包括L_p-Busemann-Petty质心不等式的一种隔离,同时探讨了新几何体Γ_(-p)K的单调性. 相似文献
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Lutwak et al.(2010) established the Orlicz centroid inequality for convex bodies and conjectured that their Orlicz centroid inequality could be extended to star bodies. Zhu(2012) confirmed the conjectured Lutwak, Yang and Zhang(LYZ) Orlicz centroid inequality and solved the equality condition for the case that φis strictly convex. Without the condition that φ is strictly convex, this paper studies the equality condition of the conjectured LYZ Orlicz centroid inequality for star bodies. 相似文献
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Lutwak, Yang and Zhang established the Orlicz centroid inequality for convex bodies and conjectured that their inequality can be extended to star bodies. In this paper, we confirm this conjecture. 相似文献
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《Advances in Applied Mathematics》2012,48(4):820-828
In this paper, the Orlicz centroid body, defined by E. Lutwak, D. Yang and G. Zhang, and the extrema of some affine invariant functionals involving the volume of the Orlicz centroid body are investigated. The reverse form of the Orlicz Busemann–Petty centroid inequalities is obtained in the two-dimensional case. 相似文献
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Using M-addition,an asymmetric Orlicz centroid inequality for absolutely continuous probability measures is established corresponding to Paouris and Pivovarov’s recent result on the symmetric case.As an application,we extend Haberl and Schuster’s asymmetric Lp centroid inequality from star bodies to compact sets. 相似文献
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Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities. 相似文献