| L_p-混合质心体和对偶L_p-混合质心体 |
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| 引用本文： | 马统一. L_p-混合质心体和对偶L_p-混合质心体[J]. 数学学报, 2010, 53(2): 301-314 |
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| 作者姓名： | 马统一 |
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| 作者单位： | 河西学院数学系; |
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| 基金项目： | 国家自然科学基金资助项目(10971128); 甘肃省教育厅科研资助项目(0709-03) |
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| 摘 要： | 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.
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| 关 键 词： | L_p-混合质心体 对偶L_p-混合质心体 均质积分 |
| 收稿时间： | 2008-03-18 |
| 修稿时间： | 2009-09-24 |
On Lp-Mixed Centroid Bodies and Dual Lp-Mixed Centroid Bodies |
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| Tong Yi MA. On Lp-Mixed Centroid Bodies and Dual Lp-Mixed Centroid Bodies[J]. Acta Mathematica Sinica, 2010, 53(2): 301-314 |
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| Authors: | Tong Yi MA |
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| Affiliation: | Department of Mathematics, Hexi University, Zhangye 734000, P. R. China |
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| Abstract: | In this paper, the three concepts of Lp-mixed centroid bodies Γp,iK and dual Lp-mixed centroid bodies Γ-p,iK and Lp-mixed harmonic Blaschke add  of star bodies  are introduced. The Shephard's question of Lp-mixed centroid bodies and dual Lp-mixed centroid bodies are solved succeed. In addition, the Brunn--Minkowski inequalities of the quermassintegrals and dual quermassintegrals of Lp-mixed centroid bodies associated with Lp-mixed harmonic Blaschke add are established, respectively. They extend some results of before document. |
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| Keywords: | L_p-mixed centroid body dual L_p-mixed centroid body quermassintegrals |
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