| 平面凸集存在最小凸生成集的充要条件 |
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| 引用本文： | 李寿贵,龚谊承. 平面凸集存在最小凸生成集的充要条件[J]. 应用数学, 2004, 17(3): 486-490 |
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| 作者姓名： | 李寿贵 龚谊承 |
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| 作者单位： | 武汉科技大学理学院,湖北,武汉,430081 |
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| 基金项目： | 湖北省文科基地资助项目 (WH2 0 0 30 11) |
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| 摘 要： | 本文在平面上解决了StevenRLay在 [1 ]中提出的开放性问题“什么样的凸集存在唯一的最小凸生成子集” ,给出并证明了“平面上的凸集存在唯一的最小凸生成子集”的一个充要条件 .同时证明了En 中的开集一定不存在最小凸生成集 .
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| 关 键 词： | 支持线 最小凸生成集 轮廓 |
| 文章编号： | 1001-9847(2004)03-0486-05 |
| 修稿时间： | 2003-06-17 |
A Sufficient and Necessary Condition for the Unique Smallest Generating Subset''''s Existence of a Planar Convex Set |
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| LI Shou-gui,GONG Yi-cheng. A Sufficient and Necessary Condition for the Unique Smallest Generating Subset''''s Existence of a Planar Convex Set[J]. Mathematica Applicata, 2004, 17(3): 486-490 |
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| Authors: | LI Shou-gui GONG Yi-cheng |
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| Abstract: | This paper resolves partly the open problem whether there is a unique smallest subset for a convex set whose convex hull is equal to the set,which was proposed by Steven R.Lay in the material convex sets and their application.The paper provieds and proves a sufficient and necessary condition about the open problem.Moreover the paper prove the answer is negative for an open set in En. |
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| Keywords: | Supporting line Smallest generating set Profile |
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