| 伪对称点集与正则单形 |
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| 引用本文： | 沈亚军,张垚,冷岗松.伪对称点集与正则单形[J].数学学报,2012(3):561-566. |
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| 作者姓名： | 沈亚军 张垚 冷岗松 |
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| 作者单位： | 浙江农林大学应用数学系;湖南师范大学数学系;上海大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目(10971128) |
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| 摘 要： | 要证明了E~n中的有序向量集是伪对称点集的充要条件.利用这一充分必要条件,得到了有关正则单形的几个等价描述,给出了伪对称点集与正则单形的关系的一个结论:设■={A_1,A_2,…,A_(n+1)}是E~n中的点集,则■是n维对称点集的充要条件是以(?)为顶点的单形是正则单形.
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| 关 键 词： | 伪对称点集 正则单形 Legendre椭球 |
Pseudo-Symmetric Point Sets and Regular Simplices |
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| Ya Jun SHEN.Pseudo-Symmetric Point Sets and Regular Simplices[J].Acta Mathematica Sinica,2012(3):561-566. |
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| Authors: | Ya Jun SHEN |
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| Institution: | Department of Mathematics,Shanghai University,Shanghai 200436,P.R.China |
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| Abstract: | A sufficient and necessary condition that an ordered vectors-set is a pseudosymmetric point set in E~n is explored.Based on this condition,several equivalent ways of characterizing regular simplices are obtained.A relationship between a pseudosymmetric point set and a regular simplex is given,i.e.,let ■ = {A_1,A_2,...,A_(n+1)} be a point set in E~n,then ■ is an n-pseudo-symmetric point set if and only if the simplex with vertex set(?) is regular. |
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| Keywords: | pseudo-symmetric point set mass-point system Legendre ellipsoid |
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