| 标准混合差集矩阵的构造 |
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| 引用本文： | 庞善起,张应山. 标准混合差集矩阵的构造[J]. 系统科学与数学, 2010, 30(3): 410-416 |
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| 作者姓名： | 庞善起 张应山 |
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| 作者单位： | 1. 河南师范大学数学与信息科学学院,河南,453007
2. 华东师范大学金融与统计学院,上海,200241 |
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| 基金项目： | 国家自然科学基金，河南省杰出青年计划项目 |
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| 摘 要： | 通过利用差集矩阵和投影矩阵的正交分解之间的关系,首先提出了构造小的标准混合差集矩阵的一般方法.其次,给定一个阶为r+1的标准混合差集矩阵和一个阶为r的差集矩阵,首先提出了构造阶为r(r+1)的标准混合差集矩阵的一般方法.如果阶为r的差集矩阵不存在但一个试验次数为r~2的正交表存在,也可以通过它们构造阶数较大的标准混合差集矩阵.
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| 关 键 词： | 标准混合差集矩阵 Kronecker和 正交表 投影矩阵. |
| 收稿时间： | 2008-12-12 |
| 修稿时间： | 2009-08-26 |
ON THE CONSTRUCTION OF NORMAL MIXED DIFFERENCE MATRICES |
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| PANG Shanqi ZHANG Yingshan. ON THE CONSTRUCTION OF NORMAL MIXED DIFFERENCE MATRICES[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(3): 410-416 |
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| Authors: | PANG Shanqi ZHANG Yingshan |
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| Affiliation: | (1)College of Mathematics and Information Science, Henan Normal University, Henan 453007;(2)School of Finance and Statistics, East China Normal University, Shanghai 200241 |
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| Abstract: | By exploring the relationship between difference matrices and orthogonal decomposition of projection matrices, this paper presents a general method for constructing smaller normal mixed difference matrices. Moreover, given a normal mixed difference matrix of order $r+1$ and a difference matrix of order $r$, this paper also presents a general method for constructing a lager normal mixed difference matrix of order $r(r+1)$. Furthermore, if the difference matrix of order $r$ does not exist but an orthogonal array of runs $r^2$ exists, we can also construct a lager normal mixed difference matrix from the normal mixed difference matrix of order $r+1$ and the orthogonal array of runs $r^2$. |
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| Keywords: | Normal mixed difference matrix Kronecker sum orthogonal array projection matrix. |
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