Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method...Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method of the valid/invalid item is developed on the relation between reachability matrix and valid items. And valid items are explained from the perspective of graph theory. An incremental augment algorithm for constructing Qr matrix is proposed based on the idea of incremental forward regression, and its validity is theoretically considered. Results of empirical tests are given in order to compare the performance of the incremental augment algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms the Tatsuoka algorithm, and the analysis of the two algorithms also show linear growth with respect to the number of valid items. Mathematical models with 10 attributes are built for the two algorithms by the linear regression analysis.展开更多
A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
朗古来（Longuerrc）定理及其推广是平面几何中的著名定理,它有着较多的推导和论证方法。本文来用极坐标法证明,比日本东京工业大学名誉教授矢野健太郎的复数证法还要简便新颖、现介绍如下,供数学教师参考。引理设 P 为△A1A2A3的外接...朗古来（Longuerrc）定理及其推广是平面几何中的著名定理,它有着较多的推导和论证方法。本文来用极坐标法证明,比日本东京工业大学名誉教授矢野健太郎的复数证法还要简便新颖、现介绍如下,供数学教师参考。引理设 P 为△A1A2A3的外接圆上任一点,D1、D2、D3分别是 P 点在三边上的射影,求证 D1、D2、D3三点共线。这条直线叫做 P 点的关于 A1、A2、A3三点的西摩松（simson）展开更多
基金Supported by the National Natural Science Foundation of China (30860084,60673014,60263005)the Backbone Young Teachers Foundation of Fujian Normal University(2008100244)the Department of Education Foundation of Fujian Province (ZA09047)~~
文摘Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method of the valid/invalid item is developed on the relation between reachability matrix and valid items. And valid items are explained from the perspective of graph theory. An incremental augment algorithm for constructing Qr matrix is proposed based on the idea of incremental forward regression, and its validity is theoretically considered. Results of empirical tests are given in order to compare the performance of the incremental augment algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms the Tatsuoka algorithm, and the analysis of the two algorithms also show linear growth with respect to the number of valid items. Mathematical models with 10 attributes are built for the two algorithms by the linear regression analysis.
文摘A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
文摘朗古来（Longuerrc）定理及其推广是平面几何中的著名定理,它有着较多的推导和论证方法。本文来用极坐标法证明,比日本东京工业大学名誉教授矢野健太郎的复数证法还要简便新颖、现介绍如下,供数学教师参考。引理设 P 为△A1A2A3的外接圆上任一点,D1、D2、D3分别是 P 点在三边上的射影,求证 D1、D2、D3三点共线。这条直线叫做 P 点的关于 A1、A2、A3三点的西摩松（simson）
