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运用分式运算法则巧证几何题
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作者 唐国珍 《中学数学研究(华南师范大学)(上半月)》 2003年第5期30-31,共2页
先看下面一道例题:如图1,已知 AD//BE//CF,求证 1/(BE)+1/(CF)=1/(AD).解题的一般思路是:要证1/(BE)+1/(CF)=1/(AD),可证 (AD)/(BE)+(AD)/(CF)=1,即要证两个异分母分式之和为1.根据平行线分线段成比例定理,由 AD//BE 可得 (AD)/(BE)=(CD... 先看下面一道例题:如图1,已知 AD//BE//CF,求证 1/(BE)+1/(CF)=1/(AD).解题的一般思路是:要证1/(BE)+1/(CF)=1/(AD),可证 (AD)/(BE)+(AD)/(CF)=1,即要证两个异分母分式之和为1.根据平行线分线段成比例定理,由 AD//BE 可得 (AD)/(BE)=(CD)/(BC),由 AD// 展开更多
关键词 分式运算法则 几何题 证明方法 平面几何 初中 数学教学 几何教学 解题规律 创新意识
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Prediction of Instability Separation Modes and Its Application in Practical Dynamic Security Region
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作者 曾沅 余贻鑫 +3 位作者 王红梅 闵亮 张沛 LEES T 《Transactions of Tianjin University》 EI CAS 2007年第3期157-162,共6页
The transient critical boundary of dynamic security region (DSR) can be approximated by a few hyper planes correlated with instability separation modes. A method to fast predict instability separation modes is propose... The transient critical boundary of dynamic security region (DSR) can be approximated by a few hyper planes correlated with instability separation modes. A method to fast predict instability separation modes is proposed for DSR calculation in power injection space. The method identifies coherent generation groups by the developed K-medoids algorithm, taking a similarity matrix derived from the reachability Grammian as the index. As an experimental result, reachability Grammian matrices under local injections are approximately invariant. It indicates that the generator coherency identifications are nearly consistent for different injections. Then instability separation modes can be predicted at the normal operating point, while average initial acceleration is considered as the measure of the critical generator group to amend the error. Moreover, based on these predicted instability separation modes, a critical point search strategy for DSR calculation is illustrated in the reduced injection space of the critical generators. The proposed method was evaluated using New England Test System, and the computation accuracy and speed in determining the practical DSR were improved. 展开更多
关键词 instability separation mode dynamic security region K-medoids algorithm reachability Grammian
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