The Generalized Sine Theorem for Mixed Vertex Angle of Two Simplices and Applications

Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.

两个单形的k级混合顶点角

本文证明了关于两个单形的k级混合顶点角与每个单形的k级顶点角之间的一些新的重要的几何不等式。

顶点成分分析法应用于高光谱图像端元提取

高光谱图像既可以获取地面物体的空间位置信息,又能够提供任意像元对应的地面物体的光谱特征曲线,具有极强的地物分类和识别能力。利用线性混合模型对高光谱图像的光谱混合特性进行描述,并采用顶点成分分析法进行端元提取,为高光谱图像的混合像元分解和分类提供依据;以合成和真实高光谱数据作为实验数据,以均方根特征角误差作为评价指标,研究不同信噪比和不同端元数条件下端元提取的效果。实验结果表明,与USGS光谱库对比,顶点成分分析法能够有效提取到端元光谱曲线,均方根特征角误差能够保持在0.2rad以内。