投影寻踪模型在国民道德体系构建中的应用

针对目前国民道德指数体系构建标准中权重确定的片面性,本文选择5个特征指标作为国民道德指数体系,并提出应用投影寻踪模型对一些国家的道德指数进行量化与排序.分析结果表明:给出了较为准确客观的评价结果,避免了人为确定权重问题,为国民道德体系指数化提供一种计算过程科学直观的新方法.     

背投影式运动技术影片解析系统

本文介绍了一种背投影式的运动技术影片分析系统。概述了该系统的设计原理、组成和特点。该系统设计上采用了机械手的方式模拟人手采点的方法,操作无需记忆采点顺序,并有自动寻找关节坐标窗口的功能。     

阿基米德和刘徽求积的"余部分割法"

古代的西方和东方,在相距万里之遥的希腊和中国,两位数学科学的巨人--阿基米德和刘徽,在他们各自独立地解决几何学的重大课题--求积问题时,不约而同地采用了"余部分割法",而且他们论证问题的方式和步骤也有着惊人的相似之处.这不能不说是数学史上的一个奇迹.在某些特定的场合,这种"余部分割法"在讨论问题时确实有它的特别便捷之处.     

投影ESOR迭代求解双边障碍问题

在本文中我们研究了求解双边障碍问题的ESOR迭代算法.证明了由此算法产生的迭代序列至少存在一个聚点,该聚点是双边障碍问题的解.并且,当矩阵为非退化对称矩阵时,该序列收敛到双边障碍问题的解.     

试论向量在几何中的应用

向量在解决数学问题中有着广泛的用途。利用向量知识解决几何问题可以将“定性”研究转变为“定量”分析,使复杂问题简单化。从而,使学生掌握“数形”结合的方法,提高解决问题的能力。     

连续型遗传算法和遗传规划在投影变换中的应用初探

回顾了地图投影变换的基本方法,阐述连续型遗传算法和遗传规划的原理和方法,探讨这两优化方法在地图投影变换中的应用.     

Assessing the effectiveness of learning solid geometry by using an augmented reality-assisted learning system

This study integrates augmented reality (AR) technology into teaching activities to design a learning system that assists junior high-school students in learning solid geometry. The following issues are addressed: (1) the relationship between achievements in mathematics and performance in spatial perception; (2) whether system-assisted learning can improve the spatial perceptions of students; (3) whether students with high, average and low academic achievement learn effectively after taught with system assistance; (4) system usability; (5) system task load; and (6) the relationship among various factors. Study participants were 76 students from Tainan City, Taiwan. Qualitative and quantitative data are obtained using pre- and post-system-assisted learning paper–pencil tests, a system usability scale, National Aeronautics & Space Administration Task Load indeX, and observations and focus group interviews. Analysis results indicate that students' math scores and spatial perception during the test closely correspond to each other. Additionally, system-assisted can improve the spatial perceptions of student. Regarding group differences related to the significance of impact, students with average and low academic achievements exhibit small and medium levels of effectiveness, but are insignificant in high academic achievement students. As for system usability, students with low academic achievements demonstrate a positive attitude toward the intensive programs provided by the system. However, the correlation between students’ learning effectiveness and system usability/task load is low.     

高等几何与初等几何的关系

高等几何是数学学科中的一门基础课程,其中有现代数学的思想和学习方法,它是初等几何的拓展,拓展了初等几何的解题方式,使初等几何的方法更加丰富,加深了初等几何的研究内容,延伸了初等几何的学习范围。高等几何有助于培养学生的几何基础,提高学生解决几何问题的能力,因此,学生应该加大对高等几何的重视程度,并认真研究高等几何在初等几何应用中的指导作用。文章主要是探讨高等几何和初等几何的关系。     

基于几何着色器的逼真运动模糊实现

运动模糊为视频游戏提供了速度的真实感。这里通过几何着色器生成运动轨迹几何,结合顺序无关透明保证运动轨迹虚实得当,最后配合高精度的顶点纹理拾取技术形成纹理模糊。该方案在取得逼真效果的同时,受运行帧数的影响小,效果稳定。局限是几何着色器运算量较大,且当运动轨迹加长到一定程度,由于几何着色器输出流容量存在瓶颈,会影响其正常运行。     

Accelerated matrix recovery via random projection based on inexact augmented Lagrange multiplier method

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.