空间解析几何教学改革初探与实践

空间解析几何是大学数学类专业的一门重要基础课,也是数学专业学生深入学习几何学专业知识的基础课程。本文通过在课堂中引入雨课堂、数学史和MATLAB,提高了学生的学习效率。     

欧拉线定理的推广

采用质点几何学的方法证明了欧拉线定理，并将其推广到高维以及位似形的情况，并讨论了四面体的外心、内心及奈格尔点．     

呱氨托美丁合成工艺的改进

以托美丁钠为起始原料．与氯甲酸异丁酯、甘氨酸反应生成中间体托美丁甘氨酰胺,再与氯甲酸异丁酯、愈创木酚反应制得呱氨托美丁,同时对其的精制方法进行了研究。结果显示：改进后的工艺反应条件温和,操作简单,提高了目标物的质量,总收率65％,具有较大的产业化生产优势。     

Disturbance rejection control based on acceleration projection method for walking robots

This paper presents a disturbance rejection scheme for walking robots under unknown external forces and moments. The disturbance rejection strategy, which combines the inverse dynamics control with the acceleration projection onto the ZMP （zero moment point）-plane, can ensure the overall dynamic stability of the robot during tracking the pre-computed trajectories. Under normal conditions, i.e., the system is dynamically balanced, a primary inverse dynamics control is utilized. In the case that the system becomes unbalanced due to external disturbances, the acceleration projection control （APC） loop, will be activated to keep the dynamic stability of the walking robot through modifying the input torques. The preliminary experimental results on a robot leg demonstrate that the proposed method can actually make the robot keep a stable motion under unknown external perturbations.     

基于CT、MRI断层图像的人体三维建模

人体三维几何建模及其可视化显示是生物医学学科的一项基础性研究。CT和MRI等医学成像技术的断层图像可为三维建模提供基础。章论述和介绍了基于CT、MRI断层图像的三维建模系统的关键技术和相关实现原理。     

The transition to secondary school geometry: can there be a “chain of school mathematics”?

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children’s transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions about the transition to secondary school and its effect on the teaching and learning of mathematics, primary and secondary school teachers in Greece often depict school mathematics as a “chain” of concepts and procedures. With this metaphor as our reference point, we discuss how ideologies about the teaching of mathematics are enacted in both school levels. We will base our discussion on the analysis of extracts taken from dialogues in primary and secondary school mathematics classrooms in Greece. In our analysis, we employ a Peircean view of semiotics in an attempt to conceptualize students’ rushed introduction to rigor in justifying mathematical statements in secondary school. These extracts are part of a longitudinal study that aimed, on the one hand, to pinpoint discontinuities and continuities in the teaching of geometry between primary and secondary schools and, on the other, to investigate whether a set of curriculum material that we designed could serve as a link in the teaching of geometry between the two school levels.     

优化清蛋糕生产工艺的探讨

本文采用正交试验法对清蛋糕质量影响较大的几个主要的工艺参数进行了研究．通过优化组合，结果得出一条生产清蛋糕的最佳工艺模式。     

Galileo平面几何的一点注记

利用Galileo变换,建立了Galileo几何.讨论了Galileo平面几何中的距离,直线间的交角问题以及Galileo平面上三角形的一些性质.     

线性代数中若干概念在解题中的巧用

本文剖析了线性代数中伴随矩阵、行向量与列向量的乘积、正交矩阵几个较难掌握的概念,由此引出这些概念的一些基本特征和性质.举例介绍了应用这些特征和性质解决线性代数相关问题的技巧.     

Clifford代数与Minkowski平面几何

以Clifford代数为工具，讨论Minkowski平面的几何性质，指明应用Clifford代数在计算机上实现Minkowski几何研究的可行性。