三边承受线性载荷悬臂矩形板的弯曲

本文利用变分的原理讨论悬臂矩形板的弯曲问题,计算简单,精度较好。     

Construct3D: A Virtual Reality Application for Mathematics and Geometry Education

Construct3D is a three dimensional geometric construction tool based on the collaborative augmented reality system Studierstube. Our setup uses a stereoscopic head mounted display (HMD) and the Personal Interaction Panel (PIP) - a two-handed 3D interaction tool that simplifies 3D model interaction. Means of application in mathematics and geometry education at high school as well as university level are being discussed. A pilot study summarizes the strengths and possible extensions of our system. Anecdotal evidence supports our claim that the use of Construct3D is easy to learn and encourages experimentation with geometric constructions.     

The role of contradiction and uncertainty in promoting the need to prove in Dynamic Geometry environments

In many geometrical problems, students can feel that the universalityof a conjectured attribute of a figure is validated by their action in adynamic geometry environment. In contrast, students generally do not feelthat deductive explanations strengthen their conviction that a geometricalfigure has a given attribute. In order to cope with students' convictionbased on empirical experience only and to create a need for deductiveexplanations, we developed a collection of innovative activities intended tocause surprise and uncertainty. In this paper we describe two activities, thatled students to contradictions between conjectures and findings. We analyzethe conjectures, working methods, and explanations given by the studentswhen faced with the contradictions that arose.This revised version was published online in September 2005 with corrections to the Cover Date.     

韦达定理在解析几何中的应用

在平面解析几何中,经常会遇到求二次曲线的中点弦,求弦的中点,求弦长,给了定弦求关于这弦的共轭直径等问题,这些问题都可借助于韦达定理而简捷地解决。     

Ethene/norbornene copolymerization by [Me_2Si(3-~(tert)BuCp)(N~(tert)Bu)]TiCl_2/MAO-catalyst

ＩＮＴＲＯＤＵＣＴＩＯＮＦｏｒｍｏｒｅｔｈａｎ 1 0ｙｅａｒｓ,ｅｔｈｅｎｅ ｎｏｒｂｏｒｎｅｎｅｃｏｐｏｌｙｍｅｒｓ (ＣＯＣｓ)ｈａｖｅｂｅｅｎｏｆｇｒｅａｔｉｎｔｅｒｅｓｔｔｏｉｎｄｕｓｔｒｙａｎｄｓｃｉｅｎｃｅ,ｂｅｃａｕｓｅｏｆｔｈｅｉｒｅｘｃｅｌ ｌｅ     

基于Matern硬核点过程的无人机辅助蜂窝网络吞吐量分析

无人机与传统的地面蜂窝基站混合组网有望成为一种实现数据高速传输的重要手段。针对这一场景,提出一种针对下行双层异构网络吞吐量性能的分析框架,采用泊松点过程对地面基站的位置进行建模,同时考虑到无人机之间存在的最小安全距离约束,采用Matern硬核点过程对无人机的位置进行建模,利用随机几何工具推导得到用户平均数据速率的简易表达式。根据得到的解析表达式,进而讨论无人机高度和功率控制因子的最优参数组合。结果表明,在提出的网络模型下选择适当的功率控制因子可以在保证地面基站用户速率的同时,有效地提高无人机用户的平均数据速率。     

有限元误差新定义及性质

对矩形有限元误差给出了新的定义及性质,此定义不仅对光滑解适用,而且对非光滑解也适用,从而对非光滑问题的收敛及超收敛性分析找到一种新的方法。     

A general framework for progressive point-sampled geometry

INTRODUCTION With the recent advances in 3D digital photog- raphy and scanning technology, unstructured dense point sets sampled from the surfaces of physical ob- jects have become a new representation of geometric shapes. The shape thus specified is usually referred to as point-sampled geometry (Amenta and Kil, 2004; Liu et al., 2004; Pauly et al., 2003; Zwicker et al., 2002), in which two key techniques are involved: (1) The raw point data P is discrete in nature while the physical ob…     

高等代数与解析几何两课合并的可行性分析及内容编排方案

阐述了高校数学专业高等代数与解析几何这两门基础课在教学内容方面的重复与联系之处 ,对这两门课程合并教学进行了可行性分析 ,提出了两门课程合并内容编排的原则和方案     

价层电子对互斥理论及应用

叙述了价层电子对互斥理论的基础规则；计算出价层电子对数，得到了电子几何排布，从而判断出分子的几何2构型；还介绍了孤电子对存在对分子构型及键角的影响。