几类特殊四面体的外接球问题

我们知道，每个四面体都有外接球，球心就是各条棱的中垂面的交点，这个点到各个顶点的距离都相等．给出一个四面体求它的外接球半径，是一类常见的问题。下面以近几年的高考题为例来说明几类特殊四面体的外接球半径的求法．     

光学非球面二次曲面常数及顶点曲率的研究

受光学非球面制造过程中诸工艺参数的影响,能否保证非球面顶点曲率及二次曲面常数的精度是一个重要问题。基于二次曲面方程,推导出确定光学非球面二次曲面常数k以及顶点曲率半径r的一组算法,并在对一块口径为760mm×200mm标准非球面反射镜的实际测算中进行拟合,经过优化,拟合精度达到Δk=0.015,Δr=0.341mm,从而有效的控制了光学非球面制造过程中的顶点曲率及二次曲面常数的偏差。     

浅谈GSM系统

 GSM原意为移动通信特别小组(GroupSpecialMobile)。该组织成立于1982年,旨在制定一个欧洲移动通信系统的特性规范,以便使整个欧洲采用一个统一的移动通信制式,让移动通信用户在欧洲各国的移动通信成为可能。今天,所谓的GSM,就是泛欧数字移动通信系统(GiobalsystemforMobileCommunication),它有效地克服了模拟制式移动通信系统存在的频谱利用率低、容量小、制式不统一、联网漫游困难、不能提供数据等非话业务以及话音失真、保密性差等缺点。GSM的发展,弥补了有线电话的严重不足,解决了人们在任何地点、任何时间的通信联络。     

叠砖平衡的一种简单解法

 叠砖的平衡问题(见图1)是一个有趣的力学平衡问题,本文利用质点系质心的定义,介绍一种较为简单的解法。为保持本文的完整性,不妨重述叠砖的平衡问题:N块完全相同的砖块以图1所示方式叠放在一起并保持平衡,每个砖块的长度为l,质量为m,求砖块突出部分的最大长度Lmax。图1考察平衡时,前i-1块砖、第i块砖和第i+1块砖之间的关系。设第i块砖相对于第i+1块砖探出的长度为di。     

一种简易云雾室的制作

本文利用自制云雾室把微观粒子的运动转化为宏观现象，从而供实验观察和研究。     

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

THE EXISTENCE THEOREM OF THE CONE-WEAK SUBDIFFERENTIAL OF SET-VALUED MAPPING

In this paper, the existence theorem of the cone-weak subdiflerential of set-valued mapping in locally convex topological vector space is proved.     

圆锥曲线

1)重点：三种圆锥曲线的定义、标准方程、几何性质(包括范围、轴、顶点、焦点、离心率、准线，对于双曲线还有渐进线)及其应用；直线与圆锥曲线相交弦的中点轨迹问题；待定系数法、运动变化思想、数形结合思想的应用．