圆锥曲线的弦对定点张直角的一组性质

最近文[2]对文[1]中关于抛物线的弦对顶点张直角的一个充要条件作了推广,得出椭圆和双曲线的弦对顶点张直角的几个充要条件.本文我们要探讨的问题是将圆锥曲线的顶点改为圆锥曲线上其它任意的一个定点时,若所张角依然为直角,那么弦会过定点吗?反之弦过此定点时,弦所张角会为直角吗?回答是肯定的,即有下面的:     

光子晶体线缺陷波导中的光孤子通信研究

采用平面波展开法分析光子晶体线缺陷波导结构的色散效应,用理论结合数值模拟的方法研究了光孤子的产生机理,给出了波导的色散曲线和入射脉冲的透射谱。结果表明群速度色散(GVD)和自相位调制(SPM)同时起作用时能够实现光孤子传输。     

高中数学变式探究教学案例

直线和圆锥曲线位置关系的相关问题是考查学生数学综合能力的主要载体,对相关问题的变式探究也是培养学生数学基本思想方法、强化数学能力的重要途径.2013年全国高中数学联赛的一道关于抛物线的试题是研究与直线与抛物线位置关系有关的度量问题及轨迹问题的好素材.     

执著人生 无悔情怀——访北京邮电大学张晓光教授

随着Internet、数字电视、可视电话等通信工具在现代社会日新月异的发展,人们对信息传输量的要求日益增加,这促使光纤通信系统的码率不断提高。当传输码率提升到10Gb/s以上时,光纤偏振模色     

探讨抛物线的切点弦性质

圆的切点弦问题蕴涵着圆的许多别具一格的几何性质，同样地，抛物线的切点弦问题的性质也很精彩。近几年来，以抛物线的切点弦性质为背景的高考试题频频亮相，以其独特的魅力，尽显风骚。本文对抛物线的切点弦问题的性质做简单的归纳与思考。     

一个重要的结论及其推论

原型 如图1，物体做平抛运动，抛物线上任意一点P（x，y）的速度方向的反向延长线交x轴于A点，则A点的横坐标为——。     

抛物线的几个性质

在高三复习中，有这样一个问题：已知抛物线C：y=x^2，过Q（0，2）的任一直线与曲线C交于M，N两点，过点M和N的切线的交点为尺，求R的轨迹方程．     

Synthesis and properties of hyper-dispersants

The synthesis and properties of three kinds of hyper-dispersants are studied in this paper, which are non-terminated, carboxyl-terminated and polyethylene imine grafted poly(hydroxyl carboxylic acid) ester. The hyper-dispersants are synthesized by the materials of 12-hydroxy-stearic acid, stearic acid and polyethylene imine, which are used to improve the dispersion properties of nano titanium dioxide (nano-TiO₂) in low-concentration resin solution system. The influences of hyper-dispersants on the viscosity and stability of the system are studied. It is found that polyethylene imine grafted hyper-dispersant has the best dispersion performance in nano-TiO₂ dispersion system, and the optimal content of the hyper-dispersant is 4%. Project supported by the Shanghai Leading Academic Disciplines (Grant No.T0105), and the Key Laboratory of Science & Technology of Eco-Textile (Donghua University), Ministry of Education of China     

Flat-top and low-dispersion optical interleavers based on nested prism pair structure

A novel flat-top and low-dispersion optical interleaver using ring cavities (RCs) in a Mach-Zehnder interferometer (MZI) is proposed. It is composed of eight mirrors and two nested prism pairs. Each prism and the two mirrors behave as a RC. Phase shift of RC is a periodic function of the frequency of the input light which acts as a phase dispersive mirror. The two phase shifts needed to achieve a flat-top spectral passband are provided by Fresnel reffectivities at the prism-air interface of the two RCs. The...