Intermediate Self-similar Solutions of the Nonlinear Schrodinger Equation with an Arbitrary Longitudinal Gain Profile

We study pulse propagation in a normal-dispersion optical fibre amplifier with an arbitrary longitudinal gain profile by self-similarity techniques. We show the functional form of the development of low-amplitude wings on the parabolic pulse, which are associated with the evolution of an arbitrary input pulse to the asymptotic parabolic pulse solution. It is found that for the increasing gain the amplifier output corresponding to the input Gaussian pulse converges to the asymptotic parabolic pulse solution more quickly than the output obtained with the input hyperbolic secant pulse, whereas for the decreasing gain the input pulse profiles have nearly no effect on the speed of convergence to the parabolic pulse solution. These theoretical results are confirmed by numerical simulations.     

同一法证明圆锥曲线光学性质及应用举例

1 圆锥曲线的光学性质 1.1 椭圆的光学性质:从椭圆一个焦点发出的光,经过椭圆反射后,反射光线都汇聚到椭圆的另一个焦点上(如图1.1)     

三角形顶点落在函数图象上的一类问题举例解析

三角形顶点落在函数图象上的一类问题频频出现在近几年的各类考试中,也成为了中考数学试题的一个新的热点.这类问题往往将等腰三角形、正三角形、坐标、函数、方程、解直角三角形等知识结合在一起,还渗透了数形结合、转化、分类讨论等数学思想方法,因此,具有很强的综合性和探究性.本文拟举在2009年全国     

Energy of a Polaron in a Wurtzite Nitride Finite Parabolic Quantum Well

The effects of electron-phonon interaction on energy levels of a polaron in a wurtzite nitride finite parabolic quantum well （PQW） are studied by using a modified Lee-Low-Pines variational method. The ground state, first excited state, and transition energy of the polaron in the GaN/Al0.3Ga0.7N wurtzite PQW are calculated by taking account of the influence of confined LO（TO）-like phonon modes and the half-spaee LO（TO）-like phonon modes and considering the anisotropy of all kinds of phonon modes. The numerical results are given and discussed. The results show that the electron-phonon interaction strongly affects the energy levels of the polaron, and the contributions from phonons to the energy of a polaron in a wurtzite nitride PQW are greater than that in an A1GaAs PQW. This indicates that ehe electron-phonon interaction in a wurtzite nitride PQW is not negligible.     

Optical, Energetic and Exergetic Analyses of Parabolic Trough Collectors

Parabolic trough collectors generate thermal energy from solar energy. Especially, they are very convenient for applications in high temperature solar power systems. To determine the design parameters, parabolic trough collectors must be analysed with optical analysis. In addition, thermodynamics （energy and exergy） analysis in the development of an energy efficient system must be achieved. Solar radiation passes through Earth＇s atmosphere until it reaches on Earth＇s surface and is focused from the parabolic trough collector to the tube receiver with a transparent insulated envelope. A11 of them constitute a complex mechanism. We investigate the geometry of parabolic trough reflector and characteristics of solar radiation to the reflecting surface through Earth＇s atmosphere, and calculate the collecting totM energy in the receiver. The parabolic trough collector, of which design parameters are given, is analysed in regard to the energy and exergy analysis considering the meteorological specification in May, June, July and August in 1sparta/TUrkey, and the results are presented.     

从一道中考复习题谈学生发散思维的培养

发散性思维是不依常规,寻求变异,对给出的材料、信息从不同的方向、途径和角度去设想,探求多种答案,最终使问题获得圆满解决的思维方法.其特点是:不拘泥于常规,充分表现出思维的流畅、变通;追求独特新颖的设想,在解决问题的过程中,有所发现、有所创新、有所突破.教师在教学过程中需要有意识地去培养学生的这一思维能力.本文从一道中考复习题中引导学生灵活运用割补法求图形的面积这方面人手,谈谈如何让学生求变、求异,以培养他们的发散性思维能力.     

圆锥曲线定义的几何证明

用一个不垂直于圆锥的轴的平面截圆锥，当截面与圆锥的轴夹角不同时，可以得到不同的截口瞄线，分别是椭圆、双曲线、抛物线，通常把它们统称为圆锥曲线．那么，为什么截口曲线是椭圆、双曲线或抛物线呢？     

抛物线焦点弦的性质与应用

经过抛物线焦点且被抛物线截得的线段叫做抛物线的焦点弦.它引人注目,是一个非常重要的几何量,与其相关的问题是高考的一