EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above.     

ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposi-tion is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.     

Ab initio calculations on the spectroscopic constants, vibrational levels and classical turning points for the 21∏u state of dimer 7Li2

The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.     

具有转向点曲线的椭圆型方程奇摄动边值问题

The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem,the asymptotic behavior of solution for the boundary value problem is studied.     

渐变折射率光波导转折点外指数衰减场的推导

证明了渐变折射率光源导转折点外的模场呈简单的指数衰减形式,指数衰减系数可用一恒定的等效折射率定义。     

基于光反馈自混合干涉效应波形转折点的智能识别

对光反馈自混合干涉信号波形转折点的智能识别进行了理论分析和实验研究。首先经对光反馈自混合干涉信号特点的分析，发现其波形转折点可以作为外部物体运动位移实时测量的依据。通过对信号波形的逐步处理可以获得波形转折点的位置，以此为基准点可以实现位移的精测。实验测试结果同理论分析吻合较好。若系统进入较复杂状态，识别出的位置与其实际位置出现偏差，不再是单一值，可以对转折点位置的所有值取平均，从而得到其对应的精确位置。     

有效利用图像信息解决问题

在初中数学学习中,坐标系的建立是代数进入数形结合阶段的转折点.利用数形结合的思想解决函数问题,能起到直观、准确的作用,因此图像是研究函数的重要手段.下面举例简单说明如何利用图像解决函数问题.     

基于马赫-曾德干涉仪的色散转折效应及其传感性能模拟研究

设计了工作在近红外波段的硅基马赫-曾德尔干涉仪(MZI)折射率传感器。理论和仿真模拟分析表明,通过改变MZI的结构参数可以对输出干涉谱的色散转折特性进行调控,经过优化后色散转折点(DTP)所对应的波长可以调至近红外波段(1550 nm),通过改变MZI周围的环境折射率(SRI)可以使折射率灵敏度达到37500 nm/RIU。由于DTP两侧的干涉条纹对外界折射率响应有相反的特性,将干涉波谷的相对漂移量作为检测对象,能够将灵敏度提高2倍,即75000 nm/RIU。不同于常规基于光栅和波导耦合构架的DTP传感器,所设计的DTP结构中两个干涉模式互不相关且均可独立调控,并可根据需要灵活调控色散转折波长。     

迈克耳孙干涉仪测折射率时的异常现象研究

针对迈克耳孙干涉仪以激光为光源测量玻璃板折射率所产生的异常现象,本文从几何光学理论出发进行了讨论,简明直观地给出了干涉条纹吞吐转折点与零光程点、光程、虚光源相对位置之间的关系,并与实验数据进行了对比.