Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients

In this paper, we propose a variational integrator for nonlinear Schrdinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrdinger equations with variable coefficients, cubic nonlinear Schrdinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.     

THE STABILITY OF θ-METHODS FOR PANTOGRAPH DELAY DIFFERENTIAL EQUATIONS

This paper deals with the numerical solution of initial value problems for pantograph differential equations with variable delays. We investigate the stability of one leg θ-methods in the numerical solution of these problems. Sufficient conditions for the asymptotic stability of θ-methods are given by Fourier analysis and Ergodic theory.     

基于连续小波变换FTIR鉴定青葙子及鸡冠子的研究

借助OMNI采样器,应用傅里叶变换红外光谱方法直接、快速、准确地测定青葙子及其伪品鸡冠子的红外光谱。利用连续小波变换对真伪品的红外光谱进行放大处理,以有效突出真伪品间的红外光谱差异程度,从而提高鉴定正确率。采用对信号奇异性具有良好探测能力的Morlet小波做小波母函数,对青葙子真伪品的红外光谱进行若干尺度的一维连续小波变换,在各个尺度下观察青葙子的真伪品的红外光谱的差异程度,从中选择一个差异程度最为明显的尺度来区分青葙子真伪品。结果表明：基于连续小波变换的傅里叶红外光谱分析方法能够有效鉴别同科同属不同种植物中药材。