BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS

The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itself, it is proved that the maximal singular integral is bounded from L∞to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions.     

马歇尔-勒纳条件的实证研究

本文从人民币实际汇率变动是否会对我国贸易收支产生影响出发，基于马歇尔．勒纳条件，对计算贸易弹性常用的OLS回归模型进行了改进，建立了向量自回归误差修正模型来估算我国的国际贸易弹性。实证研究表明：我国进出口需求的价格弹性之和大于1。因此人民币贬值可改善贸易收支；反之升值将使贸易收支恶化。     

具有急慢性阶段的MSIS流行病模型阈值和稳定性结果

系统研究了具有急性和慢性两个阶段的MSIS流行病模型.由两节构成,第1节建立和研究了具有急慢性阶段的MSIS流行病模型;第2节在第1节的基础上建立和研究了具有慢性病病程的MSIS流行病模型.第1节的模型是四个常微分方程构成的方程组.第2节的模型既含有常微分方程,又含有偏微分方程.运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式.证明了当R0<1时,无病平衡态是全局渐近稳定性,给出了各模型地方病平衡态的存在性和稳定性条件.     

中立型脉冲微分方程正解的存在性

本文利用Banach压缩映射原理，讨论了中立型时滞脉冲微分方程正解的存在性。     

串联双环光微谐振器的滤波特性

详细研究了串联双环光微谐振器的光带通滤波特性，给出了其通带带宽的公式，分析了出／入环光耦合系数和环间光耦合系数对通带特性的影响，计算并特别强调了滤波通带的结构特点，也分析了微环中存在的光损耗对串联双环光微谐振器的滤波特性的影响。     

Optimal Control of Non-well-posed Heat Equations

This work is concerned with Pontryagin＇s maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.     

Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.     

综合题新编选登：题136

函数f(x)对一切实数x，y均有f(x y)-f(Y)=x(x 2y 1)成立，且f(1)=0．