On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.     

饮酒驾车模型

据统计,我国每天困饮酒过量而产生的车祸竟达交通事故伤亡总人数的50%-60%,酒后驾车的问题已经引起了社会各界的高度重视.为此本文建立了酒后血液中酒精含量的房室数学模型,从而为司机饮酒驾车提供合理的忠告和建议.     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

一类积分不等式的推广

对一些基本的积分不等式进行了推广，给出了含有n个无关变元的更广泛的非线性积分不等式．利用所得的不等式讨论了某些非线性积分方程解的有界性．     

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。     

四阶非线性边值问题解的存在性与上下解方法

该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.     

甲基对硫磷的快速测定及电化学性质

研究了杀虫剂甲基对硫磷的电化学性质。在pH10．38的Bdtton—Robinson缓冲溶液中，采用微分脉冲溶出伏安法在悬汞电极上得到一个还原峰，峰电位为-0．5V(vs．Ag/AgCl)，本工作对实验条件进行了深入的研究，结合线性扫描伏安法等手段。研究了体系的电化学行为。实验表明，甲基对硫磷在汞电极上具有吸附性，电极反应具有不可逆性。该法用于水果及水样中甲基对硫磷残余量的测定，结果满意。     

一类非线性微分方程的脉冲镇定

针对一般形式的常微分系统提出了脉冲指数镇定的概念，具体研究了一类分离变量型非线性常微分方程的脉冲镇定问题，得到了该方程可脉冲指数镇定的充分判据，全文的概念及结论突出了脉冲在方程稳定性方面的控制效果。