聚甲醛结晶动力学研究

用解偏振光强法和差示扫描量热法（ＤＳＣ）分别研究了聚甲醛和聚甲醛助剂Ｐ的等温结晶动力学和非等温结晶动力学。探讨了助剂Ｐ对聚甲醛的结晶成核作用。     

第三类Painlevé方程(δ=0或γ=0)解的渐近性态

对带有一般实参数第三类Painlevé方程,已有γ<0,δ>0时,解的有界性以及振荡渐近解的表达形式的结论.在本文中,我们给出当δ=0或γ=0时其振荡渐近解的表达形式.     

CH-γ方程的多孤子解

利用Darboux变换得到CH-γ方程的多孤子解, 其中一些解的性质与CH方程的不同.     

基于RBC模型的动态随机一般均衡的数值解

以一般均衡为框架,引入随机变量的动态随机一般均衡系统,由于模型的庞大和函数形式的复杂,往往不能给出明确的数值解.本文给出几种操作性强的、有效的寻求一般化模型数值解的方法,并通过介绍模型参数确定的办法,使得理论的模型有了现实的含义.     

四阶方程两点边值问题Hermite有限元解的渐近展式与外推

1引言有限元解的渐近展式是提高微分方程数值解精度的重要工具,比如亏量校正和外推就是建立在有限元解的渐近展式的基础之上．许多作者对此进行了大量的研究(见[1]-[4]),特别是文[1],提出了在研究有限元解的渐近展式中十分有用的能量嵌入技巧．本文利用能量嵌入定理得到了四阶方程两点边值问题Hermite有限元解及其二阶平均导数的渐近展式,进一步我们还讨论了它们的Richardson外推公式．考虑四阶方程两点边值问题     

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

STABLE SOLUTION OF TIME DOMAIN INTEGRAL EQUATION METHODS USING QUADRATIC B-SPLINE TEMPORAL BASIS FUNCTIONS

This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.     

关于离散HJB方程的下解与上解

本文讨论HJB方程上、下解的几个性质,并讨论了从上解出发的一个迭代法的收敛性.     

非自治时滞微分方程的正周期解

By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.     

一类具有转向点问题的n阶近似解

用Langer变换和Olver变换求得一类具有转向点问题的n阶近似解:y(x)=v(x)ψ(x),其中ψ=λ12-14×(x2-1)14,2332=-λx∫11-τ2dτ,v(z)=A(z,λ)ξ(λ23z)+B(z,λ)'ζ(λ23z).并探讨了其特征值问题,得到λn=4n+1112,n=0,1,2….由此给出了该类问题的解的一般性结论.