解椭圆型方程的有限元法

本文阐述的解椭圆型方程的有限元方法，就是由椭圆型方程得到的线性代数方程组的一个分块解法．我们对节点做适当的排序，使得系数矩阵主对角线上的子块都是（不大于３）的多对角形．这样在运用电子计算机计算时，可以有效地节省计算机的存贮和运算工作量并且程序也远较其它处理稀疏矩阵的方法简单．     

带有临界指数的Emden-Fowler方程

本文讨论了 Emden-Fowler 方程渐近边值问题解的性质,证明了解 y(t)的第j个零点 T_j(r)满足 lim_((?)→0+)T_j(r)=T_j 及 lim_((?)→+∞) T_j(r)=L_j,其中 T_j 及 L_j 为确定的常数.     

关于一类连续最优控制问题的一种可实现的离散方法

本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法，此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象，文中给出这种做法的理论证明和实现方案。     

数值求解对流占优问题的分步预估校正有限差分——拟谱杂交方法

提出了数值求解对流占优问题的一种无条件L²稳定和误差L²指数地趋于零的分步预估校正有限差分——拟谱杂交方法;对非线性的对流占优问题,在数学上严格证明了这种格式的稳定性和收敛性,给出了解的误差估计式,并通过数值实验考核了方法的优越性.     

一类非方系统的Morgan问题 *

讨论一类特殊情形的非方系统的Morgan问题,得到了问题有解的充分必要条件,给出了这一类系统判断其Morgan问题是否有解的算法.     

LINUX下一种改进的音频会议系统的实现方法

提出了一种计算缓存区大小的改进方案．根据RTCP包中反馈回的丢包率,动态地改变音频数据的发送策略,有区分地采取差错控制手段,提高了网络带宽的利用率．在此基础上,设计了一个以RTP协议为基础的音频会议系统的模型,并在Linux平台上用多线程的方法实现了各个模块．模拟实验表明,该系统能自适应地调整缓存区大小和数据包的发送策略,在实时性及带宽资源的利用上都达到了较理想的效果．     

四阶非线性特征值问题的正解

本文考虑了四阶非线性特征值问题d4u/dt4=λg(t)f(u,u″),0＜t＜1,u(0)=u(1)=0,au″(0)-bu″′(0)=0,cu″(1)+du″′(1)=0.其中g(t)∈C((0,1),[0,∞)),f(u,v)∈C([0,∞)×(-∞,0],[0,∞)),a≥0,b≥0,c ≥0,d ≥ 0,且△=ac+ad+bc＞0.利用锥压缩与拉伸不动点定理,获得了上述问题正解的存在性结果.     

Predictor-Corrector Smoothing Methods for Monotone LCP

In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1],the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1‘ is obtained under the assumption of nonsingularity of generalized Jacobian of Φ(x,y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The efficiency of the two methods is tested by numerical experiments.     

The General Solution of Ming Antu＇s Problem

In two centuries ago,Ming Autu discovered the famous Catalan numbers while he tried to expand the function sin(2px) as power series of sin(x) for the case p=1,2,3.Very recently,P.J.Larcombe shows that for any p,sin(2px) can always be expressed as an infinite power series of sin(x) involving precise combinations of Catalan numbers as part of all but the initial p terms and gave all expansions for the case p=4,5.The present paper presents the desired expansion for arbitrary integer p.     

Cauchy Problem of Some Doubly Degenerate Parabolic Equations with Initial Datum a Measure

This paper discusses the Cauchy problem of the equation