一类求解奇异延迟微分方程的两步连续Runge-Kutta方法的收敛性

本文给出了一类求解延迟落在当前积分步内延迟微分方程的两步连续Runge-Kutta方法。在一定条件下我们证明了方法收敛性,数值试验表明方法是有效的。     

关于正定可对称化线性代数方程组的预对称正则化算法

1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文[1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法[12,16,17]．但非对称的系数     

α-Fe_2O_3纳米微粒/硬脂酸交替L-B膜的结构表征

纳米微粒(NP)是一个新的物质层次,它具有一系列新异的物理、化学特性,涉及到大块样品中所忽略的,或根本不具有的基本物理、化学问题.用NP 制造新型的人工功能材料具有广泛的潜在应用.一个有意义的挑战是能否对NP 进行有序的组装.Zhao andFendler 等曾利用Fe_3O_4NP 进行有序组装的尝试.我们也在前期的初步研究中利用Langmuir-Blodgett(LB)技术对7nm 的α-Fe_2O_3 NP 进行了有序组装的探索,获得了α-Fe_2O_3 NP-硬脂酸交替LB 多层膜(FNSLF).然而这种交替膜的有序情况还不十分清楚.     

纤维素基磁性聚偕胺肟树脂吸附锂

研究了氯化锂浓度、树脂含量和溶液的ＰＨ对碱式纤维素基磁性聚偕胺肟树脂吸附Ｌｉ＾＋离子能力的影响。在适当条件下，每个偕胺肟基可吸附两个Ｌｉ＾＋离子。     

Differential geometry of tensor product immersions

In this article we obtain the best possible estimates of the type number of tensor product immersions and investigate tensor product immersions with lowest possible type. Several classification theorems in this respect are then proved.     

The Micro-Theory of Ultra-Short Pulse Propagating in Nonlinear Fiber

The modified quantum nonlinear Schrodinger equation of ultra-short pulse propagating in fiber is derived using dispersion relation and the Hamiltonian of the transmission system. The derived equation is solved with linearization approximation, and modulation instability is analyzed. The equation is also solved with Hartree approximation. The results indicate that pulse power, loss and self-steeping effect change the critical frequency, the maximum gain and the gain spectrum range, but the third order dispersion has no effect on modulation instability. The expectation value of optical field is average of a set of modified classical solitons, and higher order terms change the amplitude, pulse position and phase of soliton.