差分方程

MGM is introduced to solve field distributions in 3-D electron optical systems. The difference equation, the discrete form of Laplace's equation, is deduced in 3-D Cartesian coordinates. In view of the smooth effect, MGM combines Gauss-Seidel iteration with a technique known as coarse grid correction. Formulae for restriction and prolongation are deduced and expressed in terms of tensors.

将多重网格法引入电子光学系统中三维静电场的计算，对三维笛卡尔坐标系中的差分方程，采用高斯-赛德尔迭代法求解差分方程组，并结合迭代过程讨论了粗网格的误差校正技术；在不同网格层之间进行场值的限制和延拓，推导了三维静电场中的限制、延拓公式并以张量的形式表示。

Some known results are generalized.Second,the global asymptotic stability for a higher order rational difference equation was investigated by using "Subsequence Analysis Method " in Chapter 3,and the "Semi-cycle Analysis Method" is a extension and supplement of "Semi-cycle Analysis Method".

因此，本文第三章应用"子序列分析法"研究了一类高阶的有理差分方程解的全局动力行为，进一步得到了此类高阶有理差分程解得全局渐近稳定的一些充分条件，一些已知的结果被推广。

The key point of this paper made a study of the application of FDTD method to dispersive, nonlinear materials. Two methods are introduced to deal with the relationship between the electric flux density vector and the electric field vector: auxiliary differential equation method and Z transform method.

本文的重点在于研究时域有限差分法在非线性色散媒质中的应用，主要采用了两种方法来处理电通量密度矢量D和电场强度矢量E之间的关系：辅助差分方程法和Z变换法。

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

By applying the comparison theorem and some new analysis technique, some sufficient conditions which guarantee the permanence of the system are obtained. After that, by constructing a suitable Lyapunov function, sufficient conditions which ensure the global attractivity of the system are obtained.

利用差分方程的有关理论，使用与前面不同的分析方法，获得保证该系统永久持续生存的充分性条件；其后通过构造适当的差分Lyapunov函数，得到保证该系统全局吸引的充分性条件。

The analysis in theory proves that cellular automaton is equal with a stochastic process that described by stochastic difference equations. The primary differential equation is expectation of this stochastic process. And its variance function is controllable. These results show that cellular automata are in agreement with primary differential equation in the statistical sense.

理论分析证明：该方法设计的细胞自动机等价于一个可用随机差分方程描述的随机过程，该随机过程以原微分方程为期望函数，并且，其方差函数是可控的，表明细胞自动机和原微分方程在统计意义上是一致的。

This article use the improved integral inequalities with the deviate variable and some skills of inequalities as well as related knowledge about second-order differential equation,to obtain the following results: the classification of limit point case or limit circle case and boundedness for second order differential or difference equation with deviative variable,discussed the classification for certain n-order differential equations,Criteria for the classification of second order differential equation with deviative variable.

本文利用推广的具有偏差变元的积分不等式，结合不等式的一些技巧以及常微分方程的相关知识对一类二阶具有偏差变元的微分方程及一类二阶差分方程极限圆型的分类问题作了相关的研究工作，并且讨论了一类n阶具有偏差变元的常微分方程解的平方可积性与有界性和一类二阶非线性具有偏差变元的微分方程解的有界性。

Numerical dispersion characteristic and impedance relationship of three dimensional perfectly matched layers are analyzed under finite difference approximation in this paper, respectively, which show that numerical dispersion relationship of PML is different from that of the FDTD equations and the impedance of homogeneous PML medium is the same as that of free space.

本文分别分析了有限差分近似下三维理想匹配层的数值色散特性和阻抗关系，分析表明，理想匹配层的数值色散关系有别于时域有限差分方程的数值色散关系；有限差分近似下，均匀理想匹配层媒质的阻抗和自由空间的阻抗相同。

Basic hydro-equipments for transition process, namely movement equipment and continuity equipment, are introduced; characteristic line equipment is detruded and finite difference equipments are gained.

介绍流体过渡过程的基本方程组即运动方程和连续方程；推导了的特征线方程，得出了有限差分方程即特征线方程。

Firstly, the basic principle of Finite-Difference Time-Domain is introduced and the 2-dimensional FDTD equation is derived from the Maxwells equations, calculated by setting up the appropriate excitation source, cell size, the interval of space and time.

首先，介绍了时域有限差分法的基本原理，从麦克斯韦方程出发，建立二维空间中的时域有限差分方程，通过设置合适的激励源、网格尺寸、空间和时间步长进行计算。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。