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We found that it is the effect of odd-order term of f which describe the total energy collocation between forward wave and backward wave that causes the difference of modulation instability between normal dispersion region and abnormal dispersion region.

第三，根据增益谱的比较，我们从色散关系式中看到了产生这种变化的原因。正是由于存在f奇次项的影响而导致了这种在正常色散区和反常色散区变化趋势的不同。

Look from historical condition,; of economic technology instability looks from external environment, the infrastructure such as traffic, communication, irrigation works is backward, invest good environment difference, return rate is low.

从历史条件看，经济技术基础薄弱；从客观环境看，交通、通讯、水利等基础设施落后，投资硬环境差，回报率低。

If the starting point is so far out of focus that the sensor can't identify a phase difference, the camera racks the lens once forward and once backward to find a detectable difference.

如果起始点离聚焦点太远以至于对焦感应点无法确认相位差，相机会把镜头推拉各一次以获得可检测的相位差，否则就停止工作。

While using three—points backward finite difference to imitate the radiation condition, we accept Raven's〓 idea to shift collocation points upstream a short distance.

在用三点向后差分格式模拟辐射条件时，接受了Raven〓的建议，将单元控制点向后移动了一段距离。

Central difference method and backward difference method were used for transient thermal analyzing,and the result suggested that two methods have same accurate for this problem.

太阳辐射热流、地球红外辐射热流及地球反照热流是航天器产生不均匀时变温度场主要热量来源。

By analyzing the reason of the numerical oscillation phenomenon and computing the temperature field in plate rolling process,it is found that numerical oscillation can be restrained effectively when the heat capacity matrix is lumped by using backward difference scheme.

近年来，许多研究人员采用有限元法分析热轧和淬火等过程中的瞬态温度场。

An improved derivative estimation algorithm with a low-pass filter that can suppress the influence of high-frequency noise is suggested to remove potential drawbacks of the backward difference that was applied in neural network inversion dynamic compensation method, such as large estimation error in the presence of noise and price increase of hardware realization when high estimation accuracy is required.

针对神经网络逆动态补偿策略中基于向后差分的微分估计算法在噪声环境下存在较大的微分估计误差，且提高估计精度会增加硬件成本等缺陷，提出了改进的微分估计算法，并以加速度传感器为例，设计了动态补偿实验装置，给出了基于改进的微分估计算法的动态补偿算法的实现步骤。

The control volume integration was applied to deduce the discrete expressions of the convection-diffusion equations. The staggered grid and SIMPLE algorithm were introduced to deal with coupling between pressure and velocity, and then the numerical computation expressions of such variables as fluid flow velocity and pressure were deduced. Using the backward difference method and incremental theory to discretize the governing equations for fields of chemical reaction, material structure and chemorheology, the numerical computation expressions of variables such as the monomer conversion, average molecular weight and fluid viscosity were constructed.

应用控制容积积分法导出了对流—扩散方程的离散表达式，引入交错网格技术与SIMPLE算法，实现了耦合的压力场与速度场的分离式求解，推导得到了流体的流动速度、压力等物理量的数值计算式；采用向后差分方法和增量方法，实现了化学反应场、材料结构场、化学流变场控制方程的离散，获得了反应转化率、聚合物平均相对分子质量、流体黏度等物理量的数值计算式。

Because the diffusive term is discretized with divided forward difference or divided backward difference according to the sign of convection velocity, these methods keep first order accuracy for diffusive term.

3.2考虑规则网格上的一维和二维定常型对流占优扩散问题，离散方法采用了有限体积方法及普通的有限差分方法，基本离散思想是将对流项提高到二阶精度，扩散项则根据对流速度的方向决定采用向前或向后差商离散。

Those equations are dispersed in space by iso-parameter elementmethod and in time by using backward difference. A numerical simulator is established byFortran, the ideas of high part make the of structure program clear, maintain easy, calculationeffective.

在此基础上利用Fortran语言编制了有限元方法的油藏模拟器，采用等参元对渗流方程在空间上离散，采用向后差分在时间上离散，线性方程组的求解采用变带宽高斯消去法，该方法充分利用刚度矩阵呈条带状和其对称性的特点，大大减少了所需存储空间。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。