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Initial random imperfections of composite panels are assumed to be Gaussian random fields and simulated numerically from their mean and autocovariance functions. Lindstedt-Poincare's perturbation technique is employed to solve the resulting nonlinear equation in the vibration analysis of imperfect composite panels. Monte Carlo analyses are performed for detailed numerical calculations.

层板之随机性几何缺陷以高斯随机场来描述，并利用其平均值函数及自方差函数来做数值的模拟；以Lindstedt-Poincare微扰方法来处理缺陷复合层板之非线性运动方程式，并使用蒙地卡罗法来做详细的数值分析。

Turing Award Citation): For his work on numerical methods, automatic coding systems, and error-detecting and error-correcting codes.

( 授予 Richard Hamming 图灵奖以表彰其在)数字方法，自动编码系统和错误检测和错误纠正编码领域的杰出贡献。

Numerical experiments show that the new method of automatic programming is very practical.

计算实例表明了这种新的自动程序设计方法的可行性和实用性。

Simple upper bounds of signal to noise ratio improvement factor are derived for the suppression of a narrowband first-order autoregressive process and analytical conclusions corroborated by numerical examples.

研究了判决反馈滤波器在直扩系统中估计和抑制窄带干扰的性能，给出了判决反馈滤波器抑制一阶自回归干扰时信噪比提高因子的闭合表达式的上界。

Via these formulas, the numerical solutions are incorporated with the analytical solution on the auxiliary circle.

在此基础上进一步建立了杂交元算式，它能保证在圆形人工边界上数值解和解析解两种场函数及其导数的相容性。

Based on the chemical equilibrium flow assumption, the electron density at the exit of the nozzle is determined using the minimum free energy rule. A numerical model based on auxiliary difference equation is derived to simulate the plasma in the time domain and the calculating results are compared with that using Z transform.

以化学平衡流动为前提，采用最小自由能方法确定火箭发动机喷口处的电子密度；验证了基于辅助差分方程和Z变换方法对羽流电磁特性进行时域建模的正确性。

In the process of discretization of the auxiliary function, the traditional central difference formula is replaced by the backward difference formula, and numerical results show the method is of good stability.

在辅助函数的离散过程中用后向差分公式代替传统的中心差分公式，数值结果显示出良好的稳定性。

Although the Preissman scheme of KP equation is multisymplectic, it took too efforts to realize, Hence we elimate the auxiliary variable by a trivial computation and obtained the multisymplectic forty-five points scheme of KP equation. And then, we test this forty-five points scheme on soliton and solitary waves over long time intervals, the numerical results shows the propagation and interact of soliton and solitary waves.

但是在实际的数值实验中，由于需要计算共轭动量的值，Preissman格式需要占用的计算内存比较大，计算时间比较长，因此我们在数值格式中消去共轭动量，最后得到与多辛Preissman格式等价的一个多辛45点格式，我们用这个格式进行了数值实验，数值实验结果很好地显示了孤立子和孤立波的传播与碰撞。

The explicit form of this method is very similar to that of the Newmark explicit method while its numerical characteristics are exactly the same as those the constant average acceleration method.

此新发展的外显式积分法其一般式和Newmark外显式积分法非常相似，然而，它的数值特性却完全与等平均加速度积分法一样。

In Chapter 1,we consider the numerical methods for the averaging model.

为引言部分，给出描述问题的数学模型及假设条件。2。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新