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1·Through Taylor expansion and multi-scale technique, macroscopic equation is recovered.

通过对演化方程的泰勒展开并应用多尺度技术恢复了宏观方程。

2·An approximate solution of the paraxial ray equation for cylindrical dense electron beams was obtained by means of the Taylor expansion.

本文提出圆柱形强流电子束的傍轴轨迹方程，可以用台劳展开求出它的近似解。

3·In chapter 7, an interval dynamic optimization method for uncertain structures using the improved 1st-order Taylor expansion is presented.

第七章针对区间参数振动结构提出了一种改进的动力响应的区间优化方法。

4·Nonlinear directly estimating formula for exponential curve which, through fixed point, was derived, by using first order approximation of Taylor expansion.

运用泰勒展开的一阶近似估计推导过定点的指数曲线的非线性直接估计公式。

5·Under the first-order approximation of Taylor expansion, the analytic expression for the defect mode frequency is derived, from which the coupling factor is deduced.

利用泰勒展式的一级近似，得到了缺陷模频率的解析表达式，进而得到紧束缚理论中的耦合因子。

6·To resolve the difficulty of progressive time calculating in normal inverse-time overcurrent curve, two algorithms of zonal table-lookup and Taylor expansion are put forward.

然后针对计算比较困难的一般反时限曲线，介绍了分区查表和泰勒展开法计算时延累加量的算法。

7·The traditional method of calculation for the acceptance parameters by Taylor expansion in three wave interactions is only suitable for the condition of small acceptance parameters.

采用传统级数展开方法计算晶体非线性三波互作用的允许参量。

8·To obtain desired wave characteristics of composite laminate, the varying rate of eigenvalue with respect to the thickness change is approximated by the second order Taylor expansion.

采用一种特征值反求形式的方法用来近似层状复合板的波动特性修改。

9·By means of the Taylor expansion technique, the asymptotic expressions of the dispersion curves at the long wavelength region were derived for flexural and longitudinal vibration modes.

利用泰勒展开技术，给出了长波区域弯曲振动模式和伸缩振动模式的弥散曲线渐近表达式；

10·The stiffness matrix of a hybrid crack-tip singular element is first derived, then by use of first-order Taylor expansion the mean and variance of stress intensity factors are formulated.

文中首先给出了杂交模式的裂纹尖端奇异单元的刚度矩阵，然后基于随机场的局部平均理论和一阶泰勒展开得到了应力强度因子均值和方差的计算公式。