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On the basis of classical mechanics,the author derived a series of typical vector and matrix formulas for solving the problems of a particle that takes part in plane complex movements.

本文在经典力学的基础上，提出求解动点作平面复合运动的直接矢量导数方法和矩阵方法的定型公式。

For TSFEM, the formulas of the mean value and the variance of water head at each node are derived directly with Taylor series expansions.

由此可计算出每个节点水头的均值、方差和协方差，这样就获得模型结果的不确定性。

These formulas have been tested with several mediums and Langevin diamagnetic magnetic susceptibility of helium, and the results are in good agreement with the measured data.

应用电子云导体模型和能量守恒原理，导出介质折射率表达式，并用表达式计算了几种介质的折射率，计算结果与实测值符合很好。

Tooth Proportions.—There are 17 pitches: 2.5/5, 3/6, 4/8, 5/10, 6/12, 8/16, 10/20, 12/24, 16/32, 20/40, 24/48, 32/64, 40/80, 48/96, 64/128, 80/160, and 128/256. The numerator in this fractional designation is known as the diametral pitch and controls the pitch diameter; the denominator, which is always double the numerator, is known as the stub pitch and controls the tooth depth. For convenience in calculation, only the numerator is used in the formulas given and is designated as P. Diametral pitch, as in gears, means the number of teeth per inch of pitch diameter.

齿比——一共有17种齿比：2.5/5，3/6，4/8，5/10，6/12，8/16，10/20，12/24，16/32，20/40，24/48，32/64，40/80，48/96，64/128，80/160和128/256在这一系列的分数中的分子是径节，径节的大小决定了节圆的直径；而分数中的分母通常是分子的两倍，分母是残余径节，它的作用是控制齿槽的深度为了方便计算，在所有的公式中都使用分子作为计算参数，并且与齿轮的表示方式一样定义为径节P尺寸，也就是在节圆上，每英寸长度上的齿数

Give the structural formulas and IUPAC names for the diene isomers, C7H10, having a cyclohexyl ring.

答：给出分子式为C7H10的二烯烃的结构式，并用IUPAC命名

My performance in the graduate seminars of Differential Calculus and Mathematical and Physical Formulas shows that I have got a good grasp of the fundamentals of mathematics.

我的表现在研究生研讨会的微分学与数学和物理公式表明，我有一个很好的把握其基本的数学。

Application of FLAC and numerical differential to surface deformation observation;2. The formulas solving numerical differential and integral of discrete function arc deduced in this paper.

推导了三次样条插值在求解列表函数的数值微分与积分的公式，给出了余项估计，编写了用于求解数值微分与积分的通用程序，通过数值算例表明，三次样条在插值逼近中具有非常好的性质。

Most of tha main lateral and directional flying qualities are collected and expressed in simple formulas with which the relation between vertical tailplane area or vertical tailplane volume and the wing dihedral angle are determined.

在对主要的横航向飞行品质要求进行分析整理的基础上，本文提出了一种"界限线"法，可供飞机初步设计时，选择合适的垂尾和机翼上反角之用。

The correlative formulas for pressure drop of cross-flow rotating packed bed was deduced with the method of dimensional analysis .

采用因次分析的方法推导出错流旋转填料床气相压降的无因次关联式。

When the herbs from ancient Egypt spread to Greece, Hippocrates collected by more than 400 kinds of herbs, formulas and Dios Corris writing "drug" theory of the book's efforts to formally established the Herb in the medical field status.

当香草由古埃及传到希腊后，藉由希波克拉提斯收集的400余种香草配方与迪奥斯科里斯撰写《药物论》一书的努力，正式确立了香草在医疗领域的地位。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。