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The balance wheel of a watch is a familiar example of angular harmonic motion.

钟表的摆轮是角谐运动的常例。

On the animated drawing a complex wave is resoleved into three simple harmonic waves with different frequencies and amplitudes.

该动画是由频率和振幅各不相同的三个简谐波叠加成复杂波的情形。

Based on the three dimensional surface data of the face and skull, methods of geometric analysis on them are presented through these parameters with their numerical calculating methods under the landmarks of the anthropologist and anthropometrist are proposed,which is the foundation of the statistical model that will be used in the field; 4Geometric analysis methods that based on the approximation coefficients of spherical harmonic functions are proposed.

以三维面皮和颅骨数据为基础，分别给出了基于公安法医学标志点和人体测量学标志点的几何分析主要途径和方法，确定了几何分析的主要参量，并给出了相关的计算方法，为建立颅面统计模型奠定基础； 4基于球面调和函数的颅面形态学的几何分析方法。

By virtue of method of continuum approximate limit, we obtained the solitons of the vibration of lattice in one-dimensional harmonic and inharmonic chains of polarized molecule, under the conditions considering and inconsidering the interaction of exciton with phonon, through solving moving equations of exciton and phonon.

运用连续极限近似方法，通过求解声子和激子的运动方程，得到了在不考虑激子与声子的相互作用和考虑激子与声子相互作用两种情况下的极性分子简谐链和非简谐链中晶格振动的孤子解，并得出了激子与声子的相互作用的非线性效应类似于晶格三次势的非线性效应，以及相同的非线性效应不论是同时作用还是单独作用都具有相同的非线性效应的结论。

The approximate analytic solution of displacement response which is excited by harmonic alternating current can be ...

考虑到问题的数学模型中含有小参数，周期交变电流激励下的位移响应的近似解析解可以用摄动解法得到。

The zonal translation networks on the unit sphere is constructed with the best approximation of spherical harmonic polynomials and the Riesz means. The Jackson theorem of approximation by such kind of zonal translation is established.

借助于球调和多项式的最佳逼近多项式和Riesz平均构造出了单位球面S上的带形平移网络，并建立了球面带形平移网络对LS(上标 q中函数一致逼近的Jackson型定理。

And use frequency formula or weighted harmonic mean formula of weighted arithmetic mean formula to get its mean value.

利用加权算数平均数的频数公式或加权调和平均数公式求其平均值。

However, the second associated Legendre function is too complicated to compute, so a simple and practical ellipsoidal harmonic series expansion is introduced, and the series solution and integral solution of the Dirichlet boundary value problem and the Neumann boundary value problem under ellipsoidal boundary are given.

鉴于展开式中第二类缔合勒让德函数的计算较为复杂，接着引入一种形式简单、实用的椭球谐级数展开，介绍了椭球界面下Dirichlet边值问题和Neumann边值问题的级数解和积分解。

Further more,we compute the asymptotic expansion of sums involving generalized harmonic number by singularity analysis method.

进一步地，利用奇异性分析方法，求出涉及广义调和数的一些和式的渐近展开。

Both single and double-stable limit cycle flutter states are found in wind-tunnel test. And the conclusion is proofed that the equivalent linearization based on the second order asymptotic solution of KBM method is more accurate than that based on the first order one, which is equivalent to the conventional harmonic balance method.

风洞实验时，吹出了单、双稳定极限环颤振情形，并验证了基于KBM二次渐近解的当量线化分析比KBM法一次渐近解的当量线化分析要精确一些的结论。

In this new architectural plan the Garden of Golgotha came to be at the centre of the new city.

Aelia 是高举他自己，并在此城内朝拜罗马诸神。

The continuous nature of peat accumulation means that terrestrial coaly rocks may provide a higher resolution and more complete record of base-level change than the time-equivalent shallow-marine strata, thus enabling the identification of highfrequency cycles that are not recorded in themarine strata.

泥炭积累的持续性质的手段，陆地coaly岩石可提供较高的分辨率和更完整的记录基准面变化的影响时，相当于浅海阶层，从而使确定的高频周期，不记录在themarine 阶层。