解析式

The method based on the frequency sampling is taken from the interpolation theory. The method based on the Chebyshev best uniform approximation theory can control the precision of approximation by limiting parameters.

频率采样脉冲波形设计法源于数值逼近理论插值法，所得脉冲波形有确定解析式；Chebyshev最佳一致逼近脉冲波形设计法属于均匀一致逼近，逼近程度能够利用参数进行限定。

This paper implements the symbol analysis of circuit and obtains analytical expression with the powerful symbol operation of the Matlab,provides an efficient assistant method for circuit analysis.

由于用符号表示的解析式比数值解具有更好的

A analytical expression of spectral bandwidth is obtained through retaining term of first order(when expanding circular frequence of wave vector in Taylor series).

利用该解析式，采用数值计算的方法，分别研究了带宽随信号光波长、抽运光波长和非共线角的变化规律。

Based on the static balance among the pile and soil, the basic differential equations of the displacements of the pile and soil were deduced. Considering the compatibility condition of stress and strain , based on the vertical deformation of pile and pile-surrounding soil, the analytical formulas calculating the pile friction were drew.

本文通过建立复合地基中桩体和桩周土的基本微分方程，考虑应力协调条件，假设桩周土的位移模式，在此基础上推导出桩侧摩阻力和桩身轴力的解析式，并进一步研究相关影响因素。

Based four-level forecast model, this paper presented an improved complete graph algorithm and derived analysis formula of computational amount of algorithms to prove improvement in algorithm performance.

以四级预测模型为基础，提出改进的完全图算法，并推导出该算法计算量的解析式，从理论上证明了改进的完全图算法性能上的提高。

The derived analytical expressions indicate that regardless of the input signal correlation matrix, the convergence behavior of the proposed algorithm, in all cases, is only governed by the normalized step size.

推导出的解析式表明，算法的收敛性能与输入信号的自相关矩阵无关，完全由归一化的步长参数控制。

Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励，通过随机平均法，Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题，其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

The governing equation of in-plane vibration of cable-restraint system is derived by means of D'Alembert principle, and then those partial differential equations are transformed into a set of ordinary differential equations by Garlerkin method. The method of Runge-Kutta integration is applied to solve the equation. The simulation analysis is made to prove that this vibration control has obvious damping effects and then the influence of cable tension, support mass, natural frequency and spring stiffness on the damping are discussed. Eventually, the approximate analytic solution of the optimum damping parameter is obtained to provide a simple and effective reference and design method for the engineers.

通过D'Alembert原理建立拉索－弹性约束系统振动方程，通过Galerkin方法将偏微分方程转化为常微分方程，应用龙格－库塔积分法求解方程；经过仿真分析，验证了该振动控制具有明显的减振效果，并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响；最后给出了计算最优阻尼参数的近似解析式，为工程师提供了简便有效的参考依据及设计方法。

The analytic expression of a probability current is derived by using the power series expansion method and used to generate the curve characteristics of the current varying with other parameters.

采用幂级数展开的方法得到了几率流的解析式，给出几率流随外参数变化的特性曲线。

Based on dynamic equilibrium equations of three-dimensional elasticity, a state equation was established for orthotropic foundation plates using double Fourier series, in which no assumption about stress or displacement modes was made. Analytical solutions and frequency equations of unified formulas were presented for thin and thick laminated foundation plates.

从三维弹性力学动力平衡方程入手，抛弃应力或位移模式的人为假定，利用Fourier双重级数，建立了正交各向异性地基板的状态方程，并分别给出了地基上任意层厚薄板静力问题的统一解析式和动力问题的频率方程。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。