解析法

The quasi-analytical expressions of the relative concentrations at the mobile region and the immobile region are deduced respectively by using hypergeometric equation, hypergeometric function and the method of Laplace transform under the initial concentration zero and the first or second boundary condition of a semi-infinite one-dimensional space.

并分别在初始浓度为零，半无限一维空间内第一类边界条件和第二类边界条件下，利用超几何方程、超几何函数和Laplace变换法推导出了可动区和不动区溶质相对浓度的准解析表达式。

Aiming at reducing cogging force in tubular permanent magnet linear motors, an analytical method based on energy method and Fourier series expansion was adopted, the expression of cogging force was deduced which is related with structure parameters of the motor.

为削弱圆筒永磁直线电机的齿槽力，采用了一种基于能量法和傅里叶分解的解析分析方法，推导出了圆筒直线电机与结构参数有关的齿槽力表达式。

Based on the energy method and Fourier series expansion the general expression of cogging torque was obtained and the harmonic components of cogging torques were analyzed under both ideal and non-ideal conditions.

针对永磁电机中非理想因素对齿槽转矩的影响，基于能量法和傅里叶级数解析方法给出了齿槽转矩的一般表达形式，并分析了理想及非理想条件下齿槽转矩的谐波成分。

And a model of layer—disperising dual medium is established (2) Some new theories and methods, such as Fourier dual integral transformation and half numeral value analytic method and so on, are used to establish the calculating formula in this paper.

2本文在理论推导上，应用了数学、力学和数学物理方程方面的新理论和新方法，如：二重富里叶积分变换、板壳理论、分离变量法以及半解析数值方法等，使本论文在理论推导过程上，增加了理论的严密性和逻辑性。

As well known, modern laser diffraction has widely used in engineering measurement but it mostly limited in Fraunhofer diffraction because there is simple function between the size to be measured and space of diffraction dark spots and there are no analytic algorithm for Fresnel diffraction.

现代激光技术提供了极为良好的相干光源，该光源在工程测量，特别是衍射测量中得到广泛应用。但在实际应用中，往往局限于夫琅和费衍射，因为夫琅和费衍射法暗斑间距与被测尺寸之间具有很简单的函数关系S-n/d，而菲涅尔衍射光强分布非常复杂，缺乏解析的计算方法。

This paper mainly consists of three parts:(1) Based on the Reddy's higher-order shear deformation plate theory and general von Kármán-type equations, put forward the governing equations of pre- and post-buckled vibration of several hybrid FGM plate forms which have not been studied adequately, triumphantly applying the perturbation technique combined with Galerkin method into equations solving, and get the comparatively simple result forms with complicated deduction at last;(2) As a new type of materials, piezoelectric fiber reinforced composite actuators were applied to optimal vibration control, interrelated informatons be depicted in this paper;(3) During the investigative cource, some factors not been considered adequently in other researches were discussed fully in the postbuckled vibration analysis, such as the temperature-dependent material coefficients, heat conduction and nonlinear vibration characteristic etc.

本文的研究工作主要包括：(1)基于Reddy高阶剪切变形板理论和广义Kármán型方程，给出了几类现有研究成果较少或没有彻底解决的FGM混合板结构的屈曲前和屈曲后振动特性研究的控制方程，成功将摄动-Galerkin混合法应用于求解过程，并给出了各控制方程相对直观且易于计算的解析解形式；(2)单向压电纤维增强复合材料(Piezoelectric Fiber Reinforced Composite，简称PFRC)是一种新型压电材料，本文将其应用到了结构振动控制研究当中，发现通过压电纤维体积含量的选择可以实现混合板结构的优化振动控制；(3)围绕几种有代表性的FGM混合板结构，讨论其屈曲后的振动特性，在分析中同时考虑热传导，材料物性参数的温度相关性，以及机/热/电荷载耦合效应对非线性振动特性的影响，最后给出了大量数值计算结果。

For the plane wave of laser without pulse shape, we derive the express of electron trajectory by the relative Lorentz and energy equations. Note that the orbit of electron becomes a "fat-8" in the average rest frame. For the plane wave of Gaussian laser, we may know that, through relative Hamilton-Jacobi equation, electrons are accelerated in the front of pulse and decelerated backward. Whereas for the non-plane wave of Gaussian laser, we solve the Lorentz and energy equations by fourth order Runge-Kutta method.

对于无脉冲形状的激光平面波是从考虑了相对论效应的Lorentz方程和能量方程出发，得到了电子的运动轨迹方程表达式，在纵向平均速度参照系下该电子的轨迹呈现"8"字形；对于高斯型单色激光平面波是从相对论Hamilton-Jacobi方程出发，得到激光平面波在脉冲前沿加速电子而脉冲后沿减速电子，电子能量增益为零；而对于高斯型单色激光非平面波是从拉格朗日运动方程和能量方程出发，通过四阶Runge-Kutta法数值求解，得到电子在纵向有质动力、横向电场作用下加速电子，最后在强大的横向有质动力作用下从脉冲侧面散射出去，可以获得很大能量增益本文得到了相应的电子瞬时动量解析表达式。

Based on the analytic model of an eccentric slider crank mechanism with elastic effects at both joints of the coupler and four coupler Mathieu-typed equations of motion in terms of the generalized coordinates of the system,the extract solution is developed from the improved Hill method with accelerated convergence.

在所建立的连杆接头处具有弹性效应的曲柄滑块机构的动态解析模型以及在广义坐标下推导出的4个马修型运动方程的基础上，由具有加速收敛性的改进希尔法进行了精确求解。

This paper gives a closed-form solution to Asian option with geometric average assets prices in a continuous situation.

采用几何平均法计算资产价格的平均值，并以连续时间的情形为例，得到了亚式期权的解析定价公式

Analytical solutions for displacements of the viscoelatic half-space were obtained using Green's function method for various moving loads,including constant and harmonic point,line and area load.All velocity cases including the subsonic,transonic and supersonic velocities were considered.

首先采用Green函数法求解黏弹性半空间体在各种移动荷载模式作用下的动力响应的解析解，包括恒常和简谐移动点源、线源和面源荷载。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。