解析函数

The nonlinear equation of heat conduction is transformed into a Laplace′s equation by applying the Kirchhoff transformation ,and an analytic approximate solution of the equation is derived.

当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。

In order to solve the thermal effect problem of laser rod by diode laser end—pumped,based on the heat conduct theory,a novel eigenfunction group of heat conduction equation was es—tablished and the general solutions of temperature field and thermal distortion field within laserrod were obtained.

为了解决激光二极管端面泵浦激光棒引起的热效应问题，基于热传导理论，建构了热传导方程新的本征函数解，得出了激光棒内温度场与热形变场的一般解析表达式。

It is hardly to get and express the solution of the equation of evolution by the analysis, so it used to solve the equation by numerical method.

根据解析的方法求发展方程的解，并且通过已知函数表示出来。

The overall NOX removal efficiency is expressed as an explicit function of space velocity and other parameters, and a simple analytic solution is obtained.

NO_x转化率可以表示为空速和其它参数的显函数并获得单一的解析解。

When the target function not explicit analysis expression (for example produces with value table), or has time the integer request to the variable, with .

当指标函数没有明确的解析表达式，或者对变量有整数要求时，用表格法。

limited teaching ; continuous ; field of definition ; infinity ; infinitesimal ; boundless.

由此可看出，虽然定义中强调了"有限次"和"一个解析式"，但初等函数不排斥可化

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。

A combinatorial identity is obtained:=:~z 2r扟32-rn-iJ As main result of this paper, in section two, the convolution梩ype identities emerge from our discussion about Lagrange formula whom in author 憇 view can be taken as the inherent characteristic of Lagrange formula but have been ignored fOi so long time.

第一章对拉格朗日反演在Riordan群理论中的应用进行了介绍，证明了一个组合等式：第二章通过对拉格朗日反演定理本身的分析，得到一个对任意的形式幂级数都适用的三个拟卷积公式，这些公式体现了任意能在零点解析的函数的内在性质。

Using Landauer-Buttiker formulism the analytical expressions for the electronic transmission probability as a function of incident electron energy and geometry parameters are obtained, with which the conditions for interference maximum and minimum of electron wave are indicated analytically and verified numerically.

用Landauer-Büttiker公式解析地计算出了两种情况下系统电子透射率作为入射电子能量和系统几何参数的函数表达式，从而分析得出了由于量子干涉产生透射极大与极小值时入射能量与几何参数所满足的条件关系并得到了数值验证。

Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, a systematic study on Lamb's problems in transversely isotropic saturated half-space is performed. Integral solutions for surface radial, vertical and tangentical displacements are obtained both in the case of drained surface and in the case of undrained surface excited by vertical and tangentical harmonic resources respectively. Numerical results show the obvious difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media.

其次，基于Biot波动理论，在圆柱坐标系下求解了横观各向同性饱和土的Biot波动方程：通过引入位移函数，在圆柱坐标系下将横观各向同性饱和土的Biot波动方程转化为两个解耦的6阶和2阶控制方程，然后根据方位角的Fourier展开和径向Hankel变换，求解波动方程，得到以土骨架位移和孔隙水压力为基本未知量的积分形式一般解，并用一般解给出了饱和土总应力分量的表达式；再以基本解为基础，系统地研究了横观各向同性饱和半空间体的Lamb问题，考虑表面排水或不排水两种情况后，首次得到横观各向同性饱和半空间体在表面竖向和水平谐振力作用的下径向、竖向和周向位移的解析解。

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％。