级数展开

In chapter two, based on the property of uniform plane wave, field at boundary node is expressed with field in the computation region and expanded as Taylor's series. By truncating it at second order, a concise ABC is obtained.

首先，在第二章中，利用均匀平面波的特性，将边界节点上的场用计算区域内部的场表示，利用Taylor级数展开并截断到二阶，得出了一种形式十分简明的频域二阶吸收边界条件。

The solutions of an infinite solid with spherical inclusion under tensile force at infinite are presented.

2利用Legendre级数展开的方法，给出了类位错模型下包含球形夹杂的无限大弹性体受拉伸作用的解。

So, in this paper, a circular cavity witha large radius is used to replace the straight boundary of thehalf space, then the half space problem can be changed tothe scattering problem of two circular cavities to the steadyincident P-wave . Having the aid of the mature cylinderfunction theory, the general solutions of the wave functionscan be given, and an infinite linear algebraic equations ofthe unknown coefficients in the wave functions can be gottenwith the boundary conditions and the Fourier complex seriesexpansion technology, the infinite linear algebraic equationscan be approximately solved by the finite trunction withsatisfying some definite precision, at the basis of thissolution of the equation, the variations and the lay-outs ofthe DSCF at the circular cavity boundary vs. the differentincident angles, the different embedded depths of thecircular cavity as well as the different dimensionless wavenumber of the incident P-wave.

为此，本文采用一个半径很大的圆孔来代替半空间的直边界，将该半空间问题转化为一无限大空间中两个圆孔对稳态P波的共同散射问题，借助于成熟的柱函数理论，通过写出问题波函数的一般形式解，利用问题的边界条件，并采用复数傅立叶级数展开技术将其化为一个仅包含问题波函数中未知系数的一无穷线性代数方程组，在满足一定计算精度的前提下，通过有限项截断进行近似求解，进而讨论了圆孔边界处的动应力集中系数随不同入射角、不同的圆孔掩埋深度、入射波的不同无量纲波数以及介质的泊松比变化和分布情况。

By means of the Fourier series expansion, an approximate analytical propagation equation of flattened Gaussian beams passing through an apertured paraxial ABCD optical system is derived, and illustrated with numerical examples, when the transmissivity of the aperture is T = cos.

用傅立叶级数展开法研究了平顶高斯光束通过有光阑限制的近轴ABCD光学系统的传输特性，导出了光阑透射率为T=cos时的近似解析传输公式，硬边光阑的情况可作为Ω=0的特例得到。

By means of the Fourier series expansion,an app roximate analytical propagation equation of flattened Gaussian beams passi ng through an apertured paraxial ABCD optical system is derived,and illustr ated with numerical examples,when the transmissivity of the aperture is T=cos.

用傅里叶级数展开法研究了平顶高斯光束通过有光阑限制的近轴ABCD光学系统的传输特性，导出了光阑透射率为T =cos时的近似解析传输公式，硬边光阑的情况可作为Ω=0的特例得到。

The one is Pagano method which has been proven effective to static problems, but it is very complicate for the three-dimension dynamic problems of finitely long piezoelectric laminated plates.

同时，指出Pagano方法求解动态问题所遇到的困难，为克服这些困难，提出了一种求解压电层合板动态问题三维精确解的幂级数展开方法。

Formulas are derived to compute hydrodynamic pressures or hydrodynamic perssure influence matrices on dams using series development and linear superposition theorem with nonvertical upstream face、the compressibitily of water、the effect of absorption of the reservoir bottom ect. being taken into account.

利用级数展开和线性叠加原理，推导了坝迎水面倾斜、库水具有可压缩性、库底具有吸收性等多种情形下，重力坝迎水面上动水压力和动水压力影响系数矩阵的计算公式。

In some limit conditions, by using the perturbative method, the equations may take on concise forms, i.e Mathieu equations.

如果我们所讨论的问题仅局限于原点附近，可以对场进行泰勒级数展开，得到一个场

Because the curve radius of easement curve gradually changes, the formula for calculating the coordinates can not be obtained with the method of integration.

由于缓和曲线的曲率半径是逐渐变化的，不能用积分的方法求得其上点位坐标的计算公式，以往都是用级数展开进行近似计算。

In past, the processing mode as to the electro-hydraulic servo-system nonlinear problem is that using the Tais lux formula obtains the part linear pattern behind the series expansion at the stable state work-point. This kind of linear model is feasible to this system which work point is in small scope changing.

过去对于非线性问题的处理方式是在稳态工作点处进行泰勒级数展开后得到局部线性化模型，这种线性化模型对于系统在设计工况点附近小范围变化时是可行的。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。