展成级数

When they built up the quantum Liouville equation inthe phase-space representaiton and discussed the mathematicaltransformation of the wave functions between the coordinate ormomentum and phase space,Torres-Vega and Frederick alwaysassumed the positive series expansion in coordinate of potentialsof systems.This is obviously incomplete because potentials ofreal systems contains in general negative powers of coordiante.

Torres-Vega和Frederick在建立相空间中的量子Liouville方程以及讨论和推导相空间波函数和坐标或动量空间中的波函数之间的的数学变换时，总是假定体系的相互作用势仅能展成坐标的正项级数，这显然是不全面的，因为实际体系的相互作用往往都含有坐标的负幂项。

Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave.

其解系构成完备的加权(权函数为1)内积空间，即Hilbert空间，从而内波现象可以展成该解系的广义Fourier级数；采用差分方法，将 Sturm-Liouville 方程转化为矩阵特征值问题，每一个特征值对应一个内波波数，该特征值对应的解则是内波的某一模态。

Then the analytic functions can be expanded as Laurent seriers in this region .

然后把这个区域内的解析函数展成Laurent级数的形式。

Then the analytic functions could be expanded as Laurent seriers in this region.

然后把这个区域内的解析函数展成Laurent级数的形式。

Based on the elastic theory of large deflection and by taking into account the variation of the axial force and its effects on bending deformation of the drillstring in vertical section,the vibration of the drillstring induced by fluctuating weight-on-bit is described by a parametrically excited system.A Mathieu equation describing the system is established by Galerkin Method.By extending the solution into a Fourier series,the curves of dynamic bifurcation values and the dynamically unstable regions surrounded by the curves are presented.

基于弹性大变形理论，考虑到轴力沿钻柱轴线的变化及其对钻柱弯曲变形的影响等因素，将受自重作用的铅垂井段钻柱在波动钻压激励下的振动转化为一个参数激励系统，用Galerkin方法首次得到了描述此系统的Mathieu方程，并通过将方程的解展成富里叶级数的方法，得到了该振动系统的动力分岔值曲线及其所包围的动力不稳定区。

It is complete for continuous functions on [0,1] (C[0,1]), and the properties of quick transformation and other well properties similar to Fourier system, but its partial sum is superiority to Fourier system as the approaching tool.

在此函数系上展成的Fourier级数有许多与三角Fourier级数相似的性质，三角形Fourier级数的部分和在作为函数的逼近工具时确实要比三角Fourier级数优越一些。

Based on the elastic theory of large deflection and by taking into account the variation of the axial force and its effects on bending deformation of the drillstring in vertical section ,the vibration of the drillstring induced by fluctuating weight on bit is described by a parametrically excited system.

基于弹性大变形理论，考虑到轴力沿钻柱轴线的变化及其对钻柱弯曲变形的影响等因素，将受自重作用的铅垂井段钻柱在波动钻压激励下的振动转化为一个参数激励系统，用 Galerkin方法首次得到了描述此系统的 Mathieu方程，并通过将方程的解展成富里叶级数的方法，得到了该振动系统的动力分岔值曲线及其所包围的动力不稳定区。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。