查询词典 hankel transformation

We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion in this paper.

我们提出了一种基于Dini级数展开的准离散汉克尔变换算法。

In §5, we research a new fast triangular factorization algorithm of Hankel matrix. Then we give a numerical example.

在§5中，推导了Hankel矩阵的新的快速三角分解算法，给出了数值算例。

It is solved by means of the Fourier expansion and Hankel transform. A general solution is got on the cylindrical coordinates.

自从Biot[1，2 ] 建立饱和多孔介质本构关系和运动方程以来，人们已经作了大量研究工作[3 ，4，5] 。

A set of governing dynamic equations with different basic unknowns and with different hypotheses is presented. Thereafter, the 3-D non-axisymmetric governing dynamic equation is solved by means of Fourier expanding and Hankel integral transform method.

在Biot两相介质波动理论的基础上，直接用Fourier展开和Hankel积分变换技术分析三维非轴对称饱和弹性土层和饱和弹性半空间波动方程，首次得到用积分变换形式表示的，三维非轴对称饱和弹性土层和饱和弹性半空间，以饱和土土骨架位移和孔隙水压力为基本未知量的基本解。

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。

Based on the Biot s two-phase theory for fluid-saturated porous media, considering the inertia force of the solid and the liquid, and the coupling function between the solid and the liquid, and the compressibility of the liquid in allusion to the character of the nearly saturated soils. The dynamic governing differential equations are solved by Hankel transform. Then, considering the boundary condition, the dual integral equations of vertical vibration are established which are reduced to Fredholm integral equation of the second kind.

本文基于Biot两相介质动力固结理论，针对准饱和土地基的特点，考虑了流体的可压缩性，土体和流体的惯性及水土之间的耦合作用，运用Hankel变换技术求解动力控制方程，然后按混合边值条件建立起对偶积分方程，并将其化为易于数值计算的第二类Fredholm积分方程，分别研究了准饱和土半空间地基、上覆单相弹性层的准饱和土地基和准饱和粘弹性地基上刚性基础的竖向振动特性。

Hankel inversion is calculated by Gauss integration in integral region, which are plotted at the zero points of Bessel function.

Hankel逆变换依据Bessel函数零点划分积分段，采用高斯积分计算。

Then, with the help of Hankel integral transform, general solutions to axisymmetric problems are obtained in the frequency field, based on which the dynamic response of the unsaturated soils half-space subjected to a vertical concentrated surface load is investigated.

利用Hankel积分变换方法，对频域内的轴对称问题进行了求解。在此基础上研究了非饱和土半空间体在垂直集中力作用下的动力响应，给出了Lamb问题的积分形式解。

The fundamental solutions are obtained by Hankel integral transform and numerical inverse transform.

采用Hankel变换及数值逆变换得到饱和土的基本解。

When computing the diagonal elements of the Galerkin matrix, one will encounter the integral of Hankel function, the Green's function of 2-dimensional Helmholtz equation and the cosine weighting function, whose integrand is singular in the integration range. A new approach is proposed to deal with this kind of singular integrals, which is pivotal but have not been reported so far.

首先建立了透镜边缘上任一点的电场满足的边界积分方程，然后选择适当的正交模式函数展开端口上的电场分布，采用边界元法的思路及Galerkin法将该积分方程离散化为—矩阵方程求解即可得到透镜的多模式散射参数。

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。