查询词典 sum

The product of Fourier series and a finite sum of complex Gaussian functions is used to approximate the window function of a hard-edged aperture, an improved algorithm for the beam propagation through a paraxial ABCD optical system with hard-edged aperture is proposed.

使用傅里叶级数与有限个复高斯函数之和的乘积作为硬边光阑的窗口函数的近似式，提出了含硬边光阑近轴ABCD光学系统对光束变换的改进算法。

This paper provides the analytic method to calculate the value of Green s functions in space domain at the zero distance by the discrete complex image theory,that is ,to express the finite progressional sum of Green.

对此，本文在讨论采用离散复镜象理论计算空间域Green函数时，提出了采用该镜象理论计算空间域Green函数零距离处奇异值的解析方法，即，采用Taylor公式展开镜象理论得到的空间域Green函数的有限级数和形式，并结合特定的分域基函数来得到零距离处Green函数奇异值的解析计算式进行计算。

By substituting a definite integral for the sum of finite slices, an analytical formula for the safety factor in the simplified Bishop's method can be derived.

针对简化Bishop法，采用精确积分代替有限条块的求和，获得了边坡安全系数的解析表达式。

The detected leakage signal can be decomposed into a sum of finite intrinsic mode functions by EMD, some of IMFs embracing typical AE characteristic can be selected to be reconstructed. Thus, noise interference can be eliminated. The reconstructed signals are analyzed and their cross-correlation parameter is calculated.

该信号分析方法将管道泄漏产生的声发射信号通过EMD分解为多个平稳的固有模态函数之和，选择包含声发射特征的若干IMF分量进行重构，可以提取到管道泄漏声发射信号的本质特征，消除噪声信号的干扰。

With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented.

通过将孔径函数展开为有限项复高斯函数之和，得到了高斯光束在受孔径约束的抛物面折射系统中分数傅里叶变换较符合实际的近似解析表达式，并进行了数值模拟。

Then the detected signal was decomposed into a sum of finite intrinsic mode functions by empirical mode decomposition. The normalized kurtosis value of the main IMF components was analyzed, and the eigenvectors of the detected signal could be extracted.

用动态压力变送器获取了管道的动态压力信号，利用经验模态分解的方法将信号分解为多个固有模态函数之和，选择主要的IMF分量进行归一化峭度分析，从而提取信号的特征向量。

By using the method of expanding the aperture function into a finite sum of complex Gaussian functions, approximate closed-form propagation equations of TMn0-Gaussian beams diffracted by hard-edged parallelogram aperture s are derived.

通过将硬边光阑函数展为复高斯函数之和的方法，在直角坐标系下研究了TMn0模高斯光束通过有平行四边形光阑的衍射，得到了近似的解析传输公式。

Based on a kind of orthogonal complete functions in L2[0,1], another one (called V-system) which has equivalence relation with U-system is created. It is a kind of new and effective mathematical tool on signal multi-resolution analysis. Besides that V-system keeps the favorable properties of U-system and can accurately reconstruct geometry information which expressed in piecewise polynomials by finite sum of functions in V-system, it has more special properties, such as simple construction, abundant levels, convenience of application, quick calculation, local support, and so on. V-system is the generalization of Haar orthogonal functions, and to be a class of wavelet base. It has a good future for some applications in the fields of wavelet analysis and signal processing.

从L2[0，1]空间的一类正交完备函数系U系统出发，构造了另一类与之等价的正交完备函数系，称之为V系统，它是信号多分辨分析方面的一种新型的、有效的数学工具。V系统不仅保持了U系统的优良特性，对多项式表达的几何信息能够做到有限项精确重构，并且较之U系统，它更有结构简单、层次分明、计算快捷、局部支集等特点，应用起来将更加灵活方便。V系统可以看作是Haar函数系的推广，是一类小波基，在某些数字信号处理及小波分析问题中有良好的应用前景。

Based on the Collins formula, the analytical propagation equations for a Gaussian beam through a multiple spatial filter system are derived by using the methods of the matrix decomposition and expanding the aperture function into a finite sum of complex Gaussian function .

以Collins衍射积分公式为基础，利用A0CD矩阵分解与物理实现的技巧，以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，推导出了高斯光束通过多级空间滤波器系统的传输方程，并用数值计算加以说明。

This paper provides the analytic method to calculate the value of Green"s functions in space domain at the zero distance by the discrete complex image theory,that is ,to express the finite progressional sum of Green"s functions detained with DCIT into Taylor expansion and deduce the analytic expression of the singularities at the zero distance with the help of the specific subdomain base functions.

对此，本文在讨论采用离散复镜象理论计算空间域Green函数时，提出了采用该镜象理论计算空间域Green函数零距离处奇异值的解析方法，即，采用Taylor公式展开镜象理论得到的空间域Green函数的有限级数和形式，并结合特定的分域基函数来得到零距离处Green函数奇异值的解析计算式进行计算。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。