数值函数

In order to avoid the Maratos effect, the merit functions used are approximations to Fletchers differentiable exact penalty function. Global convergence is proved on some conditions, and some numerical results are given .

为避免Maratos效应，此方法采用Fletcher的光滑精确罚函数的逼近形式作为价值函数，在一定条件下证明了算法的全局收敛性并且给出数值结果。

The new method applies quadratic spline function to interpolate thenonharmonic function in Duhamel's integral.

本方法是利用二次样条函数对Duhamel积分中的非振荡型函数进行插值，导出了相应的数值积分公式。

Mathieu functions are frequently encountered in many radiation,scattering and guided wave problems, which are formulated in the elliptic cylindrical coordinate system.

本文给出了计算马丢函数和变型马丢函数及其导数值的程序流图和相应的有用数学公式，并讨论了算法。

According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired.

为了研究随机因素对经济系统稳定性的影响，建立了系统可靠性函数和首次穿越时间概率密度函数，并结合初始条件和边界条件得到了数值结果。

For this method, integeral was proceed by triangular Gaussian quadrature method in polygon domain, which can reduce computational time greatly. Neighbor nodes database was create which can reduce neighbor nodes searching time. Rock and soil cutting problem are two complicated problems, so a robust method is needed to treat essential boundary condition.

岩土掘削数值分析要求无网格法拥有高效而适应性强(来源：ABC论文f1网www.abclunwen.com)的本质边界条件处理方法，本文提出一种新的处理方法，该方法通过改变边界节点权函数使试函数通过边界节点，并采用对角元素改1法满足本质边界条件，该方法灵活性强，适用于各种岩土掘削问题。

In order to avoid the singularity in the integration, the integrand was expressed to be sum of complex exponential terms by using discrete complex image method. With generalized pencil of function method introduced, the number, location and intensity of images were obtained without extracting the quasi-static and surface wave terms in the integrand, which makes DCIM more efficient for multi-layered media.

为了避免积分中的奇异性，利用离散复镜像法将积分核用复镜像的指数求和式表示，引入广义函数束方法，可以在不提取积分核中表面波项的条件下，采用数值方法提取准静态项，给出复镜像点的数目、位置和强度，使得该方法在多层介质情况下对格林函数的计算更为有效。

Hence, reproducing kernel function has not only the advantage of calculation, e.g.it can transform the integration into the sum of finite function values, but also theadvantage of local characteristic of wavelet function.

所以再生核函数既具有计算优势，如能将积分计算准确地转换成有限个函数值的和来计算，又具有小波函数的局部刻画优势。

Based on Collins integral formula and the expansion of the hard aperture function into a finite sum of complex Gaussian functions,the approximate analytical expression of the diffraction field of Gaussian beam by a circular disc is derived,and its characteristics are analyzed by the numerical calculation and numerical simulation.

基于圆孔光阑函数展开为复高斯函数和的方法，用Colins积分公式，导出了高斯光束照射下圆盘衍射的光场近似解析表达式，经计算机数值计算，对高斯光束照射下圆盘衍射的衍射特性进行了详细的分析

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。

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。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。