数值函数

An instance was given by means of the numerical solution for the first boundary value inverse problem of Laplace's equation.

将直匀流绕物面作二维无旋不可压缩定常流动时的流函数表达为曲面后，利用流函数曲面控制边界与流曲线的对应关系，采用拉普拉斯方程第一边值逆问题的数值解法，提出了来流为直匀流的流曲线造型方法并给出了实例。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

Based on the method that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, the propagation characteristics of a Gaussian beam passing through apertured spatial filter systems are analysed and the corresponding analytical formulae are obtained respectively.

根据矩形函数可以展开为有限复高斯函数之和的方法，从柯林斯衍射积分公式出发，对高斯光束通过受限空间滤波器传输特性进行分析，得到了相应的近似解析式。利用Matlab对其解析式进行数值模拟，得出一组直观的结果。

Base on the fact that a hard-edge aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expressions for the propagation characters of Hermite-Guassian beams passing through double rectangular apertured are derived. The approximate analysis uses Collins formula. At last, Matlab illustrates some numerical examples.

基于硬边孔函数能拓展成一组有限复高斯函数的和，研究厄米－高斯光束通过双矩孔的传输特性，用Collins公式分析，用Matlab进行一些数值模拟。

The propagation equations for oblique and off-axial Gaussian beams passing through cat-eye optical lens are deduced by using the theory of matrix optics and expanding the aperture function into a finite sum of complex Gaussian functions.

运用矩阵光学理论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，进一步推导了倾斜离轴高斯光束通过猫眼光学镜头的解析传输公式，通过数值计算分析得到了倾斜系数和离轴量对猫眼效应反射光光强分布的影响规律。

The analysis of the examples of this class of generalized filled function show that the lower bound of the parameter is usually smaller than others.

最后的数值计算结果也进一步表明这类广义单参数填充函数是一类有效的填充函数。

A two dimensional stochastic nonlinear dynamical model of semi-active suspension system is presented considering the stochastic factor of the road. The Hamilton function is also described as one dimension diffusion process by using stochastic average method, the stationary stability is studied by solving the Fokker-Planck-Kolmogorov equation. The Backward Kolmogorov equation for reliability function had been established.

考虑路面随机因素的影响，首先建立二自由度汽车半主动悬架的随机非线性动力学模型，运用随机平均法，将Hamilton函数表示为一维扩散过程，并运用奇异边界理论分析系统的全局随机稳定性，建立可靠性函数所满足的Backward Kolmogorov方程，结合初始条件和边界条件得出数值结果。

Based on this analysis, a new method for evaluating the bluntness magnitude of a Berkovich indenter was proposed. This method was examined by the experimental results of indention loading curves for pure nickel and aluminum alloy 8009, and good agreement was obtained. For thin metal films deposited on hard substrate, a method is established for determining the yield strength and hardening index of the film from nanoindentation loading curve.

通过对理想与钝化Berkovich压头以及球形压头纳米压入软膜/硬基材料加载过程的数值研究，给出了两种压头纳米压入加载曲线的幂函数拟合指数及最大压入载荷同膜、基材料基本力学性能间的函数关系，并分别就Berkovich压头与球形压头建立了由纳米压入加载曲线确定沉积在陶瓷基体上金属薄膜屈服强度与硬化指数的方法。

We give a two-parameter penalty function and its exact penalty theorem for inequation constrain- ed optimization,meanwhile,We propose a quasi Newton algorithmfor solving the unconstrained nonlinear penalty problem and study its convergence,Numerical examples illustrate the feasibility of the algorithm.

对于含约束不等式的优化问题，构造双参数精确罚函数并给出精确罚定理，提出了一个求解这种罚函数问题的布鲁丹族拟牛顿算法，研究了算法的收敛性与收敛速度，并进行了数值试验，证明了可行性。

Boundary polynomial point interpolation mesh-free method and boundary radial point interpolation mesh-free method were presented, based on polynomial basis and radial basis respectively for transient eddy current analysis, and their interpolation shape functions satisfy the Kronecker delta function and the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column was set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM was analyzed as well.

运用多项式点插值法和径向基点插值法构造形函数，推导了适合于工程电磁场瞬态涡流问题的多项式基点插值边界无单元方法和径向基点播值边界无单元方法，这两种方法的空间插值形函数满足Kronecker delta条件，从而强加边界条件可以直接施加在边界点上，以金属长方柱的瞬态涡流分析作为数值算例，证实了两种方法的正确性和有效性，并对两种基类的点插值法进行了精度分析和比较。

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。