数值函数

Based on the Volume of Fluid Method, the wave damping absorber of the numerical wave flume for irregular waves has been investigated. Setting the Turbulence motion equation and the Renault equation as the governing equations and using the wall function technique in the near-wall region, an absorbing wave-maker is set at the left side of the flume.

本文对基于VOF方法的不规则波数值波浪水槽进行了阻尼消波研究，以湍流运动方程一雷诺方程为控制方程，在近壁区应用壁函数技术，在数值波浪水槽的左端设置了主动吸收式造波机。

In this paper the numerical solution of Green's function of potential in 2-D arbitrary inhomogeneous media with axial symmetry has been given by using the numerical mode matching theory.

利用数值模式匹配理论，对具有轴对称的任意二维非均匀介质中位场的格林函数给出数值解。

Approximating unknown function by barycentric Lagrange interpolation which has advantages of higher precision and good numerical stability, the barycentric interpolation collocation method for analyzing deformation and buckling load of ring is presented.

采用数值稳定性好、计算精度高的重心Lagrange插值近似未知函数，提出数值分析圆环变形和临界载荷的重心插值配点法。

This paper presents the boundary value problem solved as the biharmonic equation of upper plane and strip domain with Green functional method and it deals with the numerical solution of bihormonic equation, using the Matlab program calculation to realize the visualization of numeric solution.

用Green函数法求解了区域为上半平面和带形区域的双调和泊松方程的边值问题；以及探讨了双调和方程的数值解，并用Matlab编程计算实现了双调和方程数值解的可视化。

The deflection and moment wavelet parameters for common boundary conditions of beams were obtained from numerical features of interval boundary of BSWI functions.

根据BSWI函数区间边界的数值特征，得到了梁常见边界条件下的挠度和弯矩小波系数值。

In the numerical calculations,the unknown density of dislocation is approximated with the product of fundamental function and Chebyshev polynomials.The calculations show the present method yields rapidly converging and high accurate numerical results.

在数值求解这组奇异积分方程中未知位错分布密度近似为基本密度函数与Chebyshev多项式之积，计算表明，本文方法的数值结果不但收效快而且精度高。

This threshold function has not only overcome incontinuous disadvantage of the hard threshold function, but also solved constant deviation which exists in the soft threshold function, meanwhile the new function needn't selecting parameters.

该阈值函数克服了硬阈值函数值不连续的问题和软阈值函数存在恒定偏差的问题，同时新函数不需要进行参数选择。

To match the boundary conditions, the modified Bessel functions are expanded to the planar wave in the interface. Then the eigenvalue equations of different polarizations are obtained by scalar approximation. At last, the relations between propagation losses and the states of polarizations, the geometric structures of the fiber, the refractive index and thickness of the polymer are calculated.

论文首先给出其等效折射率数学模型，在纤芯和包层中，光场用贝塞尔函数及虚宗量贝塞尔函数的求和表示，在聚合物和金属中用指数函数的求和表示，交界面上采用将虚宗量贝塞尔函数用平面波展开的方法匹配边界条件，然后利用标量近似求出极化D型光纤不同偏振态光场模式的本征值方程，最后通过数值计算得到光纤的传输损耗与抛磨平面和纤芯之间的距离，聚合物粘接材料的折射率和厚度，以及偏振态之间的关系。

In NWFM,to solve self-consistently the set of DFT Kohn-Sham equations,nuclear weight function is employed for numerical solution of multicenter integra-tion,which decomposes the problem of three dimensional integration to a sum ofone-center,atomic-like integrations.

首先介绍如何利用线性组合的原子轨道方法求解密度泛函理论中的K-S方程；接着详细地说明了核权重函数的概念，并列出了两种常用的核权重函数形式，同时阐述了如何利用核权重函数求解包含多中心积分的矩阵元以及复杂的三维泊松方程以获得电子间库仑势的方法；然后给出了求解矩阵元、有效势以及体系总能的具体数值计算公式。

In the optimization iteration, the levelset function values of nodes are considered as design variables. To computedifferences normally, the Heaviside function is handled for smoothing, theregularized Heaviside function is selected to avoid the oscillation inhomogenizations method, and the results can converge smoothly.

在优化迭代过程中，节点上的Level Set函数值被看作是设计变量，并且为了便于微分计算能够正常进行，对Heaviside函数及其导函数做了光滑化处理，选取了一种正则化的Heaviside函数，避免了均匀化方法中出现的振荡现象，可以平稳地收敛到最终结果。

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。