数值函数

By both defining and quantifying of preference, four classes of preference functions and an aggregate preference function were constructed by using numerical method, and a mathematics model of physical programming was proposed.

通过定义偏好的概念及对偏好的数学量化，采用数值分析方法，构造了四种不同偏好结构的偏好函数，进而构造出综合偏好函数，并建立了物理规划数学模型。

Three different numerical iterative algorithms are developed and the accuracy and stabilities of them are compared. Tension and compression instabilities are studied and effects of Conservative Smoothing Approach and artificial viscosity on stabilities are discussed. Based on Taylor series expansion, Modified SPH method is proposed. The discrete forms of the function and its first derivative estimations of the kernel function are deduced in both one and two dimensional space.

讨论了三种不同的数值迭代算法对计算精度和稳定性的影响；分析了不稳定性产生的根源，包括拉伸不稳定和压缩不稳定，探讨了保守光滑算法和人为粘性对稳定性的影响；在Taylor展开的基础上提出了一种修正的SPH方法，并推导一维和二维情形下函数的核估计和函数的一阶导数核估计的离散形式，结果表明，二维情形下MSPH方法可以很好的改善边界粒子的计算精度。

A function f: V→{-1,1} defined on the vertices of a graph G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one.

函数f：V→{-1，1}称为图G的符号全控制函数，如果对每一个开邻域集上的点的函数值的和都大于等于1。

The analysis results of these shift orthogonal functions in GSM channel, which is compared with that of conventional shaping filters such as square root raised cosine functions, show that it has better performance.

最后通过与常用的平方根升余弦函数波形在GSM信道中的数值解比较，说明了基于小波包函数的移位正交传输波形优于传统的波形。

First of all, the basis of the MRTD method is studied. In Chapter 2, wavelets analysis and multiresolution analysis, the mathematical basis, are introduced, and the characteristics of the wavelets basis functions, including orthonormality, compact support, multiresolution and so on, are also introduced. The advantages of the applications of these functions to the numerical electromagnetic calculations are discussed. In Chapter 3, the algorithm basis of MRTD: the combination of the wavelets and the method of moments is studied. This Chapter shows that the MoM based MRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

First of all, the basis of the MRTD method is studied. In Chapter 2, waveletsanalysis and multiresolution analysis, the mathematical basis, are introduced, and thecharacteristics of the wavelets basis functions, including orthonormality, compactsupport, multiresolution and so on, are also introduced. The advantages of theapplications of these functions to the numerical electromagnetic calculations arediscussed. In Chapter 3, the algorithm basis of MRTD: the combination of the waveletsand the method of moments is studied. This Chapter shows that the MoM basedMRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

When we use boundary element method to solve problems of fluid structure interaction, large amount of calculation of Green's function and its partial derivative is required.

Green函数及其偏导数的数值计算在水动力学中起着重要作用，当用边界元法求解流体结构相互作用问题时，需要大量的计算Green函数及其偏导数。

The derivative function of the ESD as a function of α, determine the frequency of its peak value.

把各阶导函数的ESD作为α的函数，确定其峰值频率的数值。

For polydisperse systems at large Péclet number, we establish the systems of differential equations describing the leading term and the second term of the pairdistribution function via regular perturbation method.

针对高Péclet数情形，通过正则扰动法我们建立了决定对分布函数的微扰展开的主导项和一阶项的联立方程组，并用由此算出的对分布函数的数值解计算了系统的沉降系数。

In order to get the formulation,the B3 spline function is used to distribute the contact problem,and numerical examples are analyzed to show the effectiveness of the method.

该方法充分利用了样条函数的解析和数值双重性及连续性强的优点来构造杆的位移函数，因此可推广应用于分析结构在冲击荷载下的动力响应问题。

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。