多函数

In this paper, the scattering of SH wave by the structure surface with multiple semi cylindrical medium inclusion is studied by using a function of complex variable and a multi polar coordinate method .

利用复变函数和多极坐标系的方法，研究了在结构表面上含有多个半圆形介质夹杂的散射问题，首先给出 SH波对多个半圆形介质夹杂的散射波函数，并利用多极坐标系的方法，来满足介质界面上的连续条件和表面上的边界条件，归结为对一组无穷代数方程组的求解，简化了问题的求解。

New multi—objectives function (including mill stand longitudinal stiffness, distribution coefficient of loaded pressure between rolls, weight of mill stand, rolling power, rolls loaded gap profile changeability of bending force, transverse mill stand stiffness of bending force, transverse mill stand stiffness of rolling load) multi—constraints (including rolls strength, spindle strength, backup roll bearing load, minimum rollable gauge, roll surface temperature rise) rolls system parameters optimization model of four—high cold strip mill is established, and programme for mill structural illustration creation on the platform of AutoCad designs is compiled. With this as basis, rolls system parameters of Yichang thin strip corporation's 1219 cold mill are calculated using SUMT (subsequent unconstrained minimization technology).

本文建立了以板形和板凸度控制特性为目标的四辊轧机多目标函数（包括轧机纵向刚度、辊间压力分布系数、轧机重量、功率、弯辊力对轧机辊缝形状改变能力、对弯辊力的横向刚度、对轧制力的横向刚度）、多约束条件（包括轧辊强度、接轴强度、支承辊轴承负荷、最小可轧厚度、轧辊温升等）的辊系参数优化模型，以此模型为基础，利用惩罚函数法计算了益昌薄板公司1219冷轧机辊系参数，编制了AutoCAD平台下的轧机结构示意图自动图形软件。

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

In particular, Stolarsky mean are generalized from two variables to n variables. Moreover,we make ωi become weight function to diversity the kinds of mean function. For the mean family, we discuss mean family with single parameter or multi-parameter .

此外还通过改变权w_i，使之成为权函数，从而使n元平均函数的形式多样化，在n元平均族中给出了单参数和多参数平均族，并讨论了具体的单参数的幂平均族和指数平均族，多参数的Dresher平均以及由此构造的另一种形式的双参数平均族。

A generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance is proposed,which incorporates geodesic distance and generalized Gaussian function into the original Laplacian eigenmap algorithm.GGLE algorithm can adjust the similarities between nodes of neighborhood graph,and can preserve the different degrees of local properties by using super-Gaussian function,Gaussian function or sub-Gaussian function.Moreover,GGLE can avoid the deficiency of Euclidean distance by using geodesic distance when neighborhoods of data points are enlarged for preserving more neighborhood relations.Experimental results show that the global low-dimensional coordinates obtained by GGLE have different clustering properties and different degrees of preserving local neighborhood structures when different generalized Gaussian functions are used to measuring the similarities between high-dimensional data points.(3) An ensemble-based discriminant algorithm based on GGLE is proposed.

该算法将测地线距离和广义高斯函数融合到传统的拉普拉斯特征映射算法中，可以调整近邻图结点间的相似度，通过选择超高斯、高斯或者次高斯函数来实现不同程度的近邻局部特性的保持；而且当需要保持更多的近邻关系使得数据点邻域增大时，采用测地线距离可以避免欧氏距离度量不合理的缺陷；实验结果表明在用不同的广义高斯函数度量高维数据点间的相似度时，局部近邻结构保持的程度是不同的，GGLE获得的全局低维坐标也呈现出不同的聚类特性。

On the other hand, when we are proving the upper bounds of the Hausdorff measure functions for the level sets, although we get the answer to the cases for the symmetric processes, we had to consider multi-integral of highly dimensional functions, the proof is quite complex. Therefore, we suggest that the proof for the corresponding problem needs some new ways.

另一方面，我们在证明严格稳定过程的水平集的Hausdorff测度函数的上界时，虽然我们得到了对称的多参数稳定过程的水平集的Hausdorff测度函数上界，但是我们的方法必须考虑多重的高维积分，其证明过程也已经相当复杂，因此，我们认为，为了得到一般的严格稳定过程的水平集的Hausdorff测度函数上界，还需要引入其它新的研究方法。

An example is applied to show the stability of hybrid systems could be analyzed by using multiple Lyapunov function when the switching hypersurface becomes sliding mode.

针对由离散事件监控连续动态系统的这一类混杂系统稳定性问题，首先分析了多Lyapunov函数方法己有结果的不足，用一个算例来说明切换超平面成为滑动模时，基于多Q叩unov函数方法，并不能证明混杂系统的稳定性。

Especially since Lindley and Smith (1972) addressed the thought of hierarchical prior distribution and Han (1997) provided the methods to construct hierarchical prior distribution, more achievements have been made on hierarchical Bayesian methods to be used for solving zero-failure data problem.

所谓λ的多层先验分布的构造方法——减函数法，主要是选取λ的减函数作为λ的第一层先验密度函数的核，第二层先验分布——第一层先验分布中超参数的先验分布取均匀分布。

The linear approximation function uncouples the problems at different terminals so that we arrive at the local problem for each terminal at each time period.

构造线性替代函数来逼近目标函数中的期望函数部分，使问题分解为多个单时段单节点问题。

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。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

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起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。