有效函数

It provides a way to find optimal lower dimensional approximations of the given data, and It enormously reduce the storage of the data which is needed when the physical processes is recurred. The physical process can be described in series expansion function that only is related to the time and space. It is optimal approximation of the given data in a certain least squares optimal sense. The most obvious advantage of the method is that it reduces the computation cost and computation time markedly.

它提供了一种描绘物理过程的有效方法，该物理过程可以写成一个只与时间相关的函数和一个只与空间相关的函数的展开式序列，且它们在均方意义上是最优的，在展开式中只需要少量的项数就可较准确地描述该物理过程，因此降低计算维数、减少计算量和节省计算时间是这个方法最明显的优点。

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。

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。

In the modified method, we use orthogonal decomposition so as to delete items which lead to linear dependence of gradient in active constraints. Therefore the Hessian matrix of the DQP subproblem is positive definite.

在改进算法中，我们通过正交分解删去了有效约束函数中引起梯度线性相关的项，从而保证了DQP子问题中的目标函数中的Hesse阵正定。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation. The difference between the original linear solution and the solitary wave theory results from the nonlinearity and dispersion of generated waves in the flume.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

Chapter 4,based on strong efficiency rather than efficiency or weak effi-ciency,discusses the similar problem to chapter 3.The concepts of strongsupremum and strong infimum for the set in finite-dimensionalEuclidean space are given,s-conjugate functions and s-subdifferentials theory is developed,by means of which,the duality problem ofmulitobjectivre programming for strong efficient solutions or called absoluteoptimal solutions is analysed,and a new duality theory-s-conjugateduality theory is proposed.

第四章，基于强有效性而不是有效性和弱有效性，给出了类似于第三章的结果，提出了有限维欧氏空间中集合的强上、下确界等概念，研究了点集映象的强共轭函数和强次微分问题，建立了点集映象的s-共轭函数及其s-次微分理论，并借助于这一理论，讨论了多目标规划关于绝对最优解或称强有效解的对偶性问题，建立了基于强有效性的s-共轭对偶理论。

This paper expresses several kinds of functions to the differential coefficient of intermediate variable, then in means of calculus and in use of the technique of variable replacement , finding the effective way to the solution of these kinds of function ; moreover, it gives the expression to the function solved.

本文提出了若干类函数对中间变量的导数，借用微积分的方法，运用变量替换的技巧，找到了求这几类函数的有效方法。

The variational convergence of real function sequence is extended to vector function sequence and the lower semicontinuity of approximating set of weak Pareto solutions of a given multiobjective decision making problem with general constraint set is obtained by using the variational convergence.

本文将函数序列的v－收敛性推广到向量值函数，在v－收敛性的条件下得到了给定的多目标决策问题的近似弱有效解集的下半连续性并给出了若干容易验证的充分条件。

By a more precise estimation of maximum value of a B-spline basis function and utilizing of the local support property of B-spline basis function, the control points of a set of compatible B-spline curves are reduced, which makes the skinning algorithm more effective.

对B样条基函数的最大值进行了更为精确的估计，并且充分利用B样条基函数的局部支撑性，尽可能多地删除相容性处理后B样条曲线的控制点，使得蒙皮算法更加有效。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了