算子函数

We firstly look back thebirth of SD method,and then present the SD scheme presented by Johnson et.al.forlinear problem to explain the basic idea and implementation:At step 1,we change the testfunctionwhere(1,β)t is the streamline or character direction decidedby hyperbolic operator of the continuous problem,therefore the SD method belongs tothe Petrov-Galerkin method;At step 2,we adopt time-space finite element space,whoseelement is only continuous in space variables x but discontinuous in time variable t.

首先回顾了SD方法的产生过程，然后以线性问题为模型，描述了SD方法的基本思想和具体实现：第一步，将标准有限元方法的检验函数ν改成其中(1，β)t是连续问题的双曲算子部分所确定的流线方向。换言之，SD方法是一种Peterov-Galerkin有限元方法；第二步，采用时空有限元空间，其元素关于空间变量x是连续的，但关于时间变量t仅分段连续。

In view of continuous function problems, it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem. Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收效，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收效的证明。

In view of continuous function problems,it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem.Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收敛，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收敛的证明。

New image fusion method based on biorthogonal wavelet that different frequency component on each decomposition level uses different operator is proposed.

bstract 提出一种各分解层上的不同频率分量采用不同的融合算子的双正交小波函数图像融合的新方法。

A dynamic interaction schematic of an end bearing or elastic bearing pile with arbitrary force at pile top is founded. By using Helmholtz resolution and the operator decomposition method, Biots equations governing motions of a porous solid saturated with interstitial fluid are decoupled.

建立饱和土中端承桩和摩擦桩在任意激振力作用下的理论模型，利用位移势函数及微分算子分解方法，得到饱和土层Biot动力固结方程的分离变量解。

The main research aspects are as following. 1. The zero-order differential operator is constructed, based on the inside interpolation collocation method.

一、在内延拓配点的基础之上，构造了0阶导算子去对函数进行相应的级数展开和插值，证明了它对边缘效应和Gibbs现象的抑制作用。

The asymptotic estimations of solution of initial value problem are obtained for Dirac equation by use of the transformation matrix operator in this thesis.

本文运用平移算子，得到了Dirac方程初值问题解的渐近估计。构造了一个整函数ω，其零点集合与具有一般两点边界条件的Dirac特征值问题的特征值集合重合。

Image matching algorithm which based on directed Hausdorff distance and immune genetic algorithm consists of defining code and adaptive degree function, confirming intercross variation operator and immune operation.

部分Hausdorff 距离和免疫遗传算法相结合的图像匹配算法包括：定义编码与适应度函数、确定交叉变异算子及免疫操作。

The system parameters are determined by optimizing an output-error cost function. To deal with the non-uniqueness of the fully parameterized state-space system, a projected gradient search algorithm is presented by restricting the update of the parameters to the tangent space to the manifold of observationally equivalent state-space systems. The sufficient condition to employ L-M algorithm for optimizing parameters is also introduced. The proposed hierarchical optimization identificationmethod includes two steps: First, the parameter search direction is determined by the proposed adaptive L-M projected gradient approach; Second, the optimum step size is computed according to a line search method.

通过极小化输出误差目标函数获得了系统参数估计；提出了正交梯度搜索方法用于解决系统参数的非唯一性问题，正交梯度搜索的本质是在输入-输出等价类相切平面的正交垂空间更新系统参数；给出了用 L-M 算法进行参数优化的充分条件；提出的系统参数递阶优化辨识方法包括两步：首先用给出的自适应 L-M 算子正交梯度方法确定参数优化方向；其次由一维搜索方法计算最佳步长。

Although some results on convex and concave iterative roots are known, there are no results about convexity for more general iterative equations. In this chapter, convexity of both increasing solutions and decreasing solutions is investigated by the divided difference theory and fixed point theory.

本章在连续函数构成的紧凸集上构造一个连续自映射算子，利用均差理论和不动点理论证明了线性型迭代方程的凹凸解的存在唯一性及连续依赖性。

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。