算了

We establish the equivalent integral equations to these problems, and prove that the defined operator is completely continuous.

建立了与这些问题等价的算子方程，并证明了所定义的算子是全连续的。

Chapter 3 studies the compactness of product operators of a composition operator C〓 with the adjoint C〓 of another composition operator C〓 on weighted Bergman spaces A〓. We give some conditions in terms of angular derivatives of the inducing maps ψ and ψ for the operator C〓C〓 or C〓C〓 to be compact.

第三章研究了加权Bergman空间上的一个复合算子C〓与另一个复合算子C〓的共轭算子C〓的乘积C〓C〓与C〓C〓的紧性问题，我们用φ与ψ在〓D上的角导数的某种关系给出了C〓C〓与C〓C〓在A〓上为紧算子的一些判据。

First,an optimal filtering operator on the continuous fractional Fourier domain is provided according to the orthogonality principle about the linear minimum mean square error estimation,and then,a discrete algorithm of the filtering operator is further proposed.

首先由线性最小均方误差估计的正交条件出发，得到了连续分数阶傅立叶域上的等效Wiener滤波算子的求解方法；在此基础上，进一步给出了滤波算子的离散化算法。

In Chapter 3, using space decomposition and block operator matrices, we study theΓ-inverse of operators in a complex Hilbert space.

我们刻画了算子A的关于算子P和Q的Γ-广义逆A_~+存在的充要条件，并且当存在A_~+时，我们具体地给出了A_~+。

In image processing, method as follows will be introduced in this paper: a method combining image threshold iterative segmentation with threshold interpolation, edge detection operator Sobel and LoG, edge linking method using delation operator based on mathematical morphology, using boundary tracking and projection method in edge distill process. Through this method, measurement of wheelset will be met precision demand.

本文阐明了图像的分通道自动采集过程，以及对采集到的原始图像进行预处理过程，达到图像去噪声的目标，本课题采用了阈值分割中迭代阈值和阈值插值相结合的方法，Sobel算子、LoG算子边缘检测算法，基于数学形态学的膨胀运算子进行边缘断点连接以及目标提取中的投影法和边缘跟踪方法，使得提取轮对图像边缘达到测量精度的要求。

In this paper, a mathematical description of mutation operator and a concept of mutation function for the study of evolutionary programming and evolution strategies are proposed, and several methods and examples of constructing mutation operator with uniformly distributed random variables are presented.

进化算法是研究全局优化算法中最重要的随机算法之一，本文给出了进化规划和进化策略的变异算子的数学描述，并提出变异函数的概念，在此基础上，给出了用均匀分布的随机数构造变异算子的几种方法和若干例子。

A new differential operator suitable for extracting leaves'texture was studied, and the percent histogram on base of the differential operator was used in extracting texture feature of leaves.

进行了基于差分算子的相对差值百分率直方图法提取缺素叶片上颜色差形成的纹理特征研究，并且提出了适合于本研究的最大化差分算子。

Moreover, we present a lattice path interpretation of the isobaric divided difference operators, and derive an expression for the flagged Schur function in terms of isobaric operators acting on a monomial.

并且，我们提供了齐次差分算子的一个格路径解释，从而证明了每一个带标志的Schur函数可以通过作用齐次算子序列在某个单项式上得到。

Thirdly, we study the energy operator systematically and successfully use it in two important diagnosis methods (resonance demodulation and spike energy) as an envelope algorithm. This algorithm can replace the Peak-Peak demodulation circuit.

最后，系统研究了能量算子方法，将其作为一种包络算法应用于共振解调和尖峰能量法两种重要的故障诊断方法之中，其中用能量算子方法成功取代了gSE法中的峰峰值检波电路。

We proposed a scheme that processes the discrete time signals by two-pass filter and digital integrator.Thirdly, we study the energy operator systematically and successfully use it in two important diagnosis methods (resonance demodulation and spike energy) as an envelope algorithm.

最后，系统研究了能量算子方法，将其作为一种包络算法应用于共振解调和尖峰能量法两种重要的故障诊断方法之中，其中用能量算子方法成功取代了gSE法中的峰峰值检波电路。

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。