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In the section, the definitions and main properties of the operator have been discussed systematically, the operational rules of one dimensional PGOPO have been strictly established based on the theory of convergence in the mean square, error and convergence analysis of approximation by PGOPO has been discussed.

系统地论述了分段广义正交多项式算子的定义、性质，并为一维PGOPO算子严格地建立一套在均方收敛意义下的代数运算规则，给出了分段广义正交多项式算子作用下的误差及收敛性分析结果。

By analysis and comparison the algorithms, the dissertation presented an algorithm, based on the Sobel operator and frame difference method. Considering the characteristics of infrared image, the frame difference algorithm is simple and easy to be realized by hardware.

文中对多种边缘检测算子进行了分析比较，其中Sobel算子在处理该类图像时的速度与效果比较理想，且算法简单易于DSP硬件实现，所以最终采用了sobel算子。

As a consequence, we make a conclusion that the dual Toeplitz operator is normal if and only if the range of the symbol lies on a line.

在此基础上研究了对偶Toeplitz算子的正规性，得到了对偶Toeplitz算子是正规算子的充分必要条件。

Based on the improved Bajsanski-Bojanic parabolic method and the related properties of integral operators, a global saturation theorem for the mixed exponential type integral operatorLnis established.

研究了该类混合指数型积分算子的性质，利用改进的Bajsanski-Bojanic抛物线技巧及积分算子的有关性质，建立了一类混合指数型积分算子的整体饱和定理。

So, the saturation results of some operators including Baskakov operator can be obtained easily, hence laying a basis for studying the approximation transformation theoremof the mixed exponential type integral operators, and presenting a new method for studying the saturation problems.

这样，包含Baskakov型在内的相关积分算子的饱和结果便可以很容易得到，为研究混合指数型积分算子的逼近转化定理奠定了基础，也为研究算子的饱和问题提供了新的方法。

Two amelioration operators were developed, such as the triangular intuitionistic fuzzy numbers weighted arithmetic average operator, and the f interval-valued intuitionistic fuzzy numbers weighted geometric average operator.

定义了三角和区间直觉模糊集的一些运算法则，给出了直觉模糊集两个改进算子，即三角模糊数加权算术平均算子和区间直觉模糊数加权几何平均算子。

A relative Szego projection is defined in the space of small deformations of 3-d CR structures of finite type, which is Fredholm. We also prove an index theorem, in whose proof we actually have the asymptotic expansion of the Szego kernel.

在三维有限型的CR结构的小形变空间上定义了相对Szego投影算子，并证明了相对Szego投影算子是Fredholm算子和相应的指标定理。

In this paper,we build symplectic structure of 2-nd order and high order singular differential operators on infinite interval, we construct a symplectic space by the maximal and minimal operator domain .

本文研究了无穷区间上二阶、高阶奇型微分算子的辛结构，利用最大与最小算子域构造了一个辛空间，用辛空间中的线性流形来刻画定义在无穷区间上二阶、高阶奇型对称微分算子的自共轭扩张问题。

Secondly, we define a monotone operator and prove that the orthogonal projection is the solution for the monotone operator equation.

其次定义了一个单调算子，利用单调算子的理论，证明了求解这个正交投影等价于求解一个单调算子方程。

In this model, a parameterized method has been employed to decrease or eliminate vertical deflection and vertical refraction errors.4 For the long baselines of Crustal Movement Observation Network of China, using the GPS satellites orbits and stations positioning analysis software GAMIT opened up by MIT to do the single day GPS observation data processing, a synthetic solution model, which is called "the synthetic solution model of baseline vectors", has been built up with several single day baseline vectors calculated by the GAMIT software, to compute the three dimension movement velocities of sites.

对于长基线的GPS地壳变形监测网，采用MIT开发研制的精密GPS定轨定位软件GAMIT进行单天GPS观测数据的处理，提出了利用多期单天的GAMIT解算出的基线向量进行综合解算的模型："基线向量综合解算模型"，用以计算地壳监测站点的漂移速度，并通过实例验证了该计算模型的正确性和可靠性。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。