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This paper have also explored the nonwandering property of sum of operator, direct sum of operator,tensor products of operators and differentiation operators which can be viewed as weighted shifts on some space.

本文也研究了和算子，直和算子，张量积算子以及在某种意义下可看成加权移位的微分算子在一定空间上的非游荡性。

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量(地面点到地下相点的水平距离)的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

We studied the different kinds of the edge extractor and the criteria of how to evaluate the performance of different method.

一方面分析了不同类别的边缘提取算子的优缺点、评价边缘提取算子性能的准则，并对不同的算子进行了比较研究，给出了实验结果。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

Second, the theory of scale space was used to design a new operator for target detection and tracking. Then, the property of scale invariant was analyzed and proved, and a tracking scheme based on the gradient LOG operator was proposed. Experimental results show that the gradient LOG operator is appropriate to describe small target in complex background, and the detection precision is in the level of sub-pixel. Furthermore, it is efficient and robust to noise.

然后根据尺度空间的基本理论构造了一种针对该成像模型的目标检测算子，分析并证明了该算子具有尺度不变性的优点，设计并实现了基于梯度LOG算子的小目标跟踪方案，实验结果表明：梯度LOG算子能够较好地跟踪复杂背景中的光团目标，定位精度可达亚像素级，且具有计算量小，抭嗓声能力强等优点。

Second, the theory of scale space was used to design a new operator for target detection and tracking. Then, the property of scale invariant was analyzed and proved, and a tracking scheme based on the gradient LOG operator was proposed. Experimental results show that the gradient LOG operator is appropriate to describe small target in complex background, and the detection precision is in the level of sub-pixel.

然后根据尺度空间的基本理论构造了一种针对该成像模型的目标检测算子，分析并证明了该算子具有尺度不变性的优点，设计并实现了基于梯度LOG 算子的小目标跟踪方案，实验结果表明：梯度LOG 算子能够较好地跟踪复杂背景中的光团目标，定位精度可达亚像素级，且具有计算量小，抗噪声能力强等优点。

In addition, we consider some conditions under which Weyl\'s and Browder\'s theorem hold for operator matrices.In chapter 4, the relationship between the reduced minimum modulus of the left multiplicative operator L_A and the reduced minimum modulus of operator A is discussed.

第三章重点研究了Banach空间上的算子满足Weyl定理和a-Weyl定理，得到了解析余亚正规算子满足a-Weyl定理；同时也讨论了上三角算子矩阵的Weyl(来源：ABC论63文网www.abclunwen.com)定理和Browder定理。

Moreover,we consider the techniques in calculating the map\'s degree respectively in two cases that the functional responses function is monotone and differentiable or is nonmonotonic and undifferentiable.

本文深入到算子度的计算方法尤其是抽象算子同伦映射的构造，并为抽象算子同伦映射的构造提供了普遍适用的操作方法，即一步到位构造一个多项式函数作为抽象算子的同伦映射。

Edge detection is one of the important roles in the digital image processing, the Prewitt operator, LOG operator and Canny operator are adopted in the classical edge detection operator arithmetic in space domain.

边缘检测是数字图像处理的一个重要内容，讨论了经典的边缘检测算子算法，该算法更多地采用Prewitt算子、LOG算子、Canny算子等在空域中进行。

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。