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Thismethod adopted affine transformation model and a Lie derivative-based analytical algorithm.We introduced the process and characters in extracting information of biological visionsystem, studied the feasibility of the generalized Gabor function used as receptive fieldfunction in extracting information and analyzed affine transformation group and Liederivatives. Finally, we deduced the mathematical denotation for Lie derivatives, i.e. theinfinitesimal generator of the geometric distortion in affine transformation.

对生物视觉信息提取的过程及特点进行了介绍，其中主要研究了广义Gabor函数作为感受野函数提取初级视觉信息的可行性；对仿射变换作为外界图像信息在视觉成像系统上的投影模型的原理进行了初步讨论；对Lie变换群微分算子用于提取仿射变换不变量的分析方法作了剖析，并推导了该方法中关键部分——仿射变换Lie微分算子的具体表达式，也就是几何变形无限小微分算子的计算表达式，使下一步编程实现该方法成为可能。

The controller makes the closed-loop systems internally stable and minimizes the H2 norm of the transfer matrix Tzw from w to z. Two Riccati formulae based on 8 operator is deduced. The H2 problems for continuous time systems, Z operator models and 8 operator models are investigated respectively.The guaranteed cost control problem of robust stabilization and robust performance for uncertain systems which is described by 8 operator is discussed in this paper.

采用Riccati方程处理方法讨论了基于Delta算子描述下的离散系统存在输出反馈控制器的问题，得到了两个基于Delta算子的Riccati方程，设计了Delta域的输出反馈控制器，使得闭环系统内稳定，且满足从w到z的传递矩阵T_的H_2范数最小，设计了基于Delta算子描述下的离散系统的最优控制器，并与S域和Z域的H_2控制器进行了比较。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

By using the cone theory and the iterative technique, the existence and uniqueness of positive fixed point for a class noncompact mixed monotone operator are studied.

本文利用锥理论和迭代技巧，研究了一类非紧混合单调算子正不动点的存在唯一性，改进和推广了混合单调算子、增算子与减算子的某些相应结果。

Author, secondly, starts from the approximate expandness of square root operator, perform mathematical calculations for finite difference operator in frequency-space domain, Fourier finite difference operator in mixing domain(frequency-space and frequency-wavenumber domain) and general screen operator in mixing domain, compare and discuss their precision of their wavefield, adaptability for lateral velocity variations, computation efficiency and stability.

第二，从平方根算子的近似展开出发对频率—空间域的有限差分算子、混合域(频率—空间域；频率—波数域)的Fourier有限差分算子、混合域的广义屏算子进行了推导并对其波场描述精度、对横向变速的适应性、计算效率和稳定性进行了比较与评述。

The relations of geometry structures between a positive operator and its shorted operator are exposed.

使用算子分块矩阵的技巧，研究了shorted算子，揭示了任意一个正算子和它的shorted算子之间的几何结构关系。

Research on development methods and application of CAD system of prac tical sheet metal expansion ;2. A frame expansion method of operator is used to the phase shift operator of split-step Fourier propagator.

针对裂步Fourier传播算子在速度强横向变化介质中的不足，将算子的框架展开方法应用于Fourier传播算子中的相移算子，提出了一种波场传播的局部裂步Fourier传播算子，并把它应用于波动方程叠前深度偏移成像。

By constructing different quotient spaces,using the method of symplectic geometry,the self-adjoint extensions of symmetric differential operators in the direct sum spaces for the different deficiency indices at(2,2)singular points was discussed. The classification and description of complete Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given.

由于对称微分算子在端点处的亏指数取值情况不同，当微分算子在端点处的亏指数均取(2， 2)时，通过构造商空间，应用辛几何的方法讨论了直和空间的对称微分算子的自共轭扩张问题，并给出了与二阶微分算子自共轭域相对应的完全Lagrangian子流型的分类与描述。

These opera-tors include composite type weakly compact increasing operators,T-monotone op-erators and theβ-constrictive operator which relatives with the measure of weaknoncompactness.

建立了若干不连续算子的不动点定理，这些算子包括复合型弱紧增算子、T-单调算子及与弱非紧性测度有关的〓增算子。

The process of our study links some of the most basic questions about C〓 with beautiful classical results from analyticfunction theory. For instance, it is essential Littlewood subordination theorem that assures that composition operators act boundedly on many analytic function spaces. And there are close connections between the compactness of C〓 and the existence of angular derivatives of ψ at points of 〓D. It involves the classical Julia-Careatheodory theorem, Denjoy-Wolff theorem and Nevanlinna counting functions and so on. It makes many old theorems in analytic-function theory getting some new meanings, and bestows upon functional analysis an interesting class of linear operators. This thesis consists of six chapters as follows: Chapter 1 is a preparatory in nature.

从而建立了C〓的算子性质与解析函数论中许多漂亮的经典结果之间的联系，如许多解析函数空间上复合算子的有界性本质上往往是著名的Littlewood从属原理，复合算子的紧性与其诱导映射在边界〓D上的角导数之间有着紧密的联系等等，这样自然而然地涉及到经典函数论中的Julia-Caratheodory定理，Denjoy-Wolff定理及Nevanlinna计数函数等等一些结果，并以此赋予函数论中许多古老问题以新意，同时也为泛函分析提供了一类十分具体的线性算子。

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。