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We discuss the relation between elementary maps and ring isomorphisms, andwe give a characterization of elementary maps on stndard operator algebras on Banachspaces, JSL-algebras and nest algebras. For Jordan-triple elementeary maps, we provetheir additivity on a class of ring and show a relation of them with Jordan isomorphisms. Furthermore. we describe the Jordan elementary maps on standard operator algebrasand nest algebras. We also study the semi-Jordan elementary maps on effect algebrasand the space of self adjoint operators.

研究了算子代数上的初等映射和环同构的关系，完全刻画了Banach空间上标准算子代数，JSL代数和套代数上的初等映射；讨论了Jordan-triple初等映射的可加性以及它和Jordan同构的关系，进而完全刻画了Banach空间上标准算子代数和套代数上的Jordan-triple初等映射；刻画了效应代数和自伴算子空间上的semi-Jordan初等映射。

With the advancement of science and technology, some new theories and new ways emerged gradually, some of them merged with specific theoretical tools, this specific theoretical tools include mathematical morphology, fuzzy techniques, neural networks, wavelet and so on. Secondly, in this paper, it described and analyzed the segmentation method based on the edge in the domain of image segmentation in detail. It did experiments on several edge detection operators using MATLAB, it summarized the advantage and the shortcoming of traditional edge detection operators, and the operating environment. On the basis of the experimental analysis, it implemented an edge location more precise, more efficient operating speed edge extraction method——Template Vector. In this method, it optimized differential approximate calculation of first differential operators the paper mentioned. After experimented on this edge extraction method, contracted with the traditional methods, the edge outline is extracted more accurately and more exquisitely, furthermore, it retained the object outline furthest, and achieved more satisfied edge extraction result.

其次，对图像分割领域中常用的基于边缘的分割方法进行了详细的研究与分析，对各种边缘检测算子进行了MATLAB环境下的实验，分析总结了各种传统边缘检测算子的优缺点和适应环境，并针对传统边缘检测算子在处理显微图像时的缺陷，在实验分析的基础上研究并实现了一种边缘定位更加精确、运算速度更加快捷的边缘提取方法——模板向量算法，在该算法中，对文章提到的一阶微分算子中微分的近似计算作进一步优化，经过对该边缘提取方法进行实验，其结果与传统方法相比，轮廓提取更为精确细腻，且最大程度的保留了图像中物体(目标个体或者明显噪声点)的轮廓，得到了比较理想的边缘提取效果。

Based on general orthogonal polynomials and general hybrid orthogonal functions, a new linear, continuous and bounded operator has been proposed in the dissertation. The definitions and properties of PGOPO are given, a various operational rules of the operator have been set up in a systematic way, the convergence of approximate solutions has been discussed. After introducing PGOPO and discussing its main properties and operational rules, a systematic methodology for solving various control problems via PGOPO has been developed.

本文在广义正交多项式及广义混合正交函数的基础上，提出了一种新的线性、连续、有界算子—分段广义正交多项式算子，探讨了这种算子的基本性质，并系统地建立了与该算子有关的各种运算规则及收敛性结论，给出了它在控制理论中的各种应用。

For this reason, the project creates the mathematical model and numerical method of backcalculation of layer moduli in asphalt pavement based on homotopy method in accordance with the theories of differential topology and optimization. Through selecting the rational objective functions of backcalculation of moduli, a large number of deflection basins of asphalt pavement with FWD are made the backcalculation of moduli to solve effectively the present problems and ensure the reliability of backcalculation of layer moduli in asphalt pavement.

为此，本项目根据微分拓扑和最优化理论，建立了基于同伦方法的沥青路面模量反算的数学模型和计算方法，并通过选取合理的模量反算目标函数，对大量FWD实测的沥青路面弯沉盆进行了模量反算，从而有效地解决了目前存在的问题，保证了沥青路面模量反算的可靠性。

The general conditions of invertible completions of operator matrix Mx are supplied and the intersective characterization of the resolvent set of operator of Mx are been desribed.

4研究了算子逆配置的等价条件，并借助算子的ε-限制逆配置的刻画及正算子、紧算子的特性，完全刻画了算子对的逆配置。

The well-known spectrum assignment problem are discuussed and a general proofs for it and its generalization are gived. 3. The general conditions of invertible completions of operator pairs are acquired.

作为研究基础，引入了算子对可控性与可容许性指标及算子ε-限制，并利用算子闭值域特性、值域逼近及空间的不同分解，获得了算子谱配置问题及广义的算子谱配置问题一般性证明。

We also give all positive self-adjoint extensions ofsingular differential operators,and all positive self-adjoint operators generated by theproducts of differential expressions 〓,where l is an nth order differentialexpression.The result that each positive self-adjoint operator is not necessarily theform of operator product 〓.This answers an open problem proposed by theauthors recently.

我们也给出了奇型微分算子的所有正自伴扩张形式及乘积微分算式〓所诱导的所有正自伴算子形式，证明〓所诱出的正自伴算子不必须是由算子乘积〓为l所生成的算子）的形式，从而回答了作者新近提出的一个公开问题。

This chapter defines the conceptsof P linear operator,〓 linear operator and 〓 linear operator by extending theconcepts of P matrix,〓 matrix and 〓 matrix to the linear operator from thelinear space of symmetric matrices to itself.In this chapter,we also present a path-following method and a potential reduction method for solving general linear matrixcomplementary problems,and analyzes their computational complexities undersuitable assumptions.

本章将第二章中给出的P矩阵、〓矩阵及P矩阵的概念推广到由实对称矩阵构成的向量空间到其自身的线性算子L上，得到了P线性算子、〓线性算子及P线性算子的概念，给出了求解一般线性矩阵互补问题的路径跟踪法和势函数约减法，并在L为P线性算子的假设下分析了这些算法的计算复杂性。

For an abitrary set X, appropriate order relations on WCL (the set of all weak closure operators), WIN (the set of all weak interior operators), WOU (the set of all weak exterior operators), WB (the set of all weak boundary operators), WD (the set of all weak derived operators), WD*(the set of all weak difference derived operators), WR (the set of all weak remote neighborhood system operators) and WN (the set of all weak neighborhood system operators) can be defined respectively, which make WCL, WIN, WOU, WB, WD, WD*, WR and WN to be complete lattices that are ismorphic to CS(X,CS is the set of all closure systems on X.

证明了可以在WCL(X上的弱闭包算子的全体)、 WIN(X上的弱内部算子的全体)、 WOU (X上的弱外部算子的全体)、 WB (X上的弱边界算子的全体)、WD、 WD*(X上的弱差导算子的全体)、 WR(X上的弱远域系算子的全体)和WN(X上的弱邻域系算子的全体)上定义适当的序关系，使它们成为与CS(X，〖JX-*5[JX*5]同构的完备格其中CS(X是给定集合X上的闭包系统的全体。

The paper is organized as follows. In chapter 2, we introduce some concepts about SEA, the abstract SEA model and the convergence definition of algorithm. In chapter 3, we describe firstly the evolution of PMA as an abstract stochastic process, and by characterizing axiomatically the properties of the fundamental selection and evolution operators, we conclude that PMA is essentially a kind of SEA.

本文结构安排如下：第二章介绍了模拟进化算法的一些基本概念、形式化随机过程描述以及收敛性定义；第三章对改进后的 PMA 各操作作了抽象定义，得到了 PMA 的形式化随机过程描述，并公理化地证明了各操作算子为选择或繁殖算子，从而得出 PMA本质上也是一种模拟进化算法；第四章先对选择算子特征数定义作了适当改进，并通过各进化算子的具体特征数指出，如果 PMA 不采取任何执行策略时，算法本身并不收敛。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新