本质收敛

This algorithm combines the optimization of the characteristic vector and the adaptability of the neural network to improve the recognition rate and the robustness of the algorithm to noises.

事实上，学习过程的本质是特殊多元优化问题，BP算法即是以负梯度为寻查方向的线性收敛速度算法。

The essence of EGA's global convergence and its behavior characteristics are analyzed. Two kinds of realization methods of EGA are studied and convergence analysis of them is carried out.

首次给出了最优保留及最优保留GA的规范化定义，分析了EGA全局收敛的本质及表现特征。

The essence of design is to ensure trajectories of states ultimately entering into some neighborhood of the coordinate origin, and the convergence of states is evident later on.

设计的本质在于保证系统的状态最终进入坐标系原点的小邻域，而其后状态的收敛性是明显的。

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。

The findings are that the essential key of the convergence in real GDP per capita is the convergence of the potential level of GDP. The growth of potential GDP tendency slope would affect the converging speed of real income in regions.

我们发现，实质人均GDP收敛的本质关键在於潜在趋势水准收敛，潜在GDP趋势斜率的成长率将左右区域间实质所得收敛速度。

In chapter 3 constructs firstlya new differential merit function by a perturbation structure of VIP and study theproperties of this merit function.Based on this merit function,a continuation-typeNewton method is proposed,which use the technique of inexact linear search forassuring its global convergence,and improves essentially the method of Taji,Fukushima and Ibaraki which can only solve the strong monotone VIP,and has locallyquadratic convergent rate under some condition.

第三章利用变分不等式问题的一种扰动结构构造了新的可微效用函数，并研究了效用函数的性质；在此基础上，给出了一类求解一般单调变分不等式问题的连续型Newton方法CN，方法采用了不精确的线性搜索技术以确保整体收敛性，从本质上改进了Taji、Fukushima和Ibaraki方法只能求解强单调变分不等式问题的局限性，同时又保持了局部二次收敛率。

In this paper, the theory, algorithm, and experiment of automatic object detection and tracking are studied in depth. It is firstly pointed out that the essential of Mean Shift method is a special Newton-Gaussian method. A new method named Fast Mean Shift is established to stretch the conservative step of Mean Shift method. The convergence and validity of this new method are proved in theory. And it is also proved that the convergence speed of Fast Mean Shift is faster than that of Mean Shift. The contrast experiments of searching the maximum possibility density of random of data sets in plane and 3D space are done. The results show that this new method can reduce the iterations greatly. A new object tracking method based on Fast Mean Shift is built to improve the object tracking performance, which is shown in the face tracking experiment with the tennis sequence provided by the Ohio State University, and the car tracking experiment with the car sequence provided by Kalsruhe University. The face trcking experiment with highly noised images show that the object tracking method based on Fast Mean Shift has strong anti-jamming ability. A new fast color object detection technology based on characteristic color is established, which use characteristic color distribution to compute the characteristic color vector of any area in an image quickly. With the high performance search method, the fast object detection is achieved. At last, using object tracker based on Fast Mean Shift and color object detector based on characteristic color with the Kalman filter, PID controller, searial communication and other technologies, automatic object detection and tracking system with control system is built. The availability and anti-jamming ability of this system are verified by some object detection and tracking tests in different scenes.

本文对目标自动识别与跟踪进行了理论、计算、试验三方面的深入研究，主要包括：首次指出了目标跟踪技术中常用的均值迁移方法的本质为一种特殊的高斯-牛顿方法，改进了均值迁移方法步长取值保守的弱点，建立了快速均值迁移方法，证明了该方法的收敛性、有效性以及收敛速度优于均值迁移方法；进行了平面和3维随机分布数据集的最大概率密度搜索对比试验，试验结果表明，快速均值迁移方法大大减少了迭代次数；建立了基于快速均值迁移的目标跟踪方法，利用俄亥俄州立大学提供的乒乓球序列图像和卡斯鲁厄大学的汽车序列图像，对人脸和汽车目标跟踪性能分别进行了对比试验，并进行了高噪声人脸图像目标跟踪试验，结果表明，基于快速均值迁移的目标跟踪方法有效提高了目标跟踪性能，具有很强的抗干扰能力；建立了一种新型彩色目标自动识别方法，采用特征色彩分布函数实现了对任意图像区域特征色彩矢量的快速计算，建立了高效的搜索方法，实现了彩色目标的快速识别；将基于快速均值迁移方法的目标跟踪方法、基于特征色彩的目标识别方法与卡尔曼滤波、PID控制、串行通讯等技术结合，建立了带有控制系统的快速目标自动识别与跟踪系统，并在不同场景下进行了目标自动识别与跟踪试验，验证了快速目标自动识别与跟踪系统的有效性和抗干扰能力。

We can expect the algorithm to quickly converge to a minimizer once in a neighborhood of a solution on which the objective is essentially quadratic.

我们可以期望目标本质为二次的一个解的邻域里算法一次快速收敛到最小值。

By using the cone and partail ordering theory, and mixed monotone operator theory in nonlinear funtional analysis, the existence and uniqueness of the common fixed point for two non-monotone binary operator are discussed in partial ordering Banach space.

利用锥与半序理论和混合单调算子理论，讨论了半序Banach空间中两个非单调二元算子的公共不动点的存在性和唯一性，并给出了迭代序列收敛于公共不动点的误差枯计，所得结果是某些已知结果本质改进和推广。

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。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。