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This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

This course provides a basic introduction of topics such as: interpolation, solution of nonlinear equations, curve fitting to measured data, numerical linear algebra, numerical integration, numerical differentiation, etc..

本课程介绍内容包括：内插法，非线性方程式求解，曲线近似法，线性代数数值运算，数值积分，数值微分等课题。

The research on generalized numerical ranges of operator contains n-numerical ranges and numerical ranges of operator polynomial.

在广义数值域方面，深入研究了算子数值域的重要推广：算子n-次数值域、算子多项式数值域及其谱理论两大问题。

The numerical results indicate that the operator splitting method effectively suppresses numerical oscillations in the cases of high air bearing number. The numerical results show that both air lift force and pitch moment increase with the ratio of the slider's rail height to the air film characteristic height and the air bearing number, and finally reaches to stable value.

比较在不同轴承数下的气浮力和纵倾力矩发现：同一轴承数下，气浮力随气膜特征厚度减小而增加；当磁头槽台高度与气膜特征厚度的比值相同时，气浮力随轴承数增大而逐渐增加直到达到某一值后保持不变；纵倾力矩随轴承数增加而增大到某个最大值后减小。

Based on modern optimization theory and optimal control theory, this dissertation studies some questions as follows:1. The optimization model of parameter identification of three-dimensional geologic history numerical simulation, algorithm and its applicationGeologic history numerical simulation is a basic content of basin numerical simulation, and the porosity is the major parameter in the evolution and development process of oil-bearing basin. According to the sedimentation and burial mechanism, the physical and chemical principles of oil geology, the mudstone porositys non-linear parabolic partial differential equation has been established.

本文应用现代最优化及最优控制理论，对如下一些问题进行了研究： 1、三维地史数值模拟的参数辨识优化模型、算法及应用地史模拟是盆地数值模拟的一个基础性的研究内容，地层孔隙度是含油气盆地地史演化发育过程中的重要参数，根据地层沉积埋藏机理和石油地质的物理化学原理，通过引入数学物理方程概念，建立了泥岩三维孔隙度场方程，根据问题的特点，给出了方程的定解条件，对方程的动边界也给出了处理方法，并且证明了解的存在性与惟一性，在此基础上建立了以当今实测数据为拟合准则的三维地史数值模拟的参数辨识优化模型，这是一个含有二阶偏微分方程约束的泛函极值问题。

Taking Master CAM as an example, the paper introduces the technique of postposition dispose for numerical automatic control programming based on CAD/CAM integration, and explains by the example the process of postposition dispose for numerical control programming, generating the numerical control programming, and then producing and machining.

以Master CAM为例，介绍了基于 CAD /CAM一体化的数控自动编程加工中的后置处理技术，以及在当前条件下如何进行数控加工后置处理。

The classical cutting stock algorithm——column generation technology , and wrap up rectangle technology for abnormity are analyzed ; The development of AutoCAD with ObjectARX is studied and the generating method of cutting outline drawing and layout drawing were found out on the basis of analyses of the graph database structure of AutoCAD and the basic operation of it ; The process planning technology of plate material cutting orienting numerical control is studied a process planning method directly based on layout drawing is established ; The emulation technology in AutoCAD is studied and a kind of dynamic emulation method is put forward , which is realized by incrementally modifying graph entity ; The postposition of NC program of the integrated cutting system constructed on software plug-in is proposed , which can effectively solve the problem that it is difficult for a numerical control programming system to be common , which is caused by the difference of instruction format and control parameter between different type of numerical control machine .

分析了经典的矩形件优化排样算法——列生成法和针对异形件的矩形包络算法；研究了基于ObjectARX 的AutoCAD 开发技术，结合对AutoCAD 图形数据库结构及其基本操作的分析，给出了下料轮廓图和排样图的生成方法；研究了板材数控下料加工的工艺处理技术，建立了一种直接基于排样图进行的图形交互工艺规划方法；研究了在AutoCAD环境中的板材下料数控仿真技术，给出一种通过增量修改图形实体对象实现的动态仿真方法；提出以软插件技术构建集成下料系统的数控编程后置处理部分，能够有效解决因数控下料机床指令格式及控制参数不统一导致的自动编程软件系统不易实现通用性的问题。

During the four years study on the project, we develop a dynamical forecast model that describing the subtropical ridge surface. A new theory on the role of the land-sea thermal difference on the formation of the Subtropical High is advanced. It is concluded that in the summer subtropics over each continent and its adjacent ocean LO, SE, CO, and a double-dominant heating from west to east compose a LOSECOD heating quadruplet. The influence of the Eurasia continent on SH varies according to the seasonal variation. From the ideal numerical simulation it is shown the important role of the Eaiuan continent and the huge topography on the mechanism of formation and mantanence of the SH during the summer. It is verified by the numerical simulation that the extension of the subtropical continent into the tropics greatly enhances the " East Asian monsoon". Through the Rossby energy dissipation theory it is verified that the deep latent convective heating induces the onset of the South China Sea monsoon over the Bay of Bengal. The relationship and mechanism between the precipitaiton over the East Asia and the Subtropicla high is illustrated by the data. It is also found the close phase lock between the east-west shift of the SH and the disturbence of the east wind belt over the tropical troposphere. The interaction between the structure and activity feature of the SH and the Meiyu over the Yangtze-Huaihe river valley is revealed from the data. The numerical simulation verified the impact of the different SH pattern on the path of the typhoon.

本项目的研究发展了描述副热带高压脊面变化的动力模型，提出了夏季副热带地区四叶型非绝热加热分布型及相应环流拼图的创新理论；明确了大陆尺度的海陆热力差异在副热带高压形成中的作用；指出欧亚地形对副热带高压和气候的影响随季节变化而变化，通过数值试验证明春季青藏高原的感热加热对亚洲夏季风的爆发地点起了"锚定"的作用，进一步证实了副热带高压断裂和亚洲夏季风的最早爆发地点发生在孟加拉湾东岸；利用Rossby波能量频散理论证明了孟加拉湾深对流潜热释放诱导南海季风爆发的机制；揭示了东亚季风降水的季节内变化与西太副高的关系及机理；揭示了西太副高与东西风带中扰动之间的相互作用过程，指出西太副高的东西活动与热带对流层上空东风带扰动和中纬度西风带扰动的移动和锁相密切相关；研究了夏季淮河流域梅雨期间副高结构和活动特征及其与江淮暴雨的相互作用；验证了不同副热带高压形态对台风路径的不同影响；通过数值试验证明了欧亚大陆和青藏高原等大地形对副热带高压形成和维持的重要作用。

In practical application of numerical control lathe, the sice precision of numerical control turning can be conteolled and ensured effectively by effective steps considering the influence of geometrical Rarameters to the sice precision of numerical control turning .

在数控车床加工的实际应用中，针对刀具几何参数对数控车削加工尺寸精度的影响，采取有效的措施，使得数控车削加工的尺寸精度，得到有效的控制和保证。

Numerical integral method is applied in this paper to study this problem, hoping to provide a reliable, yet simple numerical model for the application in the ocean disposal of waster water.Compared with other numerical model, momentum integral method is simple.

其思想是建立在流动自相似假定的基础上，使流动的控制微分方程简化成常微分方程，并以边界条件使方程封闭，从而结合定解条件来预报浮射流的流动特性，如流速和浓度的分稚规律。

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。