算了

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

The auxiliary variable system was constituted, and the recursive algorithm that can reduce the measurement noise interference has been developed. The bias property of LS with input/output measurement noise has been derived, and the self-adaptive deviation compensation principle of measurement noise variance has been proposed, and the corresponding algorithm is designed. The influence of parameters of wavelet modulating on estimation precision is investigated with simulation examples.

2构造了能降低测量噪声干扰的辅助变量系统及递推算法，研究了输入输出端测量噪声影响下最小二乘估计的偏差特性，提出了两种基于测量噪声方差估计的自适应偏差补偿原理并设计相应算法，用仿真算例研究了调制滤波器参数对辨识精度的影响。

We study several fixed point problems of a class of nonlinear operator,and obtain some new results in partial order Banach space .

研究了一类非线性算子的几个不动点问题，在偏序Banach空间得到了若干新的结果作为其应用，得到了Wm ，q空间中不动点的存在性定理同时，所得的定理改进了一些文献中的主要结

In this paper we study the method of interpolation by radial basis functions in H~k(k ≥ 1) and give some error estimates. By means of such interpolation with a special kind of radial basis function, we construct a basis in H~k(k ≥ 1). Combined with the Galerkin method, this theory can be applied to solve boundary value problems for elliptic partial differential equations (such as the third boundary value problem for Poisson equation and the corresponding problem for the biharmonic equation), and some numerical experiments are also given.

本文从求解偏微分方程的角度出发，在被逼近函数u属于一般的Sobolev空间H~k(k≥1)的情形，引入了一种径向基函数插值方法，并建立了相应的误差估计；再利用这种插值性质，从一类特殊径向基函数出发构造Sobolev空间的一组基，针对Poisson方程第三类边值问题和重调和方程类似边值问题，为用无网格算法求解偏微分方程边值问题建立了相应的理论，并通过算例来验证了这一算法。

She said,"I was very amused" I started throwin' bass, she started throwin' back mid-range But when I sprung the question, she acted kind of strange Then when I asked,"Do ya have a man," she tried to pretend She said,"No I don't, I only have a friend" Come on, I'm not even goin' for it This is what I'm goin' sing You, you got what I need but you say he's just a friend And you say he's just a friend, oh baby You, you got what I need but you say he's just a friend But you say he's just a friend, oh baby You, you got what I need but you say he's just a friend But you say he's just a friend So I took blah-blah's word for it at this time I thought just havin' a friend couldn't be no crime 'Cause I have friends and that's a fact Like Agnes, Agatha, Germaine, and Jacq Forget about that, let's go into the story About a girl named blah-blah-blah that adored me So we started talkin', getttin' familiar Spendin' a lot of time so we can build up A relationship or some undderstanding How it's gonna be in the future we was plannin' Everything sounded so dandy and sweet I had no idea I was in for a treat After this was established, everything was cool The tour was over and she went back to school I called every day to see how she was doin' Everytime that I ccalled her it seemed somethin' was brewin' I called her on my dime, picked up, and then I called again I said,"Yo, who was that?"

她说： "我感到非常好笑"我开始投掷'低音，她开始投掷'回到中间范围但当我，涌现出了问题时，她充当种奇怪那么，当我问他："做雅有一名男子，"她试着假装她说："不，我不，我只是有一个朋友"来，我什至还不算goin '，为它这就是我goin '唱你，你明白我的需要，但你说他只是朋友你说他是一个朋友，哦宝宝你，你明白我的需要，但你说他只是朋友但你说他是一个朋友，哦宝宝你，你明白我的需要，但你说他只是朋友但你说他只是朋友所以，我接拍了怎么-怎么的字，因为它在这个时候我以为只是havin '朋友不能没有犯罪'事业，我的朋友，这是一个事实如王春波， agatha ， germaine ， jacq 忘记一点，让我们走进故事约一个女孩名叫怎么-怎么-怎么说，我喜欢所以，我们开始talkin '， getttin '熟悉 spendin '了很多时间，使我们能够建立关系或某些undderstanding 它如何的好的，在未来，我们是plannin '一切听起来那么慰问和甜我都不知道我是一个对待经过这次成立时，一切都冷静巡回赛结束，她回到了学校我打电话，每天看到她是如何被doin '每当我ccalled她，这似乎somethin '，是蒲鲁贤'我打电话给她，我一分钱，拾起，然后，我再次呼吁我说，"协青社，他们是"？

Second, according to model characteristic, such as non-linear, non-convex, multiple-peaked and so on, the paper discusses limitation of traditional solving algorithm, such as branch and bound method, GBD method and OA method, puts forward penalty function-makeup integer algorithm and genetic algorithm, analyses procedures of genetic algorithm, such as selection, crossover and mutation, brings forward modifications for specific realized problems of genetic algorithm, such as selection of initial points, operator design, adoptive value adjustment, constraint treatment and so on, and works out correlated solving program.

其次针对该模型非线性、非凸、多峰等特点，讨论了分支定界法、GBD法和OA法等传统求解算法的局限性，提出了罚函数一凑整算法和遗传算法的求解思路，对遗传算法的选择、交叉、变异等过程进行分析，对遗传算法初始点选择、算子设计、适应值调整和约束处理等具体实现问题提出了改进措施，并编制了相关的求解程序。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为（n-1）维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料（单质材料作为特殊的功能梯度材料看待）、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

To understand the performance of DOA estimation using vector hydrophone array in a reflecting boundary, based on the reflecting model of plane acoustic wave, the improved Bartlett and Capon spatial spectrum are presented, and then the general frame is set up.

为了了解复杂分界面上矢量水听器阵列的定向性能，根据分界面上平面波的反射模型，提出了改进的Bartlett和Capon空间谱，建立了统一框架，并且在绝对硬边界典型界面下，分析了基于矢量水听器阵列的定向性能，给出了具体算例。

Meanwhile, it could be seen that there does not exist a confidence interval with width less than 0.5 because of the property of Poisson distribution. Based on these conditions, the author mainly carried out research into two aspects of this problem as follows. Firstly, by numerical and theoretical analysis, the author compares some existent confidence intervals, for example,"exact" confidence interval, Wald confidence interval and Bayesian confidence interval, and finds some deficiencies points of the confidence intervals, whose modification version has been proposed .Also, several better confidence intervals such asare also presented .Secondly, for given confidence coefficient and interval width, the author constructs a class of asymptotical two-stage interval estimate procedures. At the same time, under varies restriction of confidence coefflcientent interval width, the optional sample size of the first stage has been computed by numerical computation. The numerical computation shows that the method considered in this dissertation have good properties and applied value.

同时，由于Poisson分布的特性，我们知道不存在其参数区间长度小于0.5的置信区间，基于这些情况，我们主要展开了以下两个方面的研究：一是利用数值计算分析与理论分析的方法对现有的若干置信区间如"精确"置信区间，Wald置信区间，Bayes置信区间等进行分析比较，发现了一些缺陷，针对这些缺陷，我们进行适当的修正，并得到几种性质较好的置信区间如：修正大样本区间Jeffreys原则下置信区间二是针对已给定的置信系数与区间长度，我们提出了一种渐近的两阶段区间估计程序，并利用数值计算的方法，在各种置信系数与区间长度限定下，算出了最优的第一阶段观测次数，大量数据表明，本文考虑的方法性态良好，具有应用价值。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。