维数理论

In the first part,two methods calculating the coefficients of nilpotentclass normal forms are proposed.one is the iteration search method based onrepresentation theory of Li-algebra,and another is a new matrixrepresentation method based on the adjoint operator concepts,both are ableto be used to analyse the normal form problems with high orders and largedimensions efficiently.

在第一部分工作中，对于幂零类规范形的系数计算，分别提出了基于李代数表示论的迭代搜索的理论和方法以及基于共轭算子概念的新的矩阵表示的理论和方法，从而有效地解决了维数和阶数较高时的计算问题。

We get a theoretical error of the fine antithetic variables Monte Carlo method for multidimensional integration.

对维数是s的二阶导数连续的函数来说，FAMC方法理论误差的阶是O。

Studying the positive definitiveness of the covariance matrix from discrete data is important to design the sampling plan and provides the base for the data analysis.However, there have been few outcomes about the positive definitiveness of covariance matrix, most of which have been restricted to the Covariance-matrix of continuous sample.

研究离散型样本协方差矩阵的正定性有助于判断是否可以降低样本的维数，有利于优化抽样个数，为抽样调查的优化设计方案提供一定的理论基础；为基于特征根的多元统计分析提供理论指导。

There is the Cauchy problem of hyperbolic system with weak damping in Chapter4. In the space of dimension N=1,3, exploiting the semigroup method, the global existence and the decay behavior of the solution with small initial data to problem (about problem with small initial data) is put forward.

当空间维数N=1，3和初值充分小时，利用半群理论得到问题整体解的存在性，并对于整体解给出一致衰减估计；当空间维数N=1 时，利用试验函数方法讨论解在有限时刻爆破的条件。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

Aiming at the dual affects to classification results by each input data, this method has punish item be fuzzy, compensates weight to classification, reconstructs the optimization problem and its restrictions, reconstructs Langrage formula, and presents the theories deduction. This method is applied to the credit evaluating system of personal loan.

1引言支持向量机(Support Vector Machine，SVM)是20世纪90年代中期在统计学习理论(Statistical Learning Theory，SLT)的基础上提出的一种新的机器学习方法，它基于VC维理论和结构风险最小化原理，在很大程度上克服了传统机器学习中的维数灾难以及局部极小等问题[1，2]。

With the limitation of the line detection based on traditional Hough transform that the information of the length and the end points of the line is unavailable, a new algorithm which makes use of the accessional strategy based on precognition information is put forward to meet the demand for more information of the line, simulation results show this method is effective. Finally, the whole process of airport target recognition is presented and the result images are also given.

使用分形方法提取目标的特征，在知识指导下，提出了一种基于目标特征模型的降维的形态学分形维数计算方法，对传统分形方法进行了改进，从理论上推证了算法的合理性，并对算法进行了仿真分析；针对传统Hough变换无法获得线段端点和长度信息的局限性，提出了一种基于目标特征先验知识的Hough变换融合策略，通过引入目标先验知识，可以有效地获得直线信息；对信息多而复杂的机场目标采用基于知识的目标识别方法，使用置信度模摘要型实现不确定推理，对目标进行识别判断，将知识贯穿于整个识别过程中，对目标进行了有效地识别。

This dissertation involves the study of the growth dynamics of colloidal particles under unequilibrium and irreversibility condition. Firstly, it is of interest to investigate whether the ideal diffusion or reaction-limited aggregation universal behavior can be observed for the initially polydisperse practical system of basic yttrium carbonate as well. The fractal structure of basic yttrium carbonate aggregate cluster was observed using transmission eletron microscopy. The aggregation kinetics of basic yttrium carbonate colloids was studed using dynamic 1ight-scattering techniques. At 1.00mol/l NaCl solution the fast diffusion-limited aggregation behavior was observed with an increase in the aggregate size over time described by a power law. The aggregates are characterized by a fractal dimension D=1.82. The disordered and ramified cluster is consisted of primary colloidal particles and tenuous and more open. These are in good agreement with those observed for other colloidal system such as colloidal gold (1.86), silica (1.85) and polystyrene latex (1.82) in diffusion-limited aggregation from the static and dynamic light scattering by Lin. Therefore ideal diffusion-limited aggregation behavior can be observed in practical polydisperse system as well. Smoluchwski and fractal theories were used to obtain the aggregation rate constant for initially polydisperse system for the first time.

本论文研究胶粒的非平衡不可逆聚集动态学，分为两个部分，第一部分是通过实验研究一个新的初始多分散的碱式碳酸钇胶粒实际体系中，聚集标度性质的普适性，即使用透射电子显微技术观测聚集粒子簇的分形结构，使用动态激光光散射研究碱式碳酸钇胶粒的聚集动力学，胶粒带电而产生静电排斥作用使得碱式碳酸钇胶粒处于稳定状态，当加入电解质NaCl溶液时，碱式碳酸钇胶粒间的Debye-Hückel屏蔽距离缩短，从而降低静电排斥能垒，引起胶粒发生不可逆聚集，加入电解质NaCl的浓度为1.00mol/l时，碱式碳酸钇胶粒进行快速聚集，经历扩散控制聚集机理，形成结构疏松、更为开放的分形聚集粒子簇，其分形维数为1.82，碱式碳酸钇胶粒聚集增长动力学遵循幂函数增长规律，与Lin等使用静态激光光散射和动态激光光散射测量硅胶(1.85)、金胶(1.86)和聚苯乙烯胶乳(1.82)在扩散控制聚集状态形成聚集粒子簇的分形维数值以及粒子簇聚集增长的动力学规律相一致，表明胶粒聚集标度性质的普适性质在初始多分散的实际体系中也是存在的，首次由动态激光光散射的实验数据得到初始多分散胶粒分形粒子簇的聚集速率常数，并且其值与Smoluchowski聚集速率理论预期相符。

Based on the analysis to the particularity of the cruise missile attacking, a complete recognition method based on the knowledge is developed. A new fractal-based infrared image feature extraction method is presented and the detailed theoretic analysis and implement procedure of this algorithm is submitted and tested in some experiments. With the limitation of the line detection based on traditional Hough transform that the information of the length and the end points of the line is unavailable, a new algorithm which makes use of the accessional strategy based on precognition information is put forward to meet the demand for more information of the line, simulation results show this method is effective. Finally, the whole process of airport target recognition is presented and the result images are also given.

使用分形方法提取目标的特征，在知识指导下，提出了一种基于目标特征模型的降维的形态学分形维数计算方法，对传统分形方法进行了改进，从理论上推证了算法的合理性，并对算法进行了仿真分析；针对传统Hough变换无法获得线段端点和长度信息的局限性，提出了一种基于目标特征先验知识的Hough变换融合策略，通过引入目标先验知识，可以有效地获得直线信息；对信息多而复杂的机场目标采用基于知识的目标识别方法，使用置信度模型实现不确定推理，对目标进行识别判断，将知识贯穿于整个识别过程中，对目标进行了有效地识别。

In this article, the author systematically summarizes current research and tendency of fuzzy rough set theory.

模糊粗糙集理论是解决数据集维数问题的有效工具，但基于模糊粗糙集的降维算法还不多。

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。