可变换性

In chapter four,at first,we investigate classification theory of the positive homogeneous p-Laplacian equation ,the main method is Prufer's transformation,and then we discuss the nontrivial solution for associated nonhomogeneous equation by making use of Leray-Schauder degree.

接着研究了非齐次方程的可解性。在第四章中，我们首先是建立了正齐次p-Laplacian 方程的分类理论，主要利用Prufer 变换。再应用Leray-Schauder 度理论证明非齐次方程的可解性。

Using a large data set of 1 894 images,we examine whether the colorspace transformation can increase the compactness of skin distribution and the discriminability between skin and nonskin distributions in fourteen 3D colorspaces and fourteen 2D chrominance planes.

比较结果表明：(1)颜色空间的变换并不能改善肤色紧致性、肤色-非肤色可分辨性以及分类等性能，但RGB及线性变换空间却具有较好的类可分辨性和分类性能；(2)去除亮度信息将明显降低肤色和非肤色之间的可分辨性和分类性能；(3)Bayes决策下的3维SPM的分类性能是最优和空间无关的，而其余分类器则普遍存在类似的"空间偏好性"；(4)同时采用肤色和非肤色模型的分类器的分类性能优于仅使用肤色模型的分类性能。

By the analyses of different person and the same person with different expression and gesture, the number of principal component vector is determined properly under the attention to divisibility and workload.

首先对不同人以及同一个人的人脸图像进行主成分变换，然后根据得到的人脸图像类内及类间距离数值的变化结果，在充分考虑到其可分性和计算工作量的前提下，选择适当的主成分变换向量的个数并进行人脸图像的特征提取。

Based on analyzing the separation detection conditions of imperfect superposition holes and the measurability of ballistic coordinates,the method of automatic measurement was presented on the basis of distance conversion,which is a successful application of distance conversion and watershed.

在分析了不完全重合弹孔的可分离检测条件、弹道坐标可测性的基础上，提出了基于距离变换的弹道坐标自动测量方法，是距离变换分水岭方法的一种成功应用。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

The measurement system error model analysis is introduced into power system real time network state analysis as an important part for the first time, which can improve on the state estimation quality and provide the capability to monitor the operation of the measurement system; 2. The theory and algorithm of the on-line estimation and update of measurement noise variance based on the relation between the residual variance and noise variance. The statistic properties of the sample variance are discussed and the relation between the estimation precision and sample size under given confidence level is derived; 3. The theory and algorithm of detection and identification of measurement bias are presented, which is based on the relation between residual mean and noise mean. The statistic properties of sample mean are discussed and the relation between estimation precision and sample size is derived; 4. The Givens orthogonal transformation algorithm is selected to be the essential algorithm of state estimation, the fast orthogonal transformation algorithm with damp factor and the algorithm which can handle the zero injection measurements efficiently are presented; 5. The quantity analysis theory of bad data detectivity and identifibility are presented, which describes the relation between the elements in matrix W〓 and bad data amplitude and can provide the theory base for measurement system design and valuation.

一、首次将量测系统误差模型分析做为一个环节引入电力系统实时网络状态分析中，为EMS系统增加了实时监视系统运行、修正量测系统误差模型的新功能，进一步发挥了实时网络状态分析应用软件的潜力；二、首次提出了应用样本方差在线估计与修正量测系统误差方差的基本理论，讨论了样本方差的统计性质和概率分布，推导出了样本容量、估计精度和置信度之间的关系，给出了在线估计与修正量测系统误差方差的算法；三、首次提出了应用样本均值在线检测与辨识量测偏差的基本理论，讨论了样本均值的统计性质，推导了样本容量、估计精度和置信度之间的基本关系，给出了在线检测与辨识量测偏差的算法；四、在状态估计算法设计中，以Givens变换算法做为基本算法，提出了快速正交变换阻尼因子法和可以有效地处理零注入量测的混合法，并对实时应用中的一些问题进行了讨论；五、提出了不良数据可检测性与可辨识性的定量分析理论，揭示了描述量测系统配置、网络结构与参数的残差灵敏度矩阵中的元素与不良数据的幅值在可检测、可辨识能力上的定量关系，为量测系统配置设计与评价提供了理论基础；六、综合国内外最新研究成果，采用自适应自回归预测技术和稀疏矢量技术，构造了较完善的不良数据检测与辨识算法。

Using the result for non-restricted model, we transform the restricted model to common model, and multi collectivity model to single collectivity model, thus, the necessary and sufficient conditions that nonhomogeneous linear estimators for Sβ are admissible in the class of nonhomogeneous linear estimators are obtained which filled the blank for admissibility for restricted linear model.

对线性等式约束的共同均值线性模型，利用无约束单总体模型的现有结果，通过适当变换，把等式约束模型向无约束转换，并把多总体转换为单总体，在矩阵损失下找到了均值参数β的条件可估函数Sβ的线性估计∑mAiyi+a在非齐次线性估计类中可容许的充要条件，填补了等式约束的共同均值线性模型可容许性方i=1面的空白。

First, since the GRT is linear and addible, the dissertation proposes the parallelized implementation of Generalized Radon Transform. The implementation is based on the GRT Cartesian space's decomposition.

基于广义Radon变换具有良好的线性可加性，本文提出一种以分解图像空域笛卡尔空间为基础的广义Radon变换并行化实现，从而使得广义Radon变换能有效地运用于实际应用中。

Then, the relation between vibration and sound, the acoustic holography method, the indeterminacy and identifiability of BSS, the BSS algorithm are discussed in detail. Based on above researches, the dissertation is divided in following four sections. The first section investigates the BSS algorithm suitable to acoustic feature separation. The algorithm of the joint approximate diagonalization of eigen-matrices is proposed. The spectra or the time-frequency distributions of source signals are the interesting features in ABD and they are separated from mixing signals by JADE algorithm. Then, the convolutive mixing model is transformed into a high-dimension instantaneous mixing model, and the deconvolution of source signals is achieved by the joint approximate block diagonalization of eigen-matrices. The proposed algorithm has a global minimum, and it is unsensitive to noise interference.

论文首先概述国内外声学诊断研究进展与盲分离研究进展，给出机器噪声声场与盲分离的数学描述，讨论了声振辐射、声全息、盲分离模型、盲分离可解性、盲分离结果不确定性、分离算法等基本问题，在此基础上，论文的研究工作分为以下四个部分：第一部分研究适用于声学特征分离的盲分离算法，提出基于特征提取的联合近似对角化盲分离算法，该算法以频谱特征或时频特征作为分离目标，从混合信号中分离源信号频谱特征或时频特征，最大限度地保留了与声学特征提取有关的频谱特征或时频特征，采用模型变换把卷积混合模型变换为一个高维瞬时混合模型，通过联合近似分块对角化算法实现源信号频谱特征与时频特征的盲反卷积。

With the transform analysis of the edges images, the linear characteristics of the edges of the empty-trains-images were outstood.

结果表明：形态学操作有效地减弱了其他对象的边缘，得到比较满意地空列车图像的直线性质的边缘；在不同监控对象的图像的Radon变换域中的特征最大值比Hough变换域中的特征最大值有更好的可分离性。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。