规范变换

A diffeomorphism is applied to transform the nonlinear system into a new coordinate system. The stability and robustness of the system are analysized in detail.

根据微分同胚，将含有建模误差的非线性系统变换为易于分析的规范形式，并在此基础上分析了故障诊断系统的稳定性和鲁棒性。

After defining the normal forms and quasi—linearization forms, the simplified forms of uncertain nonlinear systems abtained by means of state feedback/disturbance feedforward/diffeomorphism are derived.

通过定义不确定非线性系统的规范型和准线性化形式，推出了不确定非线性系统经状态反馈/干扰前馈/微分同胚变换后所具有的简化形式。

Summary: The concept of matrix and its determinant computing, matrix determinant, matrix sub-block with the elementary transformation, invertible matrix, rank of matrix; vector and its computation, the linear relationship between vector, vector group of rank; linear equations of the nature and structure of linear equations; matrix eigenvalue and eigenvector, similar to matrix and matrix diagonalization conditions, the standard quadratic form with the normal forms, quadratic and symmetric matrix There are qualitative.

内容提要：行列式矩阵的概念及其运算，方阵的行列式，矩阵的分块与初等变换，可逆矩阵，矩阵的秩；向量及其运算，向量间的线性关系，向量组的秩；线性方程组的性质与结构，线性方程组的求解；矩阵的特征值与特征向量，相似矩阵与矩阵可对角化条件，二次型的标准形与规范形，二次型和对称阵的有定性。

The forced oscillators have been investigated with the use of the conjugated arithmetic operators and the matrix of the normal form theory.

第三章将非线性系统转换为一个四维的一阶系统，再进行非线性变换，将规范形理论中的共轭算子法和矩阵表示法联合一起应用，研究了强迫振动问题。

There are a number of hidden contributions to this work, beyond the construction of a fully verified, optimizing compiler: The compiler was built in a modular, pipelined fashion as a series of translations between well-specified intermediate languages, making it possible to add new optimizations or reuse components for other projects.

除了构造一个完全经过验证的优化编译器之外，这项工作还有一些更多贡献：采用了模块化、管道－过滤器设计模式，将整个编译器划分为一系列规范良好的中间语言之间变换的模块，这为加入新优化算法或者是在别的项目中重用这些模块提供了可能。

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。

It can not eliminate through the unitary transformation or the re\|definition of the wave function.

评述并证明了在场强为零势不为零的复连通区域，规范势沿入射粒子运动闭合路径的不可积积分是贝里几何位相，通过么正变换或重新定义波函数不能除去

It was shown in [23] that the time-frequency pair of orhtonormal basses that are related via the Fourier transform is highly incoherent.

文献[23]证明了，通过傅里叶变换相关的规范正交的低沉音的时间－频率对是高度不相干的。

We make a rather thorough review of the QCD sum rule approach, which includes the correlation functions and the spectral representations, OPE, Borel transformation, the fixed point gauge, condensates and their empirical values, Borel stability, the dispersion relation and the commonly used

我们对于 QCD 求和规则作了比较全面的评述，包括：关联函数与谱表示；算符乘积展开；Borel变换和固定点规范；凝聚量及其经验值；Borel 稳定性；色散关系和谱密度的常用模型；Wilson 系数的计算；外场方法等。

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。