正则系统

In the spatial domain, canonical projection of the Wigner distribution function of the associated pupil function to show the insensitivity of the system's point spread function to the defocus-related aberrations is mainly used, and in the frequency domain, it is shown that the optical transfer function of such a system is also insensitive to misfocus through a geometrical description of the so-called Cornu spiral.

空域中，主要利用维格纳分布函数的正则投影来分析系统的点扩展函数对离焦像差的变化不敏感特性；频域中，则利用考纽螺线的图解方法来分析系统的光学传递函数对离焦像差的变化不敏感特性。

Firstly, based on the stability criterion for the nominal discrete singular time-delay system, a sufficient condition for the existence of the static output feedback controller in terms of linear matrix inequality with linear matrix equality constraint is established, which ensures that the resulting closed-loop system is regular, causal and robustly asymptotically stable, and the static output feedback controller is designed by the feasible solution of the linear matrix inequality with linear matrix equality constraint.

首先基于标称离散广义时滞系统的稳定条件，以受限线性矩阵不等式形式，得到闭环离散广义时滞系统正则、因果且渐近稳定的充分条件，同时利用受限矩阵不等式的可行解给出静态输出反馈控制器的设计方法；然后采用矩阵的正交补，把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式的可行解；最后的数值实例说明了所给方法的有效性和正确性。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

In the mean time we also give out a reduction way for nonlinear generalized system F =0 by use of the special projection mappings Q . Based on these we prove that the qualitative structure near the isolated equilibrium point of regular nonlinear generalized system is qualitatively equivalent with the structure near the equilibriun point of the linearization system of nonlinear generalized system, so we give out a way for qualitative analysis near equilibrium point of nonlinear generalized system.

其次，对一般形式的非线性广义系统F=0，利用特殊选择的投影函数Q，给出了一种归约方法，在此基础上，并证明了正则非线性广义系统问题的孤立平衡点的小邻域的定性结构等价于其线性化后的线性广义系统平衡点的定性结构，从而为非线性广义系统的平衡点的定性分析提供了一条途径。

For the one-dimensional p-Laplacian with indefinite weights, four sequences of periodic and anti-periodic eigenvalues are given by introducing the rotation number function, and these eigenvalues are the endpoints of the preimage intervals of the rotation number function at nonnegative integers.

本文以带变号权函数和带变号势函数的一维p-Laplacian为基本模型，系统地阐述了特征值的旋转数方法、带正权Dirichlet特征值的最佳估计、特征值在正则和奇异渐近半线性方程的可解性中的应用、Fucik谱的旋转数方法以及Fucik谱在周期解的扭转性和多解性中的应用。

To deal with the problem,a reduced order model based on time-domain proper orthogonal decomposition is investigated.

为了对主动控制系统设计提供高效高精度状态空间模型，研究了气动弹性系统的时域正则正交分解/降阶模型方法，并引入平衡截断技术进一步降低时域POD/ROM的阶数，从而有效克服了时域POD/ROM阶数过高的缺点。

Firstly, we give out a reduction way for quasilinear generalized system A〓=G , and the concept of the index κ geometrically nonsingularity, where A is singular and of smooth kernal space. By using the canonical projection mappings onto the space of ker A , a class singular pointimpasse point only owned by nonlinear generalized system is also studied and we also prove that the regular index κ quasilinear generaized system A〓=G defined on the region W is equivalent with an ODEs 〓 defined on a submanifold W〓 of the W, so we reduce the problem of quasilinear generalized system to the problem of an ODEs.

首先利用投影函数，给出了拟线性广义系统A〓=G的一种归约方法，提出了指数κ几何非奇异的概念，同时对广义系统特有的一类奇点-寂点进行了研究，证明了正则指数κ的拟线性问题A〓=G等价于在其定义域W中某一个子流形W〓上的正常微分方程〓，从而将拟线性广义系统的问题归结为常微分方程问题。

The variational equations are established for holonomic nonconservative dynamical systems in the high-dimensional ex-tended phase space.

建立了高维增广相空间中完整非保守力学系统的变分方程，并利用系统的正则方程和变分方程证明，可由第一积分直接构造系统的积分不变量，并举例说明结果的应用。

Because of this large-scale interconnected power networks which are operating closely at a limited transmission level and all kinds of fast controllers which are called on to improve systems dynamic behavior, such as fast exciters、 HVDC、 FACTS and so on, the modern power system is inherently a nonlinear system, called as a stressed power system.

对于上述重载电力系统，因为传统的线性化分析方法不容易计及系统内部非线性动态结构信息，所以很难揭示其一些非线性奇异现象的实质。所以，目前国内外，用于研究强非线性系统的动态特性的理论依据主要是向量场正则形理论。

In the following, we quantize the supersymmetric anyon system according to the rule of path integral quantization for constrained Hamiltonian system in Faddeev-Senjanovic scheme. We calculate the quantal conserved angular momentum based on the quantal canonical Noether theorem, and present the fractional spin property at the quantum level.

根据约束系统的Faddeev-Senjanovic路径积分量子化方法，我们对超对称任意子系统进行了量子化；根据经典Noether定理，得到了系统的守恒角动量；用量子正则Noether定理讨论了量子守恒角动量，我们发现了系统具有分数自旋性质。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。