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 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 insens.

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。

By using the sigular system theory of compact operator, a new regularizing filter and a new regularization method for solving ill-posed problems are established.

根据紧算子的奇异系统理论，提出了一种新的正则化子，进而建立了一类新的求解病态问题的正则化方法。

The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

To apply the method of Chapter Ⅱ to ring dynamics, we develop the streamline formalism to a canonical form in Chapter Ⅲ. The perturbation equations which describe the perturbed motion of streamlines are derived, with the general form of a near-conservative system.

为将上述映射方法应用到环动力学的研究，在第三章"流线表示法的正则描述"，我们研究该表示法的正则形式，导出描述流线运动的受振运动方程，该方程具有近保守系统的一般形式。

So it is shown that,this paper uses mass router information as researching object,gives the data regular matching algorithm.It is idea not only in the time of index searching but also in the index information storage space.It is used in the method of mass information fast regular matching in embedding software system widely.

由此可见，以海量路由信息为研究对象，给出的数字正则匹配算法，不仅在索引搜索时间上而且在索引信息存储空间上都十分理想，可广泛应用于嵌入式软件系统中的海量信息快速正则匹配。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

Representation theory of quivers is applied to system theory. As a result, the regular points in system spaces are characterized. Moreover, all prestable points in system spaces are described and another generic property of linear systems is introduced.

解决了始于二十年前的系统空间的正则点的刻画问题，证明了Tannenbaum在1983年提出的&矩阵具有极大秩是正则性的必要条件&这一猜测，纠正了其关于系统空间预稳定点的错误刻画。

According to the theory of singular system of compact operators, a new family of regularizing filter s is set forth, and then a new class of reegularization strategies for solving ill-posed problems of the first kind equations is constructed.

根据紧算子的奇异系统理论，提出一种新的正则化子进而建立了一类新的求解不适定问题的正则化方法。

Increase of the regularity of interpolating scaling functions efficiently improves the approximation power of systems, moreover, that of dual scaling functions markedly enhances the smoothness of duals and improves the frequency characteristics of analysis filters in passband and stopband.

内插尺度函数正则度的增加有效提高了系统的逼近能力，对偶正则度的提高显著增加了对偶尺度函数、对偶小波的光滑性，改善了分析滤波器组的通带、阻带特性。冗余度在一定意义下制约了小波系统的性能。

However, for the collision processes in He target, a large discrepacy between the CTMC results and experimental measurement is found. As is well known, the microcanonical distributions of bounded electrons in CTMC method is quite different from quantal distributions, we modified the initial microcanonical distribution by using eleven different ionization thresholds of electron bounded in target. With modification, we calculated the collisional process of O~(3+) with He, and the total cross sections of all processess are calculated as a function of the incident energies. The agreement with experiments is improved by the modified distributions.

但由于靶电子的微正则分布与量子分布有很大不同，在计算离子与He靶碰撞时发现结果与实验差距很大，我们基于使用多个系统总能量U值，对初始电子的微正则分布进行了优化，使其更接近于量子力学的径向空间分布，然后计算了O~(3+)与氦原子随入射离子能量变化的各种反应过程截面，发现优化极大地提高了计算精度，特别是我们的模型对于描述单电子、双电子丢失过程非常成功。

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。