线性算子

We firstly look back thebirth of SD method,and then present the SD scheme presented by Johnson et.al.forlinear problem to explain the basic idea and implementation:At step 1,we change the testfunctionwhere(1,β)t is the streamline or character direction decidedby hyperbolic operator of the continuous problem,therefore the SD method belongs tothe Petrov-Galerkin method;At step 2,we adopt time-space finite element space,whoseelement is only continuous in space variables x but discontinuous in time variable t.

首先回顾了SD方法的产生过程，然后以线性问题为模型，描述了SD方法的基本思想和具体实现：第一步，将标准有限元方法的检验函数ν改成其中(1，β)t是连续问题的双曲算子部分所确定的流线方向。换言之，SD方法是一种Peterov-Galerkin有限元方法；第二步，采用时空有限元空间，其元素关于空间变量x是连续的，但关于时间变量t仅分段连续。

In this paper discuss the some properties of convergence of operators from Banach space to Banach space and from Banach space to general limear space.

这里讨论了Banach空间到Banach空间和Banach空间到一般赋范线性空间中算子列收敛的一些性质。

The linear convex combination,subtle mutation and violent mutation,and ES-

遗传算子采用线性凸组合的杂交方式、强弱两种变异方式以及进化

The second part has summarized from the one-dimension and multivariate respects the abundant approximation properties of Bernstein polynomials, mainly including the estimation of approximation degree, derivative approximation, linear combination approximation and weighted approximation.

第二部分从一元和多元两个方面系统总结了Bernstein算子丰富的逼近性质，主要包括逼近度估计、导数逼近、线性组合逼近和加权逼近等。

The difference schema of the initial boundary value problem was converted to the step-by-step form,which was similar to the difference schema of the initial value problem.It is concluded that the difference schema satisfying the Von Neumann condition is a stable schema,and that,under the consistency condition,such stable schema is convergent.Moreover,with error estimate expression for the difference approximation to the classical solution,the linearity condition is unnecessary.

引入反投影算子将发展方程初边值问题的差分格式转化为与初值问题差分格式类似的逐步推进的形式，从而得出：满足Von Neumann条件的差分格式是稳定的格式；在相容条件下，差分格式若稳定(或满足VonNeumann条件)则格式收敛，且对古典解的差分逼近有误差估计式，不再需要线性的条件。

Finally, we study the eventual differentiability of a C_0-semigroup associated to a waveequation with boundary dissipation.

最后，我们讨论了一类具边界耗散的线性双曲型方程生成的算子半群的最终可微性，并利用这个结果得到了方程的解具有最终正则性以及半群满足谱决定增长条件。

For the dynamic system of discrete coupled and nonlinear three phase voltage source PWM rectifier, the cycle switch average operator is introduced to transform the discrete system into continuous and the small signal perturbation method is used to transform the nonlinear system into linear, the small signal dynamic mathematical models are set up.

中文摘要：针对三相电压型PWM整流器这个离散的、耦合的、非线性的动态系统，引入开关周期平均算子将离散的系统变换为连续的系统，应用小信号扰动法将非线性的系统化解为线性的系统，进而分析系统的小信号动态数学模型。

For the dynamic system of discrete coupled and nonlinear three phase voltage source PWM rectifier, the cycle switch average operator is introduced to transform the discrete system into continuous andthe small signal perturbation method is used to transform the nonlinear system into linear, the small signal dynamic mathematical models are set up.

中文摘要：针对三相电压型PWM整流器这个离散的、耦合的、非线性的动态系统，引入开关周期平均算子将离散的系统变换为连续的系统，应用小信号扰动法将非线性的系统化解为线性的系统，进而分析系统的小信号动态数学模型。

Although some results on convex and concave iterative roots are known, there are no results about convexity for more general iterative equations. In this chapter, convexity of both increasing solutions and decreasing solutions is investigated by the divided difference theory and fixed point theory.

本章在连续函数构成的紧凸集上构造一个连续自映射算子，利用均差理论和不动点理论证明了线性型迭代方程的凹凸解的存在唯一性及连续依赖性。

Introduction.We present study history of the invariant theory in linear dual system and the operator series theory.

第一章 绪论：介绍了线性对偶系统中不变性理论和算子级数理论。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。