阶

In this paper,a space fractional differential equation is considered.The equation is obtained from the advection-diffusion equation by replacing the second order derivative in space by a fractional derivative in space of order.

考虑空间分数阶微分方程(即在一个标准的扩散-对流方程中，用分数阶导数代替空间二阶导数)，给出了该分数阶微分方程的显式和隐式有限差分格式。

On the basic that existing second-order sufficient condition for an isolated minimizer of order 2 for unconstrained multi-objective optimization, using the so called oriented distance from a point to a set, l-stable function and generalized second-order Peano direction derivative, some second-order sufficient conditions for an isolated minimizer of order 2 for constrained multiobjective optimization problems with l-stable functions are obtained.

在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上，借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano方向导数，进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。

First low order approximation of generating function and approximate optimal trajectory were obtained. Then using low order approximation of generating function of Hamilton "relative motion" to the approximate optimal trajectory, improvement of the approximate optimal trajectory was iteratively made. In this way, high order approximation accuracy can be obtained by only using low order approximation, which is much cost effective in computing.

首先以较低的计算代价，获得最优控制Hamilton系统生成函数的低阶近似，得到一条近似的最优轨线，然后将最优控制Hamilton系统相对于近似最优轨线求"相对运动"，该"相对运动"仍具有Hamilton性质，利用这一"相对运动"的生成函数低阶近似，可以对近似最优轨线进行迭代修正，从而以计算代价较小的低阶近似逼近计算代价高得多的高阶近似的精度。

To our knowledge there is no work on second order impulsive differential equations on infinite dimensional spaces in literature.

二阶方程不同于一阶方程，二阶方程的困难在于若把它化为一阶方程，我们将面对一个无界算子矩阵。

In this paper,we build symplectic structure of 2-nd order and high order singular differential operators on infinite interval, we construct a symplectic space by the maximal and minimal operator domain .

本文研究了无穷区间上二阶、高阶奇型微分算子的辛结构，利用最大与最小算子域构造了一个辛空间，用辛空间中的线性流形来刻画定义在无穷区间上二阶、高阶奇型对称微分算子的自共轭扩张问题。

Three elements should be calculated in first-order circuit, which can synthesise analytical solution. Second-order series RLC and parallel RLC both can be calculated by the general function, which uses the Matlab to calculate differential equations. Generally, second-order and high-order circuits use Laplace transformation to formulate circuit equation, and get analytical solution by using Laplace inverse transform.

一阶电路先计算3要素，后合成解析结果；RLC串联和并联的二阶电路采用自编的通用函数计算，自编函数采用了Matlab求解微分方程的符号运算方法；一般的二阶电路和高阶电路采用拉氏变换列写电路方程，再用拉氏反变换得到解析结果。

At first, this paper surveys nonlinear control and the applications of neural networks in control respectively. Then it studies definitions, mathematical descriptions and conditions of invertibility for nonlinear systems, which are used to analyze the feasibility of inverse system control method. Conclusions about the feasibility of inverse control and the realizability of αth-order inverse systems in engineering are achieved. Furthermore, this paper discusses the feasibility, structure and identification of neural network αth-order inverse system for general single-input single-output continuous or discrete nonlinear systems and various composite control methods based on the αth-order inverse. At last, as a part work of an actual project, this paper focuses on the design of neural network αth-order inverse control method for thyristor controlled series compensation in power systems and its effect in improving the stability of power systems.

本文首先分别概述非线性系统的控制与人工神经网络在控制中的应用；然后研究非线性系统各种可逆性的定义、数学描述及可逆性条件，并用于分析逆系统控制方法的可行性，得出有关逆系统控制方法可行性的结论，阐明一般情况下α阶逆系统才工程可实现；接着本文针对一般单输入单输出连续、离散非线性系统，研究神经网络α阶逆系统的可行性、结构与辨识以及基于神经网络α阶逆系统的各种复合控制方法，并给出应用例子；最后本文结合实际项目，针对采用可控串补的电力系统，设计神经网络α阶逆系统控制方法，研究其对提高电力系统稳定性的作用。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃，本项目主要研究它们的极限性质，着重研究了随机风景中随机变量与随机过程的极限性质，主要取得了以下几个结果：首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近，大大减弱了前人要求任意阶矩的条件，然后对独立风景中的一般随机变量给出了强逼近的一般性结果，由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近，在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛；给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质；同时给出了一些重要的相依随机变量和过程的若干极限定理，如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

The first rank derivative is a reflection of curve change and its rate, at certain range, if the sign of the first rank derivative has changed, the logging value of the correspondence depth point means maximum in this range; the second rank derivative is the knaggy property reflection of curve, at certain range, if the sign of the second rank derivative has changed, the correspondence depth point represent the inflexion of geophysical logging curve, it＇s also a turning point of the reflection of knaggy change property of the curve, it is the interface of stratum.

测井曲线的值是深度的函数，测井曲线的一阶导数表示了曲线变化的趋势和变化的快慢，在某一范围内，当一阶导数呈现符号转换时，相对应的深度点的测井值即为该范围内极大值；测井曲线的二阶导数则表示曲线的凹凸性，在某一范围内，当二阶导数呈现符号转换时，相对应的深度点代表了测井曲线的拐点，即反映曲线凹凸性变化的转折点，亦即地层的分界面。

The technique of perturbations constraint when applied to degree reduction of Bézier curves gives fairly well results This paper discusses why these kind of technique have limitation when applied to B-spline curves, and the least squares approximation approach is presented for reducing the degree of B-spline curves Examples comparing the new method with existing ones are illustrate

将扰动约束技术应用于B啨zier曲线的降阶给出了理想的结果讨论了将这类方法应用于B样条曲线降阶时结果不理想的原因，提出了采用最佳平方逼近技术对B样条曲线做降阶运算的方法；并用实例对该方法和基于扰动约束的降阶方法进行了比

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。