中阶

And we show that random walk model converges to the stable law of Lévy-Feller advection-dispersion equation by use of a properly scaled transition to vanish-ing space and time steps,We propose an explicit finite difference approximation for Lévy-Feller advection-dispersion equation.

第三章讨论描述服从某种稳定分布反常扩散的非对称空间分数阶对流-扩散方程——Lévy-Feller对流-扩散方程，首先利用Fourier变换和Laplace变换给出方程的基本解，然后利用Grünwald-Letnikov分数阶导数移位离散算子离散方程中的Riesz-Feller分数阶导数得到离散格式，证明此格式可以解释为离散随机游走模型，并且证明了当时间和空间步长以一定的比率同时趋于0时，所提出的离散随机游走模型收敛到Lévy-Feller对流-扩散过程的稳定分布。

In Chapter 4, we consider more complex fractional nonlinear differential equation,also using the high order approximation presented by Lubich to construct correspond-ing numerical scheme and giving the error analysis of the algorithms.

在第四章中，进一步的考虑更复杂的非线性分数阶常微分方程，同样利用的是Lubich提出分数阶导数的高阶近似，构造相应的数值格式，并给出这一算法的误差分析，即相容性，收敛性和稳定性的证明。

A more general structure for the classic PID controller is proposed by using fractional integral and differential operators.

分数阶PI~λD~μ控制器是用分数阶微分、积分运算器代替经典PID控制器中微分、积分运算器，这样，使分数阶PI~λD~μ控制器和经典的PID控制器统一起来。

An optimal filter is designed specially for dq transform used in the voltage mea-surement of transfer switch,which is composed of lower-order notch filter and lower-order low pass filter with higher cut-off frequency in series.Its transfer function is presented by theoretical derivation.If the order is same,it is better in measuring the positive sequence of fundamental amplitude than the average filter and the low-pass filter.

针对转换开关电压检测法——dq变换设计了优化滤波器，该滤波器是利用低阶陷波滤波器和较高截止频率低阶低通滤波器串联形成的，通过理论推导给出了该滤波器的传递函数，在相同的滤波阶数下，该优化数字滤波器在提取基波正序幅值的性能比较中，优于平均值滤波法及低通数字滤波器法等。

The Taylor formula holds the very important status in the differential calculus, especially in solves in some concrete problems to have the extremely important application, for instance the proof inequality, the judgment improper integral collects the divergence, asks the function the limit, asks the function the higher order derivative, determines certain complex progressions to collect the divergence, solves certain differential equation, as well as approximate calculation in and so on application, therefore this article will do the thorough research to these seven aspects.

摘 要：泰勒公式在微分学中占有非常重要地地位，尤其在处理1些具体的茄题中有10分重要的应用，比如证明不等式，判断广义积分的敛散性，求函数的极限，求函数的高阶导数，判定某些复杂级数的敛散性，求解某些微分方程，以及近似计算等中的应用，因此本文将对这七个方面做深入的研究。关键词：泰勒公式；不等式；广义积分；极限；高阶导数；复杂级数；微分方程

The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

二阶线性齐次微分方程在微分方程理论中占有重要位置，但二阶变系数微分方程却没有一般的求解方法，大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式，并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。

This article discusses the use of the theorem of the residues to calculate Cauchy's Principal values of the improper integral, where auxiliary function has poles of higher order on the real axis and proposes a new theorem of culcuation.

在复函中应用留数定理计算广义积分的科希主值时，许多著作仅讨论了辅助函数在实轴上有一阶极点的情形[1-3]，有的则认为：辅助函数"在实轴上的奇点不能是二阶或二阶以上的极点["4，5]。

Firstly, by adopting the thought of Adomian's decomposition method, the generic dynamic model in mechanical systems are transformed into a standard first-orderdifferential-equations, and then the inverse operator method for the approximate analytic solution of nonlinear mechanical system is developed based on the exact solution in form.

主要研 究工作如下：利用Adomian的分解方法的思想，把机械系统中最一般的动力学模型转化为一阶标准型微分方程组，以形式上的精确解的表达式为基础构造了求解机械系统非线性模型近似解析解的逆算符方法；针对机械系统非线性模型的特点，提出了直接处理高阶方程的不降阶逆算符方法；证明了该方法的收敛性。

This proposal has been tested in the present study, in a second-order motion configuration, which was assumed to be irresolvable for the linear filter model. A luminance defined first-order motion and a motion-contrast defined first-order motion were used as control conditions. The results suggest that there was no significant difference between the amplitudes of the flash-lag effect in the second-order motion and in the first-order motion.

用视网膜外推机制不再有效的二阶运动刺激取代前人实验中的一阶运动刺激来研究闪现滞后现象，发现在视网膜推断机制失效的情况下，闪现滞后现象并没有减小，而是和一阶运动刺激条件下的量相当。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。