分数

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。

To solve the difficulties of the discretization and application of fractional order controllers, evaluation strategies of digital realization of FOC are investigated. The realization principle and process of various discretization methods are discussed.

针对分数阶控制器数值计算和应用难的问题，提出了分数阶微积分算子数字实现方法的评估策略，分析了分数阶微积分算子的多种数值计算法的机理和实现步骤。

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。

The best advantage of the method is that it can solve the complex fractional order calculus equation which can hardly be answered by the general calculus knowledge.

该方法最大的优点是能够解决由一般的分数阶微积分知识所不能或是很难求解的复杂分数阶微积分问题，对于分数阶的钱性微积分方程也完全适用。

In Chapter 3, considering fractional relaxation equation, we make use of directlythe Grunwald-Letnikov definition to discrete fractional derivative, obtain a numericalmethod of fractional relaxation equation,and give the proof of consistency ,conver-gency and stability.

第三章对于一个推广到分数阶的松驰方程，直接利用Gru¨nwald-Letnikov分数阶导数定义进行离散，得到分数阶松驰方程一个数值方法，并给出了相容性，收敛性和稳定性的证明。

One position control system is introduced as the objective controlled by FOC. Based on Mittag-Leffler function, the fractional order control system with full memory length is adopted as evaluation criterion, and an approximation performance function of discretization methods is proposed. Analyzing the time domain error and approximation performance, the investigation to various discretization methods is carried out comparatively in detail.

引入一个位置控制系统作为分数阶控制对象，将Mittag-Leffler函数的全记忆长度分数阶控制系统作为评估基准，提出了一种离散算法的近似性能函数，通过时域误差分析以及近似性能分析，对比研究了分数阶微积分算子的数字实现方法。

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。

Results show that the tensile strength and the tear strength could reach 8.71MPa and 52.14kN/m respectively in the presence of 150phr ethylene silicone rubber,1phr hydrogenous silicone oil,2phr polyvinylsilicone oil,4 phr hydroxyl silicone oil and 40phr amorphous silica.

结果表明，在150份乙烯基质量分数为0.13%的硅橡胶中加入1份硅氢基质量分数为1.65%的含氢硅油、2份乙烯基质量分数为8%的多乙烯基硅油和4份羟基硅油，用40份白炭黑增强，可得到拉伸强度为8.71 MPa，撕裂强度为52.14 kN/m的乙烯基硅橡胶。

The aim of this research was to propose an operating mechanism based on fuzzy theory to integrate scores of multiple assessments. The character of fuzzy theory was to process information vaguely, imprecisely, and uncertainly.

本研究旨在利用模糊理论符合人类语意描述与思考逻辑之特性，舍弃线性且绝对性的传统分数处理方式，改以非线性的模糊逻辑推理方式，发展一个整合多元评量分数的运算机制，经由该机制所运算所得的结果研究者称其为"模糊复合分数(fuzzy composite score，FCS)"，而该机制则称其为"FCS评分架构"。

Two special cases are discussed: flow due to a constant pressure gradient and flow due to a periodic one; In chapter 4, on the basis of the method of fractional element proposed by Schiessel et al and of the generalized fractional element networks proposed by Xu and Tan and by the use of discretization method for solving the inverse Laplace transform, we obtain the creep compliance of Zener and Poynting-Thomson models which are composed of the generalized fractional element networks.

并讨论了如下两种特殊情形：常压力梯度下的流动和周期性压力梯度下的流动；第四章在Schiessel等提出的分数阶单元法和徐明瑜等提出的广义分数阶单元网络的基础上，应用离散求逆Laplace变换的方法，给出并讨论了广义分数阶单元网络Zener和Poynting-Thomson模型的蠕变柔量。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。