分数方程

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

This paper is discussed the existence of solution for nonlinear boundary value problem of fractional differential equation which with a parameter.

本论文讨论了一类含有参数的非线性分数阶微分方程解之间的关系，写出了线性分数阶微分方程解的表达式。

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 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。

In recent years, the extensive application of the fractional differential equation in many modern scientific technique realms makes the research of its numerical method in and abroad prospers.

近年来，分数阶微分方程问题在现代科学技术领域获得了日益广泛的应用。由于其勿庸置疑的重要性，国内外对于分数阶微分方程问题数值方法的研究正在蓬勃兴起。

With the aids of qualitative analysis of the fractional differential equation, the stability of the equilibrium points of the innovative technology diffuse models based on fractional Logisitic equation are studied.

利用分数次微分方程的定性理论，给出了基于分数次Logistic方程网络式技术创新传播模式平衡点的稳定性分析，为创新技术的开发与积累提供了理论依据。

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。

The results showed that the fiber had the function of absorbing toluene and trichloroethylene after introducing HEMA into macromolecules, and the absorptive process obeyed Hill equation of sigmoidal model.Toluene and trichloroethylene absorbency increased with the increase of mass fraction of HEMA,and their maximum absorbency was 10 g/g and 21 g/g,respectively.The ratio of remaining fiber also increased with the increase of mass fraction of HEMA to make organic liquid retention ratio strengthen.Furthermore,dynamic mechanical performance of the fiber was affected by mass fraction of HEMA obviously, and the segments movement was influenced more obviously.At the same time,mass fraction of HEMA had a great impact on the surface and cross section morphologies,especially,many cavities existed in surface, and cross section had a lot of holes with asymmetric size when mass fraction of HEMA was equal to 15 wt%.

结果表明，HEMA引入大分子后，所得纤维对有机液体甲苯、三氯乙烯具有吸附功能，且吸附过程符合sigmoidal模型中的Hill方程；随HEMA质量分数的增加，纤维对甲苯和三氯乙烯的饱和吸附量增大，对甲苯和三氯乙烯的最大吸附量分别可达10 g/g和21 g/g；随HEMA质量分数的增加，纤维剩余率增加的同时，使纤维对甲苯和三氯乙烯的握持能力增强；HEMA质量分数对纤维动态力学性能有突出影响，特别是链段运动受其影响更为明显；HEMA质量分数对纤维表面和断面形貌均有显著影响，特别是当HEMA质量分数为15 wt%时，所得纤维表面出现了许多空洞，其断面存在许多尺寸不均的空洞。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

The computer programs developed for the combustion process in the chamber have applied the turbulent diffu-sion flame model.

模拟包括流体流动的连续性方程和动量方程、湍流的k－ε双方程、混合分数f方程、能量方程和浓度方程。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了