分数方程

Unfortunately, most of the analytical solution for fractional differential equation are complicated owing to complex series or special functions.

然而大多数分数阶微分方程的解析解含有复杂的级数或特殊函数，不利于近似计算。

Using this method, we will get the approximate solution of the fractional differential equations.

第三章在第二章的基础上把这个方法推广到更加复杂的分数阶微分方程，同样通过数值例子表明了该方法的高精度性和有效性。

Rules for fusing, which specify the possible values of the charge that can be obtained when two particles of known charge are combinedbtogether, used for reading out information. In the #nu=5/2# FQH state, it can be realized by measuring whether each pair annihilates fully or not with interference experiment. The representation of the braid group realized by n anyons is cmpletely characterized by the R-matrix and F-matrix which satisfy a pentagon equation and a hexagon equation, coherence conditions for the corresponding anyon model.

满足一定的聚合规则，用于信息读取（在填充因子为5/2的分数量子霍尔效应中，可以通过干涉实验测量每对相邻的粒子相聚合的湮灭情况来实现信息读取）；N个任意子组成的体系的标准基中辫子群表示可以完全由R矩阵和F矩阵决定，不同任意子模型中的R矩阵和F矩阵的具体形式可以通过五边形和六边形方程求出。

The characteristic of fractional order differential equation iscontaining the non-integer order derivative. It can effectively describe the memory andtransmissibility of many kinds of material, and plays an increasingly important role inengineering, physics, finance, hydrology and other fields.

分数阶微分方程的特点是含有非整数阶导数，能非常有效的描述各种各样的物质的记忆和遗传性质，在工程，物理，金融，水文等领域发挥越来越重要的作用。

In this thesis, a semi-classical model of the force on an atom is used to describe the motion of a two-level atom interacting with a standing wave laser field. The velocity dependent force and momentum diffusion are derived through optical Bloch equations by using the matrix form of the continued fraction technique. By investigating the dynamic properties of atoms in laser field, we can control and manipulate the mechanical motion of an atom.

本文利用半经典理论，从二能级原子在激光驻波场中所满足的运动方程出发，推导出密度矩阵元所满足的递推关系，利用矩阵连分数方法求解出密度矩阵元，从而求出依赖于原子运动速度的光压力与动量扩散系数，通过讨论原子在激光场中的动力学行为，为原子在激光场中被囚禁、形成原子列阵以及可控制的量子态，从而为量子信息处理提供理论基础。

Space fractional differential equation ; finite difference approximation ; stability ; convergence

空间分数阶微分方程；显式有限差分格式；隐式有限差分格式；稳定性分析；收敛性分析

Therefore, a similarity solution of velocity distribution exists in such unsteady Navier-Stokes equations; In chapter 3, the unsteady flow of a viscoelastic fluid with the fractional derivative Maxwell model in rectangular tube is studied.

因而，给出了不定常Navier-Stokes方程速度分布的一相似性解；第三章研究了具有分数阶Maxwell模型的粘弹性流体在矩形管内的不定常流动。

The method can beused to solve the integro-differential equation included fractional integral orfractional derivative in a long history and the difficulty of storing all history data isovercome and the error can be controlled.Two numerical examples are presented.

利用该方法可对包含分数积分和微分的积分-微分方程进行较长时间的数值模拟，克服了存储全部历史数据的困难，并能对计算误差进行控制。

Many methods have been developed in evaluating the QNMs, such as evolving the time dependent wave equation method, integration of the time independent wave equation method, semi-classical method and fraction function method.

许多方法被用来研究黑洞的似正规模：波动方程的时间数值演化方法；波动方程的时间积分方法；半经典近似方法；连分数方法。

We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control.

我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

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