分数方程

Then using classical fractional differential G-L definition deduces fractional order differential difference function and constructs an approximate fractional order differential Tiansi module.

然后由经典的分数阶微分定义出发，推导出了分数阶差分方程，构建了近似的分数阶Tiansi微分模板。

It is a generalization of the nonlinear diffusion equation proposed by Perona-Malik and the method presented by Cuesta, and interpolates between the nonlinear parabolic equation and the nonlinear hyperbolic equation, thus can effectively control the diffusion process so that noises can be removed and details of the image such as edges can be preserved as much as possible simultaneously.

提出了一种包含对时间的分数阶导数的非线性扩散方程，它是对Perona-Malik的非线性扩散方程和Cuesta提出的方程的推广，介于非线性抛物方程和非线性双曲方程之间，从而能有效地控制扩散过程，使得在去除图像噪声的同时能够尽可能地保留图像的边缘等细节信息。

The first section is to introduce some corresponding basic definiens and properties on the fractional calculous. The rest of the chapter is to present solving methods for the approximation solutions of the nonlinear fractional differential equations and their application.

首先介绍了本章涉及到的分数微积分的定义及其性质，然后介绍了非线性分数阶微分方程近似求解的方法及其应用。

As the first attempt, this paper applies the laminar flamelet model to the typical diffusion combustion in diesel engines. A database of the laminar flamelet for a DI engine is built up in the phase space of the mixture fraction with the scalar dissipation rate as parameter.

以KIVA-3程序为基础，摒弃其原有的化学反应模型，模拟内燃机缸内多维湍流流场，并补充求解混合分数的时均值及其脉动均方值的湍流输运方程，得出各曲轴转角下混合分数的时均值及其脉动均方值的缸内空间分布。

Satisfactory numerical validation is presented including a preliminary investigation of time step effect and the value of fractional derivative order for different types of fractional differential equations.

数值算例对不同的分数阶微分方程进行了讨论，探讨了不同的分数阶和时间步长对计算结果的影响，并将计算结果与文献中相关算法的计算结果进行了比较。

Fractional Fourier transform procedures for the solution of fractional order equation provided some numerical method.

详细说明：分数阶Fourier变换程序，为求解分数阶方程提供了一些数值解法。

Because the characteristic equation of fractional order system is a pseudo-polynomial function with exponential-type fractional orders of complex variable, the control of integer orders cannot be directly applied to it.

分数阶系统的特征方程是一个具有复变量的分数阶指数的伪多项式，因此不能直接应用整数阶系统的控制方法。

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 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。

The second part is the controllability of parabolic equation .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 .

第二部分写的是，抛物方程的能控性，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