分数

The sufficient conditions for achieving synchronization of this fractional differential system are derived by using the stability criterion of fractional linear equation.

用三种不同的方法考虑分数阶Lorenz混沌系统的修正投影同步，基于分数阶线性方程的稳定性理论给出了实现同步的几个充分条件，数值模拟说明了所给方法的有效性。

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。

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。

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。

After introducing the generalized strain energy function with fractional order, the constitutive equation of biological visco-elastic material was obtained by means of the fractional calculus.

摘 要：对生物粘弹性材料，引入广义分数阶应变能函数以后，应用分数阶微积分分别给出了粘弹性固体和粘弹性流体的本构关系式。

It is proved that the fractional Fourier transform has the cascade feature, and the optical transfer function is the special case of fractional transfer function.

证明了其具有分数傅里叶变换的级联性，指出常规傅里叶变换下的光学传递函数为分数传递函数的特例。

Keywords: molecular dynamics simulation; fractal theory; fractional Brown function; vapor-liquid interface.

中文关键词：分子动力学模拟；分形理论；分数布朗函数；分数维数；汽液界面

Present a Ambiguity Function based on Fractional Fourier Transform. Its properties are studied. The application is discussed carefully that how to extract cube phase information by the Fractional Ambiguity Function.

给出了基于分数阶傅立叶变换的模糊函数，研究了它们的性质，重点讨论了分数阶模糊函数在三次相位信息提取中的应用。

Based on the normative fractional Fourier transform and the concept of the optical transfer function, using the linear system theory, the mathematic expressions of fractional transfer function in Fresnel diffraction system and Fraunhofer diffraction system are given respectively.

基于规范光学分数傅里叶变换，从光学传递函数概念出发，根据菲涅耳衍射、夫琅和费衍射定义，应用线性系统理论，分别给出了菲涅耳与夫琅和费衍射系统在规范分数傅里叶变换下的光学传递函数数学表达式。

In Chapter 2,we obtain some boundedness results on MK_~for a class of higher order commutators T_~m and M_~m generated by fractional integral operators T_l and maximal fractional integral operators M_l with function bin BMOrespectively.

第二章得到了一类由分数次积分算子及分数次极大算子分别和BMO函数生成的高阶交换子T_~m及M_~m在MK_~上的有界性结果。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。