分数

The weather and climate comply with the fluid dynamical equation and appear stochastic. In order to explore the relationship between weather and climate, the fractional derivative and integration are introduced. Physically, the stochastic degrees of weather and climate are different.

天气和气候虽然遵从流体力学规律，但是却显示出随机性，研究天气和气候之间的关系必须引入分数阶的导数和积分，从物理上讲不外乎说明天气和气候的随机程度是不相同的。

Based on a sinusoidal input, force and displacement expressions of a damper are formulated by using the fractional derivative Maxwell model. The mechanical property of the damper is analyzed using these expressions.

在正弦输入的假设下，推导了用分数微分Maxwell模型建模粘弹性阻尼器时力和位移的表达式，并用该表达式分析了阻尼器的力学特性。

In the model randomness, model with constantly complex modules, Kelvin-Voigt model, fractional derivative model with three parameters and standard rheologic model with three parameters are considered.

在 模型的随机性分析中分别考察了常复数模型、Kelvin-Voigt模型、三参数分数导数模型和三参数标准流变学模型。

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。

Using difference method, the first-order and the second-order differential equations of fractional derivative can become the first-order ordinary differential equation, and the high precision direct integration can be used for the solution.

所论方法首先引入差分格式，将含有分数阶导数的一阶和二阶微分方程变为一阶的常微分方程，然后再用精细积分方法逐步积分进行求解。

The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation.

研究简支的受轴向周期激励的粘弹性柱动力稳定性，柱的材料满足分数导数型本构关系。

The main research contents and results are described as follows:The constitutive equation of the elastomer modeled by the fractional derivative Maxwell model has been investigated. Based on the thermodynamics constraints analysis of the physical parameters of the fractional derivative Maxwell model, the relaxation modulus and the creeping modulus of the model are analyzed.

本论文针对该目的，采用理论研究与试验研究相结合的方法，首先研究了胶泥缓冲器的耗能机理，进而设计开发了较理想的缓冲器产品，具体研究内容和成果如下：研究了胶泥的本构模型——分数微分Maxwell模型。

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。

In the third chapter,the Lévy-Feller advection-dispersion equation describing anomalous diffusion,with asymmetric fractional derivative,is considered.

更多程不同的是，在三维情形中，分数阶导数的复杂性使得在构造差分格式时所添加的摄动项也非常复杂，由此所构造差分格式的理论分析也变得比较复杂。

The analysis results show clearly that the fractional derivative Maxwell model can embody both the creeping and the relaxing of the viscoelastic materials.

通过分析分数微分Maxwell模型的复模量，证实该模型具有广适性。

What would he tell Judith and the children?

他将怎样告诉朱迪丝和孩子们呢？

I this is at that time, the opinion with peacockish true girl is full of in a heart.

这就是当时的我，一个心中布满虚荣的女孩子真实的想法。