查询词典 fractional derivative

The results demonstrated that the fractional conversion and reaction rate were rapidly increased in the initial curing reaction. The higher the curing temperature, the higher the fractional conversion and reaction rate was. With increasing of the curing temperature and time, the fractional conversion and reaction rate decreased and became constantly. The initial curing reaction was a first order reaction. The apparent activation energy and frequency factor of curing reaction used G- capryl ester was bigger than that of used G-oligomer.

结果表明：固化体系在研究的固化温度下，转化率和反应速率在固化反应初期增加快速，温度越高增加越快，随着固化时间的延长，这种变化逐渐变慢，并最终趋于恒定；初期固化反应为一级反应，反应初期的表观活化能和指前因子大小顺序为G-预聚体＞G-辛酯。

Based on this, aim at the disadvantage on Wigner Distribution and Fractional Fourier Transform that can't restrain noise interference effectively when be used to detect Linear Frequency Modulated signals interfered by heavy noises, we proposed a improved WD. Simulation results show that this method can restrain noise interference effectively and improve the ability of LFM signals detection. On the other hand, in multi-component cases, WD suffers from the cross-terms, which may impair some of the auto-terms. In order to separate original multi-component signals into components and reconstruct them separately, we can use the method of optimal filtering in fractional Fourier domain. But this method also has a problem that if signals have aliasing in the fractional Fourier optimal domain as well, the reconstructed signals will be distorted. In this thesis, a novel method of quasi Fourier transform is proposed in order to solve the problem of multi-component signal reconstruction, and have good results.

在此基础上，针对Wigner分布和分数维傅里叶变换在处理高噪声背景下线性调频信号检测的问题时存在不能有效抑制噪声干扰的缺点，提出了改进Wigner分布的办法，该方法能够抑制噪声，提高信号的检测能力；针对Wigner分布在处理多分量非线性调频信号时存在干扰项的缺点，以及分数域最优滤波方法在处理多分量非线性调频信号分离重构问题时存在的局限性，该局限性表现为在对最优分数域上也有信号分量重叠的情况进行处理时重构信号发生畸变，提出了新颖的类傅里叶变换的方法，该方法对在最优分数域上也有信号分量重叠的情况也能处理，得到的重构信号失真很小。

Based on the theory of fractional Fourier transform and one of its very important parameter, fractional order, the relationship between FRT and Fresnel diffraction are deduced and analyzed. The fractional Fourier transform hologram reconstructed with the Lohmann Ⅰ FRT system is presented and its computer simulation and digital reconstruction are realized. It is shown that FRT is an ideal tool to describe Fresnel diffraction,and the FRTH can record information on the object and the system at the same time,which extends the application areas of FRT and holography.

基于分数傅里叶变换理论并以分数阶这一重要参量为纽带，推导和分析了分数傅里叶变换与菲涅耳衍射之间的关系；提出了基于罗曼I型分数傅里叶变换系统的分数傅里叶变换全息图，并实现了其计算机生成及数字重现；研究表明，分数傅里叶变换是描述菲涅耳衍射的理想工具，分数傅里叶变换全息图可以同时记录物体和系统的信息，开拓了分数傅里叶变换和全息术的应用领域。

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。

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。

We give some equivalent characterizations of Bloch type functions in term of fractional derivative, via studying the relative of growth of the different order fractional derivatives of holomorphic function, including the form of supremum and limit, the form of integral and Carleson measure, which are the generalizations of some known results in the unit disc and in the unit ball.

我们从研究全纯函数分数次导数的增长性入手，利用分数次导数给出了它的一类刻画，包括上确界和极限形式的特征，积分形式的特征以及Carleson测度形式的特征，推广了单位圆盘和单位球上一些已有的结论。

It is a non-symmetirc fractional derivative, with two-side fractional derivatives and skewness parameter,which results in the complicated disposal of the discrete form.

分数阶微分方程是指方程中含有非整数阶的导数，它非常有效地描述各种各样物质的记忆和遗传性质，在工程、物理、金融、水文等领域中发挥了越来越重要的作用。

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

First of all, modeling image by fractional-order derivative and negative Sobolev space, this paper presents a fractional-order multi-scale variation PDE model, and the proposes the adaptive parameter selection method and obtains the field and scale adaptively algorithm for SAR image denoising.

首先利用分数阶导数以及负指数Sobolev 空间对图像进行建模，建立了分数阶多尺度变分PDE 模型，然后给出了模型参数自适应选择方法，并在此基础上提出了区域、尺度自适应的SAR 图像去噪算法。

The exterior are belong to structure form, geometrical topology, loading case, boundary condition and other external factors. The division will be convenient for a researcher to find the real reasons affecting the dynamic characteristics of the damper. One dimensional stress and strain formulations are deduced by means of the standard derivative and fractional derivative model using the linear viscoelastic theory.

本文主要研究橡胶类粘弹性高阻尼材料及其元件的动态特性，在分析国内外关于橡胶类阻尼材料和元件的理论分析和实验研究的基础上，将影响阻尼器的因素分成属于材料特性的内在因素和属于诸如结构形式、几何尺寸、承载方式、边界条件等外在因素两大类，以利找出影响橡胶阻尼器动特性的真正原因。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。