一元不可微函数的局部分数阶定积分的问题

利用Jumarie的分数阶微积分理论推广了Kolwankat和Gangal的局部分数阶微积分,并且重新讨论了局部分数阶定积分,讨论了局部分数阶定积分的性质及其定理.     

分数阶定积分学

分数阶定积分是积分变量在某一给定的区间下的分数阶积分值。在分数维的情况下,分数阶定积分学有着重要的数值计算意义。从介绍定义,性质入手,引入分数阶积分函数的定义与性质,导出分数阶定积分的基本定理。     

数字图像纹理细节的分数阶微分检测及其分数阶微分滤波器实现

文中提出并论述数字图像纹理细节的分数阶微分检测及其分数阶微分滤波器实现．首先，分别从信息论和动力学两个角度深刻阐述了分数阶微积分的几何意义和物理意义．然后，提出并论述了分数阶驻点、分数阶平衡系数、分数阶稳定系数、分数阶灰度共生矩阵的概念与理论，并详细论述了分数阶灰度共生矩阵对图像纹理细节特征的检测．然后，论述了在X轴负、x轴正、Y轴负、Y轴正、左下对角线、左上对角线、右下对角线、右上对角线8个方向上的数字图像任意分数阶n×n的分数阶微分掩模的构造及其数值运算规则．最后，在此基础上，提出并论述了数字图像分数阶微分滤波器的理论与构造．仿真实验分别从定性和定量两方面证实了，对于纹理细节信息丰富的图像信号而言，分数阶微分具有非线性增强图像复杂纹理细节特征的独特优势与良好效果．     

分数阶 Fourier 域带限信号多通道采样定理

提出了分数阶 Fourier域带限信号多通道采样定理, 是已有采样定理的广义形式. 利用上述结果, 并结合分数阶Fourier变换所特有的时移相移性质, 得到具有重要应用价值的周期非均匀采样序列重构原始信号的表达式. 此外, 通过设计不同的分数阶 Fourier 域滤波器, 可以得到分数阶 Fourier 域带限信号不同采样策略的重构公式.     

抽取和内插的分数阶Fourier域分析

为了节省系统中信号处理的运算量和存储量，常需要对信号进行抽样率转换．分数阶Fourier变换是分析非平稳信号的有力工具，它已在雷达、通信、电子对抗、信息内容安全等领域得到广泛的应用．文中从分数阶Fourier域的采样定理出发，定义了分数阶Fourier域的数字频率，推导了非平稳信号经抽取和内插之后分数阶Fourier谱的表达式，并设计了分数阶Fourier域的去镜像和抗混叠滤波器，进而总结出了非平稳信号经过有理数倍抽样率转换之后其分数阶Fourier谱的变化规律，最后导出了抽取和内插在分数阶Fourier域内的恒等关系．此研究成果为基于分数阶Fourier变换的多抽样信号处理理论体系奠定了基础．仿真实验验证了所提理论的正确性。     

分数阶傅里叶域循环多抽样率信号处理理论

从分数阶圆周卷积定理和离散信号在分数阶傅里叶域的chirp周期性出发，研究了分数阶傅里叶域循环多抽样率信号处理理论，包括有限长非平稳信号循环内插和循环抽取的分数阶傅里叶域分析，分数阶傅里叶域循环抽取和循环内插的恒等关系、分数阶傅里叶域循环滤波器组的多相结构和准确重建条件，并在此基础上提出了分数阶傅里叶域M通道准确重建循环滤波器组和分数阶傅里叶域chirp调制循环滤波器组的设计方法．所提理论丰富了分数阶傅里叶域多抽样率信号处理理论体系，也为分数阶傅里叶域滤波器组理论在数字图像处理等有限长离散信号处理领域中的应用奠定了基础．最后，通过仿真实验验证了所提分数阶傅里叶域循环滤波器组设计方法的有效性．     

基于分数阶微积分的电感电流断续模式下Boost变换器的建模与分析

基于实际电容和实际电感在本质上是分数阶的事实,采用分数阶微积分理论建立电感电流断续模式下Boost变换器的分数阶数学模型.依据状态平均建模方法,建立电感电流断续模式下Boost变换器的分数阶状态平均模型,并进行理论分析.然后,比较电感电流断续模式下Boost变换器的分数阶模型与整数阶模型的区别.最后,基于分数阶微积分的改进Oustaloup滤波器算法,建立电感电流断续模式下Boost变换器分数阶模型的Matlab/Simulink仿真模型,并进行数值仿真分析以验证分数阶建模与理论分析的正确性.     

分数阶Fourier域过采样分析

过采样广泛应用于实际数字信号处理过程中。随着分数阶Fourier变换在信号处理领域的不断发展和应用,研究分数阶Fourier域过采样理论就显得十分必要.文中深入研究了分数阶Fourier域的过采样理论:导出了过采样序列与其子序列的分数阶Fourier谱关系;然后利用此关系得到了过采样序列子序列准确重建丢失采样点的表达式.最后以chirp信号为例,利用分数阶Fourier域过采样理论,证明了对于时频分布在分数阶Fourier域具有最小支撑宽度的信号,对其过采样重建更适合在分数阶Fourier域进行。     

四轮转向车辆分数阶控制方法研究

四轮转向系统(4WS)可根据前轮转向和车辆的状态通过后轮的转向提高车辆转弯能力, 同样, 利用这一转向系统可以改进车辆的横向稳定性和操纵性能. 当前轮转向相同时四轮转向车辆的转弯半径大于两轮转向, 而且普通的控制方法不考虑前轮转向的动态过程影响. 本文利用分数阶导数理论提出一种新的四轮转向控制方法, 其不仅考虑前轮转角和横摆角速度的大小, 而且也考虑到转向角速度的影响. 同时也给出控制方法的一些设计方法, 数值计算结果验证了该控制方法的有效性. 通过对两轮转向和四轮转向的转弯车辆的侧偏角、车辆绕质心的横摆角速度和转弯半径等动力学和运动学特性的计算结果比较, 本文的控制方法对四轮转向车辆在转向过程中的瞬态响应有所改进, 并减小了转弯半径.     

分数阶Fourier域多通道采样的滤波器组高效实现

研究了分数阶Fourier域周期非均匀采样以及多通道采样的滤波器组高效插值和重建方法．首先，根据分数阶Fourier变换的性质，得到了分数阶Fourier域插值和采样的恒等结构；然后根据该恒等结构，得到了从分数阶Fourier域多通道采样和周期非均匀采样中重建原始信号的滤波器组高效实现方法；最后建立了分数阶Fourier域多通道采样和分数阶Fourier域滤波器组的关系，并进一步说明可以通过分数阶Fourier域准确重建滤波器组，导出分数阶Fourier域新的采样和重建策略．     

Long‐Run and Cyclical Dynamics in the US Stock Market

This paper uses fractional integration to examine the long‐run dynamics and cyclical structure of US inflation, real risk‐free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 2000. It implements a procedure which allows consideration of unit roots with possibly fractional orders of integration both at zero (long‐run) and cyclical frequencies. When focusing exclusively on the former, the estimated order of integration varies considerably, and non‐stationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long‐run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, six different criteria are applied to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results, based on a 15‐year horizon, show that the former outperforms the others in a number of cases. Copyright © 2013 John Wiley & Sons, Ltd.     

Efficient forecasting in nearly non‐stationary processes

This paper proposes a procedure to make efficient predictions in a nearly non‐stationary process. The method is based on the adaptation of the theory of optimal combination of forecasts to nearly non‐stationary processes. The proposed combination method is simple to apply and has a better performance than classical combination procedures. It also has better average performance than a differenced predictor, a fractional differenced predictor, or an optimal unit‐root pretest predictor. In the case of a process that has a zero mean, only the non‐differenced predictor is slightly better than the proposed combination method. In the general case of a non‐zero mean, the proposed combination method has a better overall performance than all its competitors. Copyright © 2002 John Wiley & Sons, Ltd.     

烟曲霉素生物素标记衍生物的合成及体外测试

为了深入研究烟曲霉素及其衍生物的作用机理,合成了烟曲霉素的生物素标记衍生物6。化合物6是以辛二胺为连接臂通过酰胺键和氨基甲酸酯键把烟曲霉素的衍生物Fumagillol（compound2）和生物素连接而成,各中间体和目标化合物均经^1HNMR、^13CNMRMS表征,结构正确。体外活性测试结果表明目标化合物6可以高效的并且细胞选择性的抑制人脐静脉内皮细胞（HUVEC）增殖。体外受体结合实验证明化合物6与人甲硫氨酸氨肽酶-2（MetAP2）有很高的亲和力。     

The Realised–Implied Volatility Relationship: Recent Empirical Evidence from FTSE‐100 Stocks

This paper examines the long‐run relationship between implied and realised volatility for a sample of 16 FTSE‐100 stocks. We find strong evidence of long‐memory, fractional integration in equity volatility and show that this long‐memory characteristic is not an outcome of structural breaks experienced during the sample period. Fractional cointegration between the implied and realised volatility is shown using recently developed rank cointegration tests by Robinson and Yajima (2002). The predictive ability of individual equity options is also examined and composite implied volatility estimates are shown to contain information on future idiosyncratic or stock‐specific risk that is not captured using popular statistical approaches. Implied volatilities on individual UK equities are thus closely related to realised volatility and are an effective forecasting method particularly over medium forecasting horizons. Copyright © 2011 John Wiley & Sons, Ltd.     

A fractionally integrated exponential model for UK unemployment

Fractionally integrated models with the disturbances following a Bloomfield ( 1973 ) exponential spectral model are proposed in this article for modelling UK unemployment. This gives us a better understanding of the low‐frequency dynamics affecting the series without relying on any particular ARMA specification for its short‐run components which, in general, require many more parameters to estimate. The results indicate that this exponential model, confounded with fractional integration, may be a feasible way of modelling unemployment. It also shows that its order of integration is much higher than one and thus leads to the conclusion that the standard practice of taking first differences may lead to erroneous results. Copyright © 2001 John Wiley & Sons, Ltd.     

力学中非线性方程常用解法的比较及其改进

详细分析了力学中非线性问题常用解法Euler—Cauchy及Newton-Raphson法。论证了这两种方法均是将原非线性方程在求解过程中线性化，用一系列线性方程去逼近原非线性问题导致了误差存在。本文详细分析了上述两种算法的优缺点。将两种算法的优点进行组合，推荐一种基于梯形公式的改良算法。在不增加计算工作量的前提下该法不仅收敛快、收敛半径大，而且计算精度高。最后基于Lagrange微分中值定理论述了加权平均刚度法。     

基于周期FRFT的LFMCW信号检测与参数估计

线性调频连续波(LFMCW)含有多个线性调频信号分量,具有低截获概率特性,雷达情报侦察系统对此类信号的检测与参数估计十分困难.针对这个问题,首先分析了LFMCW的分数阶Fourier变换(FRFT),通过对FRFT核函数的周期调制,定义了周期分数阶Fourier变换(PFRFT),推导了PFRFT和FRFT的关系.然后分析了LFMCW的PFRFT,提出了一种基于PFRFT的未知LFMCW检测和参数估计方法,并对其检测和估计性能进行了理论分析.最后仿真验证了该方法的有效性和合理性.相比FRFT,PFRFT通过对LFMCW的周期性积累提高了信噪比,适合处理具有周期调制的类似LFMCW信号.     

壳聚糖磁性光敏剂血卟啉衍生物微球的制备及其体外表征研究

目的制备壳聚糖包覆的磁性光敏剂血卟啉衍生物微球并考察其体外表征。方法以五羰基铁为原料制备羰基铁粉纳米颗粒,非溶剂法将羰基铁粉纳米颗粒与光敏剂血卟啉衍生物HPD复合,并用壳聚糖包覆制备成壳聚糖包覆磁性血卟啉衍生物微球(CS-M-HPD)。使用电子显微镜、激光粒度仪、X-射线衍射仪和磁力测定仪考察微球的表征。结果检测结果表明该微球为球形,分散性良好,粒径大多集中在290～300 nm。微球羰基铁粉纯度高,呈现优良磁性。结论本研究实现了壳聚糖对磁性HPD的包覆,得到了单分散性磁性HPD微球,为进一步研究该微球靶向光动力治疗肿瘤的生物活性奠定了实验基础。     

On fractional control method for four-wheel-steering vehicle

Four-wheel-steering (4WS) system can enhance vehicle cornering ability by steering the rear wheels in accordance with the front wheels steering and vehicle status.With such steering control system,it becomes possible to improve the lateral stability and handling performance.In this paper,a new control method for 4WS vehicle is proposed,its rear wheels steering angle is in accordance with the angle of front wheels steering and vehicle yaw rate,and the effects of front wheels steering angle velocity are consi...     

Forecasting the conditional covariance matrix of a portfolio under long‐run temporal dependence

Long‐range persistence in volatility is widely modelled and forecast in terms of the so‐called fractional integrated models. These models are mostly applied in the univariate framework, since the extension to the multivariate context of assets portfolios, while relevant, is not straightforward. We discuss and apply a procedure which is able to forecast the multivariate volatility of a portfolio including assets with long memory. The main advantage of this model is that it is feasible enough to be applied on large‐scale portfolios, solving the problem of dealing with extremely complex likelihood functions which typically arises in this context. An application of this procedure to a portfolio of five daily exchange rate series shows that the out‐of‐sample forecasts for the multivariate volatility are improved under several loss functions when the long‐range dependence property of the portfolio assets is explicitly accounted for. Copyright © 2006 John Wiley & Sons, Ltd.