带p-Laplacian算子的分数阶微分方程边值问题在无穷区间中解的存在性

借助无穷区间中判别相对紧的方法,研究了一类带p-Laplacian算子的分数阶微分方程边值问题.在非线性函数给定的增长条件下,利用Schauder不动点定理得到了边值问题在无穷区间中解存在的充分条件.     

混合分数阶微分方程初值问题解的局部存在性

利用Schauder不动点定理,研究混合分数阶微分方程的带权初值问题,建立解的局部存在性的充分条件.     

过采样下分数阶傅里叶变换的改进算法

针对Ozaktas采样型分数阶傅里叶变换(fractional Fourier transform, FRFT)的计算量偏大以及分辨率较低的弱点,研究了过采样条件下采样型FRFT的计算,提出了一种改进算法。在过采样条件下,通过减小变换阶的取值范围,使在时频平面上的频率分布范围缩小,时域离散间隔保持不变,避免了插值运算,计算量明显减小,且算法具有可逆性。经过进一步拓展,改进算法具有分辨率可调,输出区域可选,输出长度可变的特点。最后通过数值仿真对改进算法进行了验证。     

Improved Oustaloup approximation of fractional-order operators using adaptive chaotic particle swarm optimization

A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning frequency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization (PSO). The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.     

几个涉及参数的分式不等式(Ⅰ)

使用基本的与已知的不等式,将田彦武的一类涉及参数的分式不等式推广为更为一般情形与别的情形.例如,设ai>0(i=1,2,…,n),n 2,an+1=a1,an+2=a2,∑in=1api/2=1,且p 2,μ>0,λ>0,则有,∑ni=1aipλapi/+21+μapi+2>(1-4λ)-4μ,(ⅰ),如果在上述假设下还有0相似文献   

可转换债券的最优发行策略设计

综合考虑可转换债券发行条件中所涉及的相关因素,以公司总价值最大化为目标,建立了转换速率与公司资产变化量之间的关系模型.运用泛函变分原理,求出最优转换速率,并且进一步得到可转换债券的最优发行策略,为可转换债券发行条件的设计提供了一种新的方法.以首钢转债为例,利用该方法分析了票面利率和最优转股期限对初始转股溢价率的影响,得出的结论与发行公司对可转换债券发行条款的实际运用一致,证明了该方法的有效性.     

A novel algorithm for fractional resizing of digital image in DCT domain

Fractional resizing of digital images is needed in various applications, such as displaying at different resolution depending on that of display device, building image index for an image database, and changing resolution according to the transmission channel bandwidth. With the wide use of JPEG and MPEG, almost all digital images are stored and transferred in DCT compressed format. In order to save the computation and memory cost, it is desirable to do resizing in DCT domain directly. This paper presents a fast and efficient method, which possesses the capability of fractional resizing in DCT domain. Experimental results confirm that this scheme can achieve significant computation cost reduction while maintain better quality.     

Fourier变换的改进形式--分数傅立叶变换

分数Fourier变换是对经典Fourier变换的改进,在处理非平稳信号时效果明显,且具有很好的可重构性。本文介绍了分数Fourier变换FRFT的定义、性质及变换图像的物理意义。     

变指数Herz型空间上分数次算子交换子的有界性(英文)

主要研究分数次算子和Lipschitz函数产生的交换子.利用Lipschitz函数和变指标函数空间的相关性质,证明了交换子在变指标的Herz型空间和Morrey-Herz空间上的有界性.     

分数阶半正边值问题一个正解的存在性定理

考虑分数阶半正边值问题:
D^α₀₊u(t)=λf(t,u(t)),0         u(0)=u(1)=u′(0)=u′(1)=0
正解的存在性. 其中: 3<α≤4是一个实数; D^α₀₊是标准的Riemann-Liouville微分, 非线性项没有数值下界. 应用Krasnosel’skii不动点定理证明该方程一个正解的存在性.