M-带正交插值小波的构造

考虑由M-带正交插值函数构造相应小波函数的矩阵扩充问题。利用插值特性,给出插值函数相应正交小波符号函数的显式构造公式。最后以算例说明该算法。     

一种加权有理三次插值函数的凸性分析

利用带导数的和仅基于函数值的分母为二次的有理三次插值样条构造了一类加权有理三次插值函数.在给定的插值数据条件下,通过调整插值函数中的参数和权系数,给出了插值曲线的保凸方法和该方法得以实现的充分必要条件,推广和改进了一些相关结论.这种条件是对参数和权系数的简单的线性的不等式约束,容易在计算机辅助几何设计中得到实际应用.     

插值正交向量尺度函数

插值正交尺度函数在抽样理论、信号处理和计算机图形学等方面有重要应用,本文给出了紧支撑正交插值向量尺度函数的定义,并对它们进行了刻画。我们证明了向量小波子空间的抽样定理问题能被转化为每个分量所在的闭空间的抽样定理问题。进一步,我们得到了向量小波子空间中抽样定理的具体表达形式。最后,我们构造了两个例子。     

一类正交基插值尺度函数

本文给出一类正交基插值尺度函数,讨论了这类尺度函数的光滑性和衰减性,特别研究了两种情况下这类尺度函数的光滑性和衰减性。     

一类紧支撑对称双正交小波(英文)

摘要:研究伸缩因子为3紧支撑对称双正交小波的构造问题.任给一个插值对称的加细函数,本文提供 一个构造其对偶尺度函数的迭代算法,其对偶尺度函数的正则性可以达到任意水平,讨论了它的一些性 质,如对称性和衰减性.最后,给出构造算例.     

基于一种特殊变换的多小波构造

本文引入一种矩阵滤波器的特殊变换。任一紧支撑正交多尺度函数都可由一个简单的矩阵滤波器通过这种变换得到。由此给出一种由多尺度函数构造相应紧支撑正交多小波的算法。与传统方法相比,这种方法既不需要对罗朗多项式矩阵逐行降次,也不需要将多项矩阵分解成特殊的形式,并且不受滤波器长度的限制。可以利用该方法构造出GHM正交多小波。     

基于分形插值函数的分形插值曲面的变差与计盒维数

分形插值是拟合数据的一种新方法,它可以反映出曲线和曲面上的粗糙性质.本文介绍了基于仿射分形插值函数的分形插值曲面的构造方法,给出了连续函数中心变差的概念,讨论了中心变差与变差、中心变差与计盒维数之间的关系.研究了这类分形插值曲面所对应的二元连续函数中心变差的性质,并根据二元连续函数中心变差与函数图像计盒维数之间的关系,得到了这类分形插值曲面的计盒维数.     

a尺度正交的多尺度函数的构造

给出α尺度正交多尺度函数一种新的构造方法。α尺度正交的多尺度函数可由任意α尺度正交的单尺度函数及滤波器组构造出来的。由于α尺度单正交尺度函数选取的任意性和用于构造的滤波器组具有相当大的自由度，从而使得有可能构造出大量的具有很好性质的α尺度的多尺度函数，进而得到良好性质的多小波。     

高阶Coiflet小波系构造与应用

利用改进的Coiflet设计算法,得到了阶为12,14,16,18,20的高阶Coiflet滤波器系数。通过与Daubechies构造的低阶Coiflet滤波器系数的比较,改进算法的计算结果更精确。对高阶Coiflet滤波器的相频特性进行了计算和验证,结果表明高阶Coiflet的尺度和小波函数图形与低阶基本相似。小波滤波器线性相位特性比尺度滤波器好。尺度滤波器相位线性差,而小波滤波器相位近似线性。随着Coiflet阶数的提高,小波滤波器线性相位变化更快。尺度滤波器相位在低频段近似为0。给出了5个新的高阶和具有更高精度的5个低阶Coiflet滤波器系数表,同时还给出了构造高阶区间Coiflet尺度函数的应用。     

2重正交多尺度函数和多小波的构造

基于正交单尺度函数,给出一种构造2重正交多尺度函数的方法。也给出对应正交多小波的显式构造公式。由于构造的2重正交多尺度函数中的个是所给的正交单尺度函数,另一个是新构造出的函数,因此这种多小波比相关的单小波具有更好的频率局部性。     

一类二元分形函数及其维数

基于一元不可微函数,本文首先构造了一类二元分形函数,然后研究了这类函数图象的分形维数。给出了这类函数图的box维数、packing维数以及Hausdorff维数的若干结果。     

复多值函数动力系统的广义M-J分形图

在研究一般复幂函数f(z)=z^α iβ C的动力系统分形图的结构时,针对在其构造其动力系统分形图时,无法确定其符合Mandelbrot集定义的迭代初始点Z。而无法得到严格意义下的Mandelbrot集分形图的问题,提出一种研究动力系统性质的方法,即构造由这些多值函数各分枝组成的随机复迭代动力系统的广义Mandelbrot集与广义Julia集。     

反周期函数的一种Hermite仿三角多项式插值逼近

杜金元等在2004年给出了Hermite仿三角多项式插值问题的基函数,且在插值函数具有一定解析性的条件下给出了余项公式。本文给出了反周期函数的一种Hermite仿三角多项式插值逼近,其对任意反周期连续函数都是收敛的。我们给出了收敛速度的一种估计。     

Digital-Analog Converter for Reproducing Trigonometric Functions

A method is given for constructing nonlinear digital-analog converters for reproducing trigonometric functions. The method is based on modeling these functions by segments of a power series. Three approaches are considered to calculating the coefficients of the polynomial giving the best approximation (Taylor, Chebyshev, and interpolation methods). It is shown that smaller errors are obtained in the case when the coefficients are calculated using the interpolation and Chebyshev methods.     

A multiscale virtual element method for the analysis of heterogeneous media

We introduce a novel heterogeneous multiscale method for the elastic analysis of two-dimensional domains with a complex microstructure. To this end, the multiscale finite element method is revisited and originally upgraded by introducing virtual element discretizations at the microscale, hence allowing for generalized polygonal and nonconvex elements. The microscale is upscaled through the numerical evaluation of a set of multiscale basis functions. The solution of the equilibrium equations is performed at the coarse scale at a reduced computational cost. We discuss the computation of the multiscale basis functions and corresponding virtual projection operators. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples.     

Boundary value problems defined on stochastic self‐similar multiscale geometries

A method for solving elasticity problems defined on composite bodies with a stochastic multiscale microstructure is presented. It is considered that the composite is made from two types of materials with different elastic moduli. One of these is taken as the matrix, while the other forms the inclusions. The inclusions form a stochastic fractal with a finite, but potentially large, number of scales and are randomly distributed within the matrix. The method presented here leads to the statistics of the solution, i.e. the mean and the variance of the stress and displacement fields. It is based on the stochastic finite element method (spectral approach, second‐order technique) and on scaling properties of the spatial distribution of inclusions over the problem domain. This scaling allows for a simple formulation of the multiscale problem and leads to significant computation cost savings, especially when the fractal has a large number of relevant scales. Several examples are presented and used to verify the proposed method against computationally intensive classical finite element models in which the mesh is refined down to the scale of the finest inclusions. Copyright © 2007 John Wiley & Sons, Ltd.     

基于迭代函数系统的分形算法及其应用

给出了基于迭代函数系统的分形内插管法控制系数的一个计算公式，并将其机制随机化，同时，给出了模拟平面分形图的一个新算法，结合两种算法，对四川丹凤场气田阳新统断层的分布进行了计算机模拟，其结果对油气勘察开发有一定实际意义。     

对流-扩散-反应方程的变分多尺度解法

根据变分多尺度的思想求解了对流项和反应项占优的对流-扩散-反应方程.在变分多尺度思想的理论框架内,推导了附加于Galerkin变分弱形式的稳定化结构和具体的稳定化系数;阐述了这种稳定化结构和经典的SUPG稳定化结构之间的关系;数值算例表明,该稳定化系数可以适应均匀和非均匀的计算网格.通过网格的恰当加密,变分多尺度方法消除了算例中的数值伪振荡.     

Simulated shift work in rats perturbs multiscale regulation of locomotor activity

Motor activity possesses a multiscale regulation that is characterized by fractal activity fluctuations with similar structure across a wide range of timescales spanning minutes to hours. Fractal activity patterns are disturbed in animals after ablating the master circadian pacemaker (suprachiasmatic nucleus, SCN) and in humans with SCN dysfunction as occurs with aging and in dementia, suggesting the crucial role of the circadian system in the multiscale activity regulation. We hypothesized that the normal synchronization between behavioural cycles and the SCN-generated circadian rhythms is required for multiscale activity regulation. To test the hypothesis, we studied activity fluctuations of rats in a simulated shift work protocol that was designed to force animals to be active during the habitual resting phase of the circadian/daily cycle. We found that these animals had gradually decreased mean activity level and reduced 24-h activity rhythm amplitude, indicating disturbed circadian and behavioural cycles. Moreover, these animals had disrupted fractal activity patterns as characterized by more random activity fluctuations at multiple timescales from 4 to 12 h. Intriguingly, these activity disturbances exacerbated when the shift work schedule lasted longer and persisted even in the normal days (without forced activity) following the shift work. The disrupted circadian and fractal patterns resemble those of SCN-lesioned animals and of human patients with dementia, suggesting a detrimental impact of shift work on multiscale activity regulation.