Multifractal analysis of infinite products

We construct a family of measures called infinite products which generalize Gibbs measures in the one-dimensional lattice gas model. The multifractal properties of these measures are studied under some regularity conditions. In particular, if the -function is differentiable, we prove a formula which gives the Hausdorff dimension and packing dimension of the set of singularity points of a given order. Mathematical examples include Riesz products,g-measures, andG-measures.     

亚像素多重分形方法在图像处理中的应用

提出了一种用亚像素多重分形原理求取图像奇异性的新型算法,降低了单纯依靠整数像素位置灰度级梯度信息计算边缘测度所产生的误差。该算法结合CCD成像机理给出在亚像素位置的灰度级梯度分布规律,利用多重分形理论将实际图像分割成一系列具有不同奇异性指数的分形集合,对应着从边缘到纹理各层面的图像内容。模拟计算了投影小波中心点改变单位距离对边缘测度的影响程度,得出亚像素分割梯度的方法可以增加计算结果鲁棒性的结论。此方法用于标准图像的分割中,选用5×5亚像素数目提取的最奇异性集合与索贝尔(Sobel)算子(默认阈值为36.7920)提取的边缘的峰值信噪比为9.3981 dB。应用于复杂路面的裂纹提取中,其结果更符合人类的视觉观测。     

连接复分形测度的维数及热力学公式

文中在证明三个联合集分形测度维数的基础上，通过一个假设，证明了连接复分形集的维数．同时，利用复分形的热力学形式来处理连接复分形测度．     

Cookie-Cuter集的多重Fractal分解的Packing维数

直线上的Ｃｏｏｋｉｅ－Ｃｕｔｔｅｒ集是一个扩张动力系统的不变集，并且是一个Ｆｒａｃｔａｌ集合．本文得到Ｃｏｏｋｉｅ－Ｃｕｔｔｅｒ集的多重Ｆｒａｃｔａｌ分解的Ｐａｃｋｉｎｇ维数，从而证明其是Ｔａｙｌｏｒ意义下的Ｆｒａｃｔａｌ集合     

足球机器人通讯系统的可靠性分析与设计

文章分析了影响足球机器人无线通讯系统的噪声和干扰，设计出具抗干扰能力的无线通讯接收与发射电路和通讯协议，实验结果表明本无线通讯系统能有效地抑制噪声，克服干扰、满足足球机器人比赛要求。     

Multifractal Analysis of Morphology of TiO2 Nano—films

The SEM and AFM images of three TiO2 nano-films prepared at different conditions were obtained and transformed into digital format.The multifractal analyses for three films were made using height from a depth of thickness of film B and q from 55 to -55.The scaleinvariance is very good for all inΧq(ε)-lnε plots and τ(q)-q plots at least close to three orders of magnitude.But the multifractal spectra f(a) of the films are quite distinct due to their different height distribution.     

低成本型工频电压／电流谐波在线检测仪的原理及工程实现

本文介绍了一种基于快速电压／电流数据采集结果的直接谐波分析方法及其工程实现。该方法在硬件实现快速电量采集的基础上，利用一个周波内的采样数据，可以快速计算出高次谐波的相关参数。相对于传统的FFT（快速傅里叶分解），该方法对硬件的依赖性小，无需DSP支持，在普通单片机上就可以实现。而且，对于不同种类的应用，可以只计算所关心的某次谐波，计算量相对较小。这对于电力系统中某些基于固定次谐波的控制、保护的工程实现具有重要意义。     

A NOTE ON MULTIFRACTAL PACKING DIMENSION OF MEASURES

The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function Ф＊（x）=limsup logv（B（x,r））-qlogu（B（x,r））/logr are discussed and some applications are given.     

Fractals in DNA sequence analysis

Fractal methods have been successfully used to study many problems in physics,mathematics,engineering,finance,and even in biology,There has been an increasing interest in unravelling the mysteries of DNA;for example,how can we distinguish coding and noncoding sequences,and the problems of classification and evolution relationship of organisms are key problems in bioinformatics,Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences,and the global fractal dimension has been used in these works by other people,the models and methods are somewhat rough and the results are not satisfactory.In recent years,our group has introduced a time series model(statistical point of view)and a visual representation (geometrical point of view) to DNA sequence analysis.We have also used fractal dimension,correlation dimension,the Hurst exponent and the dimension spectrum (multifractal analysis)to discuss problems in this field.In this paper,we introduce these fractal models and methods and the results of DNA sequence analysis.     

有限义性质下一类广义MORAN集的重分形分解

本文在一类广义Moran集上定义了一种弱分离条件－有限交性质,并证明了重分形分解在广泛的一类分形上仍然成立。本文部分的推广了Cawley和Manlain的结果。