Fractal Function Estimation via Wavelet Shrinkage

In scientific studies objects are often very rough. Mathematically these rough objects are modelled by fractal functions, and the fractal dimension is usually used to measure their roughness. This paper investigates fractal function estimation by wavelet shrinkage. It is shown that wavelet shrinkage can estimate fractal functions with their fractal dimensions virtually preserved.     

基于分形理论下的外汇市场的预测

在全球金融一体化的大背景下，汇率的变动作为一个重要指标越来越被人们所重视，利用非线性特征来研究汇率问题已经成为研究的前沿和热点，将混沌与分形运用到汇率预测与汇率控制中是汇率研究的一个重要的分支。为此，分析了分形中的R/S方法，研究了转折点的选择；并以外汇市场中的美元、日元、欧元为例进行了实证分析，指出外汇市场服从分形分布； 运用该方法对外汇的变化进行分析，不仅得出汇率变化遵循有偏的随机游走，而且还预测出这三种汇率未来的走势。     

Idempotent and multivariate copulas with fractal support

Using special iterated function systems (IFS) Fredricks et al. (2005) constructed two-dimensional copulas with fractal supports and showed that for every s∈(1,2)$s\in (\mathrm{1,2})$ there exists a copula A whose support has Hausdorff dimension s. In the current paper we present a stronger version and prove that the same result holds for the subclass of idempotent copulas. Additionally we show that every doubly stochastic idempotent matrix N (having neither minimum nor maximum rank) induces a family of idempotent copulas such that, firstly, the corresponding Markov kernels transform according to N   and, secondly, the set of Hausdorff dimensions of the supports of elements of the family covers (1,2). Furthermore we generalize the IFS approach to arbitrary dimensions d≥2$d\ge 2$ and show that for every s∈(1,d)$s\in (1,d)$ we can find a d-dimensional copula whose support has Hausdorff dimension s.     

分形插值在储层参数预测中的应用

岩心分析和测井分析表明,沉积岩的物性分布常常具有分形特征;文中用改进实验变差函数分析某油田X探区测井和取心的孔渗数据,得到在某些井中孔渗参数具有分形特征,并采用fGn分形插值技术,得到井间参数的空间分布。     

上海股票市场分形特征的实证研究

以有效市场假说为基础的现代资本市场理论被越来越多的实践证明与现实情况不符,而分形理论则考虑到资本市场的复杂性和EMH的缺陷,以非线性范式为分析基础,解释了有效市场理论无法解释的许多市场现象,为更深入地分析资本市场提供了新的思路和方法。文章以上海股票市场为例,用分形理论对上海股市的分形特征进行了研究,其结果表明上海股票市场具有明显的分形特征。     

分形理论及其在管理领域中的应用

本文简述了分形理论及其理论体系 ,综合论述并探讨了新环境下分形理论在经济管理、知识管理、企业管理、教育管理、城市管理等领域的实际应用价值和意义。     

Fractal analysis of surface roughness by using spatial data

We develop fractal methodology for data taking the form of surfaces. An advantage of fractal analysis is that it partitions roughness characteristics of a surface into a scale-free component (fractal dimension) and properties that depend purely on scale. Particular emphasis is given to anisotropy where we show that, for many surfaces, the fractal dimension of line transects across a surface must either be constant in every direction or be constant in each direction except one. This virtual direction invariance of fractal dimension provides another canonical feature of fractal analysis, complementing its scale invariance properties and enhancing its attractiveness as a method for summarizing properties of roughness. The dependence of roughness on direction may be explained in terms of scale rather than dimension and can vary with orientation. Scale may be described by a smooth periodic function and may be estimated nonparametrically. Our results and techniques are applied to analyse data on the surfaces of soil and plastic food wrapping. For the soil data, interest centres on the effect of surface roughness on retention of rain-water, and data are recorded as a series of digital images over time. Our analysis captures the way in which both the fractal dimension and the scale change with rainfall, or equivalently with time. The food wrapping data are on a much finer scale than the soil data and are particularly anisotropic. The analysis allows us to determine the manufacturing process which produces the smoothest wrapping, with least tendency for micro-organisms to adhere.     

一类广义Weierstrass函数图形的盒维数

本文主要给出了一类广义Weierstrass函数图形的盒维数。     

3D dynamic forward modeling of polar plumes using Hidden Markov Trees

The polar plumes are very fine structures of the solar K-corona lying around the poles and visible during the period of minimum of activity. These poorly known structures are linked with the solar magnetic field and with numerous coronal phenomena such as the fast solar wind and the coronal holes. The SOHO space mission has provided some continuous observations to high cadence (each 10 min). From these observations the images of the K-corona have been derived and preprocessed with an adapted anisotropic filtering. Then, a peculiar type of sinogram called Time Intensity Diagram (TID) has been built. It is adapted to the evolution of polar plumes with the time. A multiresolution wavelet analysis of the TID has then revealed that the spatial distribution of the polar plumes as well as their temporal evolution were fractal. The present study consists in simulating polar plumes by forward modeling techniques in order to validate several assumptions concerning their nature and their temporal evolution. Our work involves two main steps. The first one concerns the simulation of polar plumes and the computation of their corresponding TID. The second one concerns the estimation of analysis criteria in order to compare the original TID and the simulated ones. Static and dynamic models were both used in order to confirm the fractal behavior of the temporal evolution of plumes. The most recent and promising model is based on a Hidden Markov Tree. It allows us to control the fractal parameters of the TID.     

热线温度场稳定性的实验研究——李雅普诺夫指数和分形数

对热线温度场的稳定性进行了实验研究.得到了周期解和准周期解的自相关功率谱线.李雅普诺夫指数可以表征动力系统的形态.分形数则可以表征混沌程度.李雅普诺夫指数和分形数随参数的变化,定量地表征了非线性系统运动形态的演变,用实验数据计算得到该动力系统的李雅普诺夫指数LE_1>0,但LE_1《1,且LE_1→0,分形致为2相似文献