一类复映射$z\leftarrow e^{i\phi}(\bar{z})^\alpha+c~ (\alpha<0)$的广义M集

本文分析了一类复映射$z \leftarrow e^{i\phi }(\bar {z})^\alpha +c\{\alpha < 0,\phi \in [0,2\pi)\}$的临界点的性质,给出了广义Mandelbrot集 (简称广义M集)的定义,并构造出一系列广义M集.利用复变函数理论和计算机制图相结合的实验数学的方法,本文对广义M集的结构和演化进行了研究,结果表明: 1). 广义M集的几何结构依赖于参数$\alpha$, $R$和$\phi$; 2). 整数阶广义M集具有对称性和分形特征; 3). 小     

Chain Dominated Orders

We study finite partial orders which have a chain such that every element of the order either belongs to this chain or has all its covers in this chain. We show that such orders are exactly the orders being both interval orders and truncated lattices. We prove that their jump number is polynomially tractable and that their dimension is unbounded. We also show that every order admits a visibility model having such an order as host.     

高阶分形特征在目标特征提取中的应用

将分形理论用于空中人造目标红外图像的分析，提取出用于区分目标和干扰物的新的分形特征的缝隙特征，实验证明，此特征与传统特征相比具有较好和几何不变性，是一种较可靠的识别特征。     

Fractal dimension at the phase transition of inhomogeneous cellular automata

For random binary mixtures of cellular automata in the square lattice, calculations are made of the fractal dimensions associated with the damage spreading and the propagation time of damage at the transition to chaos. Two rules are mixed and universalities of these quantities are sought with respect to change of the rules.     

Variation in surface fractal of graphite due to the adsorption of polyoxyethylene sorbitan monooleate

The fractal analysis is carried out to study the influence of adsorption of polyoxyethylene sorbitan monooleate (Tween 80) on the surface properties of graphite. The surface fractal dimension (d_SF), BET surface area (S_BET) and pore size distribution (PSD) are calculated from low temperature nitrogen adsorption isotherms. The decline in the d_SF of graphite surface is found as the adsorption amount of Tween 80 increases, which suggests that the adsorbed Tween 80 smoothes the graphite surface. Additionally, the observation of atomic force microscopy (AFM) proves that the original slit pores in pure graphite are blocked up and the step defect sites are screened by Tween 80, which may result in the reduction of graphite roughness. The PSD pattern of graphite changes after the adsorption due to the pore blocking effect. S_BET of the graphite decreases as the adsorption amount of Tween 80 increases, which is attributed to both pore blocking effect and surface screening effect.     

New Fractal Localized Structures in Boiti-Leon-Pempinelli System

A novel phenomenon that the localized coherent structures of a (2 1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2 1)-dimensional Boiti-Leon Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.     

改进分形模型的图像降噪算法

利用分形几何中的迭代函数系统理论，针对空间域建立图像分形模型存在相似匹配速度慢的缺点，提出了一种变换域的改进分形模型方法，该方法用频域的搜索匹配代替空间域的搜索匹配，不但域块和区块达到相似匹配的速度更快，而且可以自适应的调整参与计算相似匹配的参数个数．实验结果表明改进的分形模型应用于图像降噪不但可以有效的保护图像的细节和边缘信息，并避免原方法在降噪的同时带来块效应的缺点．     

Faces of a Hyperplane Arrangement Enumerated by Ideal Dimension, with Application to Plane, Plaids, and Shi

The ideal dimension of a real affine set is the dimension of the intersection of its projective topological closure with the infinite hyperplane. We obtain a formula for the number of faces of a real hyperplane arrangement having given dimension and ideal dimension. We apply the formula to the plane, to plaids, which are arrangements of parallel families in general position, and to affinographic arrangements. We compare two definitions of ideal dimension and ask about a complex analog of the enumeration.     

On Hypereuclidean Manifolds

We show that the universal cover of an aspherical manifold whose fundamental groups has finite asymptotic dimension in sense of Gromov is hypereuclidean after crossing with some Euclidean space     

基于数据变换的维数消减方法

为了提高高维数据集合数据挖掘效率，探讨了采用数据变换进行数据维数消减的方法及其应用，提出了一个通用的数据变换维数消减模型，给出了应用主成分分析方法计算模型中的数据变换矩阵的方法，相应的数据变换应用实例表明，通过数据变换用相当少的变量来捕获原始数据的最大变化是可能的．