Absolute continuity of vector-valued self-affine measures

This paper is devoted to the absolute continuity of (scalar-valued or vector-valued) self-affine measures and their properties on the boundary of an invariant set. We first extend the definition of WSC to self-affine IFS, and then obtain a necessary and sufficient condition for the vector-valued self-affine measures to be absolutely continuous with respect to the Lebesgue measure. In addition, we prove that, for any IFS and any invariant open set V, the corresponding (scalar-valued or vector-valued) invariant measure is supported either in V or in ∂V.     

新IFS分形图象盒维数的EMMS位模拟计算

针对新获取的IFS分形图像进一步分析的需要,提出位模拟分维计算,极大地改进了原有盒维数计算的诸多不便,在普通PC机上一次性的计算即可满足一般性要求,或提供进一步处理的精质数据。完成了完整的实用软件,并采用该算法具体计算了墨竹叶分形集和扩散集及另外几种标准IFS集合的盒维数     

The chaos game revisited: Yet another, but a trivial proof of the algorithm’s correctness

The aim of this work is to explain why the most popular algorithm for approximating IFS fractals, the chaos game, works. Although there are a few proofs of the algorithm’s correctness in the relevant literature, the majority of them utilize notions and theorems of measure and ergodic theories. As a result, paradoxically, although the rules of the chaos game are very simple, the logic underlying the algorithm seems to be hard to comprehend for non-mathematicians. In contrast, the proof presented in this work uses only fundamentals of probability and can be understood by anyone interested in fractals.     

三角剖分上的仿射迭代函数系统分形插值曲面

对二维平面上三角形区域进行三角剖分,构造仿射变换,由二元分形插值函数引入第三维的值,构成迭代函数系统(IFS).利用此IFS构造了一类山状分形插值曲面.通过数值实验对比分析表明:它比人们以往用矩形剖分得出的分形图形效果更逼真,更接近于自然.     

Construction of Continuous Functions with Prescribed Local Regularity

In this paper we investigate from both a theoretical and a practical point of view the following problem: Let s be a function from [0;1] to [0;1] . Under which conditions does there exist a continuous function f from [0;1] to R such that the regularity of f at x , measured in terms of H?lder exponent, is exactly s(x) , for all x ∈ [0;1] ? We obtain a necessary and sufficient condition on s and give three constructions of the associated function f . We also examine some extensions regarding, for instance, the box or Tricot dimension or the multifractal spectrum. Finally, we present a result on the ``size' of the set of functions with prescribed local regularity. November 30, 1995. Date revised: September 30, 1996.     

FT-IR and FT-Raman, UV spectroscopic investigation of 1-bromo-3-fluorobenzene using DFT (B3LYP, B3PW91 and MPW91PW91) calculations

The FT-IR and FT-Raman spectra of 1-bromo-3-fluorobenzene (C₆H₄FBr) molecule have been recorded using Bruker IFS 66 V spectrometer in the range of 4000–100 cm⁻¹. The molecular geometry and vibrational frequencies in the ground state are calculated using the DFT (B3LYP, B3PW91 and MPW91PW91) methods with 6-31++G(d,p) and 6-311++G(d,p) basis sets. The computed values of frequencies are scaled using a suitable scale factor to yield good coherence with the observed values. The isotropic DFT (B3LYP, B3PW91 and MPW1PW91) analysis showed good agreement with the experimental observations. Comparison of the fundamental vibrational frequencies with calculated results by B3LYP methods. The complete data of this molecule provide the information for future development of substituted benzene. The influence of bromine and fluorine atom on the geometry of benzene and its normal modes of vibrations has also been discussed. A study on the electronic properties, such as absorption wavelengths, excitation energy, dipole moment and frontier molecular orbital energies, was performed by time dependent DFT (TD-DFT) approach. The electronic structure and the assignment of the absorption bands in the electronic spectra of steady compounds were discussed. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. On the basis of the thermodynamic properties of the title compound at different temperatures have been calculated in gas phase, revealing the correlations between standard heat capacities (C) standard entropies (S), standard enthalpy changes (H) and temperatures.     

基于阿基米德范数的广义直觉模糊Bonferroni平均及其多属性决策方法

主要提出了一种基于阿基米德T-范数和S-范数的广义直觉模糊Bonferroni平均算子.首先利用广义直觉模糊运算法则和阿基米德T-范数和S-范数,构建了一种新的广义直觉模糊Bonferroni平均算子,并详细研究了该算子的一些优良性质,包括幂等性、单调性、有界性以及置换不变性等;然后探究了广义直觉模糊Bonferroni平均算子的几类特殊形式;最后在直觉模糊环境下,基于提出的算子建立了一种新的多属性决策方法,并以图书馆空调系统的选择为例,分析说明了提出的决策方法的可行性和有效性.     

关于IVIFS算子与IFS算子关系的讨论

Atanassov教授在给出区间教直觉模糊集算子的定义以后曾给出断语:直觉模糊集算子满足的结论,都可以推广到相应的区问数直党模糊集算子.本文详细分析多条直觉模糊集算子的性质与相应区间数直党模糊集算子的性质之间的关系,证明这些直觉模糊集算子的性质都不能推广到区间数直党模糊集算子,因而对Atanassov的论断进行了澄清.     

直觉模糊集运算性质

针对Atanassov(Intuitionistic Fuzzy Sets. Heidelberg: Springer,1999)给出的直觉模糊集运算,指出并修正一些直觉模糊集运算的错误性质,这将有利于对直觉模糊集的进一步研究.     

基于迭代函数系统和编码空间的数字图像置乱方法研究

针对数字图像的安全保密问题 ,本文介绍了一种基于位置空间的数字图像置乱技术 .首先利用伴随于迭代函数系统 ( IFS)的编码空间对数字图像各像素赋予不同编码 ,然后通过对编码的特定置换使各像素位置改变以达到图像置乱的目的 .本文讨论了置乱变换对原图信息分散的规律以及变换的周期性 .理论和实践表明 ,该方法克服了图像信息量大造成的编码上的困难 ,置乱变换后原图的信息按照特定的规律分散开 ,增强了信息隐藏的不可感知性 .