关于Carotid-Kundalini函数的分形集

Cooper考虑了用f(z)=cos(Nzarccos(z))+c,cosz=(eiz+e-iz)/2定义的复Carotid-Kundalini函数,并研究了该函数的分形集.本文研究了该分形集的对称性和无界性,给出了在Julia型、Mandelbrot型分形集中用迭代方法产生的无界分形集.     

高阶Julia集的逃逸时间算法的计算机实现

Julia集是分形理论中具有重要地位的集合,近些年来有很多对于变换f(z)=z2+c生成分形图形的扩展研究,主要针对高阶非线性复映射迭代函数f(z)=zn+c,给出利用具体的逃逸时间算法生成分形图的具体步骤以及生成的Julia集图案。     

基于Julia集的非线性分形图像的快速压缩方法

传统的分形图像压缩方法是基于图像局部之间的自相似进行编码。提出一种快速的Julia分形压缩方法:首先利用对称性快速生成4×4的Julia图像块,其次利用传统的数据图像匹配算法对原始图像进行压缩,最后,和论文[1]所用的方法相比,可以节省60%的时间,而压缩效果和重建图像质量也十分接近。     

Julia集和Mandelbrot集的反演变换

论文讨论了居里叶集与曼德尔布罗特集的反演变换问题,通过扩充复平面上关于任意定点的反演变换,获得了两类共轭函数。使得这两类共轭函数的居里叶集与曼德尔布罗特集,恰好是原居里叶集与曼德尔布罗特集关于定点的反演变换,并运用逃逸时间算法绘制居里叶集和曼德尔布罗特集的反演图。     

模拟自然景观的分形方法

用分形L系统形象地模拟了植物的结构，绘制了三维L系统对植物模拟的分形图，复分图可以绘制出各种奇特的形状，进行艺术图案设计，根据不同的常量值绘制了Julia集的分形图，用分形迭代函数系统（IFS）绘制了分形山，同时进行了虚拟自然景物模拟，最后根据每种方法的优缺点以及适用的不同情况对3种方法进行了比较。     

三维Julia集的控制

通过对四元数动力系统的状态变量作矩阵变换,实现了系统所生成的三维Julia集的整体缩放、沿坐标轴的放大、缩小以及错切旋转等仿射变换,并从理论上证明了通过变换后的动力系统的Julia集的拓扑性质并没有发生变化.该方法克服了对图像仿射变换所产生的图像分辨率降低的缺点,对生成高分辨率图像提供了简便可靠的方法.     

三阶广义牛顿变换的Julia集

阐述了Julia集理论在牛顿法上的应用，推广了Walter的牛顿迭代法，分析了正切法和Richardson外推法的误差，提出了牛顿下山法、动态参数法和异步牛顿迭代法，利用上述方法构造并研究了三阶广义牛顿变换的Julia集。结果发现：①三阶简化牛顿变换的Julia集中含有经典Mandelbrot集的结构；②Richardson外推法的误差小于正切法；③动态参数法所构造的Julia集形态各异，结构千变万化；④广义牛顿变换的Julia集之间存在某些联系；⑤广义牛顿变换的Julia集具有对称性。     

分形集逼近算法的效率分析

本文就分形集的逼近效率进行了探讨,对几个著名的分形集给出了数值实验的效率报告,对分形集逼近算法存在的问题和发展进行了分析。     

可交换超复数Julia集的生成与研究

四元数不满足乘法交换律,可交换超复数存在一个逆复变量,满足交换律。以后者作为迭代变量,以fc(z)=z2 c作为迭代函数生成可交换超复数Julia集。通过与四元数Julia集的比较,在分析它们之间联系的同时,着重研究三维可视化模型之间的区别,证明了存在于不同基向量之间的等价性。最后总结出一种创造新型分形的方法。     

分形图形在包装装潢中的研究

研究分形图的三种算法并在包装CAD中运用分形理论模拟自然景物及不规则图形。     

四元数分形的生成与研究

为实现三维分形,应用四元数作为迭代变量生成四维Julia集。在介绍了如何实现三维显示以及迭代方法选择之后,详细说明了生成四元数分形的具体过程,并给出图形实例。因为改进了逃逸时间算法的判别标准,因此,目标集合是边界点集。最后通过观察与分析,总结了四元数Julia集的某些特征,比较了它与复平面Julia集异同点,说明了两者之间的联系。     

Systematical decision-making approach for quality function deployment based on uncertain linguistic term sets

A systematical decision-making approach is constructed for quality function deployment (QFD) in uncertain linguistic situations. The mathematical expression and operation of linguistic terms play important roles in the proposed approach in terms of customer requirements (CRs) and design requirements (DRs) in QFD. First, hesitant fuzzy linguistic term sets are designed to conveniently express uncertain linguistic terms and compute with words after the data derived from customers are pretreated and integrated in the decision-making process. Second, the tolerance deviation is defined to restrict innovatively the deviation range of fuzzy linguistic terms in the assessment stage of relative importance for CRs. Third, information entropy is originally designed to determine the final importance of DRs. Moreover, an empirical study on the research project called vortex recoil hydraulic retarder is conducted to demonstrate the performance of the systematical decision-making approach. The proposed approach can be applied to a wide variety of new product development problems in uncertainty settings.     

A possible method for retrieval of particle size distribution from its phase function in a fractal tissue model

In problems relating to light propagation in soft biomedical tissues, the tissue is generally modeled as a turbid medium. In one of the often used models, the suspended scatterers have been assumed to be of spherical shape following a fractal size distribution law. This paper studies the relationship between scattering phase function features of tissue and the fractal dimension within the framework of a fractal tissue model. It is demonstrated that witin the framework of this model the measurement of scattering phase function at two or three near-forward angles can be employed to infer fractal dimension of the model tissue. This method for tissue characterization therefore could be a potentially useful method for early detection of cancer of soft tissues.     

涡轮增压机组的功率平衡计算方法

介绍了舰船蒸汽动力装置中增压锅炉的计算特性,并在对已有的一些相关计算模型分析的基础上,描述了涡轮增压机组的功率平衡计算难题。针对该难题给出了涡轮增压机组的功率平衡计算流程和计算中有关问题的处理方法,在确保计算完备可行的前提下,该方法适合于工程应用。     

The mechanics of self-similar and self-affine fractal cracks

In this paper we study the mechanical attributes of the fractal nature of fracture surfaces. The structure of stress and strain singularity at the tip of a fractal crack, which can be self-similar or self-affine, is studied. The three classical modes of fracture and the fourth mode of fracture are discussed for fractal cracks in two-dimensional and three- dimensional solid bodies. It is discovered that there are six modes of fracture in fractal fracture mechanics. The J-integral is shown to be path-dependent. It is explained that the proposed modified J-integrals in the literature that are argued to be path-independent are only locally path-independent and have no physical meaning. It is conjectured that a fractal J-integral should be the rate of potential energy release per unit of a fractal measure of crack growth. The powers of stress and strain singularities at the tip of a fractal crack in a strain-hardening material are calculated. It is shown that stresses and strains have weaker singularities at the tip of a fractal crack than they do at the tip of a smooth crack.