分形理论

通过对不同pH值红土试样的颗粒成分进行测试，借助分形理论得到不同pH值红土粒度成分分维值。

After grain structure analysis , using the fractal theory we get the fractal dimension of granulometric composition of red soil with different pH.

得出基于分形理论和AFM观测结果计算分形维数D的方法。

Base on fractal theory and the observation result by AFM , the fractal dimension D is calculated .

多重分形理论中q值临界阈的探讨

Research on the value of limit q in multifractals theory

基于分形理论的RIFLE线表面磨损动态模型

Dynamic Model for Wear of Rifle Surface Based on Fractal Theory Dynamic State Trends

基于分形理论与BSP技术的植物形态模拟方法

Method of Simulate Plants Morphology Based on fractal theory and BSP Technique

基于IFS分形理论的信源编码技术的研究

A Study of IFS Fractal Based Source Coding Techniques

将SAR图像的特点与分形理论相结合，提出了一种新的基于区域自选的多尺度分形维数边缘检测方法。

With the combination of SAR image features and fractal theory , a new method of edge detection by calculating the fractal dimension multiscalely is proposed .

将分形理论应用到探地雷达（GPR）资料处理解释中，以提高探地雷达剖面的分辨率。

We have tried to introduce the fractal theory into GPR data processing and interpretation for improving its resolution .

结合分形理论，给出了定量计算混凝土裂缝的面积、分形维数、长度、宽度等特征参数的算法，并采用MATLAB编写计算混凝土裂缝特征参数的应用程序。

An algorithm which was derived from fractal theory was proposed and programmed with MATLAB to calculate the characteristic parameters of concrete cracks , such as area , fractal dimension , length and width .

本文应用分形理论中的Yardstick定律编制测量程序，定量分析了拉伸断裂机理。

Employing Yardstick 's law in fractal theory , the measurement program is implemented to analysis the tensile break mechanisms quantitatively .

分形理论及分形结构研究，并采用本文提出的优化算法对PreMinkowski分形微带天线进行了优化设计，证明了该算法在天线设计中的有效性。

Pre_Minkowski fractal microstrip antenna was optimized with the optimization algorithm proposed in this paper and proved the effectiveness of the algorithm in antenna design .

为了检测舰船辐射噪声中的非线性特征，本文采用混沌、分形理论从信号产生的机理、相空间轨迹、分形维数和Lyapunov指数等4个方面着重研究了舰船辐射噪声的混沌现象。

Applying the theory of chaos and fractal to ship radiated noise , this paper analyzes signal generation and phase space portraits , calculates correlation dimension and estimates Lyapunov exponent .

近年来，随着分形理论在地理学领域的应用及计量地理学与分形地貌学的兴起和GIS技术的深入应用，流域地貌分形学研究也日益深入。

In recent years , with the fractal theory in geography and the application of quantitative geography and fractal geomorphology of the rise and in-depth application of GIS technology , fractal basin geomorphological study has become more in depth .

运用分形理论，定性解释了在超声条件下金属Ag粒子的分形生长过程和树枝晶产生的原因，并利用盒维数法求出晶形分形生长过程中的分形维数，其分形维数在1.8~1.9之间。

The growth process and the reasons to form dendrites were qualitatively explained using fractal theories . The fractal dimension of the dendrites was calculated as 1.8 ~ 1.9 using the box-counting dimension method .

方法：应用非线性动力学的混沌与分形理论对正常受试者和患者的TMJ音进行分形分析。

Methods : Fractal analysis of TMJ sounds in normal subjects and patients were done by the theory of chaos and fractal in nonlinear dynamics .

由于逐步回归分析筛选核函数中心点的计算繁琐，文中提出根据分形理论和Shannon取样定理来确定核函数中心点。

For complication of central points of the kernel functions through regression analysis , it is advised that the central points are determined by fractal theory and Shannon 's theorem .

生长模式符合计算机模拟的DLA模型，并用分形理论初步探讨了这种生长机理。

The mechanism , which was discussed by the fractal theory , was well accordant with the diffusion-limited aggregation ( DLA ) mode simulated by computer .

本研究针对SAP环境下的石化企业，以海量历史数据为依据，综合运用分形理论、网络层次法、模糊粗糙法及马尔卡夫链理论对供应商风险进行分析及预测。

This study is based on the large amount of historical data of petrochemical enterprises using SAP , integrated using fractal theory , analytic network process , fuzzy rough law and Markov chain theory to do risk analysis and forecast .

利用分形理论构建了木材细胞壁中的分形木质纤维，并计算了分形木质纤维S1层和S2层的扭曲分形维数，指出木材中具有纳米尺度的纤维结构；

The fractal theory was used to build fractal microfibril in wood cell wall , and fractal dimension of fractal microfibril layer S1 and layer S2 were calculates , then wood fiber frame with nanometer scale was pointed out .

几种典型织物疵点的分析表明，基于Wold纹理模型和分形理论的分析方法能准确地检测出织物表面的多种疵点。

After analysing several typical samples , it can be concluded that many fabric defects can be detected with the method combining the Wold - based texture model and fractal theory .

介绍分形理论的起源与发展，概述分形理论的主要内容；重点介绍经济系统分形时间序列与Hurst指数以及如何运用R/S分析法求解Hurst指数；

This dissertation introduces the origin and development of fractal theory , summarizes its main content , recommends fractal time series in economic system and Hurst exponent and how to calculate Hurst exponent by R / S analysis .

结果表明分形理论值在Forchheimer区和紊流区中比传统Ergun型经验公式据有更准确的预测值，而且比Ergun型经验公式有更准确的物理意义。

The results show that the theoretical value of fractal theory is better than traditional Ergun-type empirical formula in the Forchheimer and turbulent area , and more accurate physical meaning .

文章提出了将小波包分析数据压缩和消噪并与迭代函数系统（IFS）分形理论相结合用以研究汽液两相流动不稳定性的一种新方法。

A novel method is put forward for studying the instability of vapor-water ( two - ) phase flow . This method combines data compression and denoising based on wavelet ( analysis ) with the iterated function system ( IFS ) fractal image code techniques .

以分形理论和现场实测数据为基础，提出了节理间距的Cantor集分布和岩体天然块度的计算方法，用随机分形构造模型描述爆破岩块的形成过程。

Based on fractal theory and practical data , the Cantor set distribution of joint spacings and the method of calculating natural fragment sizes are put forward , and the process of blasted fragmentation formation is described by a stochastic fractal structure model .

Mandelbrot的分形理论认为，自然界中的大量图像都可以用分形布朗运动模型来描述，而分形维数可以表征图像自相似性和灰度表面粗糙度。

According to mandelbrot 's theory , the nature images can be regarded as the result of FBM ( fractional brownian motion ) and fractal dimension can describe excellently the character of image self-similitude and coarseness of its gray surface .

因此，应用分形理论和方法来研究机织增强材料的渗透率比Kozeny-Carman方程具有明显的优越性。

Therefore , the application is divided the shape theory and the method studies weave reinforced material the permeability to have the obvious superiority compared to the Kozeny-Carman equation .

给出了用扫描隧道显微镜测量的一组微镜的表面形貌，进而将分形理论应用在微镜表面的分析上，同时一种三维的Weierstrass-Mandelbrot（W-M）函数被用以模拟各种不同的表面形貌。

The topographies of various micro-mirror surfaces have been measured by scanning tunneling microscope . These rough surfaces have been analyzed by a fractal theory , and a three-dimensional Weierstrass-Mandelbrot ( W-M ) function has been used to simulate the topographies of the rough surfaces .

本论文依托国家重点自然科学基金项目：基于子波和分形理论的水文尺度分析新途径（NO.40271024）；水文水资源子波分析新途径（No.50279023）开展研究。

This paper gets the support of Chinese National Nature Science Fund : the analysis of many New methods in hydrology based on wavelet and fractal theory ( NO.40271024 ), and Wavelet method in water resources and hydrology ( NO.50279023 ) .

图形分形理论在沙漠化定量研究中的应用

Graphic fractionation and its application based on quantitative research of desertification

分形理论在油田开发指标预测中的应用

The Application of Fractal Theory to Predict Development Targets in Oilfield