1.3．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.
3．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；
2.Hurst parameter is important to measure the self-similarity degree and bustiness of network traffic. Based on R? S statistic, variance-time plots and periodogram-based analysis methods, an optimal linear regression wavelet model is proposed to perform the accurate, quick and effective estimation of the Hurst parameter in wavelet field.
Hurst参数是衡量网络流量自相似程度和突发性的重要参数,在时域R/S统计、方差-时间图法和频域周期图法的基础上,提出一种最优化线性回归小波模型,实现小波域内Hurst参数的准确有效快速辨识.
3.1. Fractal Brownian Motion(FBM) was made from Gauss Noise and compared with pressure fluctuation signal of gas-solid fluidization,which demonstrated the similarity between the FBM and the signal. Then,Hurst Exponent was calculated from time series of the signal with R/S method. The exponent was applied in research of the identification and the diagnosis.
1．在通过FBM(分数布朗运动)数据仿真证明了气固流化床压力波动信号与分数布朗运动是相似的基础上，提出了用分数布朗运动来模拟气固流化床压力波动信号，并采用R／S分析法从信号时间序列中提取出Hurst指数，通过分析信号Hurst指数值对流化床流型和结块故障进行了研究。
4.Fractional Brownian motion(FBM) is used in the parameterized modeling of base distributing of DNA sequence. Using mexihat wavelet do wavelet transform and Hurst index is calculated which can describes the self-similarity of DNA sequence.
采用分数布朗运动(FBM)来对DNA序列的碱基分布进行参数化建模，用墨西哥帽小波变换来计算DNA序列的Hurst指数，通过Hurst指数来刻画DNA序列的自相似特性。
5.The Hurst empirical formula in the R/S method is modified and used for the analysis of the dynamic process of groundwater.
对R/S分析法中的Hurst经验公式进行了修正 ,并采用修正后的Hurst经验公式分析了地下水动态过程 .
6.he concept of reseated -range (R/S) analysis of fractal theory is introduced in this paper. It is discussed that the theoretical significance and the practical computing method of the Hurst exponent H,and use H for the prediction of heavy metals pollution in mine.
介绍了分形理论中的时间序列(R/S)分析方法,讨论了赫斯特(Hurst)指数的理论意义和实际计算方法,并将其应用于矿山重金属污染预测。
7.The Hurst indexes of the four proxies are FeO 0.85, Fe 2O 3 0.76, Fe 2O 3/FeO 0.65 and organic carbon 0.74 respectively, indicating that they have obviously long run dependence persistence. This is in accordance with previous studies [13-15] .
4项指标的Hurst指数 (FeO 0 .85;Fe2 O3 0 .76 ;Fe2 O3/FeO 0 .6 5;有机碳 0 .74 )显示该地区气候环境演化存在明显的持续性成分 .
8.Furthermore, having measured local network traffic with intrusion detect system of network center, we deal with packet arrival process and adopt R/S method to estimate Hurst parameter, which is used to distinguish wheather packet arrival process is self-similar or not in statistics.
然后，利用院网络中心的入侵检测系统对局域网流量进行测量，通过处理得到不同时段的分组到达过程，采用经验R／S分析方法，对Hurst参数进行估计，判断此分组到达过程的统计特征是否具有自相似性。
9.In this paper, using R/S analysis method, through fractal noise that describes fractional Brownian motion and the relationship between fractal noise and H value of Hurst exponent, the noise color of price behavior of Shanghai stock market is tested empirically.
运用R/S分析方法,通过分析分形布朗运动的分形噪声及其与Hurst指数H值之间的对应关系,实证检验了上海股市价格行为中存在的噪声色彩。
10.In order to model self-similar network traffic source and make simulation in NS, we use the superposition of an infinite number of source traffic whose durations of the On/Off periods according to Pareto distribution. Comparing with measured traffic based on the same estimating method of Hurst, we validate the effectiveness of the way for creating self-similar traffic.
同时，通过采用多个独立的On／Off周期内Pareto分布的流量进行叠加产生自相似过程的方法，在网络模拟器NS下对生成具有自相似特征的网络流量进行建模仿真，同样采用经验的Hurst参数估计方法，与测量得到的实际流量进行比较，验证仿真流量可以有效地反映真实网络流量。
