The experiment shows that the simulated rough surfaces exhibit statistical resemblance to the real ones, which lays the foundation for a further study of multi fractal surfaces.
实验结果证明，模拟表面的统计特性接近于真实表面，为进一步研究多重分形表面打下基础。
In this paper, the multi fractal statistical characteristics of earthquake distribution are summarized.
讨论了地震分布的多重分形统计特征。
The calculation method of earthquake multi fractal features are presented and the possibility of its application in earthquake prediction research is studied.
研究了地震多重分形性质的计算方法及其应用于地震预报的可能性。
The results show that the medium term symptoms of strong earthquakes in some regions can be proposed from the multi fractal dimension spectrum and singularity spectrum of earthquake distribution.
研究结果表明：地震分布的多重分形维数谱和奇异性谱对于一些典型震区的强震发生具有中期预报价值。
At first, the fractal dimension is extracted from the original image and special gray image for the rough classification, and then the multi-fractal dimension is used for further classification.
首先通过计算原始图像和特征灰度图像的分形维数实现第一次的粗分类提取，然后采用多重分形奇异谱方法进一步完成了细分。
Known from the theory of chaos, multi-fractal of stochastic process is a key characteristic of its dynamics, of which entropy rate is a special fractal dimension named information dimension.
从混沌的角度来看，随机过程的多重分形谱是动力系统的重要特征，熵率只是多重分形维中特殊的一维，即信息维。
We can replace the HOLDER exponent by a simple calculation method and find a suitable segmentation threshold by calculating its multi-fractal spectrum.
利用一个简单的计算方法来近似代替HOLDER指数并通过计算其多重分形谱以寻求合适的分割阈值。
A new probabilistic function for studying the multi-fractal features on the volatility of variance of financial time series is proposed.
提出了一种新的概率函数计算方法，用于研究金融时间序列在方差波动方面的多重分形特征。
The space-time distribution of earthquakes is usually multi-fractal Set.
地震时空分布通常是多重分形集。
The results indicate that multi-fractal characteristics of pores of marine soft soil are different from one to another among the three regions.
结果表明三个地点的海积软土孔隙多重分形特征存在差异。
The result above shows that it is significant to apply the multi-fractal characteristic in mid-strong earthquake prediction of one year to one and half year scale in this area.
上述结果说明利用地震时序的多标度分形特征对于该地区的半年至一年尺度的中强地震预报是有意义的。
The result above shows that it is significant to apply the multi-fractal characteristic in mid-strong earthquake prediction of one year to one and half year scale in this area.
上述结果说明利用地震时序的多标度分形特征对于该地区的半年至一年尺度的中强地震预报是有意义的。
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