2014 # Fractal dimension for fractal structures: A Hausdorff approach revisited

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“…S(I) i is the cumulative sum sequences that can be built from the monitoring data sequence. 40,41 A detailed computation of fractal dimensions was performed by Wu et al 26 After the calculation of the fractal dimension, the mine slope deformation N i + 1 can be obtained as follows…”

confidence: 99%

“…S(I) i is the cumulative sum sequences that can be built from the monitoring data sequence. 40,41 A detailed computation of fractal dimensions was performed by Wu et al 26 After the calculation of the fractal dimension, the mine slope deformation N i + 1 can be obtained as follows…”

confidence: 99%

“…(9). In fact, notice that we assume here that the satellite is describing 50 revolutions following an elliptical orbit around a planet whose gravity field has been approximated by the field of a point mass.…”

confidence: 99%

“…In this way, some definitions of fractal dimension for a fractal structure have been already studied in [7][8][9]11] and applied in [10,23], to quote some of them.…”

confidence: 99%

“…The new algorithm that the authors introduce in this paper is based on both [14, Definition 3.2] (for k = 4) and [14,Theorem 3.13]. Thus, while that definition provided a new discrete model to calculate the fractal dimension of any space with respect to a fractal structure by means of finite coverings (which is very suitable for computational purposes), the latter result implies that this new fractal dimension is equal to the Hausdorff dimension for compact Euclidean subsets.…”

confidence: 99%

“…This novel approach is based on both a new discrete model of fractal dimension for a fractal structure which considers finite coverings and a theoretical result that the authors contributed previously in [14]. This new procedure combines fractal techniques with tools from Machine Learning Theory.…”

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confidence: 99%