The effects of ash and sulfur content on the morphology particulate matter (PM) in diesel particle filter (DPF) were investigated with five different components lubricants. aggregate primary particles analyzed using transmission electron microscopy (TEM). fractal dimensions carbon calculated by box-counting method (BCM), differential (DBC), relative (RDBC) MAD-based box counting (MAD-DBC), resu...

[1] Box counting is widely used for characterizing fracture networks as fractals and estimating their fractal dimensions (D). If this analysis yields a power law distribution given by N / r , where N is the number of boxes containing one or more fractures and r is the box size, then the network is considered to be fractal. However, researchers are divided in their opinion about which is the bes...

This paper introduces a method for modification of the formula of the fractal box counting dimension. The method is based on the utilization of the probability distribution formula in the fractal box count. The purpose of this method is to use it for the discrimination of oil spill areas from the surrounding features e.g., sea surface and look-alikes in RADARSAT-1 SAR data. The result shows tha...

The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in determining the scaling range. These issues lead...

In addition to the general-purpose SSE-based utility evaluation conducted and discussed in the body of the article, in this appendix we provide evaluation results for a specific data use, namely counting queries. The reason of focusing on this data use is that many related works on differentially-private data publishing aim at preserving the utility for counting queries over protected data [12–...

We present compact formulas for the box coefficients of the six-point NMHV one-loop amplitudes in N = 8 supergravity. We explicitly demonstrate that the corresponding box integral functions, with these coefficients, have the complete IR singularities expected of the one-loop amplitude. This is strong evidence for the conjecture that N = 8 one-loop amplitudes may be expressed in terms of scalar ...

Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Ghirardi, Rimini, and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that ‘if marble 1 is in the box and marb...

Most soil parameters as the spatial variability of preferential pathways for water and chemical transport in field soils show complex variations at different scales that cannot accurately described with stationary assumptions. This is why multifractal formalism or the wavelet transform reveals as useful tools for classifying and quantifying the spatial variability of these preferential pathways...