Fractal characterization of the distribution of reactive sites over a rough catalyst surface

Enhancement of catalytic activity in NH3-SCR reaction by promoting dispersibility of CuCe/TiO2-ZrO2 with ultrasonic treatment

“…The catalysts dispersed with metal oxide crystals of various particle sizes promoted by ultrasound treatment need to be further explored by a depth theoretical analysis of experimental data to enhance the catalytic performance. According to the previous literatures [16] , [17] , [18] , the particle size and distribution of active sites on the catalyst surface can be better described by the multifractal method with the generalized dimension and singularity spectra.…”

The rescaled variance statistic and the determination of the Hurst exponent

“…A major issue in the empirical literature is the study of the long range dependence phenomenon usually presented in natural [2,15], industrial [1], economic [6,19], internet trafic [21] and financial processes [3,10].…”

“…1 The literature can be actually divided in two different strands: (1) a parametric approach to determine the parameter known as the Hurst exponent or a parameter related to it (see, for example [5,8,9]) and (2) a non-parametric approach that develops statistics to test, through a hypothesis, the presence of long range dependence (see, for example [7,11,12]). …”