Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.Comment: 30 pages, 3 figure

Utilization of Calcined Gypsum in Water and Wastewater Treatment: Removal of Phenol

The release of phenol-containing effluents above the phenol permissible limit has triggered a lot of concern over the world due to their toxic nature. The adsorptive potential of gypsum on the removal of phenol was investigated. The effect of gypsum loading (0.5–3 g), contact time (2.5–20 min) and solution temperature (298 to 318 K) on the removal of phenol by gypsum was studied at neutral pH. The thermodynamics of the adsorption process was also studied. The kinetic data were fitted into the pseudo-second-order, Elovich, and intraparticle diffusion models. The removal efficiency of phenol increased along with the mass of gypsum, contact time and temperature. The results of the thermodynamics study indicate that the adsorption process is spontaneous and endothermic in nature. The change in free energy (ΔG0) was found to increase with temperature. The values of the estimated ΔG0 suggest that the phenol adsorption on gypsum is a physical adsorption process. Additionally, the kinetic data fitted best into the pseudo-second-order than the other kinetic models. This study proved that phenol can be used effectively for the reduction of phenol concentrations in water and wastewater