Acidity / basicity and electron donor properties and catalytic activity of sulphated titania

The surface acidity/ basicity of TiO2 (rutile) and its sulphate modified form have been determined by titration method using Hammett indicators after activation at different temperatures. The electron donating properties of these oxides are also studied from the adsorption of electron acceptors of different electron affinity values. The data have been correlated with the catalytic activity of these oxides towards esterification of acetic acid using n-butanol, reduction of cyclohexanone in isopropanol and oxidation of cyclohexanol in benzophenone. Catalytic activity for esterification and oxidation reaction parallels the acidity while that for reduction reaction parallels the basicity of these oxides.

Dynamic cumulative residual Renyi’s entropy

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon’s entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi’s entropy, and study its properties.We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models