Toroidal vertex algebras and their modules

We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal Lie algebras.Comment: 36 page

Photocatalytic oxidation in phenol removal using Ru/TiO2 and Ru/Al2O3 catalysts

Ru/TiO2 and Ru/Al2O3 catalyst have been synthesized using impregnation method followed by calcinations at temperature of 550 0C. The synthesized catalysts were characterized by XRD, SEM and EDS. Based on characterization result, the active phase of Ru in form of RuO2 was well coated and dispersed on the support surface. The catalysts were then used in photocatalytic oxidation of phenol in the presence of peroxymonosulphte (PMS) as an oxidant and UV-light from Mercury lamp which is categorized as UV-C, with wave length in range of 200-280 nm. Both catalyst are effective for application of photocatalytic oxidation of phenol in the present PMS and UV. Further, activation of PMS for the production of sulphate radicals for phenol degradation in this study is generated by the interaction PMSCatalyst and PMS-UV. The photocatalytic catalyst of Ru/TiO2 and Ru/Al2O3 can increase the removal efficiency of 10-15%. The activity in phenol removal of Ru/TiO2-PMS-UV is slightly higher than Ru/Al2O3-PMS-UV. Both catalysts also showed good performance in the second and third runs after regeneration for multiple uses. Kinetic studies showed that phenol oxidation on the catalysts, Ru/TiO2 and Ru/Al2O3 in the present of PMS and UV follows the first order reaction