A generalization of a previous group manifold quantization formalism is proposed. In the new version the differential structure is circumvented, so that discrete transformations in the group are allowed, and a nonabelian group replaces the ordinary (central) 1/(1) subgroup of the Heisenberg-Weyl-like quantum group. As an example of the former we obtain the wave functions associated with the system of two identical particles, and the latter modification is used to account for the Virasoro constraints in string theory.

In this study we report, the synthesis of ZnO and its doping with Transition Metal Oxides -TMO-, such as Cr2O3, MnO2, FeO, CoO, NiO, Cu2O and CuO. Various characterization techniques were employed to investigate the structural properties. The X-ray diffraction (XRD) data and Rietveld refinement confirmed the presence of TMO phases and that the ZnO structure was not affected by the doping with TMO which was corroborated using transmission Electron microscopy (TEM). Surface areas were low due to blockage of adsorption sites by particle aggregation. TMO doping concentration in the range of 3.7–5.1% was important to calculate the catalytic activity. The UV–Visible spectra showed the variation in the band gap of TMO/ZnO ranging from 3.45 to 2.46 eV. The surface catalyzed decomposition of H2O2 was used as the model reaction to examine the photocatalytic activity following the oxygen production and the systems were compared to bulk ZnO and commercial TiO2-degussa (Aeroxyde-P25). The results indicate that the introduction of TMO species increase significantly the photocatalytic activity. The sunlight photocatalytic performance in ZnO-doped was greater than bulk-ZnO and in the case of MnO2, CoO, Cu2O and CuO surpasses TiO2 (P25-Degussa). This report opens up a new pathway to the design of high-performance materials used in photocatalytic degradation under visible light irradiation.

A study was conducted on the transformation of SnO to SnO2 using X-ray diffraction and subjecting the SnO to heat treatments between 300 °C < T < 600 °C in two different atmospheres, argon and air. The intermediary oxide that appears in the disproportionation process was identified as Sn2O3. In an argon atmosphere, decomposition occurs in three stages: (1) a direct transformation of SnO to SnO2, (2) the formation of some intermediary Sn2O3 from SnO, and (3) the conversion of the Sn2O3 to SnO2 with the formation of metallic tin, Sn (l). When an atmosphere of air is used, however, a reaction occurs, concurrent with the decomposition reactions, that relates to the specific oxidation of the metallic tin produced in the course of the three process stages.

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Co 3 O 4 particles were supported on a series of activated carbons (G60, CNR, RX3, and RB3). Incipient wetness method was used to prepare these catalysts. The effect of the structural and surface properties of the carbonaceous supports during oxidation of benzyl alcohol was evaluated. The synthetized catalysts were characterized via IR, TEM, TGA/MS, XRD, TPR, AAS, XPS, and N 2 adsorption/desorption isotherm techniques. Co 3 O 4 /G60 and Co 3 O 4 /RX3 catalysts have high activity and selectivity on the oxidation reaction reaching conversions above 90% after 6 h, without the presence of promoters. Catalytic performances show that differences in chemistry of support surface play an important role in activity and suggest that the presence of different ratios of species of cobalt and oxygenated groups on surface in Co 3 O 4 /G60 and Co 3 O 4 /RX3 catalysts, offered a larger effect synergic between both active phase and support increasing their catalytic activity when compared to the other tested catalysts.