Graph theory for fused cubic clusters of water dodecamer

The stable structures of the fused cubic water cluster (H2O)12 are examined using graph theoretical techniques and ab initio calculations. The calculations are obtained by scanning the symmetry of digraph structures of hydrogen-bond network spanning 12 oxygen atom vertexes. Using the Pólya theorem the cycle index expressions for 12 vertexes and 20 edges of a cuboid in point-group symmetry D(4h) are developed. A total of 91 energy-allowed fused cubic structures are obtained, which are classified by 8 point-group symmetries: 1 D(2h), 2 S4, 5 C4, 1 D2, 11 C2, 10 C(i), 1 C(s), and 60 C1. An energy level diagram of the structures reveals 14 bands that correspond to 14 unique two-colored graphs derived from the distributions of four free hydrogens of the cluster.     

Influence of the intensity gradient upon HHG from free electrons scattered by an intense laser beam

When an electron is scattered by a tightly focused laser beam in vacuum, the intensity gradient is a critical factor to influence the electron dynamics. In this paper, we have further investigated its influence upon the electron high-harmonic generation (HHG) by treating the spacial gradient of the laser intensity as a ponderomotive potential. Based upon perturbative quantum electrodynamics calculations, it has been found that the main effect of the intensity gradient is the broadening of the originally line HHG spectra. A one-to-one relationship can be built between the beam width and the corresponding line width. Hence, this finding may provide us a promising way to measure the beam width of intense lasers in experiments. In addition, for a laser pulse, we have also studied the different influences from transverse and longitudinal intensity gradients upon HHG.     

Stabilité des sous-algèbres paraboliques des algèbres de Lie simples exceptionnelles

Let K$\mathbb{K}$ be an algebraically closed field of characteristic 0. In this paper, we prove the equivalence between stability and quasi-reductivity for parabolic subalgebras of exceptional Lie algebras. Therefore, and considering the results of [1], we give a positive answer to the assertion (ii) of the conjecture (5.6) in [11] for parabolic Lie algebras.     

Synthesis,characterization of SiO2 supported-industrial phosphoric acid catalyst for hydrolysis of NaBH4 solution

Abstract

Tunisian industrial phosphoric acid H₃PO₄ was supported on silica gel SiO₂ (SIPA) to catalyze the hydrolysis reaction of aqueous alkaline sodium borohydride (NaBH₄). The SiO₂ was produced from purified quartz sand using alkali fusion-acidification chemical process. The BET surface area results indicate that the prepared silica gel could reach a specific surface area up to 585 m²/g. The addition of PO₃H₂ functional groups resulted in an increase of surface acidity of SiO₂ catalyst as shown by FT-IR and DTA-DTG spectra. The total acidity of SIPA catalyst was determined by titration to be 2.8?mmol H⁺/g. SEM/EDS maps reveal the distribution of heavy metals on the silica surface. The effect of supported PO₃H₂ functional groups and heavy metals on the NaBH₄ hydrolysis reaction was studied for different ratios of SIPA catalyst to NaBH₄. The sample 12SIPA/NaBH₄ leads to a very high hydrogen generation rate (up to 90%). The activation energy of hydrogen generation by NaBH₄ hydrolysis was 25.7?kJ mol^?1.