A Predictor-Corrector Method for the Numerical Simulation of Sea Pollution

The behaviour of pollutants in the sea is described by parabolicequations with dominant advection terms, mixed derivatives andnon-linear interaction terms; these equations are solved bya special predictor-corrector scheme, consisting of 3 distinctsteps. The mixed derivative is split up into second derivativesalong the grid axes and an auxiliary axis. The 2 first steps(implicit and locally one dimensional) form the predictor. Thethird one is the corrector and yields a consistent discreteapproximation of the time derivative. The accuracy is O(²+h+h²)and a stability condition is derived.     

LIFTING DIFFERENTIABLE CURVES FROM ORBIT SPACES

Let ρ: G → O(V) be a real finite dimensional orthogonal representation of a compact Lie group, let σ = (σ ₁, ?, σn): V → ? ⁿ , where σ ₁, ?, σn n form a minimal system of homogeneous generators of the G-invariant polynomials on V, and set d = max_i deg σ _i . We prove that for each C ^d?1,1-curve c in σ(V) ?? ⁿ there exits a locally Lipschitz lift over σ, i.e., a locally Lipschitz curve \( \overline{c} \) in V so that c = σ ° \( \overline{c} \), and we obtain explicit bounds for the Lipschitz constant of \( \overline{c} \) in terms of c. Moreover, we show that each C ^d -curve in σ(V) admits a C ¹-lift. For finite groups G we deduce a multivariable version and some further results.     

稻壳SiO_2/钒催化剂上苯乙酮液相氧化(英文)

Rice husk silica catalyst loaded with 10 wt% vanadium was synthesized from agricultural biomass via a sol-gel synthetic route at pH = 9. The catalyst was characterized by different physico-chemical methods. The FTIR spectra showed the formation of Si–O–V and V=O stretching bands. The presence of vanadium was confirmed by EDX elemental analysis. RH-10V possessed a high specific surface area of 276 m2/g and pore volume of 0.83 ml/g. The prepared catalyst possessed a narrow pore size distribution centered around 7.9 nm. The catalytic performance of RH-10V was tested in the oxidation of acetophenone at 70 ℃. RH-10V was found to be an active catalyst in the oxidation of acetophenone, producing 36.28% conversion efficiency. The products identified were benzoic acid, 2-hydroxyacetophenone, phenol, acetic acid, and 3-hydroxyacetophenone.     

Magnetic shielding tensors of carbon nuclei in 3,5-dichlorophenylacetylene,a theoretical ab initio and experimental study

Ab initio GIAO-CHF and DFT(B3LYP) molecular geometry optimization and magnetic shielding tensor calculations of carbon nuclei of 3,5-dichlorophenylacetylene have been performed using 6–311G?? and 6–311+G(2d,p) basis sets. The isotropic ¹³C chemical shifts, needed for comparison, have been measured in C₆D₁₂ solution. The principal elements of the shielding tensor of the carbon nuclei in the investigated molecule in the solid state have been determined from an intensity analysis of the spinning sidebands in ¹H-¹³C CP/MAS NMR spectra. Shielding anisotropy parameters of the acetylenic carbons have been independently determined using the method based on proton-coupled ¹³C nematic phase spectra as well as from the interpretation of the ¹³C longitudinal relaxation rates. The latter data have been analysed assuming the molecular reorientation to be the rotational diffusion of an asymmetrical top, which has provided, apart from the diffusion coefficients, an additional check on the reliability of the theoretical calculation of the shielding tensors. In general, satisfactory agreement between the theoretical and experimental results has been achieved.