An efficient extraction−oxidation catalytic system for deep desulfurization of a model fuel was explored. First, Mo/γ-Al 2 O 3 catalysts were prepared using an impregnation method and were characterized using X-ray diffraction, temperatureprogrammed reduction, and N 2 physical adsorption isotherms. Acetonitrile, methanol, N,N-dimethylformamide, Nmethylpyrrolidone, and H 2 O were added to investigate the influences of different extracting agents for extraction−oxidation desulfurization. Acetonitrile showed synergistic action for dibenzothiophene oxidation and a comparatively low dissolving capacity for aromatic compounds. Under a n(H 2 O 2 )/n(S) molar ratio of 2.3 and v(oil)/v(acetonitrile) of 3:1, benzothiophene, dibenzothiophene, and 4,6-dimethyldibenzothiophene were almost completely removed in the presence of the 16 wt % Mo/γ-Al 2 O 3 catalyst over 40 min at 333 K. A reaction pathway based on extraction−oxidation was proposed in which the sulfur compounds were transferred to the extracting phase before oxidizing to form sulfones in the extracting phase. The extraction process was rapid relative to the oxidation process. The advantages of the extraction−oxidation catalytic system are that a high sulfur removal can be achieved under a lower n(H 2 O 2 )/n(S) molar ratio and that the stability of the catalyst is significantly improved.
The associativity of the multiplication on a Frobenius manifold is equivalent to the WDVV equation of a symmetric cubic form in flat coordinates. Frobenius manifold could be regarded a very special type of statistical manifold. There is a natural commutative product on each tangent space of a statistical manifold. We show that it is associative, hence making it into a manifold with Frobenius algebra structure, if and only if the sectional K-curvature vanishes. In other words, WDVV equation is equivalent to zero sectional K-curvature. This gives a curvature interpretation for WDVV equation.
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