Colloidal gold immobilized on mesoporous silica as a highly active and selective catalyst for styrene epoxidation with H2O2

Colloidal gold nanoparticles were synthesized by different procedures affording suspensions with two different mean sizes (2 and 5 nm). Au catalysts were prepared by sol immobilization onto several silica frameworks with different 2D and 3D mesoporosities. The catalysts were tested in styrene oxidation reactions showing excellent efficiency and selectivity. The effect of nanoparticle size and mesoporous framework on the physical and catalytic properties of the final materials was studied. The most selective catalyst was prepared from the 5 nm Au nanoparticles and the more interconnected silica framework (3D mesoporosity).

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.