No abstract

Abstract. Regularized minimization problems with nonconvex, nonsmooth, perhaps nonLipschitz penalty functions have attracted considerable attention in recent years, owing to their wide applications in image restoration, signal reconstruction, and variable selection. In this paper, we derive affine-scaled second order necessary and sufficient conditions for local minimizers of such minimization problems. Moreover, we propose a global convergent smoothing trust region Newton method which can find a point satisfying the affine-scaled second order necessary optimality condition from any starting point. Numerical examples are given to demonstrate the effectiveness of the smoothing trust region Newton method.

Gold (Au) on ceria-zirconia is one of the most active catalysts for the low-temperature water-gas shift reaction (LTS), a key stage of upgrading H reformate streams for fuel cells. However, this catalyst rapidly deactivates on-stream and the deactivation mechanism remains unclear. Using stop-start scanning transmission electron microscopy to follow the exact same area of the sample at different stages of the LTS reaction, as well as complementary X-ray photoelectron spectroscopy, we observed the activation and deactivation of the catalyst at various stages. During the heating of the catalyst to reaction temperature, we observed the formation of small Au nanoparticles (NPs; 1-2 nm) from subnanometer Au species. These NPs were then seen to agglomerate further over 48 h on-stream, and most rapidly in the first 5 h when the highest rate of deactivation was observed. These findings suggest that the primary deactivation process consists of the loss of active sites through the agglomeration and possible dewetting of Au NPs.

We report here a synthesis method for single-crystal monodisperse GeO2 nanocubes in a reverse micelle system. Hydrolysis of germanium tetrachloride (GeCl4) in a micelle system produces GeO2 nanocubes in the presence of oleylamine and cetyltrimethylammonium (CTAB). The average edge length of the cubes varies from 50 to 520 nm depending on the concentration of CTAB in the solution. The perfection and monodispersity of the nanocubes are greatly improved by decreasing the pH value of the water solution. Different morphologies such as capsules can be prepared by using octane as the oil phase. The BFDH and Hartman-Perdok methods were used to predict the morphology evolution during the growth of GeO2 nanocubes.