Boundary Regularity for Viscosity Solutions of Fully Nonlinear Elliptic Equations

We provide regularity results at the boundary for continuous viscosity solutions to nonconvex fully nonlinear uniformly elliptic equations and inequalities in Euclidian domains. We show that (i) any solution of two sided inequalities with Pucci extremal operators is C ^{1, α} on the boundary; (ii) the solution of the Dirichlet problem for fully nonlinear uniformly elliptic equations is C ^{2, α} on the boundary; (iii) corresponding asymptotic expansions hold. This is an extension to viscosity solutions of the classical Krylov estimates for smooth solutions.     

Effects of Fe-doping of ceria-based materials on their microstructural and dynamic oxygen storage and release properties

The structural/textual characteristics and dynamic oxygen storage capacity (DOSC) of Fe_0.1Ce_0.9O_x and Fe_0.1Ce_0.6Zr_0.3O_x samples prepared by sol–gel method are investigated by X-ray powder diffraction (XRD), Raman, Hydrogen temperature-programmed reduction (H₂-TPR), X-ray photoelectron spectroscopy (XPS) and mass spectrometry with CO/O₂ transient pulses. The dynamic oxygen storage capacity and rate are largely promoted by Fe doping, and their thermal stability is enhanced by Fe and Zr co-doping. The DOSC (at 673 K) are ordered as: Fresh: Fe_0.1Ce_0.6Zr_0.3O_x (566.6 μmol/g) > Fe_0.1Ce_0.9O_x (551.8 μmol/g) > Ce_0.67Zr_0.33O₂ (287.5 μmol/g) > CeO₂ (140.3 μmol/g); Annealed_1,173K: Fe_0.1Ce_0.6Zr_0.3O_x (101.6 μmol/g) > Ce_0.67Zr_0.33O₂ (45.3 μmol/g) > Fe_0.1Ce_0.9O_x (44.9 μmol/g) > CeO₂ (43.3 μmol/g). The H₂-TPR results showed that Fe-incorporation improve the total oxygen storage capacity (TOSC) of mixed oxide and low temperature activity. The TOSC are ordered as: Fe_0.1Ce_0.9O_x (1.53 mmol/g) > Fe_0.1Ce_0.6Zr_0.3O_x (1.42 mmol/g) > Ce_0.67Zr_0.33O₂ (1.16 mmol/g) > CeO₂ (0.88 mmol/g). XRD and Raman results indicate that Fe_0.1Ce_0.9O_x and Fe_0.1Ce_0.6Zr_0.3O_x are characterized with the fluorite-type cubic structure similar to CeO₂. TPR and XPS analyses reveal that the introduction of Fe into ceria and ceria-zirconia mixed oxides strongly modified the structural and textural properties, which influenced the kinetics of bulk oxygen diffusion.     

Dual facet of gold(III) in the reactions of gold(III) and porphyrins

We have firstly demonstrated the dual facet of gold(III) in the reaction between gold(III) and porphyrins, which could be tuned through changing the counter ions, ligands and the electronic effect of the substituents of the porphyrins.