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The structures and energies of the B and Ga incorporated γ-alumina surface as well as the adsorption of water are investigated using dispersion corrected density functional theory. The results show that the substitution of surface Al atom by B atom is not so favored as Ga atom. The substitution reaction prefers to occur at the tricoordinated A(4) sites. However, the substitution reaction becomes less thermodynamically favored when more Al atoms are substituted by B and Ga atoms on the surface. Moreover, the substitution of bulk Al atoms is not so favored as the Al atoms by B and Ga on the surface. The γ-alumina surface is found to have stronger adsorption ability for water than the B and Ga incorporated surface. The total adsorption energy increases as water coverage increases, while the stepwise adsorption energy decreases. The studies show the coverage of water at 7.5 H2O/nm2 (five H2O molecules per unit cell) can fully cover the active sites and the further water molecule could only be physically adsorbed on the surface.

We characterize the difference of derivative weighted composition operators on the Bergman space in the unit disk and determine when linear-fractional derivative weighted composition operators belong to the same component of the space of derivative weighted composition operators on the Bergman space under the operator norm topology.

This paper characterizes the boundedness and compactness of the product of extended Cesàro operator and composition operator from Lipschitz space toF(p,q,s)space on the unit ball ofℂn.

This paper gives some estimates of the essential norm for the difference of composition operators induced byφandψacting on the space,H∞(Dn), of bounded analytic functions on the unit polydiscDn, whereφandψare holomorphic self-maps ofDn. As a consequence, one obtains conditions in terms of the Carathéodory distance onDnthat characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators onH∞(Dn)is compact.