Metal oxide hollow structures are of great inter- est in many current and emerging areas of technology. This paper presents a facile and controlled protocol for the syn- thesis of Al-doped CeO2 hollow-shell spheres （...Metal oxide hollow structures are of great inter- est in many current and emerging areas of technology. This paper presents a facile and controlled protocol for the syn- thesis of Al-doped CeO2 hollow-shell spheres （CHS）, where the dopant confers enhanced stability and activity to the ma- terial. These Al-doped CeO2 hollow-shell spheres （ACHS） possess a controllable shell number of up to three, where the sizes of the exterior, middle, and interior spheres were about 250-100 nm,150-50 nm, and 40-10 nm, respectively, and the average shell thickness was -15 nm. The thermal stability of the ACHS structure was enhanced by the homogeneous in- corporation of AI atoms, and more active oxygen species were present compared with those in the non-doped congener. Au NPs supported on ACHS （Au/ACHS） showed superior cat- alytic performance for the reduction of p-nitrophenol. For the same Au NP content, the reaction rate constant （k） of the Au/ACHS was nearly twice that of the non-doped Au/CHS, indicating that AI doping is promising for improving the per- formance of inert or unstable oxides as catalyst supports.展开更多
The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T ...The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.展开更多
基金financially supported by the National Natural Science Foundation of China (51472025 and 21671016)Beijing Nova Programme Interdisciplinary Cooperation Project
文摘Metal oxide hollow structures are of great inter- est in many current and emerging areas of technology. This paper presents a facile and controlled protocol for the syn- thesis of Al-doped CeO2 hollow-shell spheres （CHS）, where the dopant confers enhanced stability and activity to the ma- terial. These Al-doped CeO2 hollow-shell spheres （ACHS） possess a controllable shell number of up to three, where the sizes of the exterior, middle, and interior spheres were about 250-100 nm,150-50 nm, and 40-10 nm, respectively, and the average shell thickness was -15 nm. The thermal stability of the ACHS structure was enhanced by the homogeneous in- corporation of AI atoms, and more active oxygen species were present compared with those in the non-doped congener. Au NPs supported on ACHS （Au/ACHS） showed superior cat- alytic performance for the reduction of p-nitrophenol. For the same Au NP content, the reaction rate constant （k） of the Au/ACHS was nearly twice that of the non-doped Au/CHS, indicating that AI doping is promising for improving the per- formance of inert or unstable oxides as catalyst supports.
基金supported by the National Natural Science Foundation of China (No. 10671040)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200522) the Program for the New Century Excellent Talents in University of China (No. 06-0359)
文摘The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.
