Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iterat...Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.展开更多
Photocatalytic splitting of water over p-type semiconductors is a promising strategy for production of hydrogen.However,the determination of rate law is rarely reported.To this purpose,copper oxide(CuO)is selected as ...Photocatalytic splitting of water over p-type semiconductors is a promising strategy for production of hydrogen.However,the determination of rate law is rarely reported.To this purpose,copper oxide(CuO)is selected as a model photocathode in this study,and the photogenerated surface charge density,interfacial charge transfer rate constant and their relation to the water reduction rate(in terms of photocurrent)were investigated by a combination of(photo)electrochemical techniques.The results showed that the charge transfer rate constant is exponential-dependent on the surface charge density,and that the photocurrent equals to the product of the charge transfer rate constant and surface charge density.The reaction is first-order in terms of surface charge density.Such an unconventional rate law contrasts with the reports in literature.The charge density-dependent rate constant results from the Fermi level pinning(i.e.,Galvani potential is the main driving force for the reaction)due to accumulation of charge in the surface states and/or Frumkin behavior(i.e.,chemical potential is the main driving force).This study,therefore,may be helpful for further investigation on the mechanism of hydrogen evolution over a CuO photocathode and for designing more efficient CuO-based photocatalysts.展开更多
基金Foundation item： Projects（60835005, 90820302） supported by the National Natural Science Foundation of China Project（2007CB311001） supported by the National Basic Research Program of China
文摘Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.
基金the National Basic Research Development of China(2011CB936003)the National Natural Science Foundation of China(50971116)。
文摘Photocatalytic splitting of water over p-type semiconductors is a promising strategy for production of hydrogen.However,the determination of rate law is rarely reported.To this purpose,copper oxide(CuO)is selected as a model photocathode in this study,and the photogenerated surface charge density,interfacial charge transfer rate constant and their relation to the water reduction rate(in terms of photocurrent)were investigated by a combination of(photo)electrochemical techniques.The results showed that the charge transfer rate constant is exponential-dependent on the surface charge density,and that the photocurrent equals to the product of the charge transfer rate constant and surface charge density.The reaction is first-order in terms of surface charge density.Such an unconventional rate law contrasts with the reports in literature.The charge density-dependent rate constant results from the Fermi level pinning(i.e.,Galvani potential is the main driving force for the reaction)due to accumulation of charge in the surface states and/or Frumkin behavior(i.e.,chemical potential is the main driving force).This study,therefore,may be helpful for further investigation on the mechanism of hydrogen evolution over a CuO photocathode and for designing more efficient CuO-based photocatalysts.
