A novel palladium-catalyzed coupling reaction for the preparation of derivatives of stilbazoles was presented. A series of stilbazoles were synthesized firstly by this highly efficient method. From this reaction it wa...A novel palladium-catalyzed coupling reaction for the preparation of derivatives of stilbazoles was presented. A series of stilbazoles were synthesized firstly by this highly efficient method. From this reaction it was found that reaction solvent is one of important factors in this catalytic system.展开更多
In the case of Pd(PPh3)4 as catalyst and toluene as reaction solvent, the desired biaryls and polyaryls were synthesized in excellent yield and on a large scale.
This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonline...This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonlinear parabolic, fourth order Cahn-Hilliard equation with degenerate mobility M(u)= u^m(1-u)^m which is allowed to vanish at 0 and 1. The existence and regularity of weak solutions to the degenerate Cahn-Hilliard equation are obtained by getting the limits of Cahn-Hilliard equation with non-degenerate mobility. We explore the initial value problem with compact support and obtain the local non-negative result. Further, the above derivation process is also suitable for the viscous Cahn–Hilliard equation with degenerate mobility.展开更多
基金This work was supported by Foundation from President of the Chinese Academic of Science and NSFC.
文摘A novel palladium-catalyzed coupling reaction for the preparation of derivatives of stilbazoles was presented. A series of stilbazoles were synthesized firstly by this highly efficient method. From this reaction it was found that reaction solvent is one of important factors in this catalytic system.
基金Support from the University of Science and Technology of China the National Natural Science Foundation of China are gratefully acknowledged (NO. 50073021).
文摘In the case of Pd(PPh3)4 as catalyst and toluene as reaction solvent, the desired biaryls and polyaryls were synthesized in excellent yield and on a large scale.
基金Supported by NSF of Shanghai University of Engineering Science(Grant No.0244-E3-0507-19-05155)
文摘This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonlinear parabolic, fourth order Cahn-Hilliard equation with degenerate mobility M(u)= u^m(1-u)^m which is allowed to vanish at 0 and 1. The existence and regularity of weak solutions to the degenerate Cahn-Hilliard equation are obtained by getting the limits of Cahn-Hilliard equation with non-degenerate mobility. We explore the initial value problem with compact support and obtain the local non-negative result. Further, the above derivation process is also suitable for the viscous Cahn–Hilliard equation with degenerate mobility.
