In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi e...In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.展开更多
A convenient photocatalytic multi-component reaction of alkenes,quinoxalin-2(1H)-ones,and diazo compounds has been developed in the presence of water.A number of ester-containing quinoxalin-2(1H)-ones could be efficie...A convenient photocatalytic multi-component reaction of alkenes,quinoxalin-2(1H)-ones,and diazo compounds has been developed in the presence of water.A number of ester-containing quinoxalin-2(1H)-ones could be efficiently obtained in moderate to good yields at room temperature.This metal-free visiblelight-driven tandem reaction was conducted through proton-coupled electron transfer(PCET)process using water as the hydrogen donor and 1,2,3,5-tetrakis(carbazol-9-yl)-4,6-dicyanobenzene(4CzIPN)as the photocatalyst.展开更多
基金supported by NNSFC(11001219,10925104)the Scientific Research Program Funded by Shaanxi Provincial Education Department(2010JK860)
文摘In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.
基金supported by Sichuan Science and Technology Program(No.2023NSFSC0101)the 2024 Provincial platform project of Chengdu Normal University(No.GNFZ202404)+1 种基金Natural Science Foundation of Shandong Province(No.ZR2021MB065)National Natural Science Foundation of China(No.22101237)。
文摘A convenient photocatalytic multi-component reaction of alkenes,quinoxalin-2(1H)-ones,and diazo compounds has been developed in the presence of water.A number of ester-containing quinoxalin-2(1H)-ones could be efficiently obtained in moderate to good yields at room temperature.This metal-free visiblelight-driven tandem reaction was conducted through proton-coupled electron transfer(PCET)process using water as the hydrogen donor and 1,2,3,5-tetrakis(carbazol-9-yl)-4,6-dicyanobenzene(4CzIPN)as the photocatalyst.
