The ability to selectively introduce diverse functionality onto hydrocarbons is of substantial value in the synthesis of both small molecules and pharmaceuticals.In this endeavour,as a photocatalyst-and metalfree proc...The ability to selectively introduce diverse functionality onto hydrocarbons is of substantial value in the synthesis of both small molecules and pharmaceuticals.In this endeavour,as a photocatalyst-and metalfree process,the electron donor–acceptor(EDA)strategy has not been well explored.Here we report an approach to aliphatic carbon-hydrogen bond diversification through an EDA complex constituted by HCl and S^(IV)=O groups.As an efficient hydrogen atom transfer(HAT)reagent,chlorine radical can be produced via a proton-coupled electron transfer process in this system.Based on this unusual path,a photopromoted versatile aliphatic C–H functionalization is developed without photo-and metal-catalysts,including thiolation,arylation,alkynylation,and allylation.This conversion has concise and ambient reaction conditions,good functional group tolerance,and substrate diversity,and provides an alternative solution for the high value-added utilization of bulk light alkanes.展开更多
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m...In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.展开更多
基金supported by the National Key Research and Development Program of China(2022YFC2804105)the Joint Fund of Shandong Natural Science Foundation(ZR2021LSW013)+5 种基金Natural Science Foundation of Shandong Province(ZR2020QB044,ZR2020QH364,ZR2023MH245,and ZR2022QB090)Postdoctoral Science Foundation of China(2020M682157)Qingdao Emerging Industry Cultivation Project in 2023(23-1-4-xxgg-19-nsh)Shandong Provincial Science and Technology SME Innovation Capacity Improvement Project(2022TSGC2204)the National Natural Science Foundation of China(82003787)Postdoctoral Innovation Project of Shandong Province。
文摘The ability to selectively introduce diverse functionality onto hydrocarbons is of substantial value in the synthesis of both small molecules and pharmaceuticals.In this endeavour,as a photocatalyst-and metalfree process,the electron donor–acceptor(EDA)strategy has not been well explored.Here we report an approach to aliphatic carbon-hydrogen bond diversification through an EDA complex constituted by HCl and S^(IV)=O groups.As an efficient hydrogen atom transfer(HAT)reagent,chlorine radical can be produced via a proton-coupled electron transfer process in this system.Based on this unusual path,a photopromoted versatile aliphatic C–H functionalization is developed without photo-and metal-catalysts,including thiolation,arylation,alkynylation,and allylation.This conversion has concise and ambient reaction conditions,good functional group tolerance,and substrate diversity,and provides an alternative solution for the high value-added utilization of bulk light alkanes.
文摘In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.
