An efficient visible-light induced nickel-catalyzed reductive Heck reaction of alkenes by using mild organic reductant Hantzsch ester(HEH)instead of traditional metal reductants or hydride reagents was developed.The r...An efficient visible-light induced nickel-catalyzed reductive Heck reaction of alkenes by using mild organic reductant Hantzsch ester(HEH)instead of traditional metal reductants or hydride reagents was developed.The reductive hydroarylation of acrylates with aryl halides was successfully achieved without requiring exogenous photoredox catalysts.This reaction is highlighted by the simple and mild conditions,good functional group tolerance,thus providing a complementary approach for alkenes reductive Heck reaction.展开更多
Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized...Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized Fourier coefficients,respectively.In this paper,we investigate the correlations of triple sums associated to these Fourier coefficientsλ_(f)(n),λ_(g)(n),λ_(h)(n)over certain polynomials,and obtain some power-saving asymptotic estimates which beat the trivial bounds.展开更多
文摘An efficient visible-light induced nickel-catalyzed reductive Heck reaction of alkenes by using mild organic reductant Hantzsch ester(HEH)instead of traditional metal reductants or hydride reagents was developed.The reductive hydroarylation of acrylates with aryl halides was successfully achieved without requiring exogenous photoredox catalysts.This reaction is highlighted by the simple and mild conditions,good functional group tolerance,thus providing a complementary approach for alkenes reductive Heck reaction.
基金Supported in part by NSFC(Nos.12401011,12201214)National Key Research and Development Program of China(No.2021YFA1000700)+3 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics(No.23JSQ053)Science and Technology Program for Youth New Star of Shaanxi Province(No.2025ZC-KJXX-29)Natural Science Basic Research Program of Shaanxi Province(No.2025JC-YBQN-091)Scientific Research Foundation for Young Talents of WNU(No.2024XJ-QNRC-01)。
文摘Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized Fourier coefficients,respectively.In this paper,we investigate the correlations of triple sums associated to these Fourier coefficientsλ_(f)(n),λ_(g)(n),λ_(h)(n)over certain polynomials,and obtain some power-saving asymptotic estimates which beat the trivial bounds.
