Traditional reduction coupling reactions of two bromides typically rely on transition metal catalysis.Here,we introduce the development of a visible-light catalytic direct reduction coupling reaction between α-CF_(3)...Traditional reduction coupling reactions of two bromides typically rely on transition metal catalysis.Here,we introduce the development of a visible-light catalytic direct reduction coupling reaction between α-CF_(3)-alkyl bromides and alkynyl bromides to access valuable organic frameworks.Our research confirms the excellent compatibility of this reaction with various functional groups,which could be used to modify the substrate with biologically active molecular fragments.Mechanistic investigations,including control experiments,fluorescence quenching studies,and light-switching experiments,have provided insights into the reaction mechanism.This study paves the way for the application of visible-light catalysis in diverse synthetic transformations,offering a sustainable and efficient approach to organic synthesis.展开更多
In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex represe...In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.展开更多
The intermolecular coupling of a nitro group with a cyano group mediated by a Sm(Hg) amalgam prepared from metal samarium powder and catalytic mercury dichloride was studied.
Let G be a connected complex reductive algebraic groups. The dual group ~LG^0 of G is an algebraic group whose simple root system π~v is the dual of the simple root system π of G and whose characteristic lattice is ...Let G be a connected complex reductive algebraic groups. The dual group ~LG^0 of G is an algebraic group whose simple root system π~v is the dual of the simple root system π of G and whose characteristic lattice is just the dual lattice X_*(T) of the characteristic lattice X~*(T)of G, where T is a given maximal torus of G and the simple root system π corresponds to a Borel subgroup B containing T. For the detail of the definition of a dual group see Ref. [1].展开更多
We prove that Sp(2k+l)admits at least two non-naturally reductive Einstein metrics which are Ad(Sp(k)×Sp(k)×Sp(l))-invariant ifk<1.It implies that every compact simple Lie group Sp(n)for n≥4 admits at le...We prove that Sp(2k+l)admits at least two non-naturally reductive Einstein metrics which are Ad(Sp(k)×Sp(k)×Sp(l))-invariant ifk<1.It implies that every compact simple Lie group Sp(n)for n≥4 admits at least 2[(n-1)/3]non-naturally reductive left-invariant Einstein metrics.展开更多
Let G be a connected reductive group defined over F_q, the finite field with q elements. Let B be a Borel subgroup defined over F_q. In this paper, we completely determine the composition factors of the induced module...Let G be a connected reductive group defined over F_q, the finite field with q elements. Let B be a Borel subgroup defined over F_q. In this paper, we completely determine the composition factors of the induced module M(tr) = kG ■tr(where tr is the trivial B-module) for any field k.展开更多
In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.
In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we e...In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we explore some works in the special area in Di erential Geometry,Lie Group and Complex Homogeneous Space.Together with the special area in nonlinear analysis on complex manifolds,they are the two major aspects of my research interests.展开更多
In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae...In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gr?bner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.展开更多
Let G -- Spec A be an affine K-group scheme and A = （w ∈ A＊ ： dimK A＊-w 〈 ∞, dimK w. A＊ 〈 ∞}. Let （-, -） ： A＊ × A → K, （w, w） ：= tr（ww）, be the trace form. We prove that G is linearly reductiv...Let G -- Spec A be an affine K-group scheme and A = （w ∈ A＊ ： dimK A＊-w 〈 ∞, dimK w. A＊ 〈 ∞}. Let （-, -） ： A＊ × A → K, （w, w） ：= tr（ww）, be the trace form. We prove that G is linearly reductive if and only if the trace form is non-degenerate on A＊.展开更多
The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the...The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures.展开更多
基金support was from Tianjin University(2024XJD-0062)the National Natural Science Foundation of China(No.22371203).
文摘Traditional reduction coupling reactions of two bromides typically rely on transition metal catalysis.Here,we introduce the development of a visible-light catalytic direct reduction coupling reaction between α-CF_(3)-alkyl bromides and alkynyl bromides to access valuable organic frameworks.Our research confirms the excellent compatibility of this reaction with various functional groups,which could be used to modify the substrate with biologically active molecular fragments.Mechanistic investigations,including control experiments,fluorescence quenching studies,and light-switching experiments,have provided insights into the reaction mechanism.This study paves the way for the application of visible-light catalysis in diverse synthetic transformations,offering a sustainable and efficient approach to organic synthesis.
基金supported by National Natural Science Foundation of China (Grant No. 11321101)
文摘In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.
基金National Natural Science Foundation of China (Project No. 20072033) and Natural Science Foundation of Zhejiang province for financial support.
文摘The intermolecular coupling of a nitro group with a cyano group mediated by a Sm(Hg) amalgam prepared from metal samarium powder and catalytic mercury dichloride was studied.
基金Project supported in part by the National Natural Science Foundation of China and K. C. Wong Education Foundation.
文摘Let G be a connected complex reductive algebraic groups. The dual group ~LG^0 of G is an algebraic group whose simple root system π~v is the dual of the simple root system π of G and whose characteristic lattice is just the dual lattice X_*(T) of the characteristic lattice X~*(T)of G, where T is a given maximal torus of G and the simple root system π corresponds to a Borel subgroup B containing T. For the detail of the definition of a dual group see Ref. [1].
基金This work was supported in part by the National Natural Science Foundation of China(Nos.11571182,11901300,11931009)the Natural Science Foundation of Tianjin(No.19JCYBJC 30600)the Natural Science Research of Jiangsu Education Institutions of China(No.19K JB 110015).
文摘We prove that Sp(2k+l)admits at least two non-naturally reductive Einstein metrics which are Ad(Sp(k)×Sp(k)×Sp(l))-invariant ifk<1.It implies that every compact simple Lie group Sp(n)for n≥4 admits at least 2[(n-1)/3]non-naturally reductive left-invariant Einstein metrics.
基金supported by National Natural Science Foundation of China (Grant Nos.11501546 and 11671297)。
文摘Let G be a connected reductive group defined over F_q, the finite field with q elements. Let B be a Borel subgroup defined over F_q. In this paper, we completely determine the composition factors of the induced module M(tr) = kG ■tr(where tr is the trivial B-module) for any field k.
文摘In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.
基金the Natural Science Foundation of Henan University。
文摘In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we explore some works in the special area in Di erential Geometry,Lie Group and Complex Homogeneous Space.Together with the special area in nonlinear analysis on complex manifolds,they are the two major aspects of my research interests.
基金supported by NSFC (12071228,11901300, 51535008)Natural Science Research of Jiangsu Education Institutions of China (19KJB110015)。
文摘In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gr?bner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.
基金partially supported by a National Science Foundation Grant(Grant No.ID:DMS-1601303)partially supported by a National Science Foundation Grant(Grant No.ID:DMS-1500966)+1 种基金Simons Foundation Collaboration Grant for MathematiciansSimons Fellowship
文摘This is a survey of some recent results on spherical tropical geometry.
文摘Let G -- Spec A be an affine K-group scheme and A = （w ∈ A＊ ： dimK A＊-w 〈 ∞, dimK w. A＊ 〈 ∞}. Let （-, -） ： A＊ × A → K, （w, w） ：= tr（ww）, be the trace form. We prove that G is linearly reductive if and only if the trace form is non-degenerate on A＊.
基金supported by the 973 Project Foundation of China (#TG1999075102)
文摘The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures.
