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.
Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociateds...Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.展开更多
We study the Cauchy problem for the Davey–Stewartson equation i?tu+Δu+|u|^(2) u+E1(|u|^(2))u=0,(t,x)∈R×R^(3).The dichotomy between scattering and finite time blow-up shall be proved for initial data with finit...We study the Cauchy problem for the Davey–Stewartson equation i?tu+Δu+|u|^(2) u+E1(|u|^(2))u=0,(t,x)∈R×R^(3).The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u0)E(u0)above the ground state threshold M(Q)E(Q).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 the NNSF of China(Grant Nos.12071125,12001183 and 11831007)the Hunan Provincial NSF(Grant Nos.2020JJ5097 and 2019JJ20012)the SRF of Hunan Provincial Education Department(Grant No.19B117)。
文摘Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.
基金Supported by Natural Science Foundation of China(Grant Nos.11501111,11771082 and 11601082)China Scholarship Council(Grant No.201808350018)Foundation of the Science and Technology Department of Fujian Province(Grant No.2017J05002)。
文摘We study the Cauchy problem for the Davey–Stewartson equation i?tu+Δu+|u|^(2) u+E1(|u|^(2))u=0,(t,x)∈R×R^(3).The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u0)E(u0)above the ground state threshold M(Q)E(Q).
