In this pape,we give four methods of discriminations its nonsingularity by utilizing only parametr r1,r2 and elements of the first row of level-2 (r1, r2)-circulant matrices of type (m,n).
In this paper,it is given that the new equivalent definition of level-k (r1,r2, …,rk)-cir culant matrices of type (n1,n2,…,nk) in [1] and we give the explicit expression of its the eigenval ues and four methods of d...In this paper,it is given that the new equivalent definition of level-k (r1,r2, …,rk)-cir culant matrices of type (n1,n2,…,nk) in [1] and we give the explicit expression of its the eigenval ues and four methods of discriminations its nonsingularity by utilizing only parameter r1,r2, …,rk and elements of the first row of the sorts matrices.展开更多
The precise synthesis of polymer with narrow molecular weight distribution(?)and well-defined architectures is very essential to exploring the functions and properties of polymer materials.Here,a universal polymerizat...The precise synthesis of polymer with narrow molecular weight distribution(?)and well-defined architectures is very essential to exploring the functions and properties of polymer materials.Here,a universal polymerization method capable of low?and reactive hydrogen compatibility is reported by introducing super-Grignard reagents(R_(2)Mg?Li Cl)into polymer chemistry.Under mild conditions,various monomers,including nonpolar polystyrene and 4-methoxystyrene that cannot be initiated by Grignard reagents,and polar methacrylate,are successfully polymerized with full monomer conversion and low?.This approach is amenable to wide varieties of initiators,polymerization temperature,and feed ratio,which makes it attractive for applications in polymer synthesis.By adding methanol and water during the polymerization process,the reactive hydrogen compatibility of this method is confirmed,which makes this method avoid the rigorous restriction on polymerization conditions of anionic polymerization.Moreover,chain extension polymerization and block copolymerization are achieved and demonstrate the livingness of chain propagation,enabling the facile synthesis of well-defined macromolecular architectures.This work therefore expands the methodology libraries of living polymerization,which may cause inspirations to polymer science.展开更多
文摘In this pape,we give four methods of discriminations its nonsingularity by utilizing only parametr r1,r2 and elements of the first row of level-2 (r1, r2)-circulant matrices of type (m,n).
文摘In this paper,it is given that the new equivalent definition of level-k (r1,r2, …,rk)-cir culant matrices of type (n1,n2,…,nk) in [1] and we give the explicit expression of its the eigenval ues and four methods of discriminations its nonsingularity by utilizing only parameter r1,r2, …,rk and elements of the first row of the sorts matrices.
基金funding support from National Natural Science Foundation of China(NSFC,Nos.22271286 and 21971236)the Haixi Institute of CAS(No.CXZX-2017-P01)。
文摘The precise synthesis of polymer with narrow molecular weight distribution(?)and well-defined architectures is very essential to exploring the functions and properties of polymer materials.Here,a universal polymerization method capable of low?and reactive hydrogen compatibility is reported by introducing super-Grignard reagents(R_(2)Mg?Li Cl)into polymer chemistry.Under mild conditions,various monomers,including nonpolar polystyrene and 4-methoxystyrene that cannot be initiated by Grignard reagents,and polar methacrylate,are successfully polymerized with full monomer conversion and low?.This approach is amenable to wide varieties of initiators,polymerization temperature,and feed ratio,which makes it attractive for applications in polymer synthesis.By adding methanol and water during the polymerization process,the reactive hydrogen compatibility of this method is confirmed,which makes this method avoid the rigorous restriction on polymerization conditions of anionic polymerization.Moreover,chain extension polymerization and block copolymerization are achieved and demonstrate the livingness of chain propagation,enabling the facile synthesis of well-defined macromolecular architectures.This work therefore expands the methodology libraries of living polymerization,which may cause inspirations to polymer science.
