In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We...In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra. Using the coadjoint representation, we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras. Finally, we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.展开更多
Conventional carbon materials cannot combine high density and high porosity,which are required in many applications,typically for energy storage under a limited space.A novel highly dense yet porous carbon has previou...Conventional carbon materials cannot combine high density and high porosity,which are required in many applications,typically for energy storage under a limited space.A novel highly dense yet porous carbon has previously been produced from a three-dimensional(3D)reduced graphene oxide(r-GO)hydrogel by evaporation-induced drying.Here the mechanism of such a network shrinkage in r-GO hydrogel is specifically illustrated by the use of water and 1,4-dioxane,which have a sole difference in surface tension.As a result,the surface tension of the evaporating solvent determines the capillary forces in the nanochannels,which causes shrinkage of the r-GO network.More promisingly,the selection of a solvent with a known surface tension can precisely tune the microstructure associated with the density and porosity of the resulting porous carbon,rendering the porous carbon materials great potential in practical devices with high volumetric performance.展开更多
Prior studies using single and binary adsorbates indicate that nanografting impacts the reaction pathways and local structure of self-assembled monolayers （SAMs）. This work explores the influence of nanografting in ...Prior studies using single and binary adsorbates indicate that nanografting impacts the reaction pathways and local structure of self-assembled monolayers （SAMs）. This work explores the influence of nanografting in the case of ternary SAMs. Using atomic force microscopy （AFM） as both a nanografting and imaging tool, the local structures of two ternary SAMs, SC14：SSC10CHO：SC2COOH and SC18：SSC10CHO：SC2COOH, formed under natural growth and nanografting were imaged and compared. The results indicate that nanografting impacts the degree of phase segregation and the domain height in ternary SAMs. In addition to the previously known effect of altering self-assembly pathways, this study reveals an additional impact for these ternary systems： By shaving over the previous trajectory （grafted region）, nanografting could start exchange reactions and lateral movement of surface-bound thiols, which leads to new and somewhat unanticipated local structures.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11471139)Natural Science Foundation of Jilin Province (Grant No. 20170101050JC)Nan Hu Scholar Development Program of Xin Yang Normal University
文摘In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra. Using the coadjoint representation, we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras. Finally, we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.
基金This work was supported by the National Natural Science Fund for the Distinguished Young Scholars,China(51525204)the National Natural Science Foundation of China(51702229 and 51872195)the CAS Key Laboratory of Carbon Materials(KLCM KFJJ1704).
文摘Conventional carbon materials cannot combine high density and high porosity,which are required in many applications,typically for energy storage under a limited space.A novel highly dense yet porous carbon has previously been produced from a three-dimensional(3D)reduced graphene oxide(r-GO)hydrogel by evaporation-induced drying.Here the mechanism of such a network shrinkage in r-GO hydrogel is specifically illustrated by the use of water and 1,4-dioxane,which have a sole difference in surface tension.As a result,the surface tension of the evaporating solvent determines the capillary forces in the nanochannels,which causes shrinkage of the r-GO network.More promisingly,the selection of a solvent with a known surface tension can precisely tune the microstructure associated with the density and porosity of the resulting porous carbon,rendering the porous carbon materials great potential in practical devices with high volumetric performance.
文摘Prior studies using single and binary adsorbates indicate that nanografting impacts the reaction pathways and local structure of self-assembled monolayers （SAMs）. This work explores the influence of nanografting in the case of ternary SAMs. Using atomic force microscopy （AFM） as both a nanografting and imaging tool, the local structures of two ternary SAMs, SC14：SSC10CHO：SC2COOH and SC18：SSC10CHO：SC2COOH, formed under natural growth and nanografting were imaged and compared. The results indicate that nanografting impacts the degree of phase segregation and the domain height in ternary SAMs. In addition to the previously known effect of altering self-assembly pathways, this study reveals an additional impact for these ternary systems： By shaving over the previous trajectory （grafted region）, nanografting could start exchange reactions and lateral movement of surface-bound thiols, which leads to new and somewhat unanticipated local structures.
