Motivated by the concept of matching Rota-Baxter algebras arising from polarized associative Yang-Baxter equations and Volterra integral equations,we introduce the notion of a matching Rota-Baxter system,which general...Motivated by the concept of matching Rota-Baxter algebras arising from polarized associative Yang-Baxter equations and Volterra integral equations,we introduce the notion of a matching Rota-Baxter system,which generalizes the Rota-Baxter system proposed by Brzezinski.We show that this notion is also related to Yang-Baxter pairs and to matching pre-Lie algebras.We then modify the definition of matching Rota-Baxter systems by adding a curvature term,and make a connection with matching pre-Lie algebras and with compatible associative algebras.Furthermore,we study matching Rota-Baxter systems on a dendriform algebra and show how they induce matching quadri-algebra structures.Finally,we give a linear basis of free matching Rota-Baxter system by Grobner-Shirshov bases methods.展开更多
Graphene(Gr)has unique properties including high electrical conductivity;Thus,graphene/copper(Gr/Cu)composites have attracted increasing attention to replace traditional Cu for electrical applications. However,the pro...Graphene(Gr)has unique properties including high electrical conductivity;Thus,graphene/copper(Gr/Cu)composites have attracted increasing attention to replace traditional Cu for electrical applications. However,the problem of how to control graphene to form desired Gr/Cu composite is not well solved. This paper aims at exploring the best parameters for preparing graphene with different layers on Cu foil by chemical vapor deposition(CVD)method and studying the effects of different layers graphene on Gr/Cu composite’s electrical conductivity. Graphene grown on single-sided and double-sided copper was prepared for Gr/Cu and Gr/Cu/Gr composites. The resultant electrical conductivity of Gr/Cu composites increased with decreasing graphene layers and increasing graphene volume fraction. The Gr/Cu/Gr composite with monolayer graphene owns volume fraction of less than 0.002%,producing the best electrical conductivity up to59.8 ×10^(6)S/m,equivalent to 104.5% IACS and 105.3% pure Cu foil.展开更多
基金supported by the National Natural Science Foundation of China(12161013,12101316)supported by the Belt and Road Innovative Talents Exchange Foreign Experts Project(DL2023014002L).
文摘Motivated by the concept of matching Rota-Baxter algebras arising from polarized associative Yang-Baxter equations and Volterra integral equations,we introduce the notion of a matching Rota-Baxter system,which generalizes the Rota-Baxter system proposed by Brzezinski.We show that this notion is also related to Yang-Baxter pairs and to matching pre-Lie algebras.We then modify the definition of matching Rota-Baxter systems by adding a curvature term,and make a connection with matching pre-Lie algebras and with compatible associative algebras.Furthermore,we study matching Rota-Baxter systems on a dendriform algebra and show how they induce matching quadri-algebra structures.Finally,we give a linear basis of free matching Rota-Baxter system by Grobner-Shirshov bases methods.
基金supported substantially by the Southwest Jiaotong University for Material and Financial Support。
文摘Graphene(Gr)has unique properties including high electrical conductivity;Thus,graphene/copper(Gr/Cu)composites have attracted increasing attention to replace traditional Cu for electrical applications. However,the problem of how to control graphene to form desired Gr/Cu composite is not well solved. This paper aims at exploring the best parameters for preparing graphene with different layers on Cu foil by chemical vapor deposition(CVD)method and studying the effects of different layers graphene on Gr/Cu composite’s electrical conductivity. Graphene grown on single-sided and double-sided copper was prepared for Gr/Cu and Gr/Cu/Gr composites. The resultant electrical conductivity of Gr/Cu composites increased with decreasing graphene layers and increasing graphene volume fraction. The Gr/Cu/Gr composite with monolayer graphene owns volume fraction of less than 0.002%,producing the best electrical conductivity up to59.8 ×10^(6)S/m,equivalent to 104.5% IACS and 105.3% pure Cu foil.
