In this paper, we first prove that the dual module of a rational module is still a rational module, and maximum rational modules keep their exac t properties. Then, we give the Maschke theorem of the coideal subalge...In this paper, we first prove that the dual module of a rational module is still a rational module, and maximum rational modules keep their exac t properties. Then, we give the Maschke theorem of the coideal subalgebra of qua si-Frobenius algebra, and give some equivalent conditions for the ideal subcoal gebra.展开更多
In this paper, we obtain the following main theorem for a free quadratic bialgebra J: (a) For p≠0, J is a pointed cosemisimple coalgebra. For p=0, J is a hyperalgebra. (b) For p≠0 and q≠0, J has antipode S iff p...In this paper, we obtain the following main theorem for a free quadratic bialgebra J: (a) For p≠0, J is a pointed cosemisimple coalgebra. For p=0, J is a hyperalgebra. (b) For p≠0 and q≠0, J has antipode S iff p·q+2=0 and S(x)=x. Forp=0 or q=0, J has antipode and S(x)=-x. (c) All left J*-modules are rational. Also, we give some applications in homological theory and algebraic K-theory.展开更多
Aqueous Zn-based energy-storage devices have aroused much interest in recent years.However,uncontrollable dendrite growth in the Zn anode significantly limits their cycle life.Moreover,the poor low-temperature perform...Aqueous Zn-based energy-storage devices have aroused much interest in recent years.However,uncontrollable dendrite growth in the Zn anode significantly limits their cycle life.Moreover,the poor low-temperature performance arising from the freezing of aqueous electrolytes at sub-zero temperatures restricts their practical applications in cold regions.Here,we fabricated low-temperature-tolerant and durable Zn-ion hybrid supercapacitors(ZHSCs)via modulating a co-solvent water/ethylene glycol electrolyte.The interaction of intermolecular hydrogen bonds between water and ethylene glycol as well as cation solvation was systematically investigated by tuning the co-solvent composition.The results illustrate that the ZnSO_(4)/water/ethylene glycol(65%)electrolyte possesses high ionic conductivity at low temperatures and effectively prevents the dendrite formation of the Zn anode.The as-fabricated ZHSCs exhibit long-term cyclability and are capable of working at sub-zero temperatures as low as -40℃.The present ZHSCs are anti-freezing and cost-effective,which may find new applications in the fields of next-generation electrochemical energy storage devices.展开更多
文摘In this paper, we first prove that the dual module of a rational module is still a rational module, and maximum rational modules keep their exac t properties. Then, we give the Maschke theorem of the coideal subalgebra of qua si-Frobenius algebra, and give some equivalent conditions for the ideal subcoal gebra.
基金Partially supported by the National Natural Science Foundation of China.
文摘In this paper, we obtain the following main theorem for a free quadratic bialgebra J: (a) For p≠0, J is a pointed cosemisimple coalgebra. For p=0, J is a hyperalgebra. (b) For p≠0 and q≠0, J has antipode S iff p·q+2=0 and S(x)=x. Forp=0 or q=0, J has antipode and S(x)=-x. (c) All left J*-modules are rational. Also, we give some applications in homological theory and algebraic K-theory.
基金supported by the National Natural Science Foundation of China(51772116 and 51972132)the program for HUST Academic Frontier Youth Team(2016QYTD04)。
文摘Aqueous Zn-based energy-storage devices have aroused much interest in recent years.However,uncontrollable dendrite growth in the Zn anode significantly limits their cycle life.Moreover,the poor low-temperature performance arising from the freezing of aqueous electrolytes at sub-zero temperatures restricts their practical applications in cold regions.Here,we fabricated low-temperature-tolerant and durable Zn-ion hybrid supercapacitors(ZHSCs)via modulating a co-solvent water/ethylene glycol electrolyte.The interaction of intermolecular hydrogen bonds between water and ethylene glycol as well as cation solvation was systematically investigated by tuning the co-solvent composition.The results illustrate that the ZnSO_(4)/water/ethylene glycol(65%)electrolyte possesses high ionic conductivity at low temperatures and effectively prevents the dendrite formation of the Zn anode.The as-fabricated ZHSCs exhibit long-term cyclability and are capable of working at sub-zero temperatures as low as -40℃.The present ZHSCs are anti-freezing and cost-effective,which may find new applications in the fields of next-generation electrochemical energy storage devices.
