Glycerol is a by-product of biodiesel production and is an important readily available platform chemical.Valorization of glycerol into value-added chemicals has gained immense attention.Herein,we carried out the conve...Glycerol is a by-product of biodiesel production and is an important readily available platform chemical.Valorization of glycerol into value-added chemicals has gained immense attention.Herein,we carried out the conversion of glycerol to formic acid and glycolic acid using H2O2 as an oxidant and metal(Ⅲ)triflate-based catalytic systems.Aluminum(Ⅲ)triflate was found to be the most efficient catalyst for the selective oxidation of glycerol to formic acid.A correlation between the catalytic activity of the metal cations and their hydrolysis constants(Kh)and water exchange rate constants was observed.At 70 ℃,a formic acid yield of up to 72% could be attained within 12 h.The catalyst could be recycled at least five times with a high conversion rate,and hence can also be used for the selective oxidation of other biomass platform molecules.Reaction kinetics and 1H NMR studies showed that the oxidation of glycerol(to formic acid)involved glycerol hydrolysis pathways with glyceric acid and glycolic acid as the main intermediate products.Both the [Al(OH)x]^n+ Lewis acid species and CF3SO3H Brosted acid,which were generated by the in-situ hydrolysis of Al(OTf)3,were responsible for glycerol conversion.The easy availability,high efficiency,and good recyclability of Al(OTf)3 render it suitable for the selective oxidation of glycerol to high value-added products.展开更多
Denote by Dm the dihedral group of order 2m. Let R（Dm） be its complex representation ring, and let △（Dm） be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quoti...Denote by Dm the dihedral group of order 2m. Let R（Dm） be its complex representation ring, and let △（Dm） be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quotient △^n（Dm）/△^n＋1（Dm） for each positive integer n.展开更多
Let G be a finite abelian p-group,Г the maximal Z-order of Z[G]. We prove that the 2-primary torsion subgroups of K2Z[G]) and K2(Г)are isomorphic when p ≡ 3, 5, 7 (mod 8, and K2(Z[G])■zZ[1/p] is isomorphic to K2(...Let G be a finite abelian p-group,Г the maximal Z-order of Z[G]. We prove that the 2-primary torsion subgroups of K2Z[G]) and K2(Г)are isomorphic when p ≡ 3, 5, 7 (mod 8, and K2(Z[G])■zZ[1/p] is isomorphic to K2(Г)■zZ[1/p] when p = 2,3,5,7. As an application, we give the structure of K2(Z[G]) for G a cyclic p-group or an elementary abelian p-group.展开更多
基金the National Natural Science Foundation of China(21773061,21373082)the Innovation Program of Shanghai Municipal Education Commission(15ZZ031)~~
文摘Glycerol is a by-product of biodiesel production and is an important readily available platform chemical.Valorization of glycerol into value-added chemicals has gained immense attention.Herein,we carried out the conversion of glycerol to formic acid and glycolic acid using H2O2 as an oxidant and metal(Ⅲ)triflate-based catalytic systems.Aluminum(Ⅲ)triflate was found to be the most efficient catalyst for the selective oxidation of glycerol to formic acid.A correlation between the catalytic activity of the metal cations and their hydrolysis constants(Kh)and water exchange rate constants was observed.At 70 ℃,a formic acid yield of up to 72% could be attained within 12 h.The catalyst could be recycled at least five times with a high conversion rate,and hence can also be used for the selective oxidation of other biomass platform molecules.Reaction kinetics and 1H NMR studies showed that the oxidation of glycerol(to formic acid)involved glycerol hydrolysis pathways with glyceric acid and glycolic acid as the main intermediate products.Both the [Al(OH)x]^n+ Lewis acid species and CF3SO3H Brosted acid,which were generated by the in-situ hydrolysis of Al(OTf)3,were responsible for glycerol conversion.The easy availability,high efficiency,and good recyclability of Al(OTf)3 render it suitable for the selective oxidation of glycerol to high value-added products.
文摘Denote by Dm the dihedral group of order 2m. Let R（Dm） be its complex representation ring, and let △（Dm） be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quotient △^n（Dm）/△^n＋1（Dm） for each positive integer n.
基金This work was supported by the National Natural Science Foundation for Young Scientists of China (Grant No. 11401412the National Natural Science Foundation of China (Grant No. 11771422)the Scientific Research Foundation of the Higher Education Institutions of Jiangsu Province, China (Grant No. 18KJB110025).
文摘Let G be a finite abelian p-group,Г the maximal Z-order of Z[G]. We prove that the 2-primary torsion subgroups of K2Z[G]) and K2(Г)are isomorphic when p ≡ 3, 5, 7 (mod 8, and K2(Z[G])■zZ[1/p] is isomorphic to K2(Г)■zZ[1/p] when p = 2,3,5,7. As an application, we give the structure of K2(Z[G]) for G a cyclic p-group or an elementary abelian p-group.
