In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple grap...In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.展开更多
The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left...The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.展开更多
Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be...Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.展开更多
In this paper, the notion of L-R crossed coproduct is introduced as a unified approach for smash coproducts, crossed coproducts and L-R smash coproducts of Hopf algebras.A duality theorem for L-R crossed coproduct is ...In this paper, the notion of L-R crossed coproduct is introduced as a unified approach for smash coproducts, crossed coproducts and L-R smash coproducts of Hopf algebras.A duality theorem for L-R crossed coproduct is proved.展开更多
In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduet coalgebra induced ...In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduet coalgebra induced from two coalgebras with a cotwisted map and the cocyclic object related to the diagonal of the cocylindrical object.展开更多
On November 29,2013 the Shaanxi Coal Chemicals Technology Engineering Center,Ltd.(SCCTEC),the CNOOC Huizhou Refining and Chemical Company and the SINOPEC Luoyang Engineering Company,Ltd.signed an agreement on cooperat...On November 29,2013 the Shaanxi Coal Chemicals Technology Engineering Center,Ltd.(SCCTEC),the CNOOC Huizhou Refining and Chemical Company and the SINOPEC Luoyang Engineering Company,Ltd.signed an agreement on cooperation in development of展开更多
Before proposing an innovative process for the coproduction of ethyl and butyl acetates, the individual syntheses of ethyl acetate and butyl acetate by two different routes were first studied. These syntheses involved...Before proposing an innovative process for the coproduction of ethyl and butyl acetates, the individual syntheses of ethyl acetate and butyl acetate by two different routes were first studied. These syntheses involved the reaction of ethanol or n-butanol with acetic acid or acetic anhydride in the presence of ion exchange resins: Amberlyst 15, Amberlyst 16, Amberlyst 36 and Dowex 50WX8. Kinetic and thermodynamic studies were performed with all resins. The lowest activation energy (Ea) value was obtained with Dowex 50WX8, which was identified as the best-performing resin, able to be reused at least in four runs without regeneration. The presence of water-azeotropes during the synthesis of ethyl acetate makes its purification difficult. A new strategy was adopted here, involving the use of ethanol and acetic anhydride as the starting material. In order to minimize acetic acid as co-product of this reaction, a novel two-step process for the coproduction of ethyl and butyl acetates was developed. The first step involves the production of ethyl acetate and its purification. Butyl acetate was produced in the second step: n-butanol was added to the mixture of acetic acid and the resin remaining after the first-step distillation. This process yields ethyl acetate and butyl acetate at high purity and shows an environmental benefit over the independent syntheses by green metrics calculation and life cycle assessment.展开更多
文摘In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.
基金The National Natural Science Foundation of China(No.10871042)the Natural Science Foundation of Jiangsu Province(No.BK2009258)
文摘The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.
基金Supported by the National Natural Science Foundation of China(60873267)the Ningbo Natural Science Foundation of China(2011A610172)K.C.Wang Magna Fund in Ningbo University
文摘Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.
基金Research supported by the National Natural Science Foundation of China(11261063,11471186,11501317)the Natural Foundation of Shandong Province(ZR2018MA012,ZR2016AQ03)
文摘In this paper, the notion of L-R crossed coproduct is introduced as a unified approach for smash coproducts, crossed coproducts and L-R smash coproducts of Hopf algebras.A duality theorem for L-R crossed coproduct is proved.
基金The NSF(11261063,11171183)of Chinathe Fund(2012ZDXK03)of the Key Disciplines in the General Colleges and Universities of Xinjiang Uygur Autonomous Region+1 种基金the Foundation(2013721043)for Excellent Youth Science and Technology Innovation Talents of Xinjiang Uygur Autonomous Regionthe NSF(ZR2011AM013)of Shandong Province
文摘In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduet coalgebra induced from two coalgebras with a cotwisted map and the cocyclic object related to the diagonal of the cocylindrical object.
文摘On November 29,2013 the Shaanxi Coal Chemicals Technology Engineering Center,Ltd.(SCCTEC),the CNOOC Huizhou Refining and Chemical Company and the SINOPEC Luoyang Engineering Company,Ltd.signed an agreement on cooperation in development of
基金supported by the European Union’s Seventh Framework Program for research,technological development and demonstration(FP7/2007-2013)[Grant Agreement No.605215]CONACyT for providing funding through PhD scholarship no.383910.
文摘Before proposing an innovative process for the coproduction of ethyl and butyl acetates, the individual syntheses of ethyl acetate and butyl acetate by two different routes were first studied. These syntheses involved the reaction of ethanol or n-butanol with acetic acid or acetic anhydride in the presence of ion exchange resins: Amberlyst 15, Amberlyst 16, Amberlyst 36 and Dowex 50WX8. Kinetic and thermodynamic studies were performed with all resins. The lowest activation energy (Ea) value was obtained with Dowex 50WX8, which was identified as the best-performing resin, able to be reused at least in four runs without regeneration. The presence of water-azeotropes during the synthesis of ethyl acetate makes its purification difficult. A new strategy was adopted here, involving the use of ethanol and acetic anhydride as the starting material. In order to minimize acetic acid as co-product of this reaction, a novel two-step process for the coproduction of ethyl and butyl acetates was developed. The first step involves the production of ethyl acetate and its purification. Butyl acetate was produced in the second step: n-butanol was added to the mixture of acetic acid and the resin remaining after the first-step distillation. This process yields ethyl acetate and butyl acetate at high purity and shows an environmental benefit over the independent syntheses by green metrics calculation and life cycle assessment.
