To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are pr...To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.展开更多
For two classes of right R-modules W, X such that P W X, where P is the class of projective right R-modules, we show that there is an Avramov-Martsinkovsky type exact sequence with generalized Tate homology func...For two classes of right R-modules W, X such that P W X, where P is the class of projective right R-modules, we show that there is an Avramov-Martsinkovsky type exact sequence with generalized Tate homology functor Tor^X,W, relative homology functors Tor^W and Tor^X. Many results in Iacob [Comm. Algebra, 35, 1589-1606 （2007）] and Liang [Algebr. Represent. Theory, 16, 1541-1560 （2013）] are generalized and improved.展开更多
Let A be a finite-dimensional algebra over an algebraically closed field k,E the category of all exact sequences in A-mod,MP(respectively,MI)the full subcategory of E consisting of those objects with projective(respec...Let A be a finite-dimensional algebra over an algebraically closed field k,E the category of all exact sequences in A-mod,MP(respectively,MI)the full subcategory of E consisting of those objects with projective(respectively,injective)middle terms.It is proved that MP(respectively,MI)is contravariantly finite(respectively,covariantly finite)in E.As an application,it is shown that MP=MI is functorially finite and has Auslander-Reiten sequences provided A is selfinjective.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10862003)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZZ07031)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2010MS0111)
文摘To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.
基金Supported by the Natural Natural Science Foundation of China under Grant No.10461006the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China under Grant No.NJZZ07031the Natural Science Foundation of Inner Mongolia Autonomous Region,China under Grant No.2010MS0111
基金Supported by National Natural Science Foundation of China(Grant Nos.11301240,11401475)Natural Science Foundation of Chongqing(cstc2017jcyjAX0298)
文摘For two classes of right R-modules W, X such that P W X, where P is the class of projective right R-modules, we show that there is an Avramov-Martsinkovsky type exact sequence with generalized Tate homology functor Tor^X,W, relative homology functors Tor^W and Tor^X. Many results in Iacob [Comm. Algebra, 35, 1589-1606 （2007）] and Liang [Algebr. Represent. Theory, 16, 1541-1560 （2013）] are generalized and improved.
基金supported by National Natural Science Foundation of China(Grant No.11271257)National Science Foundation of Shanghai Municiple(Granted No.13ZR1422500)
文摘Let A be a finite-dimensional algebra over an algebraically closed field k,E the category of all exact sequences in A-mod,MP(respectively,MI)the full subcategory of E consisting of those objects with projective(respectively,injective)middle terms.It is proved that MP(respectively,MI)is contravariantly finite(respectively,covariantly finite)in E.As an application,it is shown that MP=MI is functorially finite and has Auslander-Reiten sequences provided A is selfinjective.
