By a ball-covering B of a Banach space X, we mean that B is a collection of open （or closed） balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided ...By a ball-covering B of a Banach space X, we mean that B is a collection of open （or closed） balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.展开更多
Let A be a finite dimensional, connected, basic algebra over an algebraically closed field. We prove that A is of finite representation type if and only if there is a natural number m such that rad^m（End（M）） = 0, ...Let A be a finite dimensional, connected, basic algebra over an algebraically closed field. We prove that A is of finite representation type if and only if there is a natural number m such that rad^m（End（M）） = 0, for any indecomposable A-modules M. This gives a partial answer to one of problems posed by Skowrofiski.展开更多
Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is...Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is, rep.dim（A） = rep.dim（A^CaH）. Some of the applications of this equality are also given.展开更多
Non-dominated sorting genetic algorithm II（NSGA-II）with multiple constraints handling is employed for multi-objective optimization of the topological structure of telescope skin,in which a bit-matrix is used as the ...Non-dominated sorting genetic algorithm II（NSGA-II）with multiple constraints handling is employed for multi-objective optimization of the topological structure of telescope skin,in which a bit-matrix is used as the representation of a chromosome,and genetic algorithm（GA）operators are introduced based on the matrix.Objectives including mass,in-plane performance,and out-of-plane load-bearing ability of the individuals are obtained by fnite element analysis（FEA）using ANSYS,and the matrix-based optimization algorithm is realized in MATLAB by handling multiple constraints such as structural connectivity and in-plane strain requirements.Feasible confgurations of the support structure are achieved.The results confrm that the matrix-based NSGA-II with multiple constraints handling provides an effective method for two-dimensional multi-objective topology optimization.展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos. 10771175, 10801111 and 11101340)the Natural Science Foundation of Fujian Province (Grant No. 2010J05012) the Fundamental Research Funds for the Central Universities (Grant Nos. 2010121001 and 2011121039)
文摘By a ball-covering B of a Banach space X, we mean that B is a collection of open （or closed） balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.
基金Supported by the Education Department Foundation of Hunan Province (Grant No04C469)
文摘Let A be a finite dimensional, connected, basic algebra over an algebraically closed field. We prove that A is of finite representation type if and only if there is a natural number m such that rad^m（End（M）） = 0, for any indecomposable A-modules M. This gives a partial answer to one of problems posed by Skowrofiski.
基金partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100091110034)National Natural Science Foundation of China(Grant Nos. 10771095, 10801069)the Natural Science Foundation of Jiangsu Province of China (Grant No.BK2010047)
文摘Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is, rep.dim（A） = rep.dim（A^CaH）. Some of the applications of this equality are also given.
基金supported by the National Natural Science Foundation of China(Nos.50905085 and 91116020)the National Science Foundation for Post-doctoral Scientists of China(No.2012M511263)
文摘Non-dominated sorting genetic algorithm II（NSGA-II）with multiple constraints handling is employed for multi-objective optimization of the topological structure of telescope skin,in which a bit-matrix is used as the representation of a chromosome,and genetic algorithm（GA）operators are introduced based on the matrix.Objectives including mass,in-plane performance,and out-of-plane load-bearing ability of the individuals are obtained by fnite element analysis（FEA）using ANSYS,and the matrix-based optimization algorithm is realized in MATLAB by handling multiple constraints such as structural connectivity and in-plane strain requirements.Feasible confgurations of the support structure are achieved.The results confrm that the matrix-based NSGA-II with multiple constraints handling provides an effective method for two-dimensional multi-objective topology optimization.
