Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we ...Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.展开更多
In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） ...In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias＇ stability theorem that appeared in the paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 （1978）, 297-300. This is applied to investigate isometric isomorphisms between proper CQ＊-algebras.展开更多
In this paper,we prove the Langton’s type theorem on separatedness and properness for the moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k.
In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the ...In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.展开更多
Let K=F_q(t) be the rational function field with the transcendental element t over F_q, F_q the field of q elements of odd characteristic. Any finite extension of k is called an algebraic function field. In this note,...Let K=F_q(t) be the rational function field with the transcendental element t over F_q, F_q the field of q elements of odd characteristic. Any finite extension of k is called an algebraic function field. In this note, we study the展开更多
文摘Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.
基金supported by Korea Science & Engineering Foundation (Grant No. F01-2006-000-10111-0)
文摘In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias＇ stability theorem that appeared in the paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 （1978）, 297-300. This is applied to investigate isometric isomorphisms between proper CQ＊-algebras.
基金Supported by the Fundamental Research Funds for the Central Universities,Sun Yat-sen University (Grant No.34000-31610293)。
文摘In this paper,we prove the Langton’s type theorem on separatedness and properness for the moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k.
基金This paper is partially supported by the National Fundamental Research 973 Program of China under Grant No.2004CB318000.
文摘In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.
基金Project supported by the Science Fund of Academia Sinica
文摘Let K=F_q(t) be the rational function field with the transcendental element t over F_q, F_q the field of q elements of odd characteristic. Any finite extension of k is called an algebraic function field. In this note, we study the
