We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding i...We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolani to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Pade interpolation to a finite set of functions.展开更多
In this paper, we study about trigonometry in finite field, we know that , the field with p elements, where p is a prime number if and only if p = 8k + 1 or p = 8k -1. Let F and K be two fields, we say that F is an ex...In this paper, we study about trigonometry in finite field, we know that , the field with p elements, where p is a prime number if and only if p = 8k + 1 or p = 8k -1. Let F and K be two fields, we say that F is an extension of K, if K⊆F or there exists a monomorphism f: K→F. Recall that , F[x] is the ring of polynomial over F. If (means that F is an extension of K), an element is algebraic over K if there exists such that f(u) = 0 (see [1]-[4]). The algebraic closure of K in F is , which is the set of all algebraic elements in F over K.展开更多
Representations of Drinfeld doubles of Radford Hopf algebras Hua Sun&Hui-Xiang Chen Abstract In this article,we investigate the representations of the Drinfeld doubles D(R_(mn)(q))of the Radford Hopf algebras R_(m...Representations of Drinfeld doubles of Radford Hopf algebras Hua Sun&Hui-Xiang Chen Abstract In this article,we investigate the representations of the Drinfeld doubles D(R_(mn)(q))of the Radford Hopf algebras R_(mn)(q)over an algebraically closed field k,where m>1 and n>1 are integers and q∈k is a root of unity of order n.展开更多
In order to study a class of finite-dimensional representations of Uq（sl2）, we deal with the quotient algebra Uq （m, n, b） of quantum group Uq（sl2） with relations Kr=1, Emr=b, Fnr=0 in this paper, where q is a r...In order to study a class of finite-dimensional representations of Uq（sl2）, we deal with the quotient algebra Uq （m, n, b） of quantum group Uq（sl2） with relations Kr=1, Emr=b, Fnr=0 in this paper, where q is a root of unity. The algebra Uq（m, n, b） is decomposed into a direct sum of indecomposable （left） ideals. The structures of indecomposable projective representations and their blocks are determined.展开更多
文摘We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolani to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Pade interpolation to a finite set of functions.
文摘In this paper, we study about trigonometry in finite field, we know that , the field with p elements, where p is a prime number if and only if p = 8k + 1 or p = 8k -1. Let F and K be two fields, we say that F is an extension of K, if K⊆F or there exists a monomorphism f: K→F. Recall that , F[x] is the ring of polynomial over F. If (means that F is an extension of K), an element is algebraic over K if there exists such that f(u) = 0 (see [1]-[4]). The algebraic closure of K in F is , which is the set of all algebraic elements in F over K.
文摘Representations of Drinfeld doubles of Radford Hopf algebras Hua Sun&Hui-Xiang Chen Abstract In this article,we investigate the representations of the Drinfeld doubles D(R_(mn)(q))of the Radford Hopf algebras R_(mn)(q)over an algebraically closed field k,where m>1 and n>1 are integers and q∈k is a root of unity of order n.
基金Supported by Doctor Scientific Research Start Fund of He’nan University of Science and TechnologyNational Natural Science Foundation of China (Grant No. 11171296)
文摘In order to study a class of finite-dimensional representations of Uq（sl2）, we deal with the quotient algebra Uq （m, n, b） of quantum group Uq（sl2） with relations Kr=1, Emr=b, Fnr=0 in this paper, where q is a root of unity. The algebra Uq（m, n, b） is decomposed into a direct sum of indecomposable （left） ideals. The structures of indecomposable projective representations and their blocks are determined.
