In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind...In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.展开更多
In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of th...In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.展开更多
From Lax representations,recursion operators for the supersymmetric KdV and the supersymmetric Kaup-Kupershimdt (SKK) equations are proposed explicitly.Under some special conditions,the recursion operator of the super...From Lax representations,recursion operators for the supersymmetric KdV and the supersymmetric Kaup-Kupershimdt (SKK) equations are proposed explicitly.Under some special conditions,the recursion operator of the supersymmetric Sawada-Kotera equation can be recovered by the one of the SKK equation.展开更多
A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a qu...A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a quotient of some Verma-like poillted module; moreover if it is irreduciblethen it is a quotieDt of the Vermarlike poiDted module by the left kernel of some bilinearpairing K. In case the mass fUnction is symmetric, there exists a bilinear form on M(ρ). It isproved that unitals pointed modules are integrable. In addition, a characterization of the massfunctions of Kac-Moody algebras is given, which is a generalization of the finite dimensionalLie algebras case.展开更多
文摘In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.
文摘In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.
基金Supported by Zhejiang Provincial Natural Science Foundations of China under Grant No.Y6090592National Natural Science Foundation of China under Grant Nos.10735030 and 11041003+1 种基金Ningbo Natural Science Foundation under Grant Nos.2009B21003,2010A610103 and 2009B21003K.C.Wong Magna Fund in Ningbo University
文摘From Lax representations,recursion operators for the supersymmetric KdV and the supersymmetric Kaup-Kupershimdt (SKK) equations are proposed explicitly.Under some special conditions,the recursion operator of the supersymmetric Sawada-Kotera equation can be recovered by the one of the SKK equation.
文摘A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a quotient of some Verma-like poillted module; moreover if it is irreduciblethen it is a quotieDt of the Vermarlike poiDted module by the left kernel of some bilinearpairing K. In case the mass fUnction is symmetric, there exists a bilinear form on M(ρ). It isproved that unitals pointed modules are integrable. In addition, a characterization of the massfunctions of Kac-Moody algebras is given, which is a generalization of the finite dimensionalLie algebras case.
