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1.
Let A be the affine matrix of type A_1~(1), D_l~(1) or E_l~(1), g(A) the Kac-MoodyLie algebra associated with A. For any integerable g(A)-module V, suppose thatP(V) is the set of weights of V. Let λ∈P(V) and let a_i be a simple root of g(A),M =[- p_i(λ), q_i(λ)] the closed interval of intergers of all t ∈ z such that λ ta_i ∈P(V). We define the category D as follows.Its objects are integerable g(A)-modules V such that for any λ∈P(V), 0≤i≤l, p_i(λ) q_i(λ)<∞.The morphismsin D are homomorphisms of g(A)-modules. Let 相似文献
2.
Let G be a simple connected graph with pendant vertex set ?V and nonpendant vertex set V_0. The signless Laplacian matrix of G is denoted by Q(G). The signless Dirichlet eigenvalue is a real number λ such that there exists a function f ≠ 0 on V(G) such that Q(G)f(u) = λf(u) for u ∈ V_0 and f(u) = 0 for u ∈ ?V. The signless Dirichlet spectral radiusλ(G) is the largest signless Dirichlet eigenvalue. In this paper, the unicyclic graphs with the largest signless Dirichlet spectral radius among all unicyclic graphs with a given degree sequence are characterized. 相似文献
3.
Zhang Zhongzhi Liu ChangrongSchool of Math. Science Central South Univ. Changsha China Dept. of Math. Hunan City Univ. Yiyang China. Faculty of Mathematics Econometrics Hunan Univ. Changsha China. 《高校应用数学学报(英文版)》2004,(3)
§1 IntroductionWe considerthe following inverse eigenvalue problem offinding an n-by-n matrix A∈S such thatAxi =λixi,i =1,2 ,...,m,where S is a given set of n-by-n matrices,x1 ,...,xm(m≤n) are given n-vectors andλ1 ,...,λmare given constants.Let X=(x1 ,...,xm) ,Λ=(λ1 ,λ2 ,...,λm) ,then the above inverse eigenvalue problemcan be written as followsProblem Given X∈Cn×m,Λ=(λ1 ,...,λm) ,find A∈S such thatAX =XΛ,where S is a given matrix set.We also discuss the so-called opti… 相似文献
4.
JianLin Li 《中国科学 数学(英文版)》2015,58(12):2541-2548
The self-affine measure μM,D associated with an expanding matrix M ∈ Mn(Z) and a finite digit set D ? Znis uniquely determined by the self-affine identity with equal weight. The set of orthogonal exponential functions E(Λ) := {e2πiλ,x : λ∈Λ} in the Hilbert space L2(μM,D) is simply called μM,D-orthogonal exponentials. We consider in this paper the finiteness of μM,D-orthogonality. A necessary and sufficient condition is obtained for the set E(Λ) to be a finite μM,D-orthogonal exponentials. The research here is closely connected with the non-spectrality of self-affine measures. 相似文献
5.
Let μ denote the set of all n×n nonsingular M-matrices. If A∈μ, then there exists a permutation matrix p such that where B_ⅱ(1≤i≤m) is an irreducble nonsingular M-matrix, B_(ij)≤0 (ij). Let V=B~(-1). Then V is a block upper triangular matrix of the form 相似文献
6.
Xiaoping Pan Xiyan Hu Lei Zhang College of Mathematics Econometrics Hunan University Changsha China. 《高等学校计算数学学报(英文版)》2006,15(3):227-236
Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm 1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived. 相似文献
7.
《分析论及其应用》1994,(4)
Let ι be a triangulation of a polygonal domain DR~2 with vertices V={v_1:1≤i≤N,}andRS~k(D,τ)={u∈C~k(D):(T∈τ, u|_τis a rational function}.The purpose of this paper is to study the exist-ence and construction of C~~μ-rational spline functions on any triangulation τ for CAGD.The Hermite prob-lem H~μ(V,U)={find u∈ 相似文献
8.
《高等学校计算数学学报(英文版)》2000,(Z1)
Let A∈C~(m×n),set eigenvalues of matrix A with |λ_1 (A)|≥|λ_2(A)|≥…≥|λ_n(A)|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧_k (A)=diag (λ_1(A),…,λ_k(A)),∧_((n-k).(A)=diag (λ_(k+1)(A),…,λ_n(A))for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by U~(n×n).Problem of equalities to hold in eigenvalue inequalities for products of matrices was 相似文献
9.
对称正交对称矩阵反问题的最小二乘解 总被引:18,自引:0,他引:18
Let P ∈ Rn×n be a symmetric orthogonal matrix. A∈Rn×n is called a symmetric orthogonal symmetric matrix if AT = A and (PA) T = PA. The set of all n × n symmetric orthogonal symmetric matrices is denoted by SRnxnp. This paper discusses the following problems: Problem I. Given X,B∈ Rn×m, find A ∈SRn×np such that||AX - B|| = min Problem II. Given A∈ Rn×n, find A∈SL such thatwhere ||·|| is the Frobenius norm, and SL is the solution set of Problem I.The general form of SL is given. The solvability conditions for the inverseproblem AX = B in SRn×nP are obtained. The expression of the solution toProblem II is presented. 相似文献
10.
对称正交对称矩阵逆特征值问题 总被引:27,自引:0,他引:27
Let P∈ Rn×n such that PT = P, P-1 = PT.A∈Rn×n is termed symmetric orthogonal symmetric matrix ifAT = A, (PA)T = PA.We denote the set of all n × n symmetric orthogonal symmetric matrices byThis paper discuss the following two problems:Problem I. Given X ∈ Rn×m, A = diag(λ1,λ 2, ... ,λ m). Find A SRnxnP such thatAX =XAProblem II. Given A ∈ Rnδn. Find A SE such thatwhere SE is the solution set of Problem I, ||·|| is the Frobenius norm. In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. The expression of the solution A* of Problem II is presented. We have proved that some results of Reference [3] are the special cases of this paper. 相似文献