共查询到19条相似文献,搜索用时 390 毫秒
1.
两类惯量惟一的对称符号模式 总被引:4,自引:0,他引:4
邵燕灵 《高校应用数学学报(英文版)》2003,18(2):243-250
§ 1 IntroductionA sign pattern(matrix) A is a matrix whose entries are from the set{ +,-,0 } .De-note the setofall n× n sign patterns by Qn.Associated with each A=(aij)∈ Qnis a class ofreal matrices,called the qualitative class of A,defined byQ(A) ={ B =(bij)∈ Mn(R) |sign(bij) =aijfor all i and j} . For a symmetric sign pattern A∈ Qn,by G(A) we mean the undirected graph of A,with vertex set { 1 ,...,n} and (i,j) is an edge if and only if aij≠ 0 .A sign pattern A∈ Qnis a do… 相似文献
2.
Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 |Sn/n^1/r|^p(0 〈 r 〈 2,p 〉 0) are given,which are the same as that in the independent case. 相似文献
3.
An invariant σ2(G) of a graph is defined as follows: σ2(G) := min{d(u) + d(v)|u, v ∈V(G),uv ∈ E(G),u ≠ v} is the minimum degree sum of nonadjacent vertices (when G is a complete graph, we define σ2(G) = ∞). Let k, s be integers with k ≥ 2 and s ≥ 4, G be a graph of order n sufficiently large compared with s and k. We show that if σ2(G) ≥ n + k- 1, then for any set of k independent vertices v1,..., vk, G has k vertex-disjoint cycles C1,..., Ck such that |Ci| ≤ s and vi ∈ V(Ci) for all 1 ≤ i ≤ k.
The condition of degree sum σs(G) ≥ n + k - 1 is sharp. 相似文献
The condition of degree sum σs(G) ≥ n + k - 1 is sharp. 相似文献
4.
Jiang Chaowei Yang Xiaorong 《高校应用数学学报(英文版)》2007,22(1):87-94
In the case of Zd (d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k ∈ Zd } i.i.d. random variables with mean 0, Sn = ∑k≤nXk and Vn2 = ∑j≤nX2j, the precise asymptotics for ∑n1/|n|(log|n|)dP(|Sn/vn|≥ ε√loglog|n|) and ∑n(logn|)δ/|n|(log|n|)d-1 P(|Sn/Vn| ≥ ε√log n), as ε ↘ 0, is established. 相似文献
5.
Wen Jiwei Yan Yunliang 《高校应用数学学报(英文版)》2006,21(1):87-95
Let X,X1,X2 be i. i. d. random variables with EX^2+δ〈∞ (for some δ〉0). Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ* (n)=supx∈zζ(x,n),ζ(x,n) =#{0≤k≤n:[Sk]=x}. A strong approximation of ζ(n) by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ*(n) are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ*(n) is proved. 相似文献
6.
Qi Keng LU Ke WU 《数学学报(英文版)》2007,23(4):577-598
For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj (m), (j = 0, 1,..., m - 1) which satisfy γj (m)γk (m) +γk (m)γj (m) = 2ηjk (m)I[m/2], where (ηjk (m)) 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation (m) of the Lorentz Spin group is known. For m≥ 6, we prove that (i) when m = 2n, (n ≥ 3), (m) is the group generated by the set of matrices {T|T=1/√ξ((I+k) 0 + 0 I-K) ( U 0 0 U), (ii) when m = 2n + 1 (n≥ 3), (m) is generated by the set of matrices {T|T=1/√ξ(I -k^- k I)U,U∈ (m-1),ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj(m-2)+a^(m-2) In],K^-=i[m-3∑j=0 a^j γj(m-2)-a^(m-2) In]} 相似文献
7.
A general result on precise asymptotics for linear processes of positively associated sequences 总被引:2,自引:0,他引:2
Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers satisfying ∑j=0^∞|aj|〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E|ε1|^2+δ′〈 for some δ′〉0 and μ(n)=O(n^-ρ) for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}. 相似文献
8.
Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞|aj| 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj+tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}. 相似文献
9.
Let A_n={1,2,…,n} and let %={B_1,B_2,…,B_r} where B_1、B_2,…, B_r are subsets of A_n each of size m. is said to cover all the triples (i, j, k), 1≤i2/3, then V(m, n) is a function of the fraction m/n only and the values of V(m, n) are determined for all m, n with m/n≥2/3. The value of V(m, n) for m/n<2/3 is also discussed. 相似文献
10.
Let D = (V, E) be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD(v), is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD(V1) ≤ exPD(V2) …≤ exPD(Vn). Then exPD(Vk) is called the k- point exponent of D and is denoted by exPD (k), 1≤ k ≤ n. In this paper we define e(n, k) := max{expD (k) | D ∈ PD(n, 2)} and E(n, k) := {exPD(k)| D ∈ PD(n, 2)}, where PD(n, 2) is the set of all primitive digraphs of order n with girth 2. We completely determine e(n, k) and E(n, k) for all n, k with n ≥ 3 and 1 ≤ k ≤ n. 相似文献
11.
INERTIA SETS OF SYMMETRIC SIGN PATTERN MATRICES 总被引:2,自引:0,他引:2
1 IntroductionIn qualitative and combinatorial matrix theory,we study properties ofa matrix basedon combinatorial information,such as the signs of entries in the matrix.A matrix whoseentries are from the set{ + ,-,0 } is called a sign pattern matrix ( or sign pattern,or pat-tern) .We denote the setof all n× n sign pattern matrices by Qn.For a real matrix B,sgn( B) is the sign pattern matrix obtained by replacing each positive( respectively,negative,zero) entry of B by+ ( respectively,-,0 )… 相似文献
12.
Inertially arbitrary patterns 总被引:11,自引:0,他引:11
An n×n sign pattern matrix A is an inertially arbitrary pattern (IAP) if each non-negative triple (rst) with r+s+t=n is the inertia of a matrix with sign pattern A. This paper considers the n×n(n≥2) skew-symmetric sign pattern Sn with each upper off-diagonal entry positive, the (1,1) entry negative, the (nn) entry positive, and every other diagonal entry zero. We prove that Sn is an IAP. 相似文献
13.
C. M. da Fonseca 《Czechoslovak Mathematical Journal》2006,56(3):875-883
A matrix whose entries consist of elements from the set {+, −, 0} is a sign pattern matrix. Using a linear algebra theoretical
approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign
matrices. 相似文献
14.
An n×n sign pattern matrix A is an inertially arbitrary pattern (IAP) if each non-negative triple (r s t) with r+s+t=n is the inertia of a matrix with sign pattern A. This paper considers the n×n(n2) skew-symmetric sign pattern Sn with each upper off-diagonal entry positive, the (1,1) entry negative, the (n n) entry positive, and every other diagonal entry zero. We prove that Sn is an IAP. 相似文献
15.
16.
M.S. Cavers 《Linear and Multilinear Algebra》2013,61(2):257-267
A tool to study the inertias of reducible nonzero (resp. sign) patterns is presented. Sumsets are used to obtain a list of inertias attainable by the pattern 𝒜 ⊕ ? dependent upon inertias attainable by patterns 𝒜 and ?. It is shown that if ? is a pattern of order n, and 𝒜 is an inertially arbitrary pattern of order at least 2(n ? 1), then 𝒜 ⊕ ? is inertially arbitrary if and only if ? allows the inertias (0, 0, n), (0, n, 0) and (n, 0, 0). We illustrate how to construct other reducible inertially (resp. spectrally) arbitrary patterns from an inertially (resp. spectrally) arbitrary pattern 𝒜 ⊕ ?, by replacing 𝒜 with an inertially (resp. spectrally) arbitrary pattern 𝒮. We identify reducible inertially (resp. spectrally) arbitrary patterns of the smallest orders that contain some irreducible components that are not inertially (resp. spectrally) arbitrary. It is shown there exist nonzero (resp. sign) patterns 𝒜 and ? of orders 4 and 5 (resp. 4 and 4) such that both 𝒜 and ? are non-inertially-arbitrary, and 𝒜 ⊕ ? is inertially arbitrary. 相似文献
17.
Two Hermitian matrices A,B∈Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C∈Mn(C) such that B=CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible inertias of the Hermitian matrices C that carry the congruence. We also give necessary and sufficient conditions for any 2-by-2 nonsingular Hermitian matrices to be Hermitian-congruent. In both of the studied cases, we show that if A and B are real and Hermitian-congruent, then they are congruent by a real symmetric matrix. Finally we note that if A and B are 2-by-2 nonsingular real symmetric matrices having the same sign pattern, then there is always a real symmetric matrix C satisfying B=CAC. Moreover, if both matrices are positive, then C can be picked with arbitrary inertia. 相似文献
18.
A sign pattern matrix is a matrix whose entries are from the set {+,–,0}. The purpose of this paper is to obtain bounds on the minimum rank of any symmetric sign pattern matrix A whose graph is a tree T (possibly with loops). In the special case when A is nonnegative with positive diagonal and the graph of A is star-like, the exact value of the minimum rank of A is obtained. As a result, it is shown that the gap between the symmetric minimal and maximal ranks can be arbitrarily large for a symmetric tree sign pattern A.
Supported by NSF grant No. DMS-00700AMS classification: 05C50, 05C05, 15A48 相似文献
19.
The inertia set of a symmetric sign pattern A is the set i(A) = {i(B) | B = B T ∈ Q(A)}, where i(B) denotes the inertia of real symmetric matrix B, and Q(A) denotes the sign pattern class of A. In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern A in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns A with zero diagonal that require unique inertia. 相似文献