Let A be an M-matrix and B be a Z-matrix. In this paper we reveal the spectral relationship of A and B under some interesting conditions. Applying this result, we solve an open problem on splittings of an M-matrix and...Let A be an M-matrix and B be a Z-matrix. In this paper we reveal the spectral relationship of A and B under some interesting conditions. Applying this result, we solve an open problem on splittings of an M-matrix and partially answer an open problem on the level diagrams for A and B.展开更多
Let G be a finite simple graph and A(G)be its adjacency matrix.Then G is singular if A(G)is singular.The graph obtained by bonding the starting ver-tices and ending vertices of three paths Pa1,Pa2,Pa3 is calledθ-grap...Let G be a finite simple graph and A(G)be its adjacency matrix.Then G is singular if A(G)is singular.The graph obtained by bonding the starting ver-tices and ending vertices of three paths Pa1,Pa2,Pa3 is calledθ-graph,represented byθ(a1,a2,a3).The graph obtained by bonding the two end vertices of the path Ps to the vertices of theθ(a1,a2,a3)andθ(b1,b2,b3)of degree three,respectively,is denoted byα(a1,a2,a3,s,b1,b2,b3)and calledα-graph.β-graph is denoted whenβ(a1,a2,a3,b1,b2,b3)=α(a1,a2,a3,1,b1,b2,b3).In this paper,we give the necessary and sufficient conditions for the singularity ofα-graph andβ-graph,and prove that the probability that a random givenα-graph andβ-graph is a singular graph is equal to 14232048 and 733/1024,respectively.展开更多
为实现板梁桥铰接缝损伤的定量定位识别,提出了一种基于递归奇异能量指标的损伤识别方法:首先将待测桥梁各相邻梁体的竖向冲击振动响应进行交叉递归分析并得到无阈值交叉递归矩阵,其次对各递归矩阵进行奇异值分解以进一步提取损伤特征,...为实现板梁桥铰接缝损伤的定量定位识别,提出了一种基于递归奇异能量指标的损伤识别方法:首先将待测桥梁各相邻梁体的竖向冲击振动响应进行交叉递归分析并得到无阈值交叉递归矩阵,其次对各递归矩阵进行奇异值分解以进一步提取损伤特征,最后对奇异值求取能量(递归奇异能量指标(recurrence singular energy index,RSEI)),进一步建立了基于该指标的铰接缝损伤识别方法,并对其适用性进行了分析。结果表明:RSEI指标对板梁桥铰接缝损伤较为敏感,所提方法仅在板梁桥跨中布置一排传感器即可实现铰接缝平均损伤程度的定量识别,并可实现损伤铰缝的定位,识别效果良好;铰接缝损伤位置、损伤个数及噪声对识别结果的影响极小,冲击位置会对识别结果造成一定影响,但识别效果在可接受的范围之内;应用RSEI指标开展板梁桥铰接缝损伤识别时,建议将冲击位置设在边梁跨中,可避免冲击位置对识别结果造成的影响,取得更加理想的识别效果。展开更多
IN this note all graphs are undirected, finite and simple. For a subgraph H of G,ε（H） andμ（H） denote the number of edges in H and the number of cycles in H respectively. H[X]denotes the subgraph of H induced by ...IN this note all graphs are undirected, finite and simple. For a subgraph H of G,ε（H） andμ（H） denote the number of edges in H and the number of cycles in H respectively. H[X]denotes the subgraph of H induced by X. Given two disjoint subsets X and Y of V（G）, wewrite E<sub>G</sub>（X, Y）={xy∈E（G）|x∈X, y∈Y}. Sometimes E<sub>G</sub>（H, Y）=EG（V（H）,Y） is used for a subgraph H of G-Y. If T is a tree of G and e=uv∈G-E（T）with{u,v}V（T）, then T + e contains a unique cycle, denoted by C（T, e）.A tree-decomposition {T<sub>1</sub>, T<sub>2</sub>, …, T<sub>k</sub>} of a graph G is a partition of E （G）, say,E（G）=E<sub>1</sub> U E<sub>2</sub> U…U E<sub>k</sub>, such that for each i with 1≤i≤k, T<sub>i</sub>=G[E<sub>i</sub>] is a tree.展开更多
IN this note all graphs are undirected, finite and simple. For a subgraph H of G, V(H), E(H), ε(H) and μ(H) denote the set of vertices, the set of edges, the number of edges in H and the number of cycles in H respec...IN this note all graphs are undirected, finite and simple. For a subgraph H of G, V(H), E(H), ε(H) and μ(H) denote the set of vertices, the set of edges, the number of edges in H and the number of cycles in H respectively. H[X] denotes the subgraph of H induced by X. Given two disjoint subsets X and Y of V(G), we write E_G(X, Y)={xy∈E(G)展开更多
文摘Let A be an M-matrix and B be a Z-matrix. In this paper we reveal the spectral relationship of A and B under some interesting conditions. Applying this result, we solve an open problem on splittings of an M-matrix and partially answer an open problem on the level diagrams for A and B.
基金Supported by National Natural Science Foundation of China(Grant No.11561056)National Natural Science Foundation of Qinghai Provence(Grant No.2022-ZJ-924)Innovation Project of Qinghai Minzu University(Grant No.07M2022002).
文摘Let G be a finite simple graph and A(G)be its adjacency matrix.Then G is singular if A(G)is singular.The graph obtained by bonding the starting ver-tices and ending vertices of three paths Pa1,Pa2,Pa3 is calledθ-graph,represented byθ(a1,a2,a3).The graph obtained by bonding the two end vertices of the path Ps to the vertices of theθ(a1,a2,a3)andθ(b1,b2,b3)of degree three,respectively,is denoted byα(a1,a2,a3,s,b1,b2,b3)and calledα-graph.β-graph is denoted whenβ(a1,a2,a3,b1,b2,b3)=α(a1,a2,a3,1,b1,b2,b3).In this paper,we give the necessary and sufficient conditions for the singularity ofα-graph andβ-graph,and prove that the probability that a random givenα-graph andβ-graph is a singular graph is equal to 14232048 and 733/1024,respectively.
文摘为实现板梁桥铰接缝损伤的定量定位识别,提出了一种基于递归奇异能量指标的损伤识别方法:首先将待测桥梁各相邻梁体的竖向冲击振动响应进行交叉递归分析并得到无阈值交叉递归矩阵,其次对各递归矩阵进行奇异值分解以进一步提取损伤特征,最后对奇异值求取能量(递归奇异能量指标(recurrence singular energy index,RSEI)),进一步建立了基于该指标的铰接缝损伤识别方法,并对其适用性进行了分析。结果表明:RSEI指标对板梁桥铰接缝损伤较为敏感,所提方法仅在板梁桥跨中布置一排传感器即可实现铰接缝平均损伤程度的定量识别,并可实现损伤铰缝的定位,识别效果良好;铰接缝损伤位置、损伤个数及噪声对识别结果的影响极小,冲击位置会对识别结果造成一定影响,但识别效果在可接受的范围之内;应用RSEI指标开展板梁桥铰接缝损伤识别时,建议将冲击位置设在边梁跨中,可避免冲击位置对识别结果造成的影响,取得更加理想的识别效果。
文摘IN this note all graphs are undirected, finite and simple. For a subgraph H of G,ε（H） andμ（H） denote the number of edges in H and the number of cycles in H respectively. H[X]denotes the subgraph of H induced by X. Given two disjoint subsets X and Y of V（G）, wewrite E<sub>G</sub>（X, Y）={xy∈E（G）|x∈X, y∈Y}. Sometimes E<sub>G</sub>（H, Y）=EG（V（H）,Y） is used for a subgraph H of G-Y. If T is a tree of G and e=uv∈G-E（T）with{u,v}V（T）, then T + e contains a unique cycle, denoted by C（T, e）.A tree-decomposition {T<sub>1</sub>, T<sub>2</sub>, …, T<sub>k</sub>} of a graph G is a partition of E （G）, say,E（G）=E<sub>1</sub> U E<sub>2</sub> U…U E<sub>k</sub>, such that for each i with 1≤i≤k, T<sub>i</sub>=G[E<sub>i</sub>] is a tree.
文摘IN this note all graphs are undirected, finite and simple. For a subgraph H of G, V(H), E(H), ε(H) and μ(H) denote the set of vertices, the set of edges, the number of edges in H and the number of cycles in H respectively. H[X] denotes the subgraph of H induced by X. Given two disjoint subsets X and Y of V(G), we write E_G(X, Y)={xy∈E(G)
