By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipat...By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.展开更多
In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which impr...In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.展开更多
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
基金The Natural Science Foundation of Yun-nan Province of China (2001A0001M)
文摘By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.
基金The NSF (11071106) of Chinathe Program (LR2011031) for Liaoning Excellent Talents in University
文摘In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.
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.
