In this paper we study the relationship between minimum rank of graph G and the minimum rank of graph for some families of special graph G, where is the jth power of graph G.
Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the ex...Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.展开更多
Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.In this paper,we obtain some sufficient and/or necessary conditions for a sign pattern to allow diagonalizability.Mo...Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.In this paper,we obtain some sufficient and/or necessary conditions for a sign pattern to allow diagonalizability.Moreover,we determine how many entries need to be changed to obtain a matrix B′∈Q(A)with rank MR(A)from a matrix B∈Q(A)with rank mr(A).Finally,we also obtain some results on a sign pattern matrix in Frobenius normal form that allows diagonalizability.展开更多
The development of damage detection techniques for offshore jacket structures is vital to prevent catastrophic events. This paper applies a frequency response based method for the purpose of structural health monitori...The development of damage detection techniques for offshore jacket structures is vital to prevent catastrophic events. This paper applies a frequency response based method for the purpose of structural health monitoring. In efforts to fulfill this task, concept of the minimum rank perturbation theory has been utilized. The present article introduces a promising methodology to select frequency points effectively. To achieve this goal, modal strain energy ratio of each member was evaluated at different natural frequencies of structure in order to identify the sensitive frequency domain for damage detection. The proposed methodology opens up the possibility of much greater detection efficiency. In addition, the performance of the proposed method was evaluated in relation to multiple damages. The aforementioned points are illustrated using the numerical study of a two dimensional jacket platform, and the results proved to be satisfactory utilizing the proposed methodology.展开更多
文摘In this paper we study the relationship between minimum rank of graph G and the minimum rank of graph for some families of special graph G, where is the jth power of graph G.
文摘Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.
基金Supported by Research Project of Leshan Normal University(Grant No.LZD016)。
文摘Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.In this paper,we obtain some sufficient and/or necessary conditions for a sign pattern to allow diagonalizability.Moreover,we determine how many entries need to be changed to obtain a matrix B′∈Q(A)with rank MR(A)from a matrix B∈Q(A)with rank mr(A).Finally,we also obtain some results on a sign pattern matrix in Frobenius normal form that allows diagonalizability.
基金Financial Support by the Pars Oil and Gas Company(Grant No. 88-065)
文摘The development of damage detection techniques for offshore jacket structures is vital to prevent catastrophic events. This paper applies a frequency response based method for the purpose of structural health monitoring. In efforts to fulfill this task, concept of the minimum rank perturbation theory has been utilized. The present article introduces a promising methodology to select frequency points effectively. To achieve this goal, modal strain energy ratio of each member was evaluated at different natural frequencies of structure in order to identify the sensitive frequency domain for damage detection. The proposed methodology opens up the possibility of much greater detection efficiency. In addition, the performance of the proposed method was evaluated in relation to multiple damages. The aforementioned points are illustrated using the numerical study of a two dimensional jacket platform, and the results proved to be satisfactory utilizing the proposed methodology.
