Using the theory of polynomials,this paper gives a new necessary and sufficient condition for a polynomial to be Hurwitz polynomial,a simple proof of the stability criterion of Liénard and Chipart is also obtained.
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are ...Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.展开更多
文摘Using the theory of polynomials,this paper gives a new necessary and sufficient condition for a polynomial to be Hurwitz polynomial,a simple proof of the stability criterion of Liénard and Chipart is also obtained.
基金supported by the National Natural Science Foundation of China(Nos.11471097,11271257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20121303110005)+1 种基金the Natural Science Foundation of Hebei Province(No.A2013205021)the Key Fund Project of Hebei Normal University(No.L2012Z01)
文摘Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.
