with A a diagonal matrix. Appropriate boundary and initial conditions are given. The amplification matrix Q(£) need not be diagonal. However, he required that |Q(£)| ^ 1We use certain results in matrix theory and Wiener-Hopf factorization to replace this restrictive assumption by certain reasonable assumptions on accuracy of Q(£) and smoothness of an associated positive-definite symmetric matri...

Among them, Y is the n q  random observation matrix; e is the n q  random error matrix, , nm kq X Z is the design matrix that we are known, and   r X m  ,   r Z k  , B is the p k  regression parameter matrix that we are unknown, V and  are positive definite matrices with the size q q  and n n  -order respectively.  expresses product of matrix Kronecker. e expresses a column vector...

The well known Lyapunov's theorem in matrix theory/ continuous dynamical systems asserts that a (complex) square matrix A is positive stable (that is, all eigenvalues lie in the open right-half plane) if and only if there exists a positive deenite matrix X such that AX+XA is positive deenite. In this paper, we prove a complementarity form of this theorem: A is positive stable if and only if for...

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U q [osp(1/2)] and the corresponding su-pergroup OSp q (1/2). The finite dimensional representations of the quantum su-pergroup OSp q (1/2) are readily constructed employing the said universal T-matrix and the known finite dimensional representations of the dually related deformed ...