In this paper a very general matrix quadratic equation is considered. This equation is known in literature as asymmetric Algebraic Riccati Equation (ARE) and arises in the solution of many problems in system and control theory and applied mathematics. For this reason a large amount of work has been produced on this topic. We present a new parametrization of the set of solutions of such equation...

For Lindblad's master equation of open quantum systems with a general quadratic form of the Hamiltonian, the propagator of the density matrix is analytically calculated by using path integral techniques. The time-dependent density matrix is applied to nuclear barrier penetration in heavy ion collisions with inverted oscillator and double-well potentials. The quantum mechanical decoherence of pa...

Abstract. For linear time-invariant (LTI) state space systems it is well-known that its asymptotic stability can be related to solution properties of the Lyapunov matrix equation according to so-called inertia theorems. The question now arises how analogous results can be obtained for LTI descriptor systems (singular systems, differential-algebraic equations). The stability behaviour of a LTI d...

In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

We compare two methods for superreplication of options with convex pay-off functions. One method entails an overestimation of the unknown covariance matrix in the sense of quadratic forms. With this method the value of the superreplicating portfolio is given as the solution of a linear Black-Scholes type equation. In the second method the choice of quadratic form is made pointwise. This leads t...

It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially commutative monoids under the constraint that the solution is a subset of the alphabet. We prove that this problem is NP-complete for quadratic equations and that its unifor...

Abstract: The adaptive control problem for a jump linear system with quadratic cost functional on infinite time interval is solved in this paper. It is assumed that the coefficients of the state equation are unknown but a compact set that contains the parameters is known. A diminishing excitation accompanies the adaptive control signal to ensure the strong consistency of the weighted least squa...