In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrix equations X−A1XA1− . . .−A∗mXAm = Q and X+A1XA1+ . . .+ A∗mXAm = Q. In the case there is a unique solution which is positive definite an explicit expression for this solution is given.

Mirror-symmetric matrices have important applications in studying odd/even-mode decomposition of symmetric multiconductor transmission lines (MTL). In this paper, we propose an iterative algorithm to solve the mirror-symmetric solution of matrix equation AXB + CY D = E. With it, the solvability of the equation over mirror-symmetric X, Y can be determined automatically. When the equation is cons...

We present a general method for obtaining static anisotropic spherically symmetric solutions, starting from known density profiles and satisfying a nonlocal equation of state. This equation of state describes, at a given point, the components of the corresponding energymomentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. In order to es...

This paper is devoted to the study of solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions of the nonlinear Klein-Gordon equation (NKG), as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schroedinger equat...

We study symmetric correspondences with completely decomposable minimal equation on smooth projective curves C . The Jacobian of then decomposes correspondingly. For all positive integers g and ℓ , we give series examples genus n ( − 1 ) + satisfying equations degree such that the has at least 2 isogeny components.

The renormalization group flow equation obtained by means of a proper time regulator is used to calculate the two loop β-function and anomalous dimension η of the field for the O(N) symmetric scalar theory. The standard perturbative analysis of the flow equation does not yield the correct results for both β and η. We also show that it is still possible to extract the correct β and η from the fl...

We suggest a generalized Lax pair on a Hermitian symmetric space to generate a new coupled higher-order nonlinear Schrödinger equation of a dual type which contains both bright and dark soliton equations depending on parameters in the Lax pair. Through the generalized ways of reduction and the scaling transformation for the coupled higher-order nonlinear Schrödinger equation, two integrable typ...

We model the behaviour of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behaviour is a Riccati equation. We show that the Riccati equation admits two classes of new solutions in closed form. We regain particular models, obtained in previous investigations, as special case...