M. A. Al-Gwaiz

Lie algebraic approach to the coupled-mode oscillator

The coupling of electromagnetic fields for the construction of light amplifiers is described by a certain Hamiltonian which can be expressed as the sum of three differential operators. Following the method of Steinberg (1977) and Dattoli et. al. (1990), the solution of Schrodingers equation for the Hamiltonian of the system is constructed from the solutions of the corresponding equations for the components of the Hamiltonian.

The damped pulsating oscillator with a stochastic driving force

SummaryThe problem of the damped pulsating oscillator in the rotating-wave approximation frame is considered in the presence of a stochastic force. The variances of the coordinate and momentum are calculated. The Schrödinger wave functions in the pseudostationary and quasi-coherent states are obtained, as well as the expression for the probability distribution function.

Compact manifolds of constant scalar curvature

We consider a compact non-negatively curved Riemannian manifold M of constant scalar curvature and obtain a sufficient condition for it to be isometric to a sphere.

Totally real surfaces in CP2 with parallel mean curvature vector

It has been shown that a totally real surface in CP2 with parallel mean curvature vector and constant Gaussian curvature is either flat or totally geodesic.