https://www.um.edu.mt/library/oar/handle/123456789/404 2026-10-29T06:21:05Z https://www.um.edu.mt/library/oar/handle/123456789/150509 Title: On middle box products and paracompact cardinals Authors: Buhagiar, David; Džamonja, Mirna Abstract: The paper gives several sufficient conditions on the paracompactness of box products with an arbitrary number of factors and boxes of arbitrary size. The former include results on generalised metrisability and Sikorski spaces. Of particular interest are products of the type <𝜅 □ 2𝜆, where we prove that for a regular uncountable cardinal κ, if <𝜅 □ 2𝜆 is paracompact for every 𝜆 ≥𝜅, then κ is at least inaccessible. The case of the products of the type <𝜅 □ 𝑋𝜆 for κ singular has not been studied much in the literature and we offer various results. The question if <𝜅 □ 2𝜆 can be paracompact for all λ when κ is singular has been partially answered but remains open in general. 2024-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/149994 Title: Exponential stability of damped Euler-Bernoulli beam controlled by boundary springs and dampers Authors: Baysal, Onur; Hasanov, Alemdar; Kawano, Alexandre Abstract: In this paper, the vibration model of an elastic beam, governed by the damped Euler-Bernoulli equation ρ ( x ) u t t + μ ( x ) u t + ( r ( x ) u x x ) x x = 0 , subject to the clamped boundary conditions u ( 0 , t ) = u x ( 0 , t ) = 0 at x = 0 , and the boundary conditions ( − r ( x ) u x x ) x = ℓ = k r u x ( ℓ , t ) + k a u x t ( ℓ , t ) , ( − ( r ( x ) u x x ) x ) x = ℓ = − k d u ( ℓ , t ) − k v u t ( ℓ , t ) at x = ℓ , is analyzed. The boundary conditions at x = ℓ correspond to linear combinations of damping moments caused by rotation and angular velocity and also, of forces caused by displacement and velocity, respectively. The system stability analysis based on well-known Lyapunov approach is developed. Under the natural assumptions guaranteeing the existence of a regular weak solution, uniform exponential decay estimate for the energy of the system is derived. The decay rate constant in this estimate depends only on the physical and geometric parameters of the beam, including the viscous external damping coefficient μ ( x ) ≥ 0 , and the boundary springs k r , k d ≥ 0 and dampers k a , k v ≥ 0 . Some numerical examples are given to illustrate the role of the damping coefficient and the boundary dampers. 2024-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/149952 Title: Dynamical black holes Authors: Sultana, Joseph; Dyer, Charles C. Abstract: For time dependent black hole spacetimes the event horizon cannot be described by a Killing horizon. We show that when the spacetime admits a time like conformal Killing field which generates a hypersurface, called the conformal Killing horizon (CKH), one can locally describe the event horizon by using this hypersurface. When the CKH does not coincide with the conformal stationary limit surface, on which the conformal Killing field becomes null, a generalization of the weak rigidity theorem which establishes the conformal Killing property of the event horizon and the rigidity of its rotation, is obtained. A physical definition of surface gravity for CKHs is given, which is then used to formulate a generalized zeroth law of black hole physics. 2006-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/149861 Title: Conformal killing horizons Authors: Sultana, Joseph; Dyer, Charles C. Abstract: For time dependent black hole space–times the event horizon cannot be described by a Killing horizon. In the case when the space–time admits a timelike conformal Killing field, which becomes null on a boundary called the conformal stationary limit surface, one can locally describe the expanding event horizon by using this boundary, provided that it is a null geodesic hypersurface. In this case the boundary is called a conformal Killing horizon and is shown to be null and geodesic if and only if the twist of the conformal Killing trajectories on the hypersurface vanishes. Moreover if the space–time is conformally related to a stationary asymptotically flat black hole space–time, it is shown that this hypersurface is globally equivalent to the event horizon, provided that the conformal factor goes to a constant at null infinity. When the conformal stationary limit surface does not coincide with the conformal Killing horizon, a generalization of the weak rigidity theorem which establishes the conformal Killing property of the event horizon and the rigidity of its rotation is obtained. A physical definition of surface gravity for conformal Killing horizons is given, which is then used to formulate a generalized zeroth law of black hole physics. 2004-01-01T00:00:00Z