The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz’s theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wi...

The majority of computational methods applied for the analysis of homogeneous Markov reward models (MRMs) are not applicable for the analysis of inhomogeneous MRMs. By the nature of inhomogeneous models only forward differential equations can be used to describe the model behaviour. In this paper we provide forward partial differential equations describing the distribution of reward measures of...

We have analyzed epitaxial, c-axis oriented YBa,CujO, _ 6 thin films grown in situ by sequential ion-beam sputtering on (100) SiTiOs and (100) MgO substrates. X-ray diffraction studies showed the presence of both homogeneous and inhomogeneous lattice distortions along the c-direction. The c-axis lattice parameters ranged from 11.72 to 12.00 A. The broadening of the (001) Bragg peaks in excess o...

A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open linear chains with periodic (in space) changing Larmor frequencies and coupling constants is developed. As an example of application, multiple quantum dynamics of an inhomogeneous chain consisting of 1001 spins is investigated. Intensities of multiple quantum coherences are calculated for arbitrary inhomogeneous chains ...

Calculations of radiant heating by inhomogeneous hot gases require knowledge of spectral transmittances of inhomogeneous optical paths. Determination of these transmittances is a difficult problem that can be attacked by means of the Curtis-Godson approximation, which replaces each inhomogeneous optical path with a hypothetical homogeneous path that has the same transmittance. The authors have ...

In 1998, Kleinbock & Margulis [KM98] established a conjecture of V.G. Sprindzuk in metrical Diophantine approximation (and indeed the stronger Baker-Sprindzuk conjecture). In essence the conjecture stated that the simultaneous homogeneous Diophantine exponent w0(x) = 1/n for almost every point x on a non-degenerate submanifold M of Rn. In this paper the simultaneous inhomogeneous analogue of Sp...