Born-Infeld black holes coupled to a massive scalar field

Born-Infeld black holes in the Scalar-Tensor Theories of Gravity, in the case of massless scalar field, have been recently obtained. The aim of the current paper is to study the effect from the inclusion of a potential for the scalar field in the theory, through a combination of analytical techniques and numerical methods. The black holes coupled to a massive scalar field have richer causal structure in comparison to the massless scalar field case. In the latter case, the black holes may have a second, inner horizon. The presence of potential for the scalar field allows the existence of extremal black holes for certain values of the mass of the scalar field and the magnetic (electric) charge of the black hole. The linear stability against spherically symmetric perturbations is studied. Arguments in favor of the general stability of the solutions coming from the application of the "turning point" method are also presented.Comment: 26 pages, 16 figure

Riemann-Hilbert problem, integrability and reductions

The present paper is dedicated to integrable models with Mikhailov reduction groups $G_R \simeq \mathbb{D}_h.$ Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the $G_R$-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with $\mathbb{D}_h$ symmetries are presented.Comment: 19 pages, 3 figures, Dedicated to Darryl Holm's 70th birthda

CeOx/Al2O3 thin films on stainless steel substrate - Dynamical X-ray photoelectron spectroscopy investigations

Cataloged from PDF version of article.The CeOx/Al2O3 thin films on stainless steel with different ceria loading were subjected to a. c. ( square wave) pulses at various frequencies in the range 10(-3) to 100 kHz while recording X-ray photoelectron spectra. The resulting binding energy differences were derived from the frequency dependence of the corresponding Al2p, Ce3d and O1s peaks. At low ceria loadings the main constituent on the surface is CeAlO3 phase, while for high ceria loading the film is constructed from CeO2 and CeAlO3 phases spread over the Al2O3. Accordingly, it was observed that the ceria loading determines the conductivities of the investigated thin oxide films. (C) 2013 Elsevier B.V. All rights reserved

Thermoacoustic tomography arising in brain imaging

We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit inversion formula in the form of a convergent Neumann series under the assumptions that all singularities from the support of the source reach the boundary

Time-dependent angularly averaged inverse transport

This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain