Superharmonic Perturbations of a Gaussian Measure, Equilibrium Measures and Orthogonal Polynomials

This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex plane of the form $w(z) = \exp(-|z|^2 + U^{\mu}(z))$, where $U^{\mu}(z)$ is the logarithmic potential of a compactly supported positive measure $\mu$. The equilibrium measure of the corresponding weighted energy problem is shown to be supported on subharmonic generalized quadrature domains for a large class of perturbing potentials $U^{\mu}(z)$. It is also shown that the $2\times 2$ matrix d-bar problem for orthogonal polynomials with respect to such weights is well-defined and has a unique solution given explicitly by Cauchy transforms. Numerical evidence is presented supporting a conjectured relation between the asymptotic distribution of the zeroes of the orthogonal polynomials in a semi-classical scaling limit and the Schwarz function of the curve bounding the support of the equilibrium measure, extending the previously studied case of harmonic polynomial perturbations with weights $w(z)$ supported on a compact domain.Comment: CRM preprint, 28 pages. To appear in: Complex Analysis and Operator Theory (Special volume in honour of Bjorn Gustafsson). Two references added (Oct. 2, 2008

Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics

In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a $GL(2,\mathbb{C})$ transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite polynomials, which we then study in the context of a two-dimensional model of noncommutative quantum mechanics.Comment: 17 page

Magnetic and Transport Properties of Fe-Ag granular multilayers

Results of magnetization, magnetotransport and Mossbauer spectroscopy measurements of sequentially evaporated Fe-Ag granular composites are presented. The strong magnetic scattering of the conduction electrons is reflected in the sublinear temperature dependence of the resistance and in the large negative magnetoresistance. The simultaneous analysis of the magnetic properties and the transport behavior suggests a bimodal grain size distribution. A detailed quantitative description of the unusual features observed in the transport properties is given

XRound : A reversible template language and its application in model-based security analysis

Successful analysis of the models used in Model-Driven Development requires the ability to synthesise the results of analysis and automatically integrate these results with the models themselves. This paper presents a reversible template language called XRound which supports round-trip transformations between models and the logic used to encode system properties. A template processor that supports the language is described, and the use of the template language is illustrated by its application in an analysis workbench, designed to support analysis of security properties of UML and MOF-based models. As a result of using reversible templates, it is possible to seamlessly and automatically integrate the results of a security analysis with a model. (C) 2008 Elsevier B.V. All rights reserved

The intermediate-redshift galaxy cluster CL 0048-2942. Stellar populations

We present a detailed study of the cluster CL 0048-2942, located at z~0.64, based on a photometric and spectroscopic catalogue of 54 galaxies in a 5 x 5 square arcmin region centred in that cluster. Of these, 23 galaxies were found to belong to the cluster. Based on this sample, the line-of-sight velocity dispersion of the cluster is approximately 680 +- 140 km/s. We have performed stellar population synthesis in the cluster members as well as in the field galaxies of the sample and found that there are population gradients in the cluster with central galaxies hosting mainly intermediate/old populations whereas galaxies in the cluster outskirts show clearly an increase of younger populations, meaning that star formation is predominantly taking place in the outer regions of the cluster. In a general way, field galaxies seem to host less evolved stellar populations than cluster members. In fact, in terms of ages, young supergiant stars dominate the spectra of field galaxies whereas cluster galaxies display a dominant number of old and intermediate age stars. Following the work of other authors (e.g. Dressler et al. 1999) we have estimated the percentage of K+A galaxies in our sample and found around 13% in the cluster and 10% in the field. These values were estimated through means of a new method, based on stellar population synthesis results, that takes into account all possible absorption features in the spectrum and thus makes optimal use of the data.Comment: Accepted by Astronomy & Astrophysics. 24 pages, 10 figures, 10 tables (figures 3, 4, 5 and tables 1, 3, 4, 5, 6, 7, 8 will be available in electronic format only in the A&A published version