Kumar's algorithm for solving Toeplitz systems of equations over finite fields

Adaptació de l'algorisme de Kumar per resoldre sistemes d'equacions amb matrius de Toeplitz sobre els reals a cossos finits en un temps 0 (n log n).

Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3

This paper is devoted to the study of the volcanoes of l-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the l-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case l = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results are also provided.

Energy-momentum tensor for scalar fields coupled to the dilaton in two dimensions

We clarify some issues related to the evaluation of the mean value of the energy-momentum tensor for quantum scalar fields coupled to the dilaton field in two-dimensional gravity. Because of this coupling, the energy-momentum tensor for matter is not conserved and therefore it is not determined by the trace anomaly. We discuss different approximations for the calculation of the energy-momentum tensor and show how to obtain the correct amount of Hawking radiation. We also compute cosmological particle creation and quantum corrections to the Newtonian potential.

Study of the effect of oral health on physical condition of professional soccer players of the Football Club Barcelona

Objectives: The objective of this study was to evaluate the oral health status of professional soccer players of F.C. Barcelona and its relation to the incidence of sport lesions. Methods: Thirty professional soccer players were consecutively evaluated in the seasons 2003/4, 2004/5 and 2005/6. A research protocol to assess their oral health was developed. DMFT, Quigley & Hein plaque index (PI), Löe & Silness gingival index (GI), World Health Organization malocclusion index, Ramfjord teeth probing pocket depth (PPD), TMJ examination and history of dental trauma were recorded. All physical injuries sustained by players during the season were documented from F.C. Barcelona medical services. Results: Mean DMFT score was 5.7 (SD 4.1), Quigley & Hein plaque index score was 2.3 (SD 1.1), Löe & Silness gingival index was 1.1 (SD 0.8), and periodontal pocket depth was 1.9 mm (SD 0.3). Pearson"s analysis showed a significant correlation between PI and GI (p<0.01). Nine players (30%) presented bruxism - the same proportion of those with severe malocclusion. Seven (23.3%) players had suffered uncomplicated crown fractures. The mean incidence of physical injuries was 8 (SD 3.4) per player. PI and PPD showed a statistically significant correlation to muscle injuries (p<0.05). Conclusions: Soccer players, despite intensive medical follow-up, have significant oral health problems such as untreated caries, gingivitis or malocclusion, and suffer dental trauma as a result of sports activities. Their physical condition could also be associated to oral health

Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields

The contribution of the propagating and the evanescent waves associated with freely propagating non-paraxial light fields whose transverse component is azimuthally polarized at some plane is investigated. Analytic expressions are derived for describing both the spatial shape and the relative weight of the propagating and the evanescent components integrated over the transverse plane. The analysis is carried out within the framework of the plane-wave angular spectrum approach. These results are used to illustrate the behavior of a kind of donut-like beams with transverse azimuthal polarization at some plane.

Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA=0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

On the longitudinal component of paraxial fields

The analysis of paraxial Gaussian beams features in most undergraduate courses in laser physics, advanced optics and photonics. These beams provide a simple model of the field generated in the resonant cavities of lasers, thus constituting a basic element for understanding laser theory. Usually, uniformly polarized beams are considered in the analytical calculations, with the electric field vibrating at normal planes to the propagation direction. However, such paraxial fields do not verify the Maxwell equations. In this paper we discuss how to overcome this apparent contradiction and evaluate the longitudinal component that any paraxial Gaussian beam should exhibit. Despite the fact that the assumption of a purely transverse paraxial field is useful and accurate, the inclusion of the above issue in the program helps students to clarify the importance of the electromagnetic nature of light, thus providing a more complete understanding of the paraxial approach.

Transverse and longitudinal components of the propagating and evanescent waves associated to radially-polarized nonparaxial fields

A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freely propagating radially polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to two kinds of doughnut-like beams with radial polarization, and we compare the behavior of such fields at two transverse planes.

Design of highly focused fields that remain unpolarized on axis

Research on the properties of highly focused fields mainly involved fully polarized light, whereas partially polarized waves received less attention. The aim of this Letter is to provide an appropriate framework, for designing some features of the focused field, when dealing with incoming partially polarized beams. In particular, in this Letter, we describe how to get an unpolarized field on the axis of a high numerical aperture objective lens. Some numerical results that corroborate theoretical predictions are provided.