Oversampling in shift-invariant spaces with a rational sampling period

8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología

Anomalous magnetic and weak magnetic dipole moments of the τ\tau lepton in the simplest little Higgs model

We obtain analytical expressions, both in terms of parametric integrals and Passarino-Veltman scalar functions, for the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) of a charged lepton in the framework of the simplest little Higgs model (SLHM). Our results are general and can be useful to compute the weak properties of a charged lepton in other extensions of the standard model (SM). As a by-product we obtain generic contributions to the anomalous magnetic dipole moment (AMDM), which agree with previous results. We then study numerically the potential contributions from this model to the $\tau$ lepton AMDM and AWMDM for values of the parameter space consistent with current experimental data. It is found that they depend mainly on the energy scale $f$ at which the global symmetry is broken and the $t_\beta$ parameter, whereas there is little sensitivity to a mild change in the values of other parameters of the model. While the $\tau$ AMDM is of the order of $10^{-9}$, the real (imaginary) part of its AWMDM is of the order of $10^{-9}$ ($10^{-10}$). These values seem to be out of the reach of the expected experimental sensitivity of future experiments.Comment: 23 pages, 11 figures, new analysis and References adde

Ultrahigh dielectric constant of thin films obtained by electrostatic force microscopy and artificial neural networks

Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.A detailed analysis of the electrostatic interaction between an electrostatic force microscope tip and a thin film is presented. By using artificial neural networks, an equivalent semiinfinite sample has been described as an excellent approximation to characterize the whole thin film sample. A useful analytical expression has been also developed. In the case of very small thin film thicknesses (around 1 nm), the electric response of the material differs even for very high dielectric constants. This effect can be very important for thin materials where the finite size effect can be described by an ultrahigh thin filmdielectric constant.This work was supported by TIN2010-196079. G.M.S. acknowledges support from the Spanish Ramón y Cajal Program

Graded Differential Geometry of Graded Matrix Algebras

We study the graded derivation-based noncommutative differential geometry of the $Z_2$-graded algebra ${\bf M}(n| m)$ of complex $(n+m)\times(n+m)$-matrices with the ``usual block matrix grading'' (for $n\neq m$). Beside the (infinite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In particular we prove the universality of the graded derivation-based first-order differential calculus and show, that ${\bf M}(n|m)$ is a ``noncommutative graded manifold'' in a stricter sense: There is a natural body map and the cohomologies of ${\bf M}(n|m)$ and its body coincide (as in the case of ordinary graded manifolds).Comment: 21 pages, LATE

Broadening of H2_2O rotational lines by collision with He atoms at low temperature

We report pressure broadening coefficients for the 21 electric-dipole transitions between the eight lowest rotational levels of ortho-H$_2$O and para-H$_2$O molecules by collisions with He at temperatures from 20 to 120 K. These coefficients are derived from recently published experimental state-to-state rate coefficients for H$_2$O:He inelastic collisions, plus an elastic contribution from close coupling calculations. The resulting coefficients are compared to the available experimental data. Mostly due to the elastic contribution, the pressure broadening coefficients differ much from line to line, and increase markedly at low temperature. The present results are meant as a guide for future experiments and astrophysical observations.Comment: 2 figures, 2 table

Lande g-tensor in semiconductor nanostructures

Understanding the electronic structure of semiconductor nanostructures is not complete without a detailed description of their corresponding spin-related properties. Here we explore the response of the shell structure of InAs self-assembled quantum dots to magnetic fields oriented in several directions, allowing the mapping of the g-tensor modulus for the s and p shells. We found that the g-tensors for the s and p shells show a very different behavior. The s-state in being more localized allows the probing of the confining potential details by sweeping the magnetic field orientation from the growth direction towards the in-plane direction. As for the p-state, we found that the g-tensor modulus is closer to that of the surrounding GaAs, consistent with a larger delocalization. These results reveal further details of the confining potentials of self-assembled quantum dots that have not yet been probed, in addition to the assessment of the g-tensor, which is of fundamental importance for the implementation of spin related applications.Comment: 4 pages, 4 figure