Approach to Equilibrium for a Forced Burgers Equation

We show that approach to equilibrium in certain forced Burgers equations is implied by a decay estimate on a suitable intrinsic semigroup estimate, and we verify this estimate in a variety of cases including a periodic force.Comment: To appear in Journal of Evolution Equation

Lifshitz tails for alloy type models in a constant magnetic field

In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed by a random alloy-type potential constructed with single site potentials decaying at least at a Gaussian speed. We prove that, if the Landau level stays preserved as a band edge for the perturbed Hamiltonian, at the Landau levels, the integrated density of states has a Lifshitz behavior of the type $e^{-\log^2|E-2bq|}$

In-orbit Vignetting Calibrations of XMM-Newton Telescopes

We describe measurements of the mirror vignetting in the XMM-Newton Observatory made in-orbit, using observations of SNR G21.5-09 and SNR 3C58 with the EPIC imaging cameras. The instrument features that complicate these measurements are briefly described. We show the spatial and energy dependences of measured vignetting, outlining assumptions made in deriving the eventual agreement between simulation and measurement. Alternate methods to confirm these are described, including an assessment of source elongation with off-axis angle, the surface brightness distribution of the diffuse X-ray background, and the consistency of Coma cluster emission at different position angles. A synthesis of these measurements leads to a change in the XMM calibration data base, for the optical axis of two of the three telescopes, by in excess of 1 arcminute. This has a small but measureable effect on the assumed spectral responses of the cameras for on-axis targets.Comment: Accepted by Experimental Astronomy. 26 pages, 18 figure

Anodal transcranial direct current stimulation over S1 differentially modulates proprioceptive accuracy in young and old adults

Background: Proprioception is a prerequisite for successful motor control but declines throughout the lifespan. Brain stimulation techniques such as anodal transcranial direct current stimulation (a-tDCS) are capable of enhancing sensorimotor performance across different tasks and age groups. Despite such growing evidence for a restorative potential of tDCS, its impact on proprioceptive accuracy has not been studied in detail yet. Objective: This study investigated online effects of a-tDCS over S1 on proprioceptive accuracy in young (YA) and old healthy adults (OA). Methods: The effect of 15 min of a-tDCS vs. sham on proprioceptive accuracy was assessed in a cross-over, double blind experiment in both age groups. Performance changes were tested using an arm position matching task in a robotic environment. Electrical field (EF) strengths in the target area S1 and control areas were assessed based on individualized simulations. Results: a-tDCS elicited differential changes in proprioceptive accuracy and EF strengths in the two groups: while YA showed a slight improvement, OA exhibited a decrease in performance during a-tDCS. Stronger EF were induced in target S1 and control areas in the YA group. However, no relationship between EF strength and performance change was found. Conclusion: a-tDCS over S1 elicits opposing effects on proprioceptive accuracy as a function of age, a result that is important for future studies investigating the restorative potential of a-tDCS in healthy aging and in the rehabilitation of neurological diseases that occur at advanced age. Modeling approaches could help elucidate the relationship between tDCS protocols, brain structure and performance modulation

Density of Surface States in Discrete Models

We consider a simple quantum model with a surface and prove the existence of a surface density of states. We show that the energy spectrum of the model is the union of the support of the bulk densities of states of the media forming the surface and the support of the surface density of states

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

Cosmic X-ray background and Earth albedo Spectra with Swift/BAT

We use Swift/BAT Earth occultation data at different geomagnetic latitudes to derive a sensitive measurement of the Cosmic X-ray background (CXB) and of the Earth albedo emission in the 15--200 keV band. We compare our CXB spectrum with recent (INTEGRAL, BeppoSAX) and past results (HEAO-1) and find good agreement. Using an independent measurement of the CXB spectrum we are able to confirm our results. This study shows that the BAT CXB spectrum has a normalization ~8(+/-3)% larger than the HEAO-1 measurement. The BAT accurate Earth albedo spectrum can be used to predict the level of photon background for satellites in low Earth and mid inclination orbits.Comment: Accepted for publication in the Astrophysical Journal. 38 Pages, 16 Figures, 2 Table

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.Comment: 11 page

A Bayesian Approach to Inverse Quantum Statistics

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.Comment: 4 pages, 6 figures, revte

Synthesis of arylamino-thieno-oxobutanamides and reactivity studies on the cyclisation with the Lawesson´s reagent

1-aryl-2-thienyl-substituted pyrroles and 5-arylamino-2,2´-bithiophenes are synthesized by treatment of arylamino-thieno-oxobutanamides with Lawesson´s reagent. These in turn are prepared by direct amidation of 4-oxo-(2-thienyl)butanoic acid through DCC/BtOH mediated reaction.Fundação para a Ciência e Tecnologia. FEDER - POCTI/QUI/37816/2001