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We show that the power-law decay exponents in von Neumann's Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral measure at the spectral value~$1$. In this work we also prove that, under an assumption of weak convergence, in the absence of a spectral gap, the convergence rates of the time-average in von Neumann's Ergodic Theorem depend on sequences of time going to infinity., Comment: Major changes following suggestions of the referee

We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singularities, in the sense that their Radon-Nikodym derivatives diverge with a power-law order. We also discuss an application to spectral measures of finite-rank perturbations of the discrete Laplacian.

The Astronomical Observatory of the University of Coimbra has a huge collection of solar images, acquired daily since 1926. From the beginning, only spectroheliograms in the CaiiK line has been recorded, and since 1989 in the H_alpha line also. Such dataset requires efficient tools to detect and analyze solar activity features. The objective of this work is to create a tool that allows to automatic detect sunspots, umbra, and penumbra, that can be applied to the entire dataset. To achieve this, two different approaches have been developed, one based on mathematical morphology and another based on the intensities of the digital levels of the pixels. Both approaches were applied to a subset of images with features identified visually by an experimented solar observer. The performance of both methods was compared through the metrics Precision, Recall and F-score. Another evaluation was made based on the catalogs from Heliophysics Features Catalog and the SILSO catalogue., Comment: submitted to Astronomy and Computing

We present a semi-empirical calibration between the metallicity ($Z$) of Seyfert 2 Active Galactic Nuclei and the $N2$=log([N II]$\lambda$6584/H$\alpha$) emission-line intensity ratio. This calibration was derived through the [O III]$\lambda$5007/[O II]$\lambda$3727 versus $N2$ diagram containing observational data and photoionization model results obtained with the Cloudy code. The observational sample consists of 463 confirmed Seyfert 2 nuclei (redshift $z < 0.4$) taken from the Sloan Digital Sky Survey DR7 dataset. The obtained $Z$-$N2$ relation is valid for the range $0.3 < (Z/Z_{\odot}) < 2.0$ which corresponds to $-0.7 < \: (N2) < 0.6$. The effects of varying the ionization parameter ($U$), electron density and the slope of the spectral energy distribution on the $Z$ estimations are of the order of the uncertainty produced by the error measurements of $N2$. This result indicates the large reliability of our $Z-N2$ calibration. A relation between $U$ and the [O III]/[O II] line ratio, almost independent of other nebular parameter, was obtained., Comment: 10 pages, 6 figuras, accepted for publication in MNRAS

The amplification of the relative Fresnel (Goos-Haenchen) phase by an appropriate number of total internal reflections and the choice of favorable incidence angles allow to observe full oscillations in the power of a DPSS laser transmitted through sequential BK7 blocks. The experimental results confirm the theoretical predictions. The optical apparatus used in this letter can be seen as a new type of two-phase ellipsometric system where the phase of the complex refractive index is replaced by the relative Fresnel (Goos-Haenchen) phase., Comment: 7 pages, 3 figures, 1 table

Full-disk spectroheliograms have been taken in Coimbra on a daily basis since 1926 in the Ca II K-line (K1 and K3). Later, in 1989, with the upgrade of the equipment it was possible to start the observations in the H-alpha line. The spectroheliograms of Coimbra constitutes a huge dataset of solar images, which requires an efficient automatic tool to detect and analyse solar activity features. This work presents a mathematical morphology approach applied to the CaII K3 series. The objective is to create a tool based on the segmentation by watershed transform combined with other morphological operators to detect automatically and analyse chromospheric plages during the solar cycle 24. The tool is validated by comparing its results for cycle 23 with those presented by Dorotovic et al. (2007, 2010). The results obtained are in very good agreement with those, including on images obtained in non-ideal meteorological conditions (eg. some clouds in sky). The results were also qualitatively compared with the results obtained through the application of ASSA model to SDO HMI magnetograms.

There is solid observational evidence on the existence of massive, $M\sim 1~M_\odot$, highly magnetized white dwarfs (WDs) with surface magnetic fields up to $B\sim 10^9$ G. We show that, if in addition to these features, the star is fast rotating, it can become a rotation-powered pulsar-like WD and emit detectable high-energy radiation. We infer the values of the structure parameters (mass, radius, moment of inertia), magnetic field, rotation period and spin-down rates of a WD pulsar death-line. We show that WDs above the death-line emit blackbody radiation in the soft X-ray band via the magnetic polar cap heating by back flowing pair-created particle bombardment and discuss as an example the X-ray emission of soft gamma-repeaters and anomalous X-ray pulsars within the WD model., Comment: To appear in MNRAS

We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40 % deconfined quark-hybrid matter in their cores. Neutron stars with canonical masses of around $1.4\, M_\odot$ would not contain deconfined quark matter. The central proton fractions of the stars are found to be high, enabling them to cool rapidly. Very good agreement with the temperature evolution established for the neutron star in Cassiopeia A (Cas A) is obtained for one of our models (based on the popular NL3 nuclear parametrization), if the protons in the core of our stellar models are strongly paired, the repulsion among the quarks is mildly repulsive, and the mass of Cas A has a canonical value of $1.4\, M_\odot$., Comment: 10 pages, 7 figures

Globally neutral neutron stars, obtained from the solution of the called Einstein-Maxwell-Thomas-Fermi equations that account for all the fundamental interactions, have been recently introduced. These configurations have a more general character than the ones obtained with the traditional Tolman-Oppenheimer-Volkoff, which impose the condition of local charge neutrality. The resulting configurations have a less massive and thinner crust, leading to a new mass-radius relation. Signatures of this new structure of the neutron star on the thermal evolution might be a potential test for this theory. We compute the cooling curves by integrating numerically the energy balance and transport equations in general relativity, for globally neutral neutron stars with crusts of different masses and sizes, according to this theory for different core-crust transition interfaces. We compare and contrast our study with known results for local charge neutrality. We found a new behavior for the relaxation time, depending upon the density at the base of the crust, $\rho_{\rm crust}$. In particular, we find that the traditional increase of the relaxation time with the crust thickness holds only for configurations whose density of the base of the crust is greater than $\approx 5\times 10^{13}$ g cm$^{-3}$. The reason for this is that neutron star crusts with very thin or absent inner crust have some neutrino emission process blocked which keep the crust hotter for longer times. Therefore, accurate observations of the thermal relaxation phase of neutron stars might give crucial information on the core-crust transition which may aid us in probing the inner composition/structure of these objects.

The Feynman-Metropolis-Teller treatment of compressed atoms has been recently generalized to relativistic regimes and applied to the description of static and rotating white dwarfs in general relativity. We present here the extension of this treatment to the case of finite temperatures and construct the corresponding equation of state (EOS) of the system; applicable in a wide regime of densities that includes both white dwarfs and neutron star outer crusts. We construct the mass-radius relation of white dwarfs at finite temperatures obeying this new EOS and apply it to the analysis of ultra low-mass white dwarfs with $M\lesssim 0.2 M_\odot$. In particular, we analyze the case of the white dwarf companion of PSR J1738+0333. The formulation is then extrapolated to compressed nuclear matter cores of stellar dimensions, systems with mass numbers $A\approx (m_{\rm Planck}/m_n)^3$ or mass $M_{\rm core}\approx M_{\odot}$, where $m_{\rm Planck}$ and $m_n$ are the Planck and the nucleon mass. For $T \ll m_e c^2/k_B \approx 5.9\times 10^9$ K, a family of equilibrium configurations can be obtained with analytic solutions of the ultra-relativistic Thomas-Fermi equation at finite temperatures. Such configurations fulfill global but not local charge neutrality and have strong electric fields on the core surface. We find that the maximum electric field at the core surface is enhanced at finite temperatures with respect to the degenerate case., Comment: Matches version to appear in Physical Review C

We consider off-diagonal Jacobi matrices $J$ with (faster-than-exponential) sparse perturbations. We prove (Theorem \ref{onehalf}) that the Fourier transform $\hat{\left\| f\right\| ^{2}d\rho}(t)$ of the spectral measure $\rho $ of $J$, whose sparse perturbations are at least separated by a distance $\exp \left(cj(\ln j)^{2}\right) /\delta ^{j}$, for some $c>1/2,$ $0<\delta <1$ and for a dense subset of $C_{0}^{\infty}(-2,2)$-functions $f$, decays as $t^{-1/2}\Omega (t)$, uniformly in the spectrum $[-2,2]$, $\Omega (t)$ increasing less rapidly than any positive power of $t$, improving earlier results obtained by Simon (Commun. Math. Phys. \textbf{179}, 713-722 (1996)) and by Krutikov-Remling (Commun. Math. Phys. \textbf{223}, 509-532 (2001)) for Schr\"{o}dinger operators with sparse potential that increases as fast as exponential-of-exponential. Applications to the spectrum of the Kronecker sum of two (or more) copies of the model are given., Comment: 25 pages

In the present work we consider off-diagonal Jacobi matrices with uncertainty in the position of sparse perturbations. We prove (Theorem 3.2) that the sequence of Pr\"ufer angles (\theta_{k}^{\omega})_{k\geq 1} is u.d mod \pi for all \phi \in [0,\pi] with exception of the set of rational numbers and for almost every \omega with respect to the product \nu =\prod_{j\geq 1}\nu_{j} of uniform measures on {-j,...,j}. Together with an improved criterion for pure point spectrum (Lemma 4.1), this provides a simple and natural alternative proof of a result of Zlatos (J. Funct. Anal. \textbf{207}, 216-252 (2004)): the existence of pure point (p.p) spectrum and singular continuous (s.c.) spectra on sets complementary to one another with respect to the essential spectrum [-2,2], outside sets A_{sc} and A_{pp}, respectively, both of zero Lebesgue measure (Theorem 2.4). Our method allows for an explicit characterization of A_{pp}, which is seen to be also of dense p.p. type, and thus the spectrum is proved to be exclusively pure point on one subset of the essential spectrum., Comment: Submitted to Journal Functional Analysis on August 7, 2009; Submitted to Transactions of the American Mathematical Society on September 10, 2010; Submitted to Journal of Spectral Theory on March 7, 2011; 21 pages

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i. e. nonrandom, block-Jacobi matrices may be determined exactly, improving a result of Zlatos (J. Funct. Anal. 207, 216-252 (2004))., Comment: 22 pages

In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period, all non-degenerate and at least one of them is hyperbolic. Moreover, the invariant curves of two hyperbolic points are transversal. We explore these properties to give some dynamical consequences specially about the dynamics in the instability regions., Comment: 14 pages with 1 figure