La elipse y sus relaciones geométricas con las esferas de dandelin en el ambiente de geometría dinámica Cabri 3D

En este cursillo se presenta el uso del Ambiente de Geometría Dinámica (AGD), Cabri 3D, para realizar construcciones geométricas en tres dimensiones, en particular, se estudiará las propiedades geométricas de la elipse, con el fin de brindar una herramienta que permita visualizar la naturaleza de esta cónica en el espacio y de esta manera se logre comprender las propiedades geométricas y métricas de esta curva geométrica en un espacio tridimensional, utilizando las características de tangencia de una superficie cónica con esferas inscritas y con su plano de corte, denominadas Esferas de Dandelin. La intención de este cursillo, es incentivar un cambio tanto en la enseñanza como en el aprendizaje de la geometría espacial, en particular, en el estudio de la elipse, empleando las Esferas de Dandelin como una alternativa de tratamiento de esta cónica, y de esta manera evitar una enseñanza tradicionalista mediante definiciones que tal vez no se logren interiorizar por parte de los estudiantes (Ruiz, 1996)

A Consistent Picture Emerges: A Compact X-ray Continuum Emission Region in the Gravitationally Lensed Quasar SDSS J0924+0219

We analyze the optical, UV, and X-ray microlensing variability of the lensed quasar SDSS J0924+0219 using six epochs of Chandra data in two energy bands (spanning 0.4-8.0 keV, or 1-20 keV in the quasar rest frame), 10 epochs of F275W (rest-frame 1089A) Hubble Space Telescope data, and high-cadence R-band (rest-frame 2770A) monitoring spanning eleven years. Our joint analysis provides robust constraints on the extent of the X-ray continuum emission region and the projected area of the accretion disk. The best-fit half-light radius of the soft X-ray continuum emission region is between 5x10^13 and 10^15 cm, and we find an upper limit of 10^15 cm for the hard X-rays. The best-fit soft-band size is about 13 times smaller than the optical size, and roughly 7 GM_BH/c^2 for a 2.8x10^8 M_sol black hole, similar to the results for other systems. We find that the UV emitting region falls in between the optical and X-ray emitting regions at 10^14 cm < r_1/2,UV < 3x10^15 cm. Finally, the optical size is significantly larger, by 1.5*sigma, than the theoretical thin-disk estimate based on the observed, magnification-corrected I-band flux, suggesting a shallower temperature profile than expected for a standard disk.Comment: Replaced with accepted version to Ap

Bardeen-Petterson effect and the disk structure of the Seyfert galaxy NGC 1068

VLBA high spatial resolution observations of the disk structure of the active galactic nucleus NGC 1068 has recently revealed that the kinematics and geometry of this AGN is well characterized by an outer disk of H2O maser emission having a compact milliarcsecond (parsec) scale structure, which is encircling a thin rotating inner disk surrounding a ~10^7 M_\sun compact mass, likely a black hole. A curious feature in this source is the occurrence of a misalignment between the inner and outer parts of the disk, with the galaxy's radio jet being orthogonal to the inner disk. We interpret this peculiar configuration as due to the Bardeen-Petterson effect, a general relativistic effect that warps an initially inclined (to the black hole equator) viscous disk, and drives the angular momentum vector of its inner part into alignment with the rotating black hole spin. We estimate the time-scale for both angular momenta to get aligned as a function the spin parameter of the Kerr black hole. We also reproduce the shape of the parsec and kiloparsec scale jets, assuming a model in which the jet is precessing with a period and aperture angle that decrease exponentially with time, as expected from the Bardeen-Petterson effect.Comment: 12 pages, 3 figures, accepted for publication in The Astrophysical Journa

Calibration of GRB Luminosity Relations with Cosmography

For the use of Gamma-Ray Bursts (GRBs) to probe cosmology in a cosmology-independent way, a new method has been proposed to obtain luminosity distances of GRBs by interpolating directly from the Hubble diagram of SNe Ia, and then calibrating GRB relations at high redshift. In this paper, following the basic assumption in the interpolation method that objects at the same redshift should have the same luminosity distance, we propose another approach to calibrate GRB luminosity relations with cosmographic fitting directly from SN Ia data. In cosmography, there is a well-known fitting formula which can reflect the Hubble relation between luminosity distance and redshift with cosmographic parameters which can be fitted from observation data. Using the Cosmographic fitting results from the Union set of SNe Ia, we calibrate five GRB relations using GRB sample at $z\leq1.4$ and deduce distance moduli of GRBs at $1.4< z \leq 6.6$ by generalizing above calibrated relations at high redshift. Finally, we constrain the dark energy parameterization models of the Chevallier-Polarski-Linder (CPL) model, the Jassal-Bagla-Padmanabhan (JBP) model and the Alam model with GRB data at high redshift, as well as with the Cosmic Microwave Background radiation (CMB) and the baryonic acoustic oscillation (BAO) observations, and we find the $\Lambda$CDM model is consistent with the current data in 1-$\sigma$ confidence region.Comment: 15 pages, 4 figures, 2 tables; accepted for publication in IJMP

Neutrino mass spectrum from gravitational waves generated by double neutrino spin-flip in supernovae

The supernova (SN) neutronization phase produces mainly electron ($\nu_e$) neutrinos, the oscillations of which must take place within a few mean-free-paths of their resonance surface located nearby their neutrinosphere. The state-of-the-art on the SN dynamics suggests that a significant part of these $\nu_e$ can convert into right-handed neutrinos in virtue of the interaction of the electrons and the protons flowing with the SN outgoing plasma, whenever the Dirac neutrino magnetic moment be of strength $\mu_\nu < 10^{-11} \mu_{\rm B}$, with $\mu_{\rm B}$ being the Bohr magneton. In the supernova envelope, part of these neutrinos can flip back to the left-handed flavors due to the interaction of the neutrino magnetic moment with the magnetic field in the SN expanding plasma (Kuznetsov & Mikheev 2007; Kuznetsov, Mikheev & Okrugin 2008), a region where the field strength is currently accepted to be $B \gtrsim 10^{13}$ ~G. This type of $\nu$ oscillations were shown to generate powerful gravitational wave (GW) bursts (Mosquera Cuesta 2000, Mosquera Cuesta 2002, Mosquera Cuesta & Fiuza 2004, Loveridge 2004). If such double spin-flip mechanism does run into action inside the SN core, then the release of both the oscillation-produced $\nu_\mu$s, $\nu_\tau$s and the GW pulse generated by the coherent $\nu$ spin-flips provides a unique emission offset $\Delta T^{emission}_{\rm GW} \leftrightarrow \nu = 0$ for measuring the $\nu$ travel time to Earth. As massive $\nu$s get noticeably delayed on its journey to Earth with respect to the Einstein GW they generated during the reconversion transient, then the accurate measurement of this time-of-flight delay by SNEWS + LIGO, VIRGO, BBO, DECIGO, etc., might readily assess the absolute $\nu$ mass spectrum.Comment: 14 pages, 2 figures, ApJ aastex.cls style. In press by The Astrophysical Journa

Soil Carbon in Agroforestry Systems: An Unexplored Treasure?

Soil organic matter (SOM), which contains more reactive organic carbon (C) than any other single terrestrial pool, plays a major role in determining C storage in ecosystems and regulating atmospheric concentrations of carbon dioxide (CO2)^1^. Agroforestry, the practice of growing trees and crops in interacting combinations on the same unit of land^2^, primarily by resource-poor smallholder farmers in developing countries, is recognized as a strategy for soil carbon sequestration (SCS) under the Clean Development Mechanism (CDM) of the Kyoto Protocol^3^. The understanding about C storage and dynamics under agroforestry systems (AFS), however, is minimal. Our studies under various AFS in diverse ecological conditions in five countries showed that tree-based agricultural systems, compared to treeless systems, stored more C in deeper soil layers up to 1 m depth under comparable conditions. More C is stored in soil near the tree than away from the tree; higher SOC content is associated with higher species richness and tree density; and C3 plants (trees) contribute to more C in the silt- + clay-sized (&#x3c;53 &#xb5;m) fractions that constitute more stable C, than C4 plants, in deeper soil profiles4 - 8. These results provide clear indications of the possibilities for climate change mitigation through SCS in AFS, and opportunities for economic benefit - through carbon trading - to millions of smallholder farmers in developing countries

Adult-Onset Eccrine Angiomatous Hamartoma: A Case Report With Ultrasound Findings

[Abstract] Eccrine angiomatous hamartoma (EAH) is a rare, benign cutaneous tumor composed of vascular and eccrine elements. It is most commonly diagnosed during the first years of life, although there are reports of cases diagnosed in adults. We report the ultrasound findings of a 46-year-old patient with a left plantar lesion, histopathological diagnosis of which confirmed suspicion of EAH

Statistical Comparison of Classifiers Applied to the Interferential Tear Film Lipid Layer Automatic Classification

The tear film lipid layer is heterogeneous among the population. Its classification depends on its thickness and can be done using the interference pattern categories proposed by Guillon. The interference phenomena can be characterised as a colour texture pattern, which can be automatically classified into one of these categories. From a photography of the eye, a region of interest is detected and its low-level features are extracted, generating a feature vector that describes it, to be finally classified in one of the target categories. This paper presents an exhaustive study about the problem at hand using different texture analysis methods in three colour spaces and different machine learning algorithms. All these methods and classifiers have been tested on a dataset composed of 105 images from healthy subjects and the results have been statistically analysed. As a result, the manual process done by experts can be automated with the benefits of being faster and unaffected by subjective factors, with maximum accuracy over 95%