Tareas matemáticas en la formación de maestros: caracterizando perspectivas

El diseño de tareas en los programas de formación de maestros se vincula al desarrollo del conocimiento necesario para realizar diferentes tareas profesionales- organizar el contenido matemático, interpretar el aprendizaje, gestionar la enseñanza. Se ejemplifica esta perspectiva en el caso del diseño de tareas matemáticas considerando la tarea profesional del maestro de analizar libros de texto.

Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

The accretion environment in Vela X-1 during a flaring period using XMM-Newton

We present analysis of 100 ks contiguous XMM-Newton data of the prototypical wind accretor Vela X-1. The observation covered eclipse egress between orbital phases 0.134 and 0.265, during which a giant flare took place, enabling us to study the spectral properties both outside and during the flare. This giant flare with a peak luminosity of 3.92+0.42-0.09 × 1037 erg s-1 allows estimates of the physical parameters of the accreted structure with a mass of ~1021 g. We have been able to model several contributions to the observed spectrum with a phenomenological model formed by three absorbed power laws plus three emission lines. After analysing the variations with orbital phase of the column density of each component, as well as those in the Fe and Ni fluorescence lines, we provide a physical interpretation for each spectral component. Meanwhile, the first two components are two aspects of the principal accretion component from the surface of the neutron star, the third component seems to be the X-ray light echo formed in the stellar wind of the companion.

First EURONEAR NEA discoveries from La Palma using the INT

Since 2006, the European Near Earth Asteroids Research (EURONEAR) project has been contributing to the research of near-Earth asteroids (NEAs) within a European network. One of the main aims is the amelioration of the orbits of NEAs, and starting in 2014 February we focus on the recovery of one-opposition NEAs using the Isaac Newton Telescope (INT) in La Palma in override mode. Part of this NEA recovery project, since 2014 June EURONEAR serendipitously started to discover and secure the first NEAs from La Palma and using the INT, thanks to the teamwork including amateurs and students who promptly reduce the data, report discoveries and secure new objects recovered with the INT and few other telescopes from the EURONEAR network. Five NEAs were discovered with the INT, including 2014 LU14, 2014 NL52 (one very fast rotator), 2014 OL339 (the fourth known Earth quasi-satellite), 2014 SG143 (a quite large NEA), and 2014 VP. Another very fast moving NEA was discovered but was unfortunately lost due to lack of follow-up time. Additionally, another 14 NEA candidates were identified based on two models, all being rapidly followed-up using the INT and another 11 telescopes within the EURONEAR network. They include one object discovered by Pan-STARRS, two Mars crossers, two Hungarias, one Jupiter trojan, and other few inner main belt asteroids (MBAs). Using the INT and Sierra Nevada 1.5 m for photometry, then the Gran Telescopio de Canarias for spectroscopy, we derived the very rapid rotation of 2014 NL52, then its albedo, magnitude, size, and its spectral class. Based on the total sky coverage in dark conditions, we evaluate the actual survey discovery rate using 2-m class telescopes. One NEA is possible to be discovered randomly within minimum 2.8 deg2 and maximum 5.5 deg2. These findings update our past statistics, being based on double sky coverage and taking into account the recent increase in discovery.

An XMM-Newton view of FeKα in high-mass X-ray binaries

We present a comprehensive analysis of the whole sample of available XMM-Newton observations of high-mass X-ray binaries (HMXBs) until August 2013, focusing on the FeKα emission line. This line is key to better understanding the physical properties of the material surrounding the X-ray source within a few stellar radii (the circumstellar medium). We collected observations from 46 HMXBs and detected FeKα in 21 of them. We used the standard classification of HMXBs to divide the sample into different groups. We find that (1) different classes of HMXBs display different qualitative behaviours in the FeKα spectral region. This is visible especially in SGXBs (showing ubiquitous Fe fluorescence but not recombination Fe lines) and in γ Cass analogues (showing both fluorescent and recombination Fe lines). (2) FeKα is centred at a mean value of 6.42 keV. Considering the instrumental and fits uncertainties, this value is compatible with ionization states that are lower than Fe xviii. (3) The flux of the continuum is well correlated with the flux of the line, as expected. Eclipse observations show that the Fe fluorescence emission comes from an extended region surrounding the X-ray source. (4) We observe an inverse correlation between the X-ray luminosity and the equivalent width of FeKα (EW). This phenomenon is known as the X-ray Baldwin effect. (5) FeKα is narrow (σline< 0.15 keV), reflecting that the reprocessing material does not move at high speeds. We attempt to explain the broadness of the line in terms of three possible broadening phenomena: line blending, Compton scattering, and Doppler shifts (with velocities of the reprocessing material V ~ 1000 km s-1). (6) The equivalent hydrogen column (NH) directly correlates to the EW of FeKα, displaying clear similarities to numerical simulations. It highlights the strong link between the absorbing and the fluorescent matter. (7) The observed NH in supergiant X-ray binaries (SGXBs) is in general higher than in supergiant fast X-ray transients (SFXTs). We suggest two possible explanations: different orbital configurations or a different interaction compact object – wind. (8) Finally, we analysed the sources IGR J16320-4751 and 4U 1700-37 in more detail, covering several orbital phases. The observed variation in NH between phases is compatible with the absorption produced by the wind of their optical companions. The results clearly point to a very important contribution of the donor’s wind in the FeKα emission and the absorption when the donor is a supergiant massive star.

Is financial instability male-driven? Gender and cognitive skills in experimental asset markets

The hypothesis that price stability would reliably increase with the fraction of women operating in financial markets has been frequently suggested in policy discussions. To test this hypothesis we conducted 10 male-only, 10 female-only and 10 mixed-gender experimental asset markets, and compared the effects of gender composition, confidence, risk attitude and cognitive skills. Male and female markets have comparable volatility and deviations from fundamentals, whereas mixed-gender markets are substantially more stable. On the other hand, higher average cognitive skills of the group are associated with reduced market volatility. Individual-level analysis shows that subjects with higher cognitive skills trade at prices closer to fundamental values and earn significantly higher profits; similarly, mixed markets exhibit lower mispricing, particularly for traders with lower cognitive skills. Our results are demonstrated to hold in other experimental asset market studies, suggesting that a mixed-gender composition reduces mispricing across different types of asset markets.