Integrated music and math projects in secondary education

The introduction of projects involving music and mathematics in Secondary Education should allow the integration of these disciplines by nonspecialists. In the present work we describe an experience carried out with future mathematics teachers with solid scientific-technical training, but little musical training. This pilot contributes with concrete orientations and results para the creation and development of STEAM activities, which can be found in [5].This research work has been carried out within the framework of the project EDU2017-84979-R, of the Spanish State Program of R&D and Innovation Oriented to the Challenges of the Society

Observations of one young and three middle-aged γ\gamma-ray pulsars with the Gran Telescopio Canarias

We used the 10.4m Gran Telescopio Canarias to search for the optical counterparts to four isolated $\gamma$-ray pulsars, all detected in the X-rays by either \xmm\ or \chan\ but not yet in the optical. Three of them are middle-aged pulsars -- PSR\, J1846+0919 (0.36 Myr), PSR\, J2055+2539 (1.2 Myr), PSR\, J2043+2740 (1.2 Myr) -- and one, PSR\, J1907+0602, is a young pulsar (19.5 kyr). For both PSR\, J1907+0602 and PSR\, J2055+2539 we found one object close to the pulsar position. However, in both cases such an object cannot be a viable candidate counterpart to the pulsar. For PSR\, J1907+0602, because it would imply an anomalously red spectrum for the pulsar and for PSR\, J2055+2539 because the pulsar would be unrealistically bright ($r'=20.34\pm0.04$) for the assumed distance and interstellar extinction. For PSR\, J1846+0919, we found no object sufficiently close to the expected position to claim a possible association, whereas for PSR\, J2043+2740 we confirm our previous findings that the object nearest to the pulsar position is an unrelated field star. We used our brightness limits ($g' \approx 27$), the first obtained with a large-aperture telescope for both PSR\, J1846+0919 and PSR\, J2055+2539, to constrain the optical emission properties of these pulsars and investigate the presence of spectral turnovers at low energies in their multi-wavelength spectra.Comment: 10 pages, 11 figures, accpted for publication in MNRA

Observations of three young gamma-ray pulsars with the Gran Telescopio Canarias

We report the analysis of the first deep optical observations of three isolated $\gamma$-ray pulsars detected by the {\em Fermi Gamma-ray Space Telescope}: the radio-loud PSR\, J0248+6021 and PSR\, J0631+1036, and the radio-quiet PSR\, J0633+0632. The latter has also been detected in the X rays. The pulsars are very similar in their spin-down age ($\tau \sim$40--60 kyrs), spin-down energy ($\dot{E} \sim10^{35}$ erg s$^{-1}$), and dipolar surface magnetic field ($B \sim 3$--$5\times10^{12}$ G). These pulsars are promising targets for multi-wavelength observations, since they have been already detected in $\gamma$ rays and in radio or X-rays. None of them has been detected yet in the optical band. We observed the three pulsar fields in 2014 with the Spanish 10.4m Gran Telescopio Canarias (GTC). We could not find any candidate optical counterpart to the three pulsars close to their most recent radio or {\em Chandra} positions down to $3 \sigma$ limits of $g'\sim27.3$, $g'\sim27$, $g'\sim27.3$ for PSR\, J0248+6021, J0631+1036, and J0633+0632, respectively. From the inferred optical upper limits and estimated distance and interstellar extinction, we derived limits on the pulsar optical luminosity. We also searched for the X-ray counterpart to PSR\, J0248+6021 with \chan\ but we did not detect the pulsar down to a 3$\sigma$ flux limit of $5 \times 10^{-14}$ erg cm$^{-2}$ s$^{-1}$ (0.3--10 keV). For all these pulsars, we compared the optical flux upper limits with the extrapolations in the optical domain of the $\gamma$-ray spectra and compared their multi-wavelength properties with those of other $\gamma$-ray pulsars of comparable age.Comment: 12 pages, 5 figures, accepted for publication in MNRA

Unravelling the health effects of fasting : a long road from obesity treatment to healthy life span increase and improved cognition

In recent years a revival of interest has emerged in the health benefits of intermittent fasting and long-term fasting, as well as of other related nutritional strategies. In addition to meal size and composition a new focus on time and frequency of meals has gained attention. The present review will investigate the effects of the main forms of fasting, activating the metabolic switch from glucose to fat and ketones (G-to-K), starting 12-16 h after cessation or strong reduction of food intake. During fasting the deactivation of mTOR regulated nutrient signalling pathways and activation of the AMP protein kinase trigger cell repair and inhibit anabolic processes. Clinical and animal studies have clearly indicated that modulating diet and meal frequency, as well as application of fasting patterns, e.g. intermittent fasting, periodic fasting, or long-term fasting are part of a new lifestyle approach leading to increased life and health span, enhanced intrinsic defences against oxidative and metabolic stresses, improved cognition, as well as a decrease in cardiovascular risk in both obese and non-obese subjects. Finally, in order to better understand the mechanisms beyond fasting-related changes, human studies as well as non-human models closer to human physiology may offer useful clue

Pulsar Prospects for the Cherenkov Telescope Array

In the last few years, the Fermi-LAT telescope has discovered over a 100 pulsars at energies above 100 MeV, increasing the number of known gamma-ray pulsars by an order of magnitude. In parallel, imaging Cherenkov telescopes, such as MAGIC and VERITAS, have detected for the first time VHE pulsed gamma-rays from the Crab pulsar. Such detections have revealed that the Crab VHE spectrum follows a power-law up to at least 400 GeV, challenging most theoretical models, and opening wide possibilities of detecting more pulsars from the ground with the future Cherenkov Telescope Array (CTA). In this contribution, we study the capabilities of CTA for detecting Fermi pulsars. For this, we extrapolate their spectra with "Crab-like" power-law tails in the VHE range, as suggested by the latest MAGIC and VERITAS results.Comment: 4 pages, 3 figures. In Proceedings of the 2012 Heidelberg Symposium on High Energy Gamma-Ray Astronomy. All CTA contributions at arXiv:1211.184

Niveles de algebrización de la actividad matemática escolar : implicaciones para la formación de maestros

El desarrollo del razonamiento algebraico elemental desde los primeros niveles educativos es un objetivo propuesto en diversas investigaciones y orientaciones curriculares. En consecuencia, es importante que el profesor de educación primaria conozca las características del razonamiento algebraico y sea capaz de seleccionar y elaborar tareas matemáticas adecuadas que permitan la progresiva introducción del razonamiento algebraico en la escuela primaria. En este trabajo, presentamos un modelo en el que se diferencian tres niveles de razonamiento algebraico elemental que puede utilizarse para reconocer características algebraicas en la resolución de tareas matemáticas. Presentamos el modelo junto con ejemplos de actividades matemáticas, clasificadas según los distintos niveles de algebrización. Estas actividades pueden ser usadas en la formación de profesores a fin de capacitarlos para el desarrollo del sentido algebraico en sus alumnos.Developing elementary algebraic thinking since the earliest levels of education is a goal proposed in different research works and curricular guidelines. Consequently, primary school teachers should know the characteristics of algebraic reasoning and be able to select and develop appropriate mathematical tasks that serve to gradually introduce algebraic reasoning in primary school. In this paper we present a model that distinguish three levels of elementary algebraic thinking and is useful in analyzing the algebraic features in solving mathematical tasks. We describe this model with examples of mathematical activities, classified according to the different levels of algebraization. These activities can be used in the education of teachers to prepare them to develop their students' algebraic sense