Flat 3-webs of degree one on the projective plane

The aim of this work is to study global $3$-webs with vanishing curvature. We wish to investigate degree $3$ foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree $3$ foliations whose Legendre transform are webs with zero curvature.Comment: 14 page

Metastability of non-reversible mean-field Potts model with three spins

We examine a non-reversible, mean-field Potts model with three spins on a set with $N\uparrow\infty$ points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields. We illustrate the case of large external fields with some phenomena which are not present in the absence of external field.Comment: 34 pages, 12 figure

First ALMA maps of HCO, an important precursor of complex organic molecules, towards IRAS 16293-2422

The formyl radical HCO has been proposed as the basic precursor of many complex organic molecules such as methanol (CH$_3$OH) or glycolaldehyde (CH$_2$OHCHO). Using ALMA, we have mapped, for the first time at high angular resolution ($\sim$1$^{\prime\prime}$, $\sim$140 au), HCO towards the Solar-type protostellar binary IRAS 16293$-$2422, where numerous complex organic molecules have been previously detected. We also detected several lines of the chemically related species H$_2$CO, CH$_3$OH and CH$_2$OHCHO. The observations revealed compact HCO emission arising from the two protostars. The line profiles also show redshifted absorption produced by foreground material of the circumbinary envelope that is infalling towards the protostars. Additionally, IRAM 30m single-dish data revealed a more extended HCO component arising from the common circumbinary envelope. The comparison between the observed molecular abundances and our chemical model suggests that whereas the extended HCO from the envelope can be formed via gas-phase reactions during the cold collapse of the natal core, the HCO in the hot corinos surrounding the protostars is predominantly formed by the hydrogenation of CO on the surface of dust grains and subsequent thermal desorption during the protostellar phase. The derived abundance of HCO in the dust grains is high enough to produce efficiently more complex species such as H$_2$CO, CH$_3$OH, and CH$_2$OHCHO by surface chemistry. We found that the main formation route of CH$_2$OHCHO is the reaction between HCO and CH$_2$OH.Comment: Accepted in Monthly Notices of the Royal Astronomical Society; 19 pages, 12 figures, 7 table

Compositional analysis of InAs-GaAs-GaSb heterostructures by low-loss electron energy loss spectroscopy

As an alternative to Core-Loss Electron Energy Loss Spectroscopy, Low-Loss EELS is suitable for compositional analysis of complex heterostructures, such as the InAs-GaAs-GaSb system, since in this energy range the edges corresponding to these elements are better defined than in Core-Loss. Furthermore, the analysis of the bulk plasmon peak, which is present in this energy range, also provides information about the composition. In this work, compositional information in an InAs-GaAs-GaSb heterostructure has been obtained from Low-Loss EEL spectra

Teaching about Madrid: A Collaborative Agents-Based Distributed Learning Course

Interactive art courses require a huge amount of computational resources to be running on real time. These computational resources are even bigger if the course has been designed as a Virtual Environment with which students can interact. In this paper, we present an initiative that has been develop in a close collaboration between two Spanish Universities: Universidad Politécnica de Madrid and Universidad Rey Juan Carlos with the aim of join two previous research project: a Collaborative Awareness Model for Task-Balancing-Delivery (CAMT) in clusters and the “Teaching about Madrid” course, which provides a cultural interactive background of the capital of Spain

Patrones geométricos para iniciar en el álgebra a estudiantes de primaria con talento matemático

Entre las formas de iniciar la enseñanza del álgebra básica, la resolución de problemas de patrones geométricos (ppg) ha mostrado ser muy productiva, incluso en primaria (cai, knuth, 2011). En Benedicto, Jaime, Gutiérrez (2015) hemos realizado otro análisis de la resolución de este tipo de problemas. Diversos autores han descrito estilos de razonamiento y de resolución de problemas característicos de los estudiantes con talento matemático (freiman, 2006), algunos de los cuales son propios del contexto de pre-álgebra y resolución de ppg (Amit, Neira, 2008)

Movies and TV series fragments in mathematics: Epistemic suitability of instructional designs

There are plenty of books, journals and online sites devoted to the relationship between mathematics and cinema, and its educational applications, whose interest is to explore the pertinence of the instruction processes that can be designed around this resource. Instead of watching a full production, mathematics teachers that include movies and TV series in their classroom sessions, usually show short fragments, so the first step should be to consider these fragments alone to identify the mathematical objects and the involved meanings and representations. For this purpose, we use some theoretical notions from the Onto- Semiotic Approach to research in mathematics education, applying them to three excerpts from a movie and to some typical tasks designed based on them. The analysis of the involved mathematical content allows to reflect about the epistemic suitability of the instruction process, in terms of how aligned they are with the institutional meanings. The results show that it is possible to achieve a high suitability level but, most importantly, that this kind of analysis promotes teacher reflection to design teaching and learning processes