Kissing number

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Juan Carlos Naranjo del ValThe kissing number problem is a classic problem related to the Kepler conjecture and which was already the subject of discussion between David Gregory and Isaac Newton. The problem asks for the value of $κ(n)$, which is the maximal number of equal radius and nonoverlapping spheres in n-dimensional space that can touch a fixed sphere of the same radius? The answer is known for n = 1, 2, 3, 4, 8, 24, in this work we will study the proof of Oleg R. Musin in the three dimensional case and discuss his strategy in the four dimensional one

WHO CAN FISH WHAT AND WHERE: CHILE'S TRADEOFFS IN HIGH SEAS FISHING OF STRADDLING STOCKS

Chile has not yet ratified the U.N. 1995 Agreement on straddling/ highly migratory fish stocks. This paper discusses key economic issues at stake from the viewpoint of a coastal state with important stakes in a straddling stock. The Chilean jack mackerel stock, one of Chile's most important fish resources, is in this category. This stock is currently caught on adjacent high-seas only by a Chilean-flag fleet, and currently there is no evidence of imminent competition from distant water fishing nations (DWFNs). We argue that ratification of the Agreement could imply negative effects on: (i) coastal states' sovereignty upon management measures within its Exclusive Economic Zone (EEZ) and (ii) national fishing companies' competitiveness. Despite this, the net cost/benefit balance depends on how binding the threat of DWFNs' fishing competition is expected to be. If the Agreement does go into force, coastal states with important stakes in straddling fish stocks will feel increased pressure to ratify as well. For the case of states that become parties to the Agreement, we discuss pending obstacles for achieving effective fishery management in the adjacent high-seas. We speculate about possible solutions to the 'New Member' and 'Interloper' problems. Regarding the former, enforceable closed access would seem to be legally feasible under the Agreement. In terms of effective enforcement against fishing by illegal interlopers, innovation in enforcement tools would be needed. In some cases, the latter may require further adjustments to the Law of the Sea Convention.Resource /Energy Economics and Policy,

Los viajes de siete reinas de España a la corte de los Austrias (1559-1690)

Este trabajo de investigación trata, tal y como indica su título, sobre los distintos viajes que hicieron siete reinas de España a la corte de los Austrias. Mediante el análisis de estos viajes reales, el trabajo pretende ser una aproximación a los preparativos, problemáticas y dificultades con las que se encontraron las distintas reinas, desde que salían de la corte paterna hasta su entrada en la corte español

Hygroscopicity issues in powder and grain technology

The effect of hygroscopicity on flowability of powders and bulk solids with applications in the packaging industry is experimentally and numerically investigated. Firstly, four granular materials are tested at different water contents to study the impact of relative humidity on some hydro-mechanical properties, namely the hydraulic diffusivity on wetting, as well as the shear strength and compressibility properties of the materials. Next, a capillary model covering a wider water content range –compared to the previous tests– is applied to discrete element simulations of a granular column collapse set-up. These simulations give further insight into important aspects of grain hygroscopicity in packaging and other industrial applications (such as the kinematics of flow and flowability issues), which are outside the scope of conventional experimental testing.Postprint (published version

On the evolution of the molecular line profiles induced by the propagation of C-shock waves

We present the first results of the expected variations of the molecular line emission arising from material recently affected by C-shocks (shock precursors). Our parametric model of the structure of C-shocks has been coupled with a radiative transfer code to calculate the molecular excitation and line profiles of shock tracers such as SiO, and of ion and neutral molecules such as H13CO+ and HN13C, as the shock propagates through the unperturbed medium. Our results show that the SiO emission arising from the early stage of the magnetic precursor typically has very narrow line profiles slightly shifted in velocity with respect to the ambient cloud. This narrow emission is generated in the region where the bulk of the ion fluid has already slipped to larger velocities in the precursor as observed toward the young L1448-mm outflow. This strongly suggests that the detection of narrow SiO emission and of an ion enhancement in young shocks, is produced by the magnetic precursor of C-shocks. In addition, our model shows that the different velocity components observed toward this outflow can be explained by the coexistence of different shocks at different evolutionary stages, within the same beam of the single-dish observations.Comment: 7 pages, 4 figures, accepted for publication in Ap

El Raonament probabilístic en alumnes d'educació infantil i de cicle mitjà d'educació primària

Es presenta un estudi realitzat amb alumnes d'educació infantil i d'educació primària per detectar els coneixements i els raonaments previs que tenen sobre probabilitat i atzar. A partir d'una activitat senzilla, s'han analitzat els seus raonaments probabilístics i s'ha fet una comparativa entre els alumnes d'educació infantil i els d'educació primària. Els resultats no mostren diferències significatives entre les dues poblacions de l'estudi, ja que la majoria dels alumnes té una òptica totalment determinista i no entén l'atzar. Aquests resultats coincideixen amb els d'altres autors com Inhelder i Piaget (1955), que afirmen que aquest raonament no s'obté fins a finals de l'educació primària.This article presents a study of kindergarten and primary school students designed to detect pre-existing knowledge and reasoning with respect to probability and chance. A simple activity was used to analyse probabilistic reasoning and a comparison between kindergarten and primary school students made. The results show no significant differences between the two groups, as most children do not understand chance due to their completely deterministic perspective. These results align with other authors, such as Piaget and Inhelder (1951), who argue that this type of reasoning is not obtained until the end of primary education

The magnetic precursor of L1448-mm: Excitation differences between ion and neutral fluids

Shock modelling predicts an electron density enhancement within the magnetic precursor of C-shocks. Previous observations of SiO, H13CO+, HN13C and H13CN toward the young L1448-mm outflow showed an over-excitation of the ion fluid that was attributed to an electron density enhancement in the precursor. We re-visit this interpretation and test if it still holds when we consider different source morphologies and kinetic temperatures for the observed molecules, and also give some insight on the spatial extent of the electron density enhancement around L1448-mm. We estimate the opacities of H13CO+ and HN13C by observing the J=3\to2 lines of rarer isotopologues to confirm that the emission is optically thin. To model the excitation of the molecules, we use the large velocity gradient (LVG) approximation with updated collisional coefficients to i) re- analyse the observations toward the positions where the over-excitation of H13CO+ has previously been observed [i.e. toward L1448- mm at offsets (0,0) and (0,-10)], and ii) to investigate if the electron density enhancement is still required for the cases of extended and compact emission, and for kinetic temperatures of up to 400 K. We also report several lines of SiO, HN13C and H13CO+ toward new positions around this outflow, to investigate the spatial extent of the over-excitation of the ions in L1448-mm. From the isotopologue observations, we find that the emission of H13CO+ and HN13C from the precursor is optically thin if this emission is extended. Using the new collisional coefficients, an electron density enhancement is still needed to explain the excitation of H13CO+ for extended emission and for gas temperatures of\le 400 K toward L1448-mm (0,-10), and possibly also toward L1448-mm (0,0). For compact emission the data cannot be fitted. We do not find any evidence for the over-excitation of the ion fluid toward the newly observed positions around L1448-mm. The observed line emission of SiO, H13CO+ and HN13C toward L1448-mm (0,0) and (0,-10) is consistent with an electron density enhancement in the precursor component, if this emission is spatially extended. This is also true for the case of high gas temperatures (\le400 K) toward the (0,-10) offset. The electron density enhancement seems to be restricted to the southern, redshifted lobe of the L1448-mm outflow. Interferometric images of the line emission of these molecules are needed to confirm the spatial extent of the over-excitation of the ions and thus, of the electron density enhancement in the magnetic precursor of L1448-mm.Comment: Accepted for publication in A&A; 9 pages, 3 figure