SIDI SIFR. Proyecto de animación a la lectura y educación en valores desde el área de matemáticas

En la sociedad actual la educación en valores y el fomento a la lectura, entre el alumnado de la enseñanza secundaria, tiene una singular importancia. Con este trabajo, desde el área de matemáticas y de modo interdisciplinar, hemos querido contribuir al enriquecimiento de nuestro alumnado para analizar y valorar fenómenos sociales como la diversidad cultural, la igualdad entre los sexos o la convivencia pacífica, desarrollando simultáneamente contenidos específicos de las distintas disciplinas desde las cuales puede ser analizada la lectura de El señor del cero.

El perímetro de Dubai y el área de Singapur

Hasta hace poco la idea de que todo país estable tenía un perímetro de frontera y una superficie determinada formaba parte de las firmes creencias de todos nosotros. En estos sorprendentes tiempos en que vivimos hasta estas ideas firmes sobre medidas empiezan a ser superadas. Durante décadas la escasez de terreno inducía a construir edificios cada vez más altos y a ir aumentando la cotización de determinadas zonas como las de los centros y la primera línea de mar. Esto esta liquidado.

Medida del área de un recinto por procedimientos mecánicos. Fundamentos matemáticos del planímetro

El presente trabajo, sobre los fundamentos matemáticos del planímetro, viene a continuar la tarea emprendida en 1990 cuando, con un grupo de trabajo que se formó en el IB Félix de Azara de Zaragoza durante el curso 1990-91, se constituyó un grupo de investigación educativa subvencionado por el MEC para trabajar en lo que podría constituir una matemática pretécnica. En este proyecto, entre otros temas, nos dedicamos a la construcción de aparatos de medida, estudiando sus fundamentos matemáticos y sus aplicaciones. El estudio de los fundamentos matemáticos del planímetro, por su nivel, caía fuera de lo que se podría explicar a los alumnos de bachillerato, pero puede resultar interesante para despertar la curiosidad de los profesores, como nos ocurrió a nosotros. '

Un ejemplo de utilizar en el área de estadística las representaciones gráficas con ordenador

En este artículo se reflexiona sobre la incorporación de gráficos tridimensionales a la educación matemática en bachillerato mediante el uso de un sistema de cálculo simbólico, y se presenta un ejemplo de aplicación. Al final del artículo se propone una posible línea de ampliación de la actividad descrita y se hace una última reflexión sobre las posibilidades que, para el aula, nos ofrecen los sistemas de cálculo simbólico.

Fenología de la floración en un área mediterránea del noroeste ibérico: contrastes con áreas eurosiberianas próximas

Se estudia la fenología de la floración de 56 especies de angiospermas en un área mediterránea del noroeste ibérico. Esta presenta una fuerte concentración de la floración en el mes de Mayo y un predominio de períodos de floración cortos (1=4.6 semanas). Su comparación con un área Eurosiberiana próxima pone de manifiesto los fuertes contrastes existentes como respuesta a la heterogeneidad ambiental de ambas áreas.

Analysis of the footprint in school age of 8-10 years old

Biomechanical problems in children, is an important subject currently, existing controversy in different areas, for example, the majority of children have a flattened footprint, or the hypermobility joint is linked to a musculoskeletal pain. The objective of the study was to determine what kind of footprint is most frequent in school-age children (8-10 years) in the area of Plasencia. This was taken as a sign 50 children, of whom 28 were males and 22 females. All the subjects in the study underwent an assessment of footprint planted in static as well as an exploration of different parameters through inspection in a standing position (formula digital, rearfoot). The results show that excavated footprint is present in a 72% cases of the population, 16% was belonging to an excavated footprint in which we find a higher percentage of weight related.For the digital formula we find that the most common is the Egyptian foot by 40% of the cases and that the prevalence in the rearfoot, is a normal hindfoot. In relation with the hypermobility joint, we check that it is more common in girls and that none of them presents an association to musculoskeletal pain. As a future line we could establish a more comprehensive study with new techniques and valuingchild’s statics and dynamics, to have a more accurate study of the different variables in the sample population studied.

An insight into alkali promotion: a density functional theory study of CO dissociation on K/Rh(111)

The important role of alkali additives in heterogeneous catalysis is, to a large extent, related to the high promotion effect they have on many fundamental reactions. The wide application of alkali additives in industry does not, however, reflect a thorough understanding of the mechanism of their promotional abilities. To investigate the physical origin of the alkali promotion effect, we have studied CO dissociation on clean Rh(111) and K-covered Rh(111) surfaces using density functional theory. By varying the position of potassium atoms relative to a dissociating CO, we have mapped out the importance of different K effects on the CO dissociation reactions. The K-induced changes in the reaction pathways and reaction barriers have been determined; in particular, a large reduction of the CO dissociation barrier has been identified. A thorough analysis of this promotion effect allows us to rationalize both the electronic and the geometrical factors that govern alkali promotion effect: (i) The extent of barrier reductions depends strongly on how close K is to the dissociating CO. (ii) Direct K-O bonding that is in a very short range plays a crucial role in reducing the barrier. (iii) K can have a rather long-range effect on the TS structure, which could reduce slightly the barriers.

[Rh-2(COD)(2)(Dppm)(mu(2)-Cl)]BF4: Precursor for a selective hydrogenation catalyst and its recycling by silica entrapment

The synthesis of [Rh-2(COD)(2)(dppm)(mu(2)-Cl)] BF4 (1) (COD) 1,5-cyclooctadiene, dppm) bis(diphenylphosphino) methane) from simple precursors is reported. This is a rare example of a dirhodium complex with an open [Rh-2(mu(2)-dppm)(mu(2)-Cl)] core. The complex has been used to affect the hydrogenation of styrene and benzo[b] thiophene with total selectivity and competitive rates of reaction. The recycling of the catalyst has been achieved by the entrapment of 1 in silica by a sol-gel method to produce a recyclable solid catalyst.

Insight into the key aspects of the regeneration process in the NOx storage reduction (NSR) reaction probed using fast transient kinetics coupled with isotopically labelled (NO)-N-15 over Pt and Rh-containing Ba/Al2O3 catalysts

For the first time, the coupling of fast transient kinetic switching and the use of an isotopically labelled reactant (15NO) has allowed detailed analysis of the evolution of all the products and reactants involved in the regeneration of a NOx storage reduction (NSR) material. Using realistic regeneration times (ca. 1 s) for Pt, Rh and Pt/Rh-containing Ba/Al2O3 catalysts we have revealed an unexpected double peak in the evolution of nitrogen. The first peak occurred immediately on switching from lean to rich conditions, while the second peak started at the point at which the gases switched from rich to lean. The first evolution of nitrogen occurs as a result of the fast reaction between H2 and/or CO and NO on reduced Rh and/or Pt sites. The second N2 peak which occurs upon removal of the rich phase can be explained by reaction of stored ammonia with stored NOx, gas phase NOx or O2. The ammonia can be formed either by hydrolysis of isocyanates or by direct reaction of NO and H2.

The study highlights the importance of the relative rates of regeneration and storage in determining the overall performance of the catalysts. The performance of the monometallic 1.1%Rh/Ba/Al2O3 catalyst at 250 and 350 °C was found to be dependent on the rate of NOx storage, since the rate of regeneration was sufficient to remove the NOx stored in the lean phase. In contrast, for the monometallic 1.6%Pt/Ba/Al2O3 catalyst at 250 °C, the rate of regeneration was the determining factor with the result that the amount of NOx stored on the catalyst deteriorated from cycle to cycle until the amount of NOx stored in the lean phase matched the NOx reduced in the rich phase. On the basis of the ratio of exposed metal surface atoms to total Ba content, the monometallic 1.6%Pt/Ba/Al2O3 catalyst outperformed the Rh-containing catalysts at 250 and 350 °C even when CO was used as a reductant.

Chain growth mechanism in Fischer-Tropsch synthesis: A DFT study of C-C coupling over Ru, Fe, Rh, and Re surfaces

A quantitative approach is used to understand the chain growth mechanism in FT synthesis on the Ru, Fe, Rh, and Re surfaces. The C-C coupling reactions are extensively calculated on the stepped metal surfaces. Combining the coupling barriers and reactant stabilities, we investigate the reaction rates of all possible C, + C-1 coupling pathways on the metal surfaces. It is found that (i) all the transition-state structures are similar on these surfaces, while some coupling barriers are very different; (ii) the dominant chain growth pathways on these surfaces are different: C + CH and CH + CH on Rh and Ru surfaces, C + CH3 on Fe surface, and C + CH on Re surface. The common features of the major coupling reactions together with those on the Co surface are also discussed.

Insight into association reactions on metal surfaces: Density-functional theory studies of hydrogenation reactions on Rh(111)

Hydrogenation reaction, as one of the simplest association reactions on surfaces, is of great importance both scientifically and technologically. They are essential steps in many industrial processes in heterogeneous catalysis, such as ammonia synthesis (N-2+3H(2)-->2NH(3)). Many issues in hydrogenation reactions remain largely elusive. In this work, the NHx (x=0,1,2) hydrogenation reactions (N+H-->NH, NH+H-->NH2 and NH2+H-->NH3) on Rh(111) are used as a model system to study the hydrogenation reactions on metal surfaces in general using density-functional theory. In addition, C and O hydrogenation (C+H-->CH and O+H-->OH) and several oxygenation reactions, i.e., C+O, N+O, O+O reactions, are also calculated in order to provide a further understanding of the barrier of association reactions. The reaction pathways and the barriers of all these reactions are determined and reported. For the C, N, NH, and O hydrogenation reactions, it is found that there is a linear relationship between the barrier and the valency of R (R=C, N, NH, and O). Detailed analyses are carried out to rationalize the barriers of the reactions, which shows that: (i) The interaction energy between two reactants in the transition state plays an important role in determining the trend in the barriers; (ii) there are two major components in the interaction energy: The bonding competition and the direct Pauli repulsion; and (iii) the Pauli repulsion effect is responsible for the linear valency-barrier trend in the C, N, NH, and O hydrogenation reactions. For the NH2+H reaction, which is different from other hydrogenation reactions studied, the energy cost of the NH2 activation from the IS to the TS is the main part of the barrier. The potential energy surface of the NH2 on metal surfaces is thus crucial to the barrier of NH2+H reaction. Three important factors that can affect the barrier of association reactions are generalized: (i) The bonding competition effect; (ii) the local charge densities of the reactants along the reaction direction; and (iii) the potential energy surface of the reactants on the surface. The lowest energy pathway for a surface association reaction should correspond to the one with the best compromise of these three factors. (C) 2003 American Institute of Physics.

Ligand differentiated complementary Rh-catalyst systems for the enantioselective desymmetrization of meso-cyclic anhydrides

Two distinct systems for the rhodium-catalyzed enantioselective desymmetrization of meso-cyclic anhydrides have been developed. Each system has been optimized and are compatible with the use of in situ prepared organozinc reagents. Rhodium/PHOX species efficiently catalyze the addition of alkyl nucleophiles to glutaric anhydrides, while a rhodium/phosphoramidite system is effective in the enantioselective arylation of succinic and glutaric anhydrides.