Cuadriláteros con GeoGebra. Una secuencia de formación docente en la enseñanza de la geometría con tecnologías libres

En la actualidad, un desafío en la formación del profesorado de Matemática es diseñar oportunidades que le permitan al docente desarrollar conocimiento y destrezas para enseñar adecuadamente los contenidos escolares. Este trabajo describe el diseño de una secuencia instruccional para la formación permanente de profesores de Matemática en la enseñanza de cuadriláteros, apoyada en el uso de un programa de Geometría Dinámica. La propuesta es parte de un “experimento de enseñanza”, un tipo de investigación de diseño que lleva a cabo el Grupo TEM, con el propósito de elaborar un modelo de aprendizaje del conocimiento sobre los cuadriláteros como objeto de enseñanza en un entorno dinámico. La secuencia articula objetivos, contenidos, actividades y una trayectoria hipotética de aprendizaje; elementos característicos del diseño del experimento. Además, la instrucción se organiza alrededor de tres grandes núcleos temáticos,referidos a las funcionalidades y características dinámicas del programa, los cuadriláteros y una clasificación de éstos

Petrología y geoquímica isotópica de los depósitos de magnesita de la cuenca de Calatayud (provincia de Zaragoza). Interpretación paleoambiental

Los sedimentos miocenos de la Cuenca de Calatayud, en particular los correspondientes a las unidades Inferior e Intermedia, contienen nllmerosos niveles de magnesita, que aparecen comúnmente asociados con depósitos lacustres sulfatados (anhidrita, yeso, glauberita), así como con margas y arcillas. L¡t magnesita de la Cuenca de Calatayud es de tipocriptocristalino, presentándose en capas masivas de color blanquecino, de espesor variable (mm a dm), entre arcillas, margas, niveles de yeso laminado y yeso nodular. Se han distinguido cuatro asociaciones de facies (MLH, Mys, Myp, MIN) con presencia de magnesita. Estas asociaciones de facies se ordenan básicamente en dos tipos de secuencias sedimentarias principales que reflejan, en un caso, la evolución de subambientes lacustres de alta salinidad y, en otro, de salinidad moderada a alta. La textura de la magnesita, observada mediante M.E.B. en muestras con alta pureza en este mineral, se caracteriza por presentar mosaicos densos y homogéneos de cristales romboédricos euhedrales a subeuhedrales, con tamaño alrededor de 1 m.Los valores de isótopos estables (0180, 013C) de la magnesita (n=34) muestran una ciertadispersión, con valores de 0180 de -4,8 a +4,9 %0 PDB y valores negativos de 013C, de -9,3 a +0,4 %0 PDB, más bajos en los niveles de magnesita correspondientes a las asociaciones de facies MLH y Mys. Las características estratigráficas, texturales e isotópicas sugieren que la magnesita se formó en condiciones evaporíticas, posiblemente por precipitación primaria a partir de soluciones concentradas con mezcla de aguas meteóricas, ricas en CO2 biogénico, aunque los valores negativos de o\3C pueden interpretarse también como reflejo de la actividad bacteriana en la precipitación de la magnesita. El análisis de las asociaciones de facies en que aparece la magnesita y su evolución secuencial permiten concluir que los depósitos de magnesita de la Cuenca de Calatayud se formaron tanto en condiciones lacustres hipersalinas como de salinidad moderada a alta

On the Discretization of a Class of Homogeneous Differentiators

This paper proposes explicit and implicit discrete-time realizations for a class of homogeneous sliding-mode-based differentiators. The proposed approach relies on the exact discretization of the continuous differentiator. Also, it is demonstrated that the proposed implicit discretization always exists, is non-anticipative and unique. A numerical simulation shows the better performance of the implicit scheme over the proposed and the referenced explicit implementations.ITESO, A.C

Discretization of the Robust Exact Filtering Differentiator Based on the Matching Approach

This paper presents a time discretization of the robust exact filtering differentiator, a sliding mode differentiator coupled to filter, which provides a suitable approximation of the derivatives for some noisy signals. This realization rely on the stabilization of a pseudo linear discrete-time system, it is attained through the matching approach. As in the original case, the convergence of the robust exact filtering differentiator depends on the bound of a higher-order derivative. Nevertheless, this new realization can be implemented with or without the knowledge of such constant. It is demonstrated that the system trajectories converge to a neighborhood of the origin for a free-noise input. Finally, comparisons between the behavior of the differentiator with different design parameters are presented.ITESO, A.C

Dark matter from primordial black holes would hold charge

We explore the possibility that primordial black holes (PBHs), formed early in the history of the Universe, contain electric charge down to the present day. We find that PBHs should hold a non-zero charge at their formation, sourced by both Poisson fluctuations and collisions of charged particles in the early universe. Although initial charges could be of either sign and are thought to be subject to fast discharge processes, we show that dipolar magnetic fields from rotating black holes can deviate them, avoiding their accretion or emission to infinity, regardless of the PBH mass. Moreover, we find that charged, maximally rotating PBHs produce magnetic fields able to cancel the Schwinger effect for all masses, and the Hawking emission for PBHs with M>1\,\mbox{kg}. These mechanisms could allow PBHs to maintain their charge for extended periods. At late times, we conclude that the plasma within virialised dark matter haloes can endow PBHs with a net average negative charge. We report resulting charges Q/M \sim -10^{-32}\,C/\mbox{kg} and Q/M \sim -10^{-22}\,C/\mbox{kg} for two current windows where PBHs can make up all of the dark matter; being respectively M\sim 10^{20}\,\mbox{kg} and M\sim 10^{30}\,\mbox{kg}. The charge of PBHs in haloes lies below the Schwinger limit for discharge, which would effectively make PBH dark matter slightly non-neutral to the present day. Altogether, the initial PBH charge, possible shielding against discharge, and late time negative charge accretion, show that PBHs of all masses could hold a net charge, with values about two to ten orders of magnitude lower than the maximal bound imposed by subextremal Reissner-Nordstr\"om (RN) PBHs, and even the extremal charge for Planck mass PBHs. The latter are of particular interest, as they could constitute charged stable relics, composing the entirety of dark matter in the Universe.Comment: 24 pages, 6 figures, minor changes, matches the version submitted to the journa

Investigation of patterned and non-patterned poly(2,6-dimethyl 1,4-phenylene) oxide based anion exchange membranes for enhanced desalination and power generation in a microbial desalination cell

© 2017 The Authors Quaternary ammonium poly(2,6-dimethyl 1,4-phenylene oxide) (QAPPO) anion exchange membranes (AEMs) with topographically patterned surfaces were assessed in a microbial desalination cell (MDC) system. The MDC results with these QAPPO AEMs were benchmarked against a commercially available AEM. The MDC with the non-patterned QAPPO AEM (Q1) displayed the best desalination rate (a reduction of salinity by 53 ± 2.7%) and power generation (189 ± 5 mW m− 2) when compared against the commercially available AEM and the patterned AEMs. The enhanced performance with the Q1 AEM was attributed to its higher ionic conductivity and smaller thickness leading to a reduced area specific resistance. It is important to note that Real Pacific Ocean seawater and activated sludge were used into the desalination chamber and anode chamber respectively for the MDC – which mimicked realistic conditions. Although the non-patterned QAPPO AEM displayed better performance over the patterned QAPPO AEMs, it was observed that the anodic overpotential was smaller when the MDCs featured QAPPO AEMs with larger lateral feature sizes. The results from this study have important implications for the continuous improvements necessary for developing cheaper and better performing membranes in order to optimize the MDC

Searching for solutions to the conflict over Europe's oldest forest

The Białowieża Forest World Heritage site is one of the last remaining primeval forests in lowland Europe and is a refuge for European Bison (Bison bonasus), the largest land mammal on the continent (Table 1)