Automatic Deduction in Dynamic Geometry using Sage

We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction. In one worksheet, diagrams constructed with the open source dynamic geometry system GeoGebra are accepted. In this worksheet, Groebner bases are used to either compute the equation of a geometric locus in the case of a locus construction or to determine the truth of a general geometric statement included in the GeoGebra construction as a boolean variable. In the second worksheet, locus constructions coded using the common file format for dynamic geometry developed by the Intergeo project are accepted for computation. The prototype and several examples are provided for testing. Moreover, a third Sage worksheet is presented in which a novel algorithm to eliminate extraneous parts in symbolically computed loci has been implemented. The algorithm, based on a recent work on the Groebner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Detailed examples are discussed.Comment: In Proceedings THedu'11, arXiv:1202.453

Electronic structure of V4_4O7_7: charge ordering, metal-insulator transition and magnetism

The low and high-temperature phases of V$_4$O$_7$ have been studied by \textit{ab initio} calculations. At high temperature, all V atoms are electronically equivalent and the material is metallic. Charge and orbital ordering, associated with the distortions in the V pseudo-rutile chains, occur below the metal-insulator transition. Orbital ordering in the low-temperature phase, different in V$^{3+}$ and V$^{4+}$ chains, allows to explain the distortion pattern in the insulating phase of V$_4$O$_7$. The in-chain magnetic couplings in the low-temperature phase turn out to be antiferromagnetic, but very different in the various V$^{4+}$ and V$^{3+}$ bonds. The V$^{4+}$ dimers formed below the transition temperature form spin singlets, but V$^{3+}$ ions, despite dimerization, apparently participate in magnetic ordering.Comment: 10 pages, 6 figures, 2 table

Enhanced thermoelectric response of hole-doped La2_2NiO4+δ_{4+\delta} by ab initio calculations

Thermoelectric properties of the system La$_2$NiO$_{4+\delta}$ have been studied ab initio. Large Seebeck coefficient values are predicted for the parent compound, and to some extent remain in the hole-doped metallic phase, accompanied of an increase in the conductivity. This system, due to its layered structure would be a suitable candidate for an improvement of its thermoelectric figure of merit by nanostructurization in thin films, that has already been shown to increase the electrical conductivity ($\sigma$). Our calculations show that in the region around La$_2$NiO$_{4.05}$ the system has a large thermopower at high temperatures and also a substantially increased $\sigma$. Films grown with this low-doping concentration will show an optimal relationship between thermopower and $\sigma$. This result is obtained for various exchange-correlation schemes (correlated, uncorrelated and parameter-free) that we use to analyze the electronic structure of the hole-doped compound.Comment: 10 pages, 6 figure

Using a free open source software to teach mathematics

We present the experience of the authors teaching mathematics to freshmen engineering students with the help of the open source computer algebra system Sage. We describe some teaching resources and present an ad hoc distribution of Sage used by the authors

Spongionella secondary metabolites protect mitochondrial function in cortical neurons against oxidative stress

Accepted: 8 January 2014 This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Acknowledgments The research leading to these results has received funding from the following FEDER cofunded-grants: From Ministerio de Ciencia y Tecnología, Spain: AGL2009-13581-CO2-01, AGL2012-40485-CO2-01. From Xunta de Galicia, Spain: 10PXIB261254 PR. From the European Union’s Seventh Framework Programme managed by REA—Research Executive Agency (FP7/2007–2013) under grant agreement Nos. 265896 BAMMBO, 265409 µAQUA, and 262649 BEADS, 315285 CIGUATOOLS and 312184 PHARMASEA. From the Atlantic Area Programme (Interreg IVB Trans-national): 2009-1/117 Pharmatlantic. MER thanks the Government of the Arab Republic of Egypt for a PhD Scholarship. MJ thanks the Scottish University Life Science Alliance which provided funding to set up the compound library.Peer reviewedPublisher PD

Fermiology and transport properties of the half-metallic itinerant ferromagnet CoS2_2: influence of spin orbit coupling

Electronic structure calculations were performed on the compound CoS$_2$, an itinerant ferromagnet whose magnetic properties can be understood in terms of spin fluctuation theory. We have identified nesting features in the Fermi surface of the compound, active for long wavelength spin fluctuations. The electronic structure of the material is close to a half-metal. We show the importance of introducing spin-orbit coupling (SOC) in the calculations, that partially destroys the half-metallicity of the material. By means of transport properties calculations, we have quantified the influence of SOC in the conductivity at room temperature, with an important decrease comparing to the GGA alone conductivity. SOC also helps to understand the negative 0 of the material, whose conductivity varies by a few percent with the introduction of small perturbations in the states around the Fermi level.Comment: 8 pages, 8 figure