A case of the Rodriguez Villegas conjecture

Let L be a number field and let E be any subgroup of the units O_L^* of L. If rank(E) = 1, Lehmer's conjecture predicts that the height of any non-torsion element of E is bounded below by an absolute positive constant. If rank(E) = rank(O_L^*), Zimmert proved a lower bound on the regulator of E which grows exponentially with [L:Q]. Fernando Rodriguez Villegas made a conjecture in 2002 that "interpolates" between these two extremes of rank. Here we prove a high-rank case of this conjecture. Namely, it holds if L contains a subfield K for which [L:K] >> [K:Q] and E contains the kernel of the norm map from O_L^* to O_K^*

Solar Energy Harvesting on S- and N-doped nanoporous Carbons

Nowadays heteroatom-containing carbonaceous materials such as graphene or CNT have gained more and more attention of the scientists searching for inexpensive substitutes of the catalysts for energy related applications such an oxygen reduction reactions. Discovery of graphene and an extensive characterization of its electronic properties caused that the surface of traditional activated carbon has been viewed from other, unexplored before, angles. The main advantage of activated or nanoporous carbons, within the family of carbonaceous materials, is their porosity where the confined pore space effect can be utilized. Recently we have shown that specific nanoporous carbons obtained from commodity polymers can catalyze oxygen evolution reactions1, oxygen reduction reaction2 and exhibit photoluminescence properties3. This behavior was attributed to the specificity of surface microstructure, texture, and chemistry. It was found that the carbons obtained at relatively low temperature (800 oC) contain 10 nm graphic units enhancing their DC conductivity. They have also rich surface chemistry based on sulfur, nitrogen and oxygen containing groups. Even though small sp2 clusters should be important to affect the width of the band gap, the sulfur and nitrogen containing groups are hypothesized to act as chromophores/antenna accepting visible light energy. Electron deficiency on them promotes water splitting in small pores. These groups also change the electronic structure of the carbons surface and bring some level hydrophobicity to it. These features were found as important for oxygen reduction reactions4. These reactions enhance the performance of carbons as supercapcitors when the process takes place in the visible light5. References 1. Ania, C.O.; Seredych, M.; Rodriguez-Castellon, E.; Bandosz, T.J. Visible light driven photoelectrochemical water splitting on metal free nanoporous carbon promoted by chromophoric functional groups. Carbon 79 (2014) 432–441. 2. Seredych, M.; Idrobo, J-C.; Bandosz, T.J. Effect of confined space reduction of graphite oxide followed by sulfur doping on oxygen reduction reaction in neutral electrolyte. J. Mater. Chem. A. 1 (2013) 7059-7067. 3. Bandosz, T.J.; Rodriguez-Castellon, E.; Montenegro J.M.; Seredych, M. Photoluminescence of nanoporous carbons: Opening a new application route for old materials.. Carbon 77 (2014) 651–659. 4. Confined space reduced graphite oxide doped with sulfur as metal-free oxygen reduction catalyst. Seredych, M.; Rodriguez-Castellon, E.; Bandosz, T.J. Carbon 66 (2014) 227-233. 5. Seredych, M.; Rodriguez-Castellon, E.; Biggs, MJ. Skinner, W.l Bandosz, T.J. Effect of visible light and electrode wetting on the capacitive performance of S- and N-doped nanoporous carbons: Importance of surface chemistry. Carbon 78 (2014) 540–558.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Spin fluctuations and superconductivity in powders of Fe_1+xTe_0.7Se_0.3 as a function of interstitial iron concentration

Using neutron inelastic scattering, we investigate the role of interstitial iron on the low-energy spin fluctuations in powder samples of Fe_{1+x}Te_{0.7}Se_{0.3}. We demonstrate how combining the principle of detailed balance along with measurements at several temperatures allows us to subtract both temperature-independent and phonon backgrounds from S(Q,\omega) to obtain purely magnetic scattering. For small values of interstitial iron (x=0.009(3)), the sample is superconducting (T_{c}=14 K) and displays a spin gap of 7 meV peaked in momentum at wave vector q_{0}=(\pi,\pi) consistent with single crystal results. On populating the interstitial iron sites, the superconducting volume fraction decreases and we observe a filling in of the low-energy magnetic fluctuations and a decrease of the characteristic wave vector of the magnetic fluctuations. For large concentrations of interstitial iron (x=0.048(2)) where the superconducting volume fraction is minimal, we observe the presence of gapless spin fluctuations at a wave vector of q_{0}=(\pi,0). We estimate the absolute total moment for the various samples and find that the amount of interstitial iron does not change the total magnetic spectral weight significantly, but rather has the effect of shifting the spectral weight in Q and energy. These results show that the superconducting and magnetic properties can be tuned by doping small amounts of iron and are suggestive that interstitial iron concentration is also a controlling dopant in the Fe_{1+x}Te_{1-y}Se_{y} phase diagram in addition to the Te/Se ratio.Comment: (10 pages, 8 figures, to be published in Phys. Rev. B

Liquid phase reactions of hypergolic propellants Final report

Measuring heat and gas release rates for initial reaction of liquid nitrogen tetroxide with hydrazine, monomethyl hydrazine, and unsymmetric dimethyl hydrazin

The Gremlin Graph Traversal Machine and Language

Gremlin is a graph traversal machine and language designed, developed, and distributed by the Apache TinkerPop project. Gremlin, as a graph traversal machine, is composed of three interacting components: a graph $G$, a traversal $\Psi$, and a set of traversers $T$. The traversers move about the graph according to the instructions specified in the traversal, where the result of the computation is the ultimate locations of all halted traversers. A Gremlin machine can be executed over any supporting graph computing system such as an OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph traversal language, is a functional language implemented in the user's native programming language and is used to define the $\Psi$ of a Gremlin machine. This article provides a mathematical description of Gremlin and details its automaton and functional properties. These properties enable Gremlin to naturally support imperative and declarative querying, host language agnosticism, user-defined domain specific languages, an extensible compiler/optimizer, single- and multi-machine execution models, hybrid depth- and breadth-first evaluation, as well as the existence of a Universal Gremlin Machine and its respective entailments.Comment: To appear in the Proceedings of the 2015 ACM Database Programming Languages Conferenc