Primitive geodesic lengths and (almost) arithmetic progressions

In this article, we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsification of arithmetic progressions, and prove that every negatively curved, closed Riemannian manifold has arbitrarily long almost arithmetic progressions in its primitive length spectrum. Concerning genuine arithmetic progressions, we prove that every non-compact, locally symmetric, arithmetic manifold has arbitrarily long arithmetic progressions in its primitive length spectrum. We end with a conjectural characterization of arithmeticity in terms of arithmetic progressions in the primitive length spectrum. We also suggest an approach to a well known spectral rigidity problem based on the scarcity of manifolds with arithmetic progressions.Comment: v3: 23 pages. To appear in Publ. Ma

An Explicit Framework for Interaction Nets

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard's Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets

Avisos de nuevos ejemplares incorporados a la biblioteca con Sierra

En la Biblioteca de la Universidad de Navarra los usuarios tienen un parte muy activa en el desarrollo de la colección. Ello implica que la Biblioteca esté muy interesada en avisarles cuando se incorporan los ejemplares que han pedido. Cuando se genera una nueva order (tanto en Sierra como en Millenniun) en el campo ‘SOLICITANTE” se puede cumplimentar los datos de la persona que ha pedido la compra del ejemplar. La notificación al usuario cuando se ha catalogado el ejemplar y se incorpora a la colección se realizaba, hasta hace poco, de manera manual. En la Biblioteca de la Universidad de Navarra se ha desarrollado una aplicación que recibe los datos de los ejemplares que se han incorporado durante la semana y permite gestionar las alertas a los usuarios que los han solicitado en compra.Comunicación presentada en la XIII Asamblea de GEUI

Quantum Hall resistance standards from graphene grown by chemical vapor deposition on silicon carbide

Replacing GaAs by graphene to realize more practical quantum Hall resistance standards (QHRS), accurate to within $10^{-9}$ in relative value, but operating at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date, the required accuracy has been reported, only few times, in graphene grown on SiC by sublimation of Si, under higher magnetic fields. Here, we report on a device made of graphene grown by chemical vapour deposition on SiC which demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4 K. This is explained by a quantum Hall effect with low dissipation, resulting from strongly localized bulk states at the magnetic length scale, over a wide magnetic field range. Our results show that graphene-based QHRS can replace their GaAs counterparts by operating in as-convenient cryomagnetic conditions, but over an extended magnetic field range. They rely on a promising hybrid and scalable growth method and a fabrication process achieving low-electron density devices.Comment: 12 pages, 8 figure

La biblioteca jurídica y los bibliotecarios en las universidades: el ejemplo de Estados Unidos y la realidad española

Las bibliotecas jurídicas y los bibliotecarios de Derecho en otros países realizan una labor activa e importante en el ámbito jurídico y especialmente en el universitario. En este trabajo se indican algunas de sus características, especialmente en las universidades de los Estados Unidos y se analiza cual es la situación en las bibliotecas de las universidades españolas que tienen Facultad de Derecho. Se plantean cuestiones como el grado de presencia de la figura del bibliotecario temático de Derecho en las mismas así como sus efectos positivos, el estado de la formación de usuarios y su integración en los programas de grado así como las políticas de desarrollo de la colección jurídica que están siguiendo las bibliotecas universitarias españolas.-------------------Law libraries and law librarians in other countries play an active and significant part in the legal field in general, and the university sector, in particular. This paper outlines some of the key features in this regard, especially in US university context. In light of this analysis, the situation of Spanish libraries in universities that have a law school is discussed. Questions arise as to the status and role of the law librarian and his/her positive contribution, as well as the state of user training, integration within degree programs and the development policies in relation to legal collections adopted by Spanish university libraries