A note on primes of the form a2 + 1

In this note I prove using an algebraic identity and Wilson's Theorem

A new perspective on the integrability of Inozemtsev's elliptic spin chain

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane-Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev's chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane-Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane-Shastry chain.Comment: Pdflatex, 35 pages, 6 figures. Minor changes, to appear in Annals of Physic

Exact solution and thermodynamics of a spin chain with long-range elliptic interactions

We solve in closed form the simplest (su(1|1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions, and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit, and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1|1) elliptic chain behaves as a critical XX model, and deviates in an essential way from the Haldane-Shastry chain.Comment: Typeset with LaTeX, 7 figures, 30 pages; considerably enlarged version of previous submissio

Compact modes in quasi one dimensional coupled magnetic oscillators

In this work we study analytically and numerically the spectrum and localization properties of three quasi-one-dimensional (ribbons) split-ring resonator arrays which possess magnetic flatbands, namely, the stub, Lieb and kagome lattices, and how their spectra is affected by the presence of perturbations that break the delicate geometrical interference needed for a magnetic flatband to exist. We find that the Stub and Lieb ribbons are stable against the three types of perturbations considered here, while the kagome ribbon is, in general, unstable. When losses are incorporated, all flatbands remain dispersionless but become complex, with the kagome ribbon exhibiting the highest loss rate.Comment: 11 pages, 15 figure

Electronic Ticket and Check-in System for Indico Conferences

Project Specification: This project should build on the existing participant registration module of Indico and provide additional functionalities for managing the check-in process. While in small conferences it is easy to keep track of participants with a simple paper list, such techniques become inefficient when the need to scale the process up arises. Therefore Indico’s participant registration module would be extended with the functionality to generate electronic tickets. This will allow conference organizers to keep track of attendees after they finish the registration process. As part of this project it is also necessary to develop a mobile application that will be used to scan the electronic tickets, identify the user and mark them as checked in when they arrive at the conference. Additionally Indico’s HTTP API would be extended to be used by the mobile application to retrieve data about conferences and attendees. Abstract: The main goal of this project is to simplify the check-in process for conferences that use the Indico conference management system. This is archived by extending Indico’s core to include electronic ticket generation functionality and developing a mobile application that is used to scan the electronic tickets during the check-in process. Indico’s HTTP API is also extended to provide the mobile application with the necessary data

La reestructuración económico-territorial de la megalópolis de México ante la globalización (2a parte)

Es común plantear que los procesos de ampliación territorial de las actividades económicas supone una tendencia centrífuga, que, partiendo del centro se irradia en forma concéntrica hacia el resto del Área urbana

La reestructuración económico-territorial de la megalópolis de México ante la globalización (1a Parte)

El presente artículo aborda el análisis del proceso de configuración económico-territorial de la Megalópolis de México (MM) 3 , de la década de los ochenta a la fecha. Formulando, para tal fin, preguntas tales como ¿cuáles son las principales transformaciones económicas y territoriales que se han presentado en este ámbito territorial?, ¿en qué han consistido los principales planteamientos de ordenamiento económico- territorial durante este periodo?, y, ¿se presenta alguna correspondencia entre los procesos económico-territoriales y los planteamientos vertidos? Al respecto, las respuestas que adelantamos en este trabajo son: Los principales cambios económico-territoriales de la MM no se circunscriben sólo hacia la desindustrialización y la disminución relativa del grado de concentración económica con respecto al total nacional; sino, y sobre todo, hacia la especialización productiva y territorial. El principal cambio entre los planteamientos de los documentos generales de ordenamiento territorial que se analizan consiste en el traslado de la prioridad del control en la zona metropolitana y de la desconcentración nacional hacia la competitividad internacional. Y, por último, si bien existe una correspondencia entre los procesos económico-territoriales y los planteamientos vertidos, es pertinente plantear que estos últimos son insuficientes que dificulta plantear tanto que los cambios de los procesos respondan a dichas políticas como que en la actualidad se cuenta con un proyecto económico-territorial que posibilite elevar las condiciones económicas de la MM