Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations

In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solutions to the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.Comment: 29 page

Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties

We investigate the equation $$(-\Delta_{\mathbb H^n})^{\gamma} w=f(w)\quad in \mathbb H^{n},$$ where $(-\Delta_{\mathbb H^n})^\gamma$ corresponds to the fractional Laplacian on hyperbolic space for $\gamma \in (0,1)$ and $f$ is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connections in the following sense; a so-called layer solution is a smooth solution of the previous equation converging to $\pm 1$ at any point of the two hemispheres $S_\pm \subset \partial_\infty \mathbb H^n$ and which is strictly increasing with respect to the signed distance to a totally geodesic hyperplane $\Pi.$ We prove that under additional conditions on the nonlinearity uniqueness holds up to isometry. Then we provide several symmetry results and qualitative properties of the layer solutions. Finally, we consider the multilayer case, at least when $\gamma$ is close to one

Some Necessities in Teaching on Administration and Management of Companies: Of Theory to the Practice Through TICs

Tras exponer brevemente algunas necesidades en la enseñanza en Administración y Dirección de Empresas, presentamos una herramienta que consideramos que permite solucionar aquéllas. Se trata de un simulador de empresas en competencia desarrollado con Dinámica de Sistemas y en el que se hace uso de las Tecnologías de la Información y de las Comunicaciones. Tras describir brevemente los distintos módulos de los que consta el simulador, procedemos a realizar una breve descripción de su empleo, en la que esperamos haber puesto de manifiesto sus potencialidades para resolver algunas de las deficiencias existentes en los instrumentos de formación actuales.After briefly setting out some teaching requirements in Business Administration, we introduce a tool that, we believe, would allow these to be met: a competing-company simulator with Systems Dynamics which makes use of Information and Communications Technologies. A short description of the various modules that make up the simulator is followed by a brief description of the way it is used which, we hope, amply shows its potential for resolving some of the shortcomings found in today s training tools

Renormalized weighted volume for the conformal fractional Laplacian

We give a notion of renormalized weighted volume in the setting of conformal geometry following the ideas of Fefferman-Graham. Indeed, it is a precise term in the asymptotic expansion near the boundary for a weighted volume related to the conformal fractional Laplacian operator and fractional order Q-curvaturePreprin

"Hablando a través de otra cultura": la versión de Frank McGuinness de La casa de Bernarda Alba, de Federico García Lorca

Translation and adaptation play an essential role in Irish contemporary theatre. Irish playwrights have turned to continental writers, such as Federico García Lorca, to rewrite their culture through another culture. Frank McGuinness has followed this tradition but, while his rewritings of Euripides or Sophocles have been widely discussed by scholarship, his version of Lorca’s The House of Bernarda Alba (1991) remains an unpublished text and, consequently, has not been the object of critical attention. This article intends to engage in close analysis of the play, addressing the strategies used by McGuinness to accommodate Lorca in the Irish context, and how the Lorquian themes voice the situation of women in the Northern Ireland of the 1990s, where McGuinness’s play was first produced. La traducción y la adaptación desempeñan un papel esencial en el teatro irlandés contemporáneo. Los dramaturgos y las dramaturgas han recurrido al teatro escrito en el continente por autores como Federico García Lorca para reescribir su cultura a través de otra cultura. Frank McGuinness ha seguido esta tradición, aunque, si bien la crítica ha estudiado sus revisiones de clásicos como Eurípides o Sófocles, su versión de La Casa de Bernarda Alba no ha recibido demasiada atención académica porque aún no se ha publicado. En este artículo se analiza con detalle el manuscrito y se abordan las estrategias que utiliza McGuinness para contextualizar a Lorca en el nuevo espacio irlandés. Además se examina cómo los temas lorquianos se utilizan para hacer visible la situación de la mujer de los años 1990 en Irlanda del Norte, donde la obra se representó por primera vez.&nbsp

Admissible surfaces in progressive addition lenses

Progressive addition lenses contain a surface of spatially-varying curvature, which provides variable optical power for different viewing areas over the lens. We derive complete compatibility equations that provide the exact magnitude of cylinder along lines of curvatures on any arbitrary PAL smooth surface. These equations reveal that, contrary to current knowledge, cylinder, and its derivative, does not only depend on principal curvature and its derivatives along the principal line but also on the geodesic curvature and its derivatives along the line orthogonal to the principal line. We quantify the relevance of the geodesic curvature through numerical computations. We also derive an extended and exact Minkwitz theorem only restricted to be applied along lines of curvatures, but excluding umbilical points

Singularities for a fully non-linear elliptic equation in conformal geometry

Peer ReviewedPostprint (published version