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

Existence and uniqueness to a fully non-linear version of the Loewner-Nirenberg problem

We consider the problem of finding on a given Euclidean domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a problem considered by Loewner and Nirenberg for the scalar curvature. We prove the existence and uniqueness of such metric when the boundary $\partial\Omega$ is a smooth bounded hypersurface (of codimension one). When $\partial\Omega$ contains a compact smooth submanifold $\Sigma$ of higher codimension with $\partial\Omega\setminus\Sigma$ being compact, we also give a `sharp' condition for the divergence to infinity of the conformal factor near $\Sigma$ in terms of the codimension

El movimiento sostenible en el mundo del café

En el siguiente trabajo se hará un análisis del movimiento sostenible a través del caso del mercado de café. Tras una breve introducción a la cultura del café y su industrialización, se pasará a analizar el concepto de sostenibilidad según los informes y medidas llevados a cabo por las Naciones Unidas. Una vez esclarecidos los conceptos, expondremos las diferentes iniciativas y subculturas generadas en el mundo del café que representen al movimiento sostenible. Se explorará entonces las distintas opiniones y actitudes hacia la sostenibilidad por parte de los ciudadanos españoles. Todo ello nos permitirá esclarecer, a modo de conclusión, el futuro del movimiento sostenible

Re-thinking Eating Disorders as Cultural Pathologies in Contemporary Irish Poetry: A Case Study

Eating disorders—a generic term that includes anorexia nervosa, bulimia, binge eating and many other subtypes of problematic relationships with food and eating—are situated at the interface of disciplines as varied as medicine, biology, history, cultural studies, gender studies and the social sciences. Although the reasons behind the development and experience of an eating disorder are individual as well as cultural, these pathologies tend to be analysed from either an exclusively biomedical perspective—which often excludes the cultural factor—or oversimplified as being the result of the stereotypes of beauty imposed on the female body in western cultural traditions. This essay, in contrast, looks at eating disorders as multi-layered metaphors of cultural dissidence within the social order and literary traditions of contemporary Ireland. It is divided into distinct, though interrelated, sections: a brief introduction to eating disorders; a consideration of the problems posed in the representation of emaciated corporealities; a taxonomical classification of the primary sources found in the course of my research; and the analysis of Mary O’Donnell’s poem “Reading the Sunflowers in September” as a case study to illustrate the literal and metaphorical employment of anorexia in contemporary Irish poetry. Although the análisis is philological, the perspective adopted is that of the Medical Humanities, in that I will make use of literary, cultural and biomedical literature in order to provide a view that is complementary to the scientific discourse around anorexia nervosa. O’Donnell’s poem will be considered in relation to European visual arts, particularly photography, in order to enhance the transnational dimension of eating disorders. At the same time, the close reading of the poem under analysis will be complemented by a comparative analysis with other Irish poems of the late 20th and early 21st centuries to underline the relevance of the national context in interpreting the representation of this disease. Ultimately, this essay aims to proffer new perspectives on the pathology and to contribute to the social understanding of those who experience it.The author of this essay wants to acknowledge her participation in the research project “End: Illness in the Age of Extinction,” funded by the Spanish Ministry of Research, Science and Technology (ref.: PID2019-109565RB-I00/AEI)

Determinants of the outcomes of services outsourcing: an empirical study of transport services.

The purpose of our study is to examine whether the design and management of the interfaces and interaction processes between customer and provider in services outsourcing are determinants of the results achieved by the outsourcing company. Following the conceptual framework initiated in the study by Wynstra et al. [11], this study focuses on transport services and hypothesized relationships are tested using the Partial Least Squares (PLS) statistical technique. The primary data used was obtained from a survey in three different countries (Germany, Japan and Spain), and from manufacturing companies in the electronics, automotive and machinery sectors. Among other things, the results show that both the structural dimensions of interaction (the organization's resources that it must commit) and the process dimensions of interaction (that consider the dynamic nature of the relationships), are important for obtaining adequate performance from transport services outsourcing.Spanish National Program of Industrial Design and Production DPI 2009 11148PAIDI Excellence Projects P08-SEJ0384

An extension problem for the CR fractional Laplacian

We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre.Comment: 33 pages. arXiv admin note: text overlap with arXiv:0709.1103 by other author