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A Liouville type result for fractional Schrödinger operators in 1D

  • Felipe Navarro, Juan Carlos
The aim of this master's thesis is to obtain an alternative and original proof of a Liouville type result for fractional Schrödinger operators in 1D without using a local extension problem, in the spirit of the recent work of Hamel et al. Thanks to this new proof we can extend the Liouville theorem to other nonlocal operators that do not have a local extension problem, being the first time that a result of this kind is proven. First, we introduce Schrödinger operators, the fractional Laplacian and its local extension problem. Then, we present a recent work about a nonlocal and nonlinear problem, where the prior study of fractional Schrödinger operators is needed. We also present the most important motivation for the study of Liouville type results: the conjecture of De Giorgi, and we review some Liouville type results both with local and nonlocal operators. Finally, we give the proof of the main theorems of the thesis.
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Environmental performance of rainwater harvesting strategies in Mediterranean buildings

  • Angrill Toledo, Sara
  • Segura Castillo, Luis
  • Petit Boix, Anna
  • Rieradevall Pons, Joan
  • Gabarrell Durany, Xavier
  • Josa Garcia-Tornel, Alejandro
Purpose: The rapid urbanization and the constant expansion of urban areas during the last decades have locally led to increasing water shortage. Rainwater harvesting (RWH) systems have the potential to be an important contributor to urban water self-sufficiency. The goal of this study was to select an environmentally optimal RWH strategy in newly constructed residential buildings linked to rainwater demand for laundry under Mediterranean climatic conditions, without accounting for water from the mains. Methods: Different strategies were environmentally assessed for the design and use of RWH infrastructures in residential apartment blocks in Mediterranean climates. The harvested rainwater was used for laundry in all strategies. These strategies accounted for (i) tank location (i.e., tank distributed over the roof and underground tank), (ii) building height considering the number of stories (i.e., 6, 9, 12, and 15), and (iii) distribution strategy (i.e., shared laundry, supply to the nearest apartments, and distribution throughout the building). The RWH systems consisted of the catchment, storage, and distribution stages, and the structural and hydraulic calculations were based on Mediterranean conditions. The quantification of the environmental performance of each strategy (e.g., CO2eq. emissions) was performed in accordance with the life cycle assessment methodology. Results and discussion: According to the environmental assessment, the tank location and distribution strategy chosen were the most important variables in the optimization of RWH systems. Roof tank strategies present fewer impacts than their underground tank equivalents because they enhance energy and material savings, and their reinforcement requirements can be accounted for within the safety factors of the building structure without the tank. Among roof tanks and depending on the height, a distribution strategy that concentrates demand in a laundry room was the preferable option, resulting in reductions from 25 to 54 % in most of the selected impact categories compared to distribution throughout the building. Conclusions: These results may set new urban planning standards for the design and construction of buildings from the perspective of sustainable water management. In this sense, a behavioral change regarding demand should be promoted in compact, dense urban settlements., Peer Reviewed
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La xarxa Ibercom

  • Santos Boada, Germán
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Bifurcation of 2-periodic orbits from non-hyperbolic fixed points

  • Cima Mollet, Anna
  • Gasull Embid, Armengol
  • Mañosa Fernández, Víctor
Prepublicació, We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2-periodic orbits that can bifurcate from the fixed point. As an application we study the 2-cyclicity of some natural families of polynomial maps.
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A subsystem identification method based on the path concept with coupling strength estimation

  • Magrans Fontrodona, Francesc Xavier
  • Poblet-Puig, Jordi
  • Rodríguez Ferran, Antonio
For complex geometries, the definition of the subsystems is not a straightforward task. We present here a subsystem identification method based on the direct transfer matrix, which represents the first-order paths. The key ingredient is a cluster analysis of the rows of the powers of the transfer matrix. These powers represent high-order paths in the system and are more affected than low-order paths by damping. Once subsystems are identified, the proposed approach also provides a quantification of the degree of coupling between subsystems. This information is relevant to decide whether a subsystem may be analysed in a computer model or measured in the laboratory independently of the rest or subsystems or not. The two features (subsystem identification and quantification of the degree of coupling) are illustrated by means of numerical examples: plates coupled by means of springs and rooms connected by means of a cavity., Peer Reviewed
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Estación ligera y móvil potabilizadora de agua mediante energía renovable

  • Moreno Ruz, Agustín
En el Informe de las Naciones Unidas sobre los recursos hídricos en el mundo 2015 1 indican que 748 millones de personas no disfrutan de una buena fuente de agua potable y 2.500 millones no gozan de buenas instalaciones de saneamiento (2014), estadística inmersa en una población mundial de 7.400 millones. El fenómeno atmosférico sequía meteorológica lleva a la sequía hidrológica, y tal como indica Global Water Parternship2: El fenómeno de ENOS ha afectado Centroamérica causando sequía y estaciones lluviosas irregulares con repercusiones económicas y sociales. En el caso de Centroamérica, en el 2014 tuvo lugar un evento de déficit de lluvias que afectó a la región, vinculado a un periodo de manifestación de El Niño (GWP, 2015) El efecto en el desabastecimiento de agua potable por cualquier causa: esperanza de vida reducida; coste de oportunidad; desaparición de personas con capacidad intelectual y reducción del potencial del progreso humano. Ante lo cual el argumento de la confrontación en términos políticos de la izquierda y la derecha se ha visto superado por la consideración del término Conservador - Progresista3 Conservador, a quien la situación actual, apoyada en la personal, es favorable a mantener los valores tradicionales frente a las innovaciones y los cambios radicales. Progresista para quien se trata de avanzar, personal y generalmente, en ideas y actitudes. Se ha de afrontar por tanto esa situación con pequeñas y móviles instalaciones existentes en diseño, sin importar dónde, capaces de potabilizar agua con riesgo para la salud humana, con energía renovable, sea solar, eólica, entre otras.
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