We study several mathematical aspects of a system of equations modelling the interaction between short waves, described by a nonlinear Schrödinger equation, and long waves, described by the equations ...of magnetohydrodynamics for a compressible, heat conductive fluid. The system in question models an aurora-type phenomenon, where a short wave propagates along the streamlines of a magnetohydrodynamic medium. We focus on the one dimensional (planar) version of the model and address the problem of well posedness as well as convergence of the sequence of solutions as the bulk viscosity tends to zero together with some other interaction parameters, to a solution of the limit decoupled system involving the compressible Euler equations and a nonlinear Schrödinger equation. The vanishing viscosity limit serves to justify the SW–LW interactions in the limit equations as, in this setting, the SW–LW interactions cannot be defined in a straightforward way, due to the possible occurrence of vacuum.
We study the well-posedness of the initial value problem and the long-time behavior of almost periodic solutions to stochastic scalar conservation laws in any space dimension, under the assumption of ...Lipschitz continuity of the flux functions and a non-degeneracy condition. We show the existence and uniqueness of an invariant measure in a separable subspace of the space of Besicovitch almost periodic functions.
ResumenEl Nuevo Urbanismo americano es un enfoque de planificación y desarrollo urbano en EEUU, basado en cómo se han construido ciudades y pueblos antes de la invención del automóvil. Calles ...peatonalizadas, viviendas y tiendas en las proximidades, parques y espacios públicos accesibles junto a oficinas, escuelas y edificios gubernamentales. Cada uno contribuyendo a la dinámica de un tejido urbano de alta calidad. Los 10 Principios del Nuevo Urbanismo son un conjunto de principios aplicables a cualquier proyecto urbano, de cualquier escala, desde un edificio hasta la escala metropolitana. A continuación, os expongo un sistema de puntuación que he creado para evaluar y clasificar en un ranking las sedes internacionales de las grandes empresas tecnológicas de Silicon Valley para comprobar si estas grandes empresas tecnológicas contribuyen al Nuevo Urbanismo de ciudades peatonalizadas y densas, o favorecen la dispersión suburbana, dependiente del uso del automóvil.AbstractNew Urbanism is an American urban planning and development approach based on the principles of how urban areas used to be built before the invention of the automobile. Cities were built as dense urban environments with lots of life and vibrancy at street level with a mix of homes, shops and restaurants next to offices, schools and government buildings, surrounded by parks and public spaces, each one contributing to the dynamics of a high-quality urban fabric. The 10 Principles of New Urbanism are urban planning guidelines that can be applied to any project site of any size, from the small scale of a single building to the large metropolitan scale. I have created a point system to evaluate the international headquarters of Silicon Valley's Big Tech giants to see if these global tech companies are contributing to automobile-based suburban sprawl or to a pedestrian-friendly New Urbanist environment.
We establish the well-posedness of an initial-boundary value problem of mixed type for a stochastic nonlinear parabolic-hyperbolic equation on a space domain O=O′×O″ where a Neumann boundary ...condition is imposed on ∂O′×O″, the hyperbolic boundary, and a Dirichlet condition is imposed on O′×∂O″, the parabolic boundary. Among other points to be highlighted in our analysis of this problem we mention the new strong trace theorem for the special class of stochastic nonlinear parabolic-hyperbolic equations studied here, which is decisive for the uniqueness of the kinetic solution, and the new averaging lemma for the referred class of equations which is a vital part of the proof of the strong trace property. We also provide a detailed analysis of the approximate nondegenerate problems, which is also made here for the first time, as far as the authors know, whose solutions we prove to converge to the solution of our initial-boundary value problem.
We consider the generalized almost periodic homogenization problem for two different types of stochastic conservation laws with oscillatory coefficients and multiplicative noise. In both cases the ...stochastic perturbations are such that the equation admits special stochastic solutions which play the role of the steady-state solutions in the deterministic case. Specially in the second type, these stochastic solutions are crucial elements in the homogenization analysis. Our homogenization method is based on the notion of stochastic two-scale Young measure, whose existence is established here.
Idiopathic acute recurrent pancreatitis (IARP) is defined as at least two episodes of acute pancreatitis with the complete or near-complete resolution of symptoms and signs of pancreatitis between ...episodes, without an identified cause. There is a paucity of information about the usefulness of endoscopic ultrasound (EUS) in IARP.ObjectivesTo determine the diagnostic yield of EUS in IARP.DesignA retrospective study was performed in patients with IARP evaluated by EUS between January 2009 and December 2016. Follow-up assessments of acute pancreatitis recurrence were carried out.ResultsSeventy-three patients with 102 EUS procedures were included. EUS was able to identify the cause of IARP in 55 patients (75.3%). The most common findings were chronic pancreatitis in 27 patients (49.1%), followed by lithiasic pathology in 24 patients (43.6%), and intraductal papillary mucinous neoplasm in four patients (7.3%). A directed treatment against EUS findings had a protective tendency associated with the final resolution of recurrence. There were no complications reported.ConclusionEUS performed in patients with IARP helped to identify a possible cause in 2/3 of the cases. The majority of patients have a treatable disease.
Resumen El Nuevo Urbanismo americano es un enfoque de planificación y desarrollo urbano en EEUU, basado en cómo se han construido ciudades y pueblos antes de la invención del automóvil. Calles ...peatonalizadas, viviendas y tiendas en las proximidades, parques y espacios públicos accesibles junto a oficinas, escuelas y edificios gubernamentales. Cada uno contribuyendo a la dinámica de un tejido urbano de alta calidad. Los 10 Principios del Nuevo Urbanismo son un conjunto de principios aplicables a cualquier proyecto urbano, de cualquier escala, desde un edificio hasta la escala metropolitana. A continuación, os expongo un sistema de puntuación que he creado para evaluar y clasificar en un ranking las sedes internacionales de las grandes empresas tecnológicas de Silicon Valley para comprobar si estas grandes empresas tecnológicas contribuyen al Nuevo Urbanismo de ciudades peatonalizadas y densas, o favorecen la dispersión suburbana, dependiente del uso del automóvil. Abstract New Urbanism is an American urban planning and development approach based on the principles of how urban areas used to be built before the invention of the automobile. Cities were built as dense urban environments with lots of life and vibrancy at street level with a mix of homes, shops and restaurants next to offices, schools and government buildings, surrounded by parks and public spaces, each one contributing to the dynamics of a high-quality urban fabric. The 10 Principles of New Urbanism are urban planning guidelines that can be applied to any project site of any size, from the small scale of a single building to the large metropolitan scale. I have created a point system to evaluate the international headquarters of Silicon Valley's Big Tech giants to see if these global tech companies are contributing to automobile-based suburban sprawl or to a pedestrian-friendly New Urbanist environment.
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