On the numerical stability of Fourier extensions

An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically fast in the truncation parameter. Unfortunately, computing a Fourier extension requires solving an ill-conditioned linear system, and hence one might expect such rapid convergence to be destroyed when carrying out computations in finite precision. The purpose of this paper is to show that this is not the case. Specifically, we show that Fourier extensions are actually numerically stable when implemented in finite arithmetic, and achieve a convergence rate that is at least superalgebraic. Thus, in this instance, ill-conditioning of the linear system does not prohibit a good approximation. In the second part of this paper we consider the issue of computing Fourier extensions from equispaced data. A result of Platte, Trefethen & Kuijlaars states that no method for this problem can be both numerically stable and exponentially convergent. We explain how Fourier extensions relate to this theoretical barrier, and demonstrate that they are particularly well suited for this problem: namely, they obtain at least superalgebraic convergence in a numerically stable manner

Propagation studies for the construction of atomic macro-coherence in dense media as a tool to investigate neutrino physics

In this manuscript we review the possibility of inducing large coherence in a macroscopic dense target by using adiabatic techniques. For this purpose we investigate the degradation of the laser pulse through propagation, which was also related to the size of the prepared medium. Our results show that, although adiabatic techniques offer the best alternative in terms of stability against experimental parameters, for very dense media it is necessary to engineer laser-matter interaction in order to minimize laser field degradation. This work has been triggered by the proposal of a new technique, namely Radiative Emission of Neutrino Pairs (RENP), capable of investigating neutrino physics through quantum optics concepts which require the preparation of a macrocoherent state.Ministerio de Economía y Competitividad (Spain) FIS2014-53371-C4-3-RMinisterio de Economía y Competitividad (Spain) FIS2014-53371-C4-1-

Numerical schemes for general Klein–Gordon equations with Dirichlet and nonlocal boundary conditions

In this work, we address the problem of solving nonlinear general Klein–Gordon equations (nlKGEs). Different fourth- and sixth-order, stable explicit and implicit, finite difference schemes are derived. These new methods can be considered to approximate all type of Klein–Gordon equations (KGEs) including phi-four, forms I, II, and III, sine-Gordon, Liouville, damped Klein–Gordon equations, and many others. These KGEs have a great importance in engineering and theoretical physics.The higher-order methods proposed in this study allow a reduction in the number of nodes, which might also be very interesting when solving multi-dimensional KGEs. We have studied the stability and consistency of the proposed schemes when considering certain smoothness conditions of the solutions. Additionally, both the typical Dirichlet and some nonlocal integral boundary conditions have been studied. Finally, some numerical results are provided to support the theoretical aspects previously considered

Synthesis of new conjugated mesomeric betaines from alkoxycarbonylazinium salts

A new series of conjugated mesomeric betaines have been synthesized from the reaction of various aminoheterocycles with 2-methylthio-4-oxo-3-phenylpyrido[2,1-φ][1,2,4]triazinium iodide, itself prepared from 2-ethoxycarbonylpyridinium N-aminide. Some of the heterobetaines and salts obtained have been studied by 1H-NMR, and their structures have been confirmed by X-ray analysis. The crystal structures reveal unexpected complementary stabilizing interactions between some betaines and their salts.We wish to express our thanks to the Comisió Interdepartamental de Reçerca i Innovació Tecnológica (CIRIT) for financial support (Project QFN94-4619) and to the Ministerio de Educación y Ciencia for a grant to one of us (JVM)

Evaluación de Competencias Matemáticas en titulaciones de Ciencias e Ingeniería

Memoria ID-027. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2018-2019

Las matemáticas en la ingeniería actual: aprendizaje basado en problemas y competencias

Memoria ID-0096. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2017-2018

Adaptación de recursos y contenidos y utilización de nuevas herramientas en la docencia en ingeniería industrial

Memoria ID-032. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2013-2014

Nanostructured porous silicon micropatterns as a tool for substrate-conditioned cell research

The localized irradiation of Si allows a precise patterning at the microscale of nanostructured materials such as porous silicon (PS). PS patterns with precisely defined geometries can be fabricated using ion stopping masks. The nanoscale textured micropatterns were used to explore their influence as microenvironments for human mesenchymal stem cells (hMSCs). In fact, the change of photoluminescence emission from PS upon aging in physiological solution suggests the intense formation of silanol surface groups, which may play a relevant role in ulterior cell adhesion. The experimental results show that hMSCs are sensitive to the surface micropatterns. In this regard, preliminary β-catenin labeling studies reveal the formation of cell to cell interaction structures, while microtubule orientation is strongly influenced by the selective adhesion conditions. Relevantly, Ki-67 assays support a proliferative state of hMSCs on such nanostructured micropatterns comparable to that of standard cell culture platforms, which reinforce the candidature of porous silicon micropatterns to become a conditioning structure for in vitro culture of hMSCsThe authors gratefully acknowledge the financial support from MICINN under research project MAT2008-06858-C02-01/NAN and Comunidad de Madrid (Spain) under Project Microseres. Technical support from L García Pelayo is greatly appreciate

Herramienta interdisciplinar para estudiantes de ingeniería

Memoria ID12-0228. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2012-2013

Desarrollo de herramientas y adecuación de contenidos para docencia virtual

Memoria ID-0272. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2014-2015