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

En torno a Rafael de Ballerna, un desconocido platero vitoriano: su testamento

El estudio se centra en Rafael de Ballerna, platero vitoriano activo en el siglo XVIII. El hallazgo de tres importantes documentos inéditos de este platero -poder para testar, testamento, e inventario de bienes- constituyen una fuente inapreciable para conocer a éste y a otros importantes plateros vitorianos del siglo XVIII. Las creencias y religiosidad en las que se desenvolvía su vida, quedan ahora perfiladas tras el análisis de los textos. Se aportan numerosos docu-mentos relacionados con su oficio.Rafael de Ballerna-z, XVIII. mendean lan egin zuen Gasteizko zilargileaz dihardu lan honek. Ballernaren hiru dokumentu garrantzitsu -testamentu egiteko ahalordea, testamentua eta ondasunen inbentarioa- aurkitu izana albiste-iturri guztiz garrantzitsua gertatu da, bai zilargile hori eta bai XVIII. mendeko Gasteizko beste zilargile gailen batzuk ezagutzeko. Horien bizitza inguratzen zuten sinesteak eta erlijiozkotasuna agerian azaltzen dira orain, testuak aztertu ondoren. Lanbide horrekin zerikusia duten dokumentu askoren ekarpena burutu da.L'étude est centrée sur Rafael de Ballerna, orfèvre de Vitoria en activité au XVIIIème siècle. La découverte de trois importants documents inédits de cet orfèvre -pouvoir pour tester, testament, et inventaire des biens- constituent une source inappréciable pour la connaissance de cet orfèvre, ainsi que de beaucoup d'autres, tout aussi importants, de Vitoria au XVIIIème siècle. Les croyances et la religiosité au sein desquels sa vie s'est déroulée sont maintenant esquis -sées après analyse des textes. On apporte de nombreux documents en relation avec son métier.This study is centred on Rafael de Ballerna, a silversmith from Vitoria who was active in the 18th century. The finding of three important unpublished documents by this silversmith - the powers to make testament, the testament, and his inventory of pro p e rties - constitute an invaluable source to understand his life and other important silversmiths in 18th century Vitoria. The beliefs and religiousness in which he led his life, are outlined after the analysis of the texts. This study includes numerous documents related to his trade

La Real Escuela de Platería "Martínez "de Madrid y su relación con la Escuela de Dibujo en Álava

Con esta comunicación pretendemos poner de manifiesto la influencia que la Escuela de Platería Martínez ha tenido en el País Vasco, con la temprana introducción del Neoclasicismo, a través de las Escuelas de Dibujo de la Real Sociedad Bascongada de los Amigos del País. El aprendizaje de los tres pensionados vascos enviados por la Sociedad a la escuela Martínez tuvo una gran repercusión en la platería local. Las obras conservadas en Álava, nos permiten seguir la evolución de la Platería Martínez, desde su fundación por el platero Antonio Martínez, a su regreso de París y Londres e instalación de la Escuela de Platería de Madri d,con las diferentes etapas por las que atravesó la Real Fábrica de Platería, después de su muerte.Komunikazio honen bidez agerian jarri nahi dugu Escuela de Platería Martínez delakoak (Martínez Zilargintza Eskola) Euskal Herrian izan duen eragina, Neoklasizismoa garai goiztiarrean sartu baitzuen gure lurraldean, Euskalerriaren Adiskideen Elkartearen Marrazki Eskolen bidez. Elkarteak Martínez Eskolara bidalitako hiru pentsiodunen ikasketak eragin handia izan zuen bertako zilargintzan. Araban kontserbaturiko obrek Martínez Zilargintzak izan zuen bilakaera jarraitzeko ahalbidea ematen digute, Antonio Martínez zilarginak sortu zuenetik, Paris eta Londresetik itzuli eta Zilargintza Eskola Madrilen jarri zuenetik, bai eta hura hil ondoren Real Fábrica de Platería-k (Zilargintza Errege Fabrika) izan zituen aldi desberdinak hautemateko ere.Par cette communication,nous prétendons mettre en évidence l'influence que l'Ecole d'Orfèvrerie Martínez a eu dans le Pays Basque,avec l'introduction précoce du Néoclassicisme,à travers les Ecoles de Dessin de la Real Sociedad Bascongada de los Amigos del País (Société Royale Basque des Amis du Pays). L'apprentissage des trois pensionnaires basque envoyés par la Société à l'école Martínez eut une grande répercussion sur l'orfèvrerie locale. Les oeuvres conservées en Alava nous permettent de suivre l'évolution de l'Orfèvrerie Martínez, depuis sa fondation par l'orfèvre Antonio Martínez, jusqu'à son retour de Paris et Londres et l'installation de l'Ecole d'Orfèvrerie de Madrid, avec les différentes étapes traversées par la Real Fábrica de Platería (Fabrique Royale d 'Orfèvrerie), après sa mort.With this communication we intend to show the influence that the Martinez Silversmith School in Madrid had in the Basque Country, with the early introduction of Neo-classicism, through the Drawing Schools of the Real Sociedad Bascongada de Amigos del País (Royal Basque Society of Friends of the Country). The training of the three Basque pensioners sent by the Society to the Martinez School had a great repercussion in local silversmithery. The works preserved in Álava allow us to follow the evolution of the Martínez Silversmithery, from its foundation by silversmith Antonio Martínez. Martinez founded this school upon his return from Paris and London and after settling down near the Silversmith School in Madrid, including the different stages followed by the Real Fábrica de Platería (Royal Silversmithery Factory), after his death

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.Comment: 10 pages, 10 figure

Work and Art: Artistic Contracts of Silverware in the 18 th - 19 th centuries

[Resumo] Con este estudo queremos contribuír a un maior coñecemento de como as relacións xurídico-laborais están presentes desde antigo a través dos contratos artísticos de aprendizaxe na ordenación do traballo e nos contratos das obras na arte da prataría dos ss. XVIII-XIX. De igual maneira buscamos achegarnos á consideración social do traballo dos artistas representado en miniaturas, gravados ou pinturas.[Abstract] With this study we want to contribute to a better understanding of how relations under employment law are present since ancient times through artistic learning contracts in the work organization and in the work contracts in the art of silverware during the 18th-19th centuries. In the same way, we seek to explore the social consideration of the work of artists represented in miniatures, engravings or paintings

Existence, uniqueness and numerical solution of a fractional PDE with integral conditions

This paper is devoted to the solution of one-dimensional Fractional Partial Differential Equation (FPDE) with nonlocal integral conditions. These FPDEs have been of considerable interest in the recent literature because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. Existence and uniqueness of the solution of this FPDE are demonstrated. As for the numerical approach, a Galerkin method based on least squares is considered. The numerical examples illustrate the fast convergence of this technique and show the efficiency of the proposed method

On the stability of θ\theta-methods for DDEs and PDDEs

In this paper, the stability of $\theta$-methods for delay differential equations is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay and $A$ is a positive definite matrix. It is mainly considered the case where the matrices $A$ and $B$ are not simultaneosly diagonalizable and the concept of field of values is used to prove a sufficient condition for unconditional stability of these methods and another condition which also guarantees their stability, but according to the step size. The results obtained are also simplified for the case where the matrices $A$ and $B$ are simultaneously diagonalizable and compared with other similar works for the general case. Several numerical examples in which the theory discussed here is applied to parabolic problems given by partial delay differential equations with a diffusion term and a delayed term are presented, too.Comment: 17 pages, 21st IMACS World Congres

Evaluando la aplicación de Lean Six Sigma en la Industria Creativa: el caso de una empresa española en un país islámico

The presence of cultural, creative and experiential projects in several Islamic countries evidences that the characterization of their main dimensions in diverse operational processes is a very interesting research question. From a comparative perspective, the application of Lean Six Sigma in the context of cultural institutions and organizations shows the usefulness to intervene on certain variables at different levels of management performance. This paper aims: 1) to describe the characterization of Lean Six Sigma as a set of techniques providing positive outcomes in the creative industry; and 2) to evaluate empirically the main dimensions for success of these core processes at a museum in an Islamic country. Firstly, this research describes a review of those approaches and secondly a rigorous managerial process is presented and validated. The results and conclusions of this research are relevant in decisions of cultural policy, but also on the operational practice and management theory in the scope of this study.La existencia de proyectos culturales, creativos y experimentales en diversos países islámicos refleja que caracterizar sus dimensiones principales en los procesos operativos es una interesante pregunta de investigación. Desde una perspectiva comparada, aplicar Lean Six Sigma en instituciones y organizaciones culturales evidencia la utilidad de intervenir en ciertas variables, a distintos niveles de gestión. Este trabajo tiene como objetivo: 1) caracterizar Lean Six Sigma como un conjunto de técnicas que proporcionan resultados positivos en la industria creativa; y 2) evaluar empíricamente las dimensiones principales para el éxito de estos procesos centrales en un museo de un país islámico. En primer lugar, esta investigación describe una revisión de esos enfoques y, en segundo lugar, se presenta y valida su proceso de gestión. Los resultados y conclusiones de este estudio resultan relevantes en las decisiones de política cultural, pero también en la práctica operacional y la teoría del management en el alcance de este estudio