Error estimates in Sobolev spaces for interpolating thin plate splines under tension

AbstractThis paper discusses Lp-error estimates for interpolation by thin plate spline under tension of a function in the classical Sobolev space on an open bounded set with a Lipschitz-continuous boundary. A property of convergence is also given when the set of interpolating points becomes more and more dense

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Priprema kromatografskog medija iz alžirskog dijatomita

X-ray photoelectron spectrometry combined with FTIR spectroscopy, X-ray diffraction analysis (XRD), and scanning electron microscopy (SEM) allowed highlighting the different interactions of grafts or impregnated polymers on the mineral surface of diatomite obtained by treatment of raw diatomite under reflux with a 5 M solution of hydrochloric acid for 24 h. This acid treatment led to almost total elimination of organic impurities with a total decalcification of the diatomite, leading to its deferrization and partial dealumination, and the obtaining of a support with a homogeneous siliceous surface mainly constituted of Si−OH and Si−O−Si functional groups. The surface of the diatomite washed with HCl became totally saturated with PEG-20M and SE30 with respective impregnation rates of 5 and 2 %. However, the grafting and/or impregnation of this diatomite with octadecyltrichlorosilane (C18) and docosane (C22) led to the formation of perfectly homogeneous surfaces. This work is licensed under a Creative Commons Attribution 4.0 International License.Rendgenska fotoelektronska spektroskopija u kombinaciji s FTIR spektroskopijom, rendgenskom difrakcijskom analizom (XRD) i skenirajućom elektronskom mikroskopijom (SEM) omogućila je uvid u različite interakcije graftova ili impregniranih polimera na mineralnoj površini dijatomita dobivenih obradom sirova dijatomita pod refluksom 5 M otopine klorovodične kiseline tijekom 24 h. Navedena kiselinska obrada gotovo je u potpunosti uklonila organske nečistoće uz potpunu dekalcifikaciju dijatomita, deferizaciju i djelomičnu dealuminaciju, uz dobivanje kvarcne površine koja se uglavnom sastojala od funkcionalnih skupina Si−OH i Si−O−Si. Površina dijatomita isprana HCl-om u postala je u potpunosti zasićena PEG-20M-om i SE30-icom s impregnacijom od 5 odnosno 2 %. Graftiranje i/ili impregnacija dijatomita oktadeciltriklorosilanom (C18) i dokozanom (C22) dovela je do stvaranja savršeno homogenih površina. Ovo djelo je dano na korištenje pod licencom Creative Commons Imenovanje 4.0 međunarodna

Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles

Cette thèse porte sur des méthode de résolution d'équations matricielles appliquées à la résolution numérique d'équations aux dérivées partielles ou des problèmes de contrôle linéaire. On s'intéressen en premier lieu à des équations matricielles linéaires. Après avoir donné un aperçu des méthodes classiques employées pour les équations de Sylvester et de Lyapunov, on s'intéresse au cas d'équations linéaires générales de la forme M(X)=C, où M est un opérateur linéaire matriciel. On expose la méthode de GMRES globale qui s'avère particulièrement utile dans le cas où M(X) ne peut s'exprimer comme un polynôme du premier degré en X à coefficients matriciels, ce qui est le cas dans certains problèmes de résolution numérique d'équations aux dérivées partielles. Nous proposons une approche, noté LR-BA-ADI consistant à utiliser un préconditionnement de type ADI qui transforme l'équation de Sylvester en une équation de Stein que nous résolvons par une méthode de Krylox par blocs. Enfin, nous proposons une méthode de type Newton-Krylov par blocs avec préconditionnement ADI pour les équations de Riccati issues de problèmes de contrôle linéaire quadratique. Cette méthode est dérivée de la méthode LR-BA-ADI. Des résultats de convergence et de majoration de l'erreur sont donnés. Dans la seconde partie de ce travail, nous appliquons les méthodes exposées dans la première partie de ce travail à des problèmes d'équations aux dérivées partielles. Nous nous intéressons d'abord à la résolution numérique d'équations couplées de type Burgers évolutives en dimension 2. Ensuite, nous nous intéressons au cas où le domaine borné est choisi quelconque. Nous établissons des résultats théoriques de l'existence de tels interpolants faisant appel à des techniques d'algèbre linéaire.This thesis deals with some matrix equations involved in numerical resolution of partial differential equations and linear control. We first consider some numerical resolution techniques of linear matrix equation. In the second part of this thesis, we apply these resolution techniques to problems related to partial differential equations.DUNKERQUE-SCD-Bib.electronique (591839901) / SudocSudocFranceF

A fusion method for creating sub-hourly DNI-based TMY from long-term satellite-based and short-term ground-based irradiation data

International audienceIn order to correctly perform Concentrated Solar Power (CSP) plant electric energy output estimation, a standard approach is to consider Typical Meteorological Year (TMY) as a reference input data in CSP simulation software such as System Advisor Model or Greenius. These TMYs may be built from satellite derived irradiation databases. In order to correctly estimate the CSP electricity production, it is highly recommended to use sub-hourly DNI information. Due to limitation in spatial and temporal resolution of geostationary satellite images, satellite-based irradiation data lack good representativity in term of any sub-hourly temporal variability. To overcome this limitation, we propose an innovative fusion method to combine a one year short time series of ground-based sub-hourly irradiation data and the long-term satellite-based one to create calibrated, sub-hourly and long-term based TMY irradiation data. This method has been successfully applied in the planning of the CSP plant project in Morocco: one year and a half of high quality 10-minute irradiation data from pyranometric ground stations belonging to the Moroccan Agency for Solar Energy (MASEN) has been used with long-term hourly satellite-based irradiation data to create calibrated 10-minute DNI based TMY. The ground-based irradiation data have passed the standard quality check procedure recommended by the Baseline Solar Radiation Network for the World Climate Research Program. The satellite hourly irradiation data has been calibrated on a one year learning period of ground station data and this calibration has been verified on a subsequent half year ground station data. This calibration has been applied to the hourly long-term satellite irradiation time series from which a TMY was computed. The final and innovative step consists in introducing the site specific sub-hourly variability into the whole set of hourly daily profiles of irradiation of the TMY time series, as needed to obtain a better estimation of the CSP producible. The method uses the whole 10-minute measured irradiation data as a store of available days, normalized in terms of time between sunrise and sunset

Métastases cutanées révélant un adénocarcinome bronchique

Nous rapportons le cas d’un cancer bronchique révélé par des nodules cutanés métastatiques du cuir chevelu. Ce mode de découverte assez fréquent est souvent associé à un mauvais pronostic. Cette observation souligne l’intérêt de rechercher un cancer primitif pulmonaire en cas de localisation secondaire cutanée.English abstractWe report the case of bronchial carcinoma revealed by metastatic skin nodules on the scalp. This fairly common mode of discovery is often associated with poor prognosis. This study aims to underline the importance of directing the search for a primary lung cancer in cases of secondary skin involvement.Key words: Cutaneous metastases, bronchial adenocarcinoma, excisional biops

Explicit processing of verbal and spatial features during letter-location binding modulates oscillatory activity of a fronto-parietal network.

The present study investigated the binding of verbal and spatial features in immediate memory. In a recent study, we demonstrated incidental and asymmetrical letter-location binding effects when participants attended to letter features (but not when they attended to location features) that were associated with greater oscillatory activity over prefrontal and posterior regions during the retention period. We were interested to investigate whether the patterns of brain activity associated with the incidental binding of letters and locations observed when only the verbal feature is attended differ from those reflecting the binding resulting from the controlled/explicit processing of both verbal and spatial features. To achieve this, neural activity was recorded using magnetoencephalography (MEG) while participants performed two working memory tasks. Both tasks were identical in terms of their perceptual characteristics and only differed with respect to the task instructions. One of the tasks required participants to process both letters and locations. In the other, participants were instructed to memorize only the letters, regardless of their location. Time–frequency representation of MEG data based on the wavelet transform of the signals was calculated on a single trial basis during the maintenance period of both tasks. Critically, despite equivalent behavioural binding effects in both tasks, single and dual feature encoding relied on different neuroanatomical and neural oscillatory correlates. We propose that enhanced activation of an anterior–posterior dorsal network observed in the task requiring the processing of both features reflects the necessity for allocating greater resources to intentionally process verbal and spatial features in this task