Search results for "functional"

The Early Bird Gets The Word Games and Play: Creating a Context For Authentic Language Learning

2022

Early foreign language teaching has recently been made compulsory in Finland, making this an area open to development and innovation where policy - makers and teachers play a significant role in creating new kinds of learning environments, operating cultures, and pedagogy for foreign language learning. This article discusses the early foreign language learning landscape in the context of early foreign language learning theory, initial education pedagogy as well as functional foreign language learning. The cornerstone of this study is the Contextual Pedagogical approach to Learning, which creates a bridge between the theory and practice of early foreign language learning, creating an inspiri…

Copper Induces a Core Plasmon in Intermetallic Au(144,145)–xCux(SR)60 Nanoclusters

2015

The electronic structure and optical absorption spectra of intermetallic thiol-stabilized gold-copper clusters, having 144-145 metal atoms and 60 thiols, were studied by ab initio computations. The widely known icosahedral-based cluster model from the work of Lopez-Acevedo et al. (2009) was used, and clusters doped with one to 30 copper atoms were considered. When doped inside the metal core, copper induces dramatic changes in the optical spectrum as compared to the previously studied all-gold Au144(SR)60. An intense broad absorption peak develops in the range 535-587 nm depending on the amount of doping and doping sites. This result agrees very well with recent experiments by the Dass grou…

Single Crystal Sub‐Nanometer Sized Cu6(SR)6 Clusters: Structure, Photophysical Properties, and Electrochemical Sensing

2016

Organic ligand-protected metal nanoclusters have attracted extensively attention owing to their atomically precise composition, determined atom-packing structure and the fascinating properties and promising applications. To date, most research has been focused on thiol-stabilized gold and silver nanoclusters and their single crystal structures. Here the single crystal copper nanocluster species (Cu6(SC7H4NO)6) determined by X-ray crystallography and mass spectrometry is presented. The hexanuclear copper core is a distorted octahedron surrounded by six mercaptobenzoxazole ligands as protecting units through a simple bridging bonding motif. Density functional theory (DFT) calculations provide…

Stability, electronic structure, and optical properties of protected gold-doped silver Ag29−xAux (x = 0–5) nanoclusters

2017

In this work, we used density functional theory (DFT) and linear response time-dependent DFT (LR-TDDFT) to investigate the stability, electronic structure, and optical properties of Au-doped [Ag29-xAux(BDT)12(TPP)4]3- nanoclusters (BDT: 1,3-benzenedithiol; TPP triphenylphosphine) with x = 0-5. The aim of this work is to shed light on the most favorable doped structures by comparing our results with previously published experimental data. The calculated relative energies, ranging between 0.8 and 10 meV per atom, indicate that several doped Ag29-xAux nanoclusters are likely to co-exist at room temperature. However, only the Au-doped [Ag29-xAux(BDT)12(TPP)4]3- nanoclusters that have direct bon…

Direct P-functionalization of azobenzene by a cationic phosphidozirconocene complex.

2016

International audience; We report that the cationic phosphidozirconocene complex [(eta(5)-C5H5)(2)Zr(PCy2)][CH3B(C6F5)(3)] (II) reacts with azobenzene, resulting in the expedient formation of Zr complex (2) bound to a tridentate PNN ligand. This reaction proceeds by a mechanism of cooperative nucleophilic substitution of hydrogen. The intermediate sigma(H) adduct (1) has been characterized by NMR spectroscopy.

Functional a posteriori error estimates for boundary element methods

2019

Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.

A posteriori error control for Maxwell and elliptic type problems

2014

Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems

2019

The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Furthermore, a p…

Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems

2018

The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example. peerReviewed

Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type

2018

Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of Mihlin--H\"ormander type and wave propagator estimates of Miyachi--Peral type for $\mathscr{L}$ cannot be wider than the corresponding ranges for the Laplace operator on $\mathbb{R}^n$. The result applies to all sub-Laplacians on Carnot groups and more general sub-Riemannian manifolds, without restrictions on the step. The proof hinges on a Fourier integral representation for the wave propagator associated with $\mathscr{L}$ and nondegeneracy properties of the sub…