Search results for "numerical"
showing 10 items of 2002 documents
Teaching Early Mathematical Skills to 3- to 7-Year-Old Children — Differences Related to Mathematical Skill Category, Children’s Age Group and Teache…
2022
Abstract This study explored teaching early mathematical skills to 3- to 7-year-old children in early childhood education and care (ECEC) and pre-primary education. Teachers in ECEC (N = 206) answered a web survey. The first aim was to determine whether teaching frequency or pedagogical awareness of teaching early mathematical skills varied according to the category of skills (numerical skills, spatial thinking skills and mathematical thinking and reasoning skills) and whether children’s age group moderated these differences. The second aim was to explore to what extent teacher-related characteristics and children’s age group explained variations in teaching frequency concerning early mathe…
On a nonlinear Schrödinger equation for nucleons in one space dimension
2021
We study a 1D nonlinear Schrödinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied numerically via the time evolution of perturbed ground states. In the time evolution of general localized initial data, they are shown to appear in the long time behaviour of certain cases.
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.
C1,α-regularity for variational problems in the Heisenberg group
2017
We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group and prove the H\"older continuity of horizontal gradient of minima.
Multi-marginal entropy-transport with repulsive cost
2020
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the $\Gamma$-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.
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
Group Identities on Units of Group Algebras
2000
Abstract Let U be the group of units of the group algebra FG of a group G over a field F . Suppose that either F is infinite or G has an element of infinite order. We characterize groups G so that U satisfies a group identity. Under the assumption that G modulo the torsion elements is nilpotent this gives a complete classification of such groups. For torsion groups this problem has already been settled in recent years.
The action of a compact Lie group on nilpotent Lie algebras of type {{n,2}}
2015
Abstract We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO 2 ( ℝ ) ${{\mathrm{SO}}_{2}(\mathbb{R})}$ . This is the first step to extend the class of nilpotent Lie algebras 𝔥 ${{\mathfrak{h}}}$ of type { n , 2 } ${\{n,2\}}$ to solvable Lie algebras in which 𝔥 ${{\mathfrak{h}}}$ has codimension one.
Testing the nature of the Λ(1520)-resonance in proton-induced production
2006
The $\Lambda(1520)$ resonance has been recently studied in a unitarized coupled channel formalism with $\pi\Sigma(1385)$, $K\Xi(1530)$, $\bar{K}N$ and $\pi\Sigma$ as constituents blocks. We provide a theoretical study of the predictions of this model in physical observables of the $pp\to pK^+K^-p$ and $pp\to pK^+\pi^0\pi^0\Lambda$ reactions. In particular, we show that the ratio between the $\pi^0\pi^0\Lambda$ and $K^-p$ mass distributions can provide valuable information on the ratio of the couplings of the $\Lambda(1520)$ resonance to $\pi\Sigma(1385)$ and $\bar{K}N$ that the theory predicts. Calculations are done for energies which are accessible in an experimental facility like COSY at …
Impurity behaviour in JET-ILW plasmas fuelled with gas and/or with pellets: a comparative study with the transport code COREDIV
2021
Abstract This study deals with the comparison of impurity behaviour in pellet and gas fuelled JET-ITER like wall pulses with the aim of finding the mechanisms leading to the generally observed higher concentration of tungsten in pellet fuelled plasmas. In fact, tungsten is the main high-Z impurity in the JET-ILW plasmas and is responsible for most of the radiative losses in the plasma core. Analysis of the experimental data pertaining to pulses at different plasma currents, different input power and different electron densities is integrated by numerical modelling with the self-consistent fluid transport code COREDIV. Experimentally, and numerically, the ratio between the radiated power in …