Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at the boundaries. The Chebyshev method is found to be more efficient. © 2009 IMACS. Published by Elsevier...

: This study investigated the impact of audio-visual input enhancement teaching techniques on improving English as Foreign Language (EFL) learnersˈ collocation learning as well as their accuracy concerning collocation use in narrative writing. In addition, it compared the impact and efficiency of audio-visual input enhancement in two learning contexts, namely traditional and mo...

The use of L1 regularisation for sparse learning has generated immense research interest, with many successful applications in diverse areas such as signal acquisition, image coding, genomics and collaborative filtering. While existing work highlights the many advantages of L1 methods, in this paper we find that L1 regularisation often dramatically under-performs in terms of predictive performa...

A goal of second language (L2) learning is to enable learners to understand and speak L2 words without mediation through the first language (L1). However, psycholinguistic research suggests that lexical candidates are routinely activated in L1 when words in L2 are processed. In this article we describe two experiments that examined the acquisition of L2 lexical fluency. In Experiment 1, two gro...

The aim of this talk is to present highly stable collocation based numerical methods for Volterra Integral Equations (VIEs). As it is well known, a collocation method is based on the idea of approximating the exact solution of a given integral equation with a suitable function belonging to a chosen finite dimensional space, usually a piecewise algebraic polynomial, which satisfies the integral ...

We evaluate the performance of global stochastic collocation methods for solving nonlinear parabolic and elliptic problems (e.g., transient and steady nonlinear di↵usion) with random coe cients. The robustness of these and other strategies based on a spectral decomposition of stochastic state variables depends on the regularity of the system’s response in outcome space. The latter is a↵ected by...

In this paper we propose a non-polynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order α, 0 < α < 1. The approach used is based on the equivalence between a problem of this type and a Fredholm integral equation of a particular form. Taking into account the asymptotic behaviour of the solution of this problem, we p...

background: l1 retrotransposons are the most active mobile dna elements in human genome. unregulated l1 retrotransposition may have deleterious effect by disrupting vital genes and inducing genomic instabilities. therefore, human cells control l1 elements by silencing their activities through epigenetic mechanisms. it has been shown that cell division and heavy metals stimulate the frequency of...

The immense explosion of geographically referenced data calls for efficient discovery of spatial knowledge. Spatial association analysis is a typical data mining approach for discovering spatial knowledge. Associate rules are patterns of form X→Y, where pattern Y is likely to occur when pattern X occurs. One of the most famous patterns, Diapers → Beer, is a typical association rule example. Spa...