SUMMARY Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The rst scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an eecient and relatively simple approach for solving two-dimensional spectral equations. Numerica...

In a paper in this journal (Nouvellet et al., 2010), we presented results from experiments on the behaviour of the Pharaoh's ant, Monomorium pharaonis, along with a substantial statistical and theoretical analysis of the results. In a minor part of our paper, we compared our results with the related work of Richardson et al. (2010a). These authors have subsequently commented on our interpretati...

magnetohydrodynamic (mhd) mixed convection flow of cu–water nanofluid inside a two-sided lid-driven square enclosure with adiabatic horizontal walls and differentially heated sidewalls has been investigated numerically. the effects of moving lids direction, variations of richardson number, hartmann number, and volume fraction of nanoparticles on flow and temperature fields have been studied. th...

Patients with corticobasal degeneration can present with several different clinical syndromes, making ante-mortem diagnosis a challenge. Corticobasal syndrome is the clinical phenotype originally described for corticobasal degeneration, characterized by asymmetric rigidity and apraxia, cortical sensory deficits, dystonia and myoclonus. Some patients do not develop these features, but instead ha...

According to Lewis Richardson, the likelihood of two nations engaging in conflict can be determined by a set of differential equations. Richardson conjectured that a nation’s probability of entering into an aggressive war is based upon its stockpiles of available weaponry, and tempered by the resistance of the citizenry. In the Richardson model, the likelihood of a small dispute erupting into a...

1. Introduction. One of the objections to the use of a one-step method to integrate a system of ordinary differential equations is that an estimate of the accumulated truncation error is difficult to make. If an attempt is made at appraising the truncation error, it is usually confined to an approximate evaluation of the local truncation error. A scheme for estimating the local truncation error...

A comparison is made between some conventional and new methods for detecting stars in crowded stellar images. The new methods are (1) Lucy-Richardson deconvolution of the image before detection, and (2) fitting the Point Spread Function to each pixel in the image. These methods are applied to both a synthetic image and a real one. The deconvolution method looks very promising, and gives better ...

Based on a generalized ordering ∝ on a set X, Schensted’s insertion mapping is defined on the set of words (W, ·) over the ordered alphabet (X,∝). In this general framework, a transparent approach to various versions of the Robinson-Schensted correspondence and of invariant properties originally due to Schützenberger, Knuth, White e.a. is obtained. Furthermore, eight combinatorial descriptions ...