In early numerical development, children have to become familiar with the Arabic number system and its place-value structure. The present review summarizes and discusses evidence for language influences on the acquisition of the highly transparent structuring principles of digital-Arabic digits by means of its moderation through the transparency of the respective language's number word system. ...

We propose a fast structured selected inversion method for extracting the diagonal blocks of the inverse of a sparse symmetric matrix A, using the multifrontal method and rank structures. When A arises from the discretization of some PDEs and has a low-rank property (the intermediate dense matrices in the factorization have small off-diagonal numerical ranks), structured approximations of the d...

The present paper is concerned with  the investigation of disturbances in a homogeneous  transversely isotropic thermoelastic rotating  medium with two temperatures, in the presence of the combined effects of   Hall currents and magnetic field due to thermomechanical sources. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi Theories of Type-II and Type-III. ...

Hyperspectral-multidirectional radiance observations of the land surface from space potentially form one of the richest sources of geobiophysical information possible. For soil-vegetation objects, the retrieval of this information can be simulated by radiative transfer modelling. In combination with a couple of atmospheric parameters, the surface reflectance model SLC (soil-leaf-canopy) has mor...

We show how certain widely used multistep approximation algorithms can be interpreted as instances of an approximate Newton method. It was shown in an earlier paper by the second author that the convergence rates of approximate Newton methods (in the context of the numerical solution of PDEs) suuer from a \loss of derivatives", and that the subsequent linear rate of convergence can be improved ...

We present a Newton-CG method for full-waveform seismic inversion. Our method comprises the adjoint-based computation of the gradient and Hessianvector products of the reduced problem and a preconditioned conjugate gradient method to solve the Newton system in matrix-free fashion. A trust-region globalization strategy and a multi-frequency inversion approach are applied. The governing equations...

In this article, we have effectively used the Numerical Inversion of Laplace transform to study the time-dependent thin film flow of a second grade fluid flowing down an inclined plane through a porous medium. The solution to the governing equation is obtained by using the standard Laplace transform. However, to transform the obtained solutions from Laplace space back to the original space, we ...

A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data...

We present an overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process (BMAP). The BMAP encompasses a wide range of arrival processes and yet, mathematically, the BMAP/G/I model is a relatively simple matrix generalization of the M/G/l queue. Stationary and transient distributions for t...

This paper discusses simulation from an absolutely continuous distribution on the positive real line when the Laplace transform of the distribution is known but its density and distribution functions may not be available. We advocate simulation by the inversion method using a modified Newton-Raphson method, with values of the distribution and density functions obtained by numerical transform in...