In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior

the structrual and mechanical properties of thin Ni films of different thicknesses deposited on coring glass substrate using lonbeam sputtering(IBS) technique under vacuum torr have been studied the TEM and electron

This conducted research,  (The Scientific Efforts of Ahmed Mustafa Al-Maraghi) deals with Al-Maraghi's life, birth, upbringing, characteristics, title, family and religion secter, as well as his general biography. And his relationship with scholars, his learning and teaching, and the introduction of the Muhammed Abdo School and the College of Dar Al Uloom, and finally the discussion  of his scientific, social and political poin of view, as an interpreter of twentieths century, was  appointed as the president of Al-Azhar and Ifta during the days of the royal era, and he studied at the College of Dar Al-Uloom

Assume that G is a finite group and X = tG where t is non-identity element with t3 = 1. The simple graph with node set being X such that a, b ∈ X, are adjacent if ab-1 is an involution element, is called the A4-graph, and designated by A4(G, X). In this article, the construction of A4(G, X) is analyzed for G is the twisted group of Lie type 3D4(3).