The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very

Samples of tea leaves (Green tea, Gugarate tea and Black tea used commonly in Iraq) are dried, grinded, pressed and submitted for the elemental analysis by x-ray fluorescence technique (XRF). The concentrations of major, minor and trace elements are determined. The major elements were Na, Mg, Al, K, Si, Ca, Mn, Fe, S and P. Of these elements, Ca, concentration in Gugarate tea leaves is three times, it's level in the other types of tea. Titanium, Cl, Rb and Sr are found as minor elements, while other elements such as Cu, Zn, V, Cr, Co, ...etc are found as trace elements. Of these trace elements considerable concentration values are found for some toxic elements Hg, Cd, Pb and As. Green tea contains 1.1 ppm Hg and 4.4 ppm Pb. Gugarate tea

Translating culture-specific proverbs (CSPs) is a challenging task since they often occur in a peculiar context. Further, CSPs are intended to imply meanings that extend far beyond the literal meaning of such a kind of proverbs. As far as English and Arabic are concerned, translators often encounter problems in translating CSPs due to cultural differences between the source language(SL) and the target language (TL) as well as what seems to be the lack of equivalence for some CSPs.

In view of this, the present study aims at investigating the translation of CSPs in three English-Arabic dictionaries of proverbs, namely Dictionary of Common English Proverbs Translated and Explained (2004), One thousand and One English Pr

Geotechnical engineers have always been concerned with the stabilization of slopes. For this purpose,
various methods such as retaining walls, piles, and geosynthetics may be used to increase the safety factor of slopes prone to failure. The application of stone columns may also be another potential alternative for slope stabilization. Such columns have normally been used for cohesive soil improvement. Most slope analysis and design is based on deterministic approach i.e a set of single valued design parameter are adopted and a set of single valued factor of safety (FOS) is determined. Usually the FOS is selected in view of the understanding and knowledge of the material parameters, the problem geometry, the method of analysis and the

A theoretical analysis of mixing in the secondary combustion chamber of ramjet is presented. Theoretical investigations were initiated to insight into the flow field of the mixing zone of the ramjet combustor and a computer program to calculate axisymmetric, reacting and inert flow was developed. The mathematical model of the mixing zone of ramjet comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy and its dissipation rate. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variable at all internal grid nodes.
The results showed that increasing air mass flow (0.32 to 0.64 kg/s) increases the development o

Characterization is commonly known in stylistics to be the cognitive process in the readers' minds when comprehending a fictional character in a literary work .In one approach, it is assumed that characters are the outcome of the interaction between the words in the text on the one hand and the contents of our heads on the other. This paper is an attempt to understand how characterization is achieved by applying Culpeper’s (2001) model which seems to be to present a method of analysis that is more objective and more systematic in analyzing characters. Two characters are selected for discussion; Ralph and Jack from Golding’s (1954) Lord of the Flies. The novel talks about the corruption of human beings and the capacity of evil th

The aim: to evaluate combined microscopy techniques for determining the morphological and optical properties of methadone hydrochloride (MDN) crystals. Materials and methods: MDN crystal formation was optimized using a closed container method and crystals were characterized using polarized light microscope (PLM), scanning electron microscopy (SEM) and confocal microscopy (CM). SEM and CM were used to determine MDN crystal thickness and study its relationship with crystal retardation colours using the Michel-Levy Birefringence approach. Results: Dimensions (mean±SD) of diamond shaped MDN crystals were confirmed using SEM and CM. Crystals were 46.4±15.2 Vs 32.0±8.3 µm long, 28.03±8.2 Vs 20.85±5.5 µm wide, and 6.62±

The production and analysis of an optimal interference pattern for the optical fiber interferometer of a 193.1THz continuous laser source was simulated by comparing the spectral spectroscopy of the two arms of interferometer to be used as a heterodyne detection in sensing the body range, speed, and direction of movement by delaying the time between the arms.

     The study showed that the fringe pattern can be sensed a range by the free spectral range FSR and the velocity by the fringe separation FS and the direction by the fringe spatial frequency FSF.

This study was chosen because of the entry of our regions into the seismic zone recently, where Diyala governorate was hit by the Halabja earthquake in 2017 by 7.3Mw. Therefore, the impact of earthquakes will be studied on the AL-Mafraq bridge foundations piles located in Iraq- east of Baghdad in Diyala Governorate and the extent of its resistance to the Halabjah, EL-Centro, and Kobe earthquakes with acceleration 0.1g, 0.34g, and 0.58g respectively. After modeling and performing the analysis by using Midas Gts-Nx software, the settlement (mm) results at nine nodes (four nodes for the pile cap and five nodes for the piles) were obtained for each of Halabjah, EL-Centro, and Kobe earthquakes to know the resistance of the br