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 detailed form
that the errors of the solutions by Jordan elimination and by Gauss-Jordan elimination cannot
be essentially greater than the possible maximal errors of the solutions by back substitution
and by Gaussian elimination, respectively. Finally, the theoretical results are illustrated by
two numerical examples.
The research discusses the need to find the innovative structures and methodologies for developing Human Capital (HC) in Iraqi Universities. One of the most important of these structures is Communities of Practice (CoPs) which contributes to develop HC by using learning, teaching and training through the conversion speed of knowledge and creativity into practice. This research has been used the comparative approach through employing the methodology of Data Envelopment Analysis (DEA) by using (Excel 2010 - Solver) as a field evidence to prove the role of CoPs in developing HC. In light of the given information, a researcher adopted on an archived preliminary data about (23) colleges at Mosul University as a deliberate sample for t
... Show MoreWater supply and distribution networks play an important role in our daily activities. They make a substantial contribution to public health by providing potable water for public consumption and non-potable applications such as firefighters and other purposes such as irrigation. This study used ArcMap 10.8 and WaterGEMS CONNECT Edition update 1 version to create a hydraulic network model to simulate the pipes’ network. Detailed network information, including pipe lengths, layouts, and diameters, was given by the Baghdad Water Department. The TUF-2000H Handheld digital ultrasonic flow meter has been used to measure the water flows in the network’s source nodes. In eight junctions,
The main purpose of this investigation is to evaluate the concentrations of six essential metals (Na+, Mg2+, K+, Ca2+, Fe2+ and Zn2+) in saffron and a farm soil using the neutron activation analysis (NAA) as a nuclear spectrometry method. The stratified random sampling method was used here. The NAA results showed the well uptake of Mg2+, K+, Ca2+, Fe2+, and Zn2+ in saffron, which is lower than the toxicity range. Based on the contamination factor and geoaccumulation index, soil contamination levels were determined uncontaminated by Zn, moderately contaminated by Na+ and Fe2+, and strongly contamin
... Show MoreChronic lymphocytic leukaemia (CLL) patients display a highly variable clinical course, with progressive acquisition of drug resistance. We sought to identify aberrant epigenetic traits that are enriched following exposure to treatment that could impact patient response to therapy.
Epigenome-wide analysis of DNA methylation was performed for 20 patients at two timepoints during treatment. The prognostic significance of differentially methylated regions (DMRs) was assessed in independent cohorts of 139 and 1
Background: The purposes of this study were to determine the photogrammetric soft tissue facial profile measurements for Iraqi adults sample with class I normal occlusion using Standardized photographic techniques and to verify the existence of possible gender differences. Materials and methods: Eighty Iraqi adult subjects (40 males and 40 females) with an age ranged between 18-25 years having class I normal occlusion were chosen for this study. Each individual was subjected to clinical examination and digital standardized right side photographic records were taken in the natural head position which is mirror position which the patient looking straight into his eyes into the mirror mounted on the stand. The photographs were analyzed using A
... Show More The ï€ ï¤
Mixing ratios of ï€ ï§
transitions from low and high spin states populated from the nuclear reaction Ni Mg pn Y 80 39 58 28 ( , ) ï§ are calculated using a new method which we called it as Improved Analysis Method. The comparison of the results of experimental values,CST method, LST and adopted ï€ ï¤ mixing ratios with the results of the presented work confirm the validity of this method.