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.
Purpose: aims the study to show How to be can to enhance measurement management by incorporating a risk-based approach and the six sigma method into a more thorough assessment of metrological performance. Theoretical framework: Recent literature has recorded good results in analyzing the impact of Six Sigma and risk management on the energy sector (Barrera García et al., 2022) (D'Emilia et al. 2015). However, this research came to validate and emphasize the most comprehensive assessment of metrological performance by integrating Risk management based approach and Six Sigma analysis. Design/methodology/approach: This study was conducted in Iraqi petroleum refining companies. System quality is measured in terms of sigmas, and t
... Show MoreFifty five surface and subsurface soil samples were taken from the area between Tigris and Euphrates Rivers along the Main Drain course from north Baghdad to Basrah to evaluate the geochemical, physical characteristics and the probability contamination of these samples. The study area is covered by Quaternary sediments of complex alternation of sand, silt and clay. Significant variation in the textural content of the present soils is observed, where the northern and southern parts are characterized by silt predominance, while sand is prevailing in the central parts as a result of the extensive spreading of aeolian deposits represented mostly by sand dunes. Mineralogical analysis explains wide variations in the heavy minerals distribution
... Show MoreBackground: Dental implants provide a unique treatment modality for the replacement of a lost dentition .This is accomplished by the insertion of relatively an inert material (a biomaterial) into the soft and hard tissue of the jaws, there by providing support and retention for dental prostheses. Low level laser therapy (LLLT) is an effective tool used to prompt bone repair and remodeling, this has referred to the biostimulation effect of LLLT. The Aim of this study was to evaluate the effects of inflammatory cells on osseointegration of CpTi implant irradiated by low level laser. Materials and Methods: thirty two adult New Zealand white rabbits, received titanium implants were inserted in the tibia. The right side is considered as experime
... Show MoreTransportation Sector classified as one of the services sectors which is without the production activities cannot be complete its rule. Is act asmoving actions which operate at production and non production goals for the organization and individuals insides the country and with others, that is why this sector act as one of the main which is occupied an important status on the way the economic activities and on the level of the economic institutions the transportation work on transforming all the commodities and products from productions locations to consumption location then its effect the productivity process and create the location utility and on the level of economic it considered as one of the economic supportive structure an
... Show MoreAl-Rustamiyah plant is the oldest and biggest sewage treatment plant in Iraq; it locates in the south of Baghdad city. The plant suffers from serious problems associated with overflow and low capacity. The present work aims to upgrade the heart of biological treatment process through suggesting the use of membrane bioreactor; (MBR). In this work, fouling of membrane during sewage treatment has been analyzed experimentally and theoretically by fouling mechanisms. Aeration has been applied in order to control fouling through producing effective diameters of air bubbles close to the membrane walls. Effect of air flow rate on flux decline was investigated. Hermia's models were used to investigate the fouling mechanisms. The results showed th
... Show MoreThe application of low order panel method with the Dirichlet boundary condition on complex aircraft configuration have been studied in high subsonic and transonic speeds. Low order panel method has been used to solve the case of the steady, inviscid and compressible flow on a forward swept wing – canard configuration with cylindrical fuselage and a vertical stabilizer with symmetrical cross section. The aerodynamic coefficients for the forward swept wing aircraft were calculated using measured wake shape from an experimental work on same model configuration. The study showed that the application of low order panel method can be used with acceptable results
This paper presents a numerical analysis of the piled-raft foundation (PRF) based on the actual behavior of supporting piles. The raft was modeled as a thin plate, while the piles were modeled as springs in different ways. This research also aims to propose an analytical model of piles based on actual behavior at fieldwork. The results proved that the structural behavior of raft member can be improved through utilizing the actual behavior of supporting piles. When the piles were modeled as non-linear stiffness springs, settlements and bending stresses of raft foundation were reduce marginally as compared with those obtained from piles with linear stiffness springs.
The significance of the research conducted in northern Iraq comes despite the expansion of afforestation projects; yet, the suffering of the forests has increased due to their lack of scientific study, unpredictability of the climate, and adverse effects on the spread and growth of plant species Therefore, the goal of the study is to understand the effects of afforestation through a statistical analysis of plant diversity in northern Iraq and its distinctivenessThe analysis revealed that natural groupings had improved qualitatively more than other groups, particularly some dwindling species that are able to compete and occupy new areas. drought-prone vegetation, vegetation, and climat
This research dealt with study of cladistics taxonomy of five species related to the genus Rumex L. and Polygonum L. from family polygonaceae in Iraq by using Mesquite software V.2.75. This research support strongly delimiting the species P. aviculare L. and P. lapathifolia L.as suggested in floras publication while R. dentatus L. is setted in single group whereas R. vesicarius L. and R. conglomeratus Murray were included in the same group. Also, this study involved characteristics of shape, dimensions, color, and ornamentation of seeds and fruits as the seed forms were ranging from lenticular to trigonous. In terms of size calculations, the seeds of R. vesicarius was recorded the higher range (4.0- 4.5) mm in length w
... Show MoreThe current research aims to analyze the chemistry books for the preparatory stage according to life skills for the academic year (2019-2020) and to know the life skills contained in the chemistry books for the preparatory stage through the following two questions:1-What life skills should be available in the content of chemistry books prescribed for middle school students approved by the Ministry of Education, General Directorate of Curricula in the academic year(2019-2020). 2-What is the percentage of life skills included in the content of chemistry textbooks prescribed for middle school students approved by the Ministry of Education, General Directorate of Curricula in the academic year (2019-2020). To achieve the objectives of the resea
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