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.
This study aims to design unified electronic information system to manage students attendance in Lebanese French university/Erbil, as a system that simplifies the process of entering and counting the students absence, and generate absence reports to expel students who passed the acceptable limit of being absent, and by that we can replace the traditional way of using papers to count absence, with a complete electronically system for managing students attendance, in a way that makes the results accurate and unchangeable by the students.
In order to achieve the study's objectives, we designed an information syst
... Show MoreThere has been a growing interest in the use of chaotic techniques for enabling secure communication in recent years. This need has been motivated by the emergence of a number of wireless services which require the channel to provide low bit error rates (BER) along with information security. The aim of such activity is to steal or distort the information being conveyed. Optical Wireless Systems (basically Free Space Optic Systems, FSO) are no exception to this trend. Thus, there is an urgent necessity to design techniques that can secure privileged information against unauthorized eavesdroppers while simultaneously protecting information against channel-induced perturbations and errors. Conventional cryptographic techniques are not designed
... Show MoreAjloun Governorate is considered the smallest governorate in Jordan in terms of area, and its population density rises to 472.2 people/ km2 and is distributed among five municipalities. The Al-Shafa municipality is one of these municipalities. Al-Shafa is rich in its natural and human resources, and the first municipal council was established in it in 2001.
This study seeks to achieve the following general objective: inventory the natural and human resources that Al-Shafa enjoys, and highlight the role of Al-Shafa municipality in achieving and settling sustainable development for the local community. Certain content, which are: the comprehensive approach to geographical reality, the descriptive
... Show MoreA load flow program is developed using MATLAB and based on the Newton–Raphson method,which shows very fast and efficient rate of convergence as well as computationally the proposed method is very efficient and it requires less computer memory through the use of sparsing method and other methods in programming to accelerate the run speed to be near the real time.
The designed program computes the voltage magnitudes and phase angles at each bus of the network under steady–state operating conditions. It also computes the power flow and power losses for all equipment, including transformers and transmission lines taking into consideration the effects of off–nominal, tap and phase shift transformers, generators, shunt capacitors, sh
The aim of this research is to identify the availability of visual thinking skills in the chemistry textbook scheduled for the third intermediate grade for the academic year (2020-2021) in the Republic of Iraq. The study sample consisted of all (85) images contained in the chemistry course for the third intermediate grade, which are (85) form using the curriculum. Analytical descriptive A list of visual thinking skills was prepared, and the unit of form was adopted as a unit of analysis and repetition as a unit of counting, and frequencies and percentages were used for statistical treatment, and validity and reliability were calculated. And using the Holste equation. The following results were reached: The skill
... Show More: zonal are included in phraseological units, form metaphorical names for a person, give him various emotional and evaluative characteristics. This article examines the topic of zoomorphic metaphors that characterize a person in the Russian and Arabic languages in the aspect of their comparative analysis, since the comparative analysis of the metaphorical meanings of animalisms is an important method for studying cultural linguistics, since zoomorphic metaphors are a reflection of culture in a language.
Determining the actual amounts of active ingredients in various pharmaceutical commercial forms is still receiving a lot of attention. Two flow injection analysis (FIA) methods were suggested for determination of mesalazine (MES) in pharmaceutical forms. Normal and reverse FIA systems (nFIA and rFIA) combined with UV-Vis spectrophotometric technique were used for the analysis. The methods involved using two mods of FIA systems for measuring a colored product result from coupling of MES with 2,2'-dihydroxybiphenyl after oxidized with sodium periodate in alkaline medium. The absorbance of the red colored dye was measured at maximum wavelength of 500 nm. The calibration graphs for MES were linear in the ranges 2.5-200 and 0.5-60 µg/mL with
... Show MoreA novel analytical method is developed for the determination of azithromycin. The method utilizes continuous flow injection analysis to enhance the chemiluminescence system of luminol, H2O2, and Cr(III). The method demonstrated a linear dynamic range of 0.001–100 mmol L-1 with a high correlation coefficient (r) of 0.9978, and 0.001–150 mmol L-1 with a correlation coefficient (r) of 0.9769 for the chemiluminescence emission versus azithromycin concentration. The limit of detection (L.O.D.) of the method was found to be 18.725 ng.50 µL−1 based on the stepwise dilution method for the lowest concentration within the linear dynamic range of the calibration graph. The relative standard deviation (R.S.D. %) for n = 6 was less than 1.2%
... Show MoreLinear motor offers several features in many applications that require linear motion. Nevertheless, the presence of cogging force can deteriorate the thrust of a permanent magnet linear motor. Using several methodologies, a design of synchronous single sided linear iron-core motor was proposed. According to exact formulas with surface-mounted magnets and concentrated winding specification, which are relying on geometrical parameters. Two-dimensional performance analysis of the designed model and its multi-objective optimization were accomplished as a method to reduce the motor cogging force using MAXWELL ANSYS. The optimum model design results showed that the maximum force ripple was approximatrly reduced by 81.24%compared to the origina
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