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.
إحدى أهم الطرق لتقصي توزيع المجرات عبر الزمن الكوني هي دالة اللمعان LF بدلالة كتلة القرص الباريوني ψS(Mb)، القدر . لقد درسنا تقديرًا لكثافة كتلة الباريون في عينة من المجرات الحلزونية القضيبية وغير القضيبية من الادبيات السابقة، والتي تتضمن فعليًا، لكل صنف من الاجرام السماوية ذات المحتوى الباريون المرئي، جزءًا لا يتجزأ من ناتج دالة الضيائية (LF) ونسبة الكتلة إلى الضوء. استخدمت تقنية الانحدار المتعدد لحزمة الب
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A field experiment was conducted at Abu-Ghrib during 2013- 2014 season to study the effect of harrowing systems on the decomposition and fermentation on organic matter(OM) when added and mixed with the soil under special technology, as well as its effect on the growth parameters and productivity of (Zea mays L. 5018). The experiment was laid out using factorial randomized complete block design (RCBD) in split-split design with three replications in SCL bare soil with a percent of moisture ranged from 16 – 18 %. The main plots were designated to the two systems of harrowing (Rotary Harrowand Disc Harrow ). The sub main plots were specified for two organic matters ( Sheep manure ,cow manure ) . Data were statistically analyzed, and
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Background: Optimal root canal retreatment was required safe and efficient removal of filling material from root canal. The aim of this in vitro study was to compare the efficacy of reciprocating and continuous motion of four retreatment systems in removal of root canal filling material. Materials and Methods: Forty distal roots of the mandibular first molars teeth were used in this study, these roots were embedded in cold clear acrylic,roots were instrumented using crown down technique and rotary ProTaper systemize Sx to size F2 ,instrumentation were done with copiousirrigation of 2.5% sodium hypochlorite and 17% buffered solution of EDTA was used as final irrigant followed by distilledwater, roots were obturated with AH26 sealer and Prota
... Show MoreThe increasing level of residents’ requirements of the local community led to the necessity for sufficient local funding to satisfy the residents’ requirements and services of the local units affiliated with the decentralized administrative systems on the one hand, and to the role of local financing in the financial independence of local units on the other hand.With the presence of local financing, the financial independence of local units is achieved and is considered one of the conditions for financial independence, which is the provision of local financing to the units away from central support. The study focused in this research to clarify the concept of local financing for local units with a statement of its conditions and importan
... Show MoreAim: To evaluate the effect of two bonding systems and two curing systems on sealing ability of class V composite restorative materials. Materials and methods: This study was performed in vitro on 40 caries free upper first premolar teeth. The Standardized class V cavity preparation on buccal and lin- gual surfaces of each tooth was done. Then the teeth were randomly divided into two major groups each of twenty. 40 cavities were performed on these teeth and the first group7th generation bonding agent (i Bond) were applied according to the manufacturer instructions and single increment of univer- sal composite (XRV Herculite) from kerr were applied and twenty of the cavities were cured with con- ventional light cure device (astralis-5) and t
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Despite Iraq's possession of the energies material, human and agricultural resources and great economic but that contribution of the agricultural sector in the total gross fixed capital formation and gross domestic product in the Iraqi economy remained low and declining continuously since the nineties of the last century, as well as the inability of agricultural production to meet the country's needs of food . The food gap increased strategic food crops until it reached 1049 thousand tons in 2010. On this basis, there is a need to study and analysis the behavior of the function of gross fixed capital format
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The researcher aims to Diagnose the reality of research variables, strategic leadership and decision support systems, and their impact on crisis management in the General Company for Steel Industries because of their important role in preventing crises and reducing their occurrence for the research company in particular and other companies in general affiliated with the Ministry of Industry and Minerals, as well as clarifying theoretical concepts of research variables As it included the answer to questions related to the research problem, including (Is there an impact of the strategic leadership in managing crises if decision support systems are used), and the researcher adopted the descriptive and analytical approach in its comp
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Environmental Control Systems form one of the integral tasks of the designer, resulting from his/her acquaintance with the nature of sites and the way they are deployed to achieve modern space entity which is witnessing significant development in the field of interior design.Good deployment of these systems offer us, as designers, high potential and several varied solutions to configure internal spaces characterised as a fertile field of study and knowledge.The research problem was identified in the marginalisation of the importance of Environmental Control Systems as an important designing factor to achieve integrated design. The research problem was demonstrated in Chapter One, along with defining the objectives and formulating
Using the Neural network as a type of associative memory will be introduced in this paper through the problem of mobile position estimation where mobile estimate its location depending on the signal strength reach to it from several around base stations where the neural network can be implemented inside the mobile. Traditional methods of time of arrival (TOA) and received signal strength (RSS) are used and compared with two analytical methods, optimal positioning method and average positioning method. The data that are used for training are ideal since they can be obtained based on geometry of CDMA cell topology. The test of the two methods TOA and RSS take many cases through a nonlinear path that MS can move through tha
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