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 location is the northern part of the Basin of Limboto Lake; the focus of the research is the limestone outcrop with 24 meter thickness in Yosonegoro area. The purpose of the study is to find out facies, standard microfacies and depositional environment on Limboto limestone. The research method carried out consisted of three methods namely the measured section, petrographic analysis and biostratigraphy analysis.
The limestone facies in the Yosonegoro area consist of two facies. Then, based on sedimentary structure, composition, color, precipitation texture, terrestrial origin components and the organism content, the two facies can divided into three different microfacies. Paleobathyme
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The general trend in Iraqi banks is focused towards the application of international financial reporting standards, especially the international financial reporting standard IFRS 9 “Financial Instruments”, in addition to the directives issued on the Central Bank of Iraq’s instructions for the year 2018 regarding the development of expected credit losses models, and not to adhere to a specific method for calculating these losses and authorizing the banks’ departments to adopt the method of calculating losses that suits the nature of the bank’s activity and to be consistent in its use from time to time. The research problem revolves around the different methodologies for calculatin
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The researchers aim of this research to analyze the reality of educational services in the city of Ramadi in order to reveal the efficiency of the spatial distribution of schools at the level of residential neighborhoods and the requirements of the population, based on the standards and indicators for this service.
The research problem related to the educational function of the city of Ramadi was formulated by asking about the efficiency of the spatial distribution of educational services and whether there is a balance in the distribution of schools to residential neighborhoods in a way that meets the requirements of the population, and in order to answer the research problem, the research hypothesis was formulated that there is
... Show MoreThe food web is a crucial conceptual tool for understanding the dynamics of energy transfer in an ecosystem, as well as the feeding relationships among species within a community. It also reveals species interactions and community structure. As a result, an ecological food web system with two predators competing for prey while experiencing fear was developed and studied. The properties of the solution of the system were determined, and all potential equilibrium points were identified. The dynamic behavior in their immediate surroundings was examined both locally and globally. The system’s persistence demands were calculated, and all conceivable forms of local bifurcations were investigated. With the aid of MATLAB, a numerical simu
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The wound healing process is incredibly intricate, consisting of a series of cellular activities. Although, this complex process has the potential to degenerate and result in chronic wound problems that are resistant to biological healing mechanisms. Nanoparticles can help to reduce inflammation, promote tissue regeneration, and accelerate wound healing. The proteolytic enzymes are believed to break down proteins and other molecules that can cause inflammation and impede the healing process. Wound was created in vivo using adult mice, and by taking blood samples the hematological parameters were evaluated to detected the effects of bromelain, silver nanoparticles and Br-AgNPs. The results shows an increased in white blood cells WBC, RBC, MC
... Show MoreThis study introduced the effect of using magnetic abrasive finishing method (MAF) for finishing flat surfaces. The results of experiment allow considering the MAF method as a perspective for finishing flat surfaces, forming optimum physical mechanical properties of surfaces layer, removing the defective layers and decreasing the height of micro irregularities. Study the characteristics which permit judgment parameters of surface quality after MAF method then comparative with grinding
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