In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior

This paper aims to introduce certain new kinds of ideals on pseudo-BG-Algebra (P-BG-A), such as pseudo-closed ideal (P-CI), pseudo-completely closed ideal (P-CCI), and pseudo-n-ideal (P-n-I). Firstly, a (P-n-I) is defined and its pertinent properties are explored. Some important properties have been proven, for example, any pseudo-ideal is a (P-n-I), but the opposite is not generally true, an example was given of the opposite direction. Also, every pseudo-subalgebra of a (P-BG-A) is a pseudo ideal and it is a (P-n-I). Secondly, (P-CI) and a (P-CCI) ideal are defined. After that, we prove that every pseudo-subalgebra of a (P-BG-A) is a (P-CI) and the converse is true. The relationship between (P-BG-A) and pseudo-BH-algebra is demonstrated un

Biodiesel production process was attracted more attention recently due to the surplus quantity of glycerol (G) as a byproduct from the process. Glycerol Utilization must take in to consideration to fix this issue also, to ensure biodiesel industry sustainability. Highly amount of Glycerol converted to more benefit material Glycerol carbonate (GC) was one of the most allurement compound derived from glycerol by transesterification of glycerol with dimethyl carbonate (DMC). Various parameters have highly impact on transesterification was investigated like catalyst loading (1-5) %wt., molar ratio of DMC: glycerol (5:1 – 1:1), reaction time (30 - 150) min and temperature (40 – 80) ᴼC. The Optimum glycerol carbonate yie

Iron is one of the abundant elements on earth that is an essential element for humans and may be a troublesome element in water supplies.  In this research an AAN model was developed to predict iron concentrations in the location of Al- Wahda water treatment plant in Baghdad city by water quality assessment of iron concentrations at seven WTPs up stream Tigris River. SPSS software was used to build the ANN model. The input data were iron concentrations in the raw water for the period 2004-2011. The results indicated the best model predicted Iron concentrations at Al-Wahda WTP with a coefficient of determination 0.9142. The model used one hidden layer with two nodes and the testing error was 0.834. The ANN model coul

Through the researchers' acquaintance with the previous studies, the problem was identified as that the preparation of training curricula in all its units must be based on accurate scientific foundations. Positively affect the type of attack and its implication in the presence of correlational relations, whether direct or indirect, i.e., precedence in training and in preparing units Therefore, the researcher decided to build a causal model to know the relationships to show the best model of the direct straight attack. The study aimed to build a causal model for the most important physical measurements and kinetic capabilities of the direct straight attack in the research sample. The two researchers used the descriptive approach in t

This study was conducted in Diyala province for renal failure patients during the periods August 2015 - April 2016. Hundred renal failure patients were enrolled in the study after diagnosis by the consultant physician at Ibn-Sina Center for Dialysis in Baquba Teaching Hospital according to criteria adopted by the World Health Organization for diagnosis of renal failure disease. The number of males in patient’s sample was 61 (61%) and females was 39 (39%) with an age range of 10 – 88 year (44.7 ± 22.1 year). In addition, the study included 50 apparently healthy individuals and considered as a group control, in which the number of males and females was similar (25 individual), with an age range of 18 – 88 year (51.7 ± 17.3 year). The

Many economic entities working in multiple industrial fields suffer fromlow techniques in using modern administrative means in their works. The mostused tool in measuring required procedures is to adopt and use quality costs. inspite of complications and bronchial of operations in construction projects, Theresearcher was able to find a structure to quality costs according to traditionclassification (prevention, Appraisal, failure) which enables the calculation ofthese costs and then analyze results and setting standards which can beimplemented in evaluating strategic performance for targeted project. and theforge research in theoretical fly to quality and costs concerning it inconstruction section , as well as strategically performance a

Abstract:
                The research seeks to explain the role of the international auditing standard (3402) in the auditor's procedures, where the importance of the research stems from the adoption of international auditing standards in the Iraqi environment, including the standard (3402) of assurance engagements that the external auditor performs by submitting reports on the design of control tools and their operational effectiveness in a service facility that provides the beneficiaries with a service. To provide useful information for service organizations The control tools are of great benefit in rationalizing decisions, and many recommen

      The service system has become a necessity of life in modern cities to be the most basic necessities of modern humans, they constitute a major base, which is based on the sustainability of life in the city and a standard measured through the degree of well-being and progress of civilized peoples and their interaction with the surrounding environment, making the services sector as a need not be an option, whenever the cities widened in population and space whenever provision of services and upgrading the quality and quantity more pressing, which made the subject of the services takes the biggest area of the trends and thinking of urban planners and those who in charge of drawing the cities policies. Consideri