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

The educational sector is one of the important sectors in the world, and it is considered one of the means of community development. In addition, it is one of the means of making the country’s renaissance and devel-opment because it represents the factory of thinking minds that make change. There is no doubt that this sector is the same as any other sector. The deficit in the studied scientific planning has been prolonged, which led to its deterioration, and the problems of education remain diverse and inherited from previous time periods, where the hierarchical cluster analysis was used on postgraduate students in universities in Iraq, except for Kurdistan region, and the number of universities that were included in the study was

The research included five sections containing the first section on the introduction of the research and its importance and was addressed to the importance of the game of gymnastic and skilled parallel effectiveness and the importance of learning, but the problem of research that there is a difference in learning this skill and difficulty in learning may be one of the most important reasons are fear and fear of falling and injury, And a lack of sense of the movement of the movement is one of the obstacles in the completion of the skill and the goal of research to design a device that helps in learning the skill of descending Almtor facing with half a cycle according to the typical locomotor track on the parallel device of the technical men'

The research aims to evaluate the direct deduction department’s procedures for the process of collecting income tax using the direct deduction method for state departments and the public sector in light of direct deduction tax instructions No. (1) of 2007 and Income Tax Law No. (113) of 1982 (amended) through Giving a clear idea of ​​the reality of tax collection procedures because this type of tax is one of great importance because it contributes to the provision of financial revenues to the state to finance its expenses and direct the economy towards achieving its social, economic and political goals. The researcher makes comparisons between the procedures of the General Tax Authority in collecting the tax and what was approved b

The talk about the relationship between the media and industrialists can be the core of a bigger and deeper subject which is the role of these means in increasing sales : First, increasing the customer’s awareness of the importance of goods and the result of the promotion of products. Secondly, increasing investments which do require continuous studies and deep research in order to understand the constantly changing market conditions, and the public’s taste. In this research, we try to find out how industrialists see the role of media in the promotion of products in Iraq today, and how it develops in the future.

There was a reluctance of the industrialists to advertise in the local media, also industrialists see the role of t

Background: Orthodontic mini-implants are increasingly used in orthodontics and the bone density is a very important factor in stabilization and success of mini-implant. The aim of this study was to observe the relationship among maximum bite force (MBF); body mass index (BMI); face width, height and type; and bone density in an attempt to predict bone density from these variables to eliminate the need for CT scan which have a highly hazard on patient. Materials and Methods: Computed tomographic (CT) images were obtained for 70 patients (24 males and 46 females) with age range 18-30 years. The maxillary and mandibular buccal cortical and cancellous bone densities were measured between 2nd premolar and 1st molar at two levels from the alveol

The study aims to identify the impact of the round-robin strategy on the logical thinking of fourth-year middle school students in chemistry. Two groups were employed:  an experimental group consisted of (30) students who were taught according to the round-robin strategy, and the control group consisted of (30) students who were taught according to the traditional method. The researcher adopted the experimental design with partial control by preparing the visual thinking test tool, which consists of (20) multiple-choice items, it was applied as a post-test on the research sample. The result showed that there was a statistically significant difference in favor of the experimental group, which was taught according to the Round Robin s

The objective of the present study is to determine the effect of Kaolin as a fuel oil additive to minimize the fireside corrosion of superheater boiler tubes of ASTM designation (A213-T22) by increasing the melting point of the formed slag on the outside tubes surface, through the formation of new compounds with protective properties to the metal surface. The study included measuring corrosion rates at different temperatures with and without additive use with various periods of time, through crucible test method and weight loss technique.

      A mathematical model represents the relation between corrosion rate and the studied variables, is obtained using statistical regression analysis. Using this model,