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 energy aimed at examining the mode of energy drinks consumption among athletes in
Baghdad and assessing their drinks were spread greatly among the athletes and students. This
study impression toward such drinks. The study sample comprised of 102 mal athletes aged
between 19-27 years and selected randomly .The obtained results showed that football was
most practiced among the test samples at 40.54% based on twice daily .The athletes
consumed one can each day at 41.18% .As the data on energy drinks was supplied from
friends .The prefared period for drinking was before or during exercise .The athletes thought
that there products can provide energy ,vitamins ,tell ale materials ,does not affect
appetite.The most f

In this paper the reinforced materials manufactured from steel continues fibers are used in Aluminum matrix to build a composite material. Most of researches concentrated on reinforced materials and its position in the matrix according to its size and distribution, and their effects on the magnitude of different kinds of the stresses, so this paper presents and concentrate on the geometrical shape of reinforced material and its effects on the internal stresses and strains on the composite strength using FEM as a method for analysis after loaded by certain force showing the deference magnitudes of stresses according to the different geometrical shapes of reinforced materials.

The need for detection and investigation of the causes of pollution of the marshes and submit a statistical study evaluated accurately and submitted to the competent authorities and to achieve this goal was used to analyze the factorial analysis and then obtained the results from this analysis from a sample selected from marsh water pollutants which they were: (Electrical Conductivity: EC, Power of Hydrogen: PH, Temperature: T, Turbidity: TU, Total Dissolved Solids: TDS, Dissolved Oxygen: DO). The size of sample (44) sites has been withdrawn and examined in the laboratories of the Iraqi Ministry of Environment. By illustrating SPSS program) the results had been obtained. The most important recommendation was to increase the pumping of addit

The current problem is summarized in what is called the development failing experience
in comprehencing the studying materials , so the students will feel worry of repeating failure
in he future , so he would seek blind keeping on heart for the studying material bond this isbad due to the forgetting in the future , one side of thesis research problem is that there is
many contradictory researches result in relation to the learning styles which impose the
nessicity to find results lessen this contradiction . the importance of the research is
summarized in the importance of the subject under the study , in that the researcher ( as in
her knowledge ) did not find a thesrs tackling the subject of the distinguished students

After this systematic presentation of the phenomenon of rotation of formulas, ie the construction of the verb and the verb, and the narrated narratives therein differed among the readers, it became clear to us how the difference was clear between reading and the other, and how readers have varied in their readings of the verb, As we have noted through our modest research that the phenomenon of building the verb for the actor and the effect have included the act of both past and present tense, and not limited to a specific time, and this difference in reading was not limited to a particular environment, but beyond To more than one environment This is evidenced by the readings of various readers from the environment of Kufa, Basra, Mecca,

the influence of permeability tensor upon drainage of anisotropic soils under ponded water and steady recharge (rainfall) is theoretically investigated. Tensorial permeability has led to the formulation of mixed type partial differential equations. Since there is no analytical solution to this problem, the formulation is therefore solved numerically by the method of finite elements. The finite element formulation is implemented into a computer model which can be applied to any problem of seepage under steady state
conditions. Two different example problems representing two different flow conditions under full anisotropy have been studied. Results of the model for the isotropic case were checked against exact mathematical solutions de