The approximate solution of a nonlinear parabolic boundary value problem with variable coefficients (NLPBVPVC) is found by using mixed Galekin finite element method (GFEM) in space variable with Crank Nicolson (C-N) scheme in time variable. The problem is reduced to solve a Galerkin nonlinear algebraic system (NLAS), which is solved by applying the predictor and the corrector method (PCM), which transforms the NLAS into a Galerkin linear algebraic system (LAS). This LAS is solved once using the Cholesky technique (CHT) as it appears in the MATLAB package and once again using the General Cholesky Reduction Order Technique (GCHROT), the GCHROT is employed here at first time to play an important role for saving a massive time. Illustrative examples are given to solve the NLPBVPVC with the GCHROT, the results are given by tables and figures which show from a side efficiency of this technique, and from another side show that the two methods GCHROT and CHM are given the same results, but the suggesting first technique is very fast than the second one.
Our research comes to shed light on Iraqi literature as literature that arose in special circumstances alongside foreign literature. Using comparative research methods, we chose to highlight two distinguished writers, who have their mark in the world of literature. The first is the Iraqi writer Maysaloun Hadi, who is considered an icon of Iraqi feminist literature, and the second is the French writer Le Clézieu, who won the Nobel in 2008. We will see through the research how the two authors expressed their views of modernity and urbanism. And how each of them separately portrayed the psychological and moral projections that formed the essence of man today.
Résumé
Notre recherche abord un des points inc
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Background: Chronic obstructive pulmonary disease causes permanent morbidity, premature mortality and great burden to the healthcare system. Smoking is it's most common risk factor and Spirometry is for diagnosing COPD and monitoring its progression.
Objectives: Early detection of chronic obstructive pulmonary disease in symptomatic smokers’ ≥ 40years by spirometry.
Methods: A cross sectional study on all symptomatic smokers aged ≥ 40 years attending ten PHCCs in Baghdad Alkarkh and Alrisafa. Those whose FEV1/FVC was <70% on spirometry; after giving bronchodilator, were considered COPD +ve.
Results: Overall, airway obstruction was seen in
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Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
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