In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

From different hospitals in Baghdad city, 25 clinical isolates of Proteus spp. were collected from different clinical samples, all isolates were identified as Proteus mirabilis by using bacteriological and biochemical assays in addition to Vitek-2 identification system. 15 (60%) isolates were identifying as Proteus mirabilis. The susceptibility of P. mirabilis isolates towards cefotaxime and ceftazidime was (66.6 %), (20%) consecutively; while extended spectrum β-lactamases producing P. mirabilis percentage was (30.7 %). Because blaVEB-1 was documented as an important indicator for increasing risk of extended spectrum beta ßlactamases producing P. mirabilis isolates that began to spread from many geographic area to Far east which inc

Al-Aziz's book was chosen as a subject for research as it is one of the important books in the Islamic world in general and the Shafi'i school in particular and its author Imam Abdul Karim bin Mohammed bin Abdul Karim Al-Rafi's, who in the doctrine of the jurisprudence has made prominent lines and left behind invaluable scientific treasures in the service of religion. Its importance is summarized as follows:
1. Being an explanation of the book (brief) of the argument of Islam Imam Ghazali (God's mercy), one of the five books adopted in Shafi'i jurisprudence.
2. His work is Imam Abu al-Qasim al-Rafii known for the brilliance of the investigation and the power of weighting in the doctrine.
3. It is considered an encyclopedia in Sh

The esterification of oleic acid with 2-ethylhexanol in presence of sulfuric acid  as homogeneous catalyst was investigated in this work to produce 2-ethylhexyl oleate (biodiesel) by using semi batch reactive distillation. The effect of reaction temperature (100 to 130°C), 2-ethylhexanol:oleic acid molar ratio (1:1 to 1:3) and catalysts concentration (0.2 to 1wt%) were studied. Higher conversion of 97% was achieved with operating conditions of reaction temperature of 130°C, molar ratio of free fatty acid to alcohol of 1:2 and catalyst concentration of 1wt%. A simulation was adopted from basic principles of the reactive distillation using MATLAB to describe the process. Good agreement was achieved.

Nanostructured Al2O3has been applied as a protective coating against corrosion of the carbon steel (C.S) in seawater environment (3.5% NaCl) at temperatures range (298-328)K. Aluminananoparticles were deposited on carbon steel substrates by cathodic electrophoretic deposition (EPD) with ethanol as suspension medium and poly(acrylic acid) (PAA) as polymeric charging agent. Meanwhile, thesurface morphology was examined using Atomic-force microscopy (AFM). The cross-section AFM showed that the particles sizes for the Al2O3 NPs is around 60-80 nm. The anticorrosion behaviour of coated C.S was investigated in 3.5% NaCl at temperature range 298-328 K by potentiodynamic polarization measurements. Results show that using PAA in suspension coat incr