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.

The aim of this research was to study the concentrations of Uranium in the phosphorus fertilizers using Nuclear track detector (CR-39). Our present investigation is based on the study of 10 types samples for different kinds of phosphorus fertilizers which were available in the local market Some of them were Iraqi made and the others from different countries like, (Iran, Italy, Holland, Lebanon and Jordan) .. The result obtained shows that the Uranium concentration in phosphorus fertilizers samples varies from (3.59ppm) to(2.59ppm). Based on the radioactive concentration of Uranium in the samples all the results obtained between(3.59ppm) in the Iraqi super phosphate to (2.59ppm) in the mixture Iraqi phosphate fertilizer are withi

Concentrations of radon were measured in this study for twenty-four samples of soil distributed in six locations on the north part of Iraq. The radon concentrations in soil samples measured by using alpha-emitters registration that emits from Radon (222Rn) in (CR-39) track detector. The concentrations values were calculated by a comparison with standard samples. The results shows that the radon gas concentrations in Darbandikhan City varies from (16.60-34.04 Bq/m3), Halabja City (16.51-23.32 Bq/m3), Al Sulaimaniya City (17.61-32.25 Bq/m3), Koisnjaq City (22.04-35.65 Bq/m3), Shaqlaua City (21.10-29.10 Bq/m3) and Erbil City (22.30-34.63 Bq/m3). The average radon gas concentration in Al Sulaimaniya and Erbil governorate are (22.30 Bq/m3)

This research presents a particular designing strategy for a free form of surfaces, constructed by the lofting design method. The regarded surfaces were created by sliding a B-spline curves (profile curves), in addition to describing an automatic procedure for selective identification of sampling points in reverse engineering applications using Coordinate Measurement Machine. Two models have been implemented from (Ureol material) to represent the different cases of B-spline types to clarify its scope of application. The interior data of the desired surfaces was designed by MATLAB software, which then were transformed to UG-NX9 software for connecting the sections that were designed in MATLAB program and obtaining G-code programs for the

This work deals with kinetics and chemical equilibrium studies of esterification reaction of ethanol with acetic acid. The esterification reaction was catalyzed by an acidic ion exchange resin (Amberlyst- 15) using a batch stirred tank reactor. The pseudo-homogenous and Eley-Rideal models were successfully fitted with experimental data. At first, Eley-Rideal model was examined for heterogeneous esterification of acetic acid and ethanol. The pseudo-homogenous model was investigated with a power-law model. The apparent reaction order was determined to be (0.88) for Ethanol and (0.92) for acetic acid with a correlation coefficient (R2) of 0.981 and 0.988, respectively. The reaction order was determined to be 4.1087x10-3 L0.8/(mol0.8.min) with

Due to the rapid advancement of technology and the technology of things, modern industries start to need a highprecision equipment and surface finishing, so many finishing processes began to develop. One of the modern processes is Magnetic Abrasive Finishing (MAF), which is a high-precision process for internal and external finishing under the influence of a magnetic field of abrasive particles. Boron Carbide (B4C) ceramics was tested by mixing it with iron (Fe) and produced abrasive particles to reduce the intensity of scraping on the surface, reduce the economic cost and achieve a high finishing addition to remove the edges at the same time. The material selected for the samples was mild steel (ASTM E415) under (Quantity of Abrasives, Mac

There are serious environmental problems in all countries of the world, due to the waste material such as crushed clay bricks (CCB) and in huge quantities resulting from the demolition of buildings. In order to reduce the effects of this problem as well as to preserve natural resources, it is possible to work on recycling (CCB) and to use it in the manufacture of environmentally friendly loaded building units by replacing percentages in coarse aggregate by volume. It can be used as a powder and replacing of percentages in cement by weight and study the effect on the physical and mechanical properties of the concrete and the masonry unit. Evaluation of its performance through workability, dry density, compressive strength, thermal conduct

As a result of the exacerbation of the problem of water pollution, research was directed towards studying the treatment using ceramic membranes, which proved to be highly effective in treating all water sources. The research aims to study the possibility of preparing a new type of ceramic membranes from Syrian zeolite that was not previously used in this field. In this research, ceramic membranes were prepared from Syrian raw zeolite in several stages. Zeolite sample was characterized, grinded, mixed with boric acid, pressed to form desks, treated thermally according to experiment program, finally coated with silver nanoparticles. Specifications of prepared membranes were determined according to reference methods, effectiveness of prepar