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.

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

In order for the process of removing pollutants, including dyes, from the aquatic environment to be effective, plant wastes such as banana peels were used as adsorbent surfaces by thermally activating them (ABP) and modifying them with iron oxide nanoparticles (MABP), which were characterized using Fourier transform infrared (FT-IR) and X-ray diffraction (XRD) techniques. They were applied in the field of Janus green (JG) dye adsorption for the batch system and studied the effect of several factors (adsorbent weight, contact time, initial concentration, and temperature). Their data were analyzed kinetically using first- and second-order kinetic models and they were found to follow the second order. Their data were also analyzed thro

Water pollution as a result of contamination with dye-contaminating effluents is a severe issue for water reservoirs, which instigated the study of biodegradation of Reactive Red 195 and Reactive Blue dyes by E. coli and Bacillus sp. The effects of occupation time, solution pH, initial dyes concentrations, biomass loading, and temperature were investigated via batch-system experiments by using the Design of Experiment (DOE) for 2 levels and 5 factors response surface methodology (RSM). The operational conditions used for these factors were optimized using quadratic techniques by reducing the number of experiments. The results revealed that the two types of bacteria had a powerful effect on biodegradable dyes. The regression analysis reveale

Background: Plaque retention during fixed orthodontic therapy is an important cause of developing enamel demineralization. The purpose of this study was to evaluate the effect of different brackets types on the count of Streptococcus Mutans in orthodontic patients using conventional fluoridated toothpaste. Materials and Methods: Plaque samples were collected from maxillary 1st premolar teeth of twenty right handed patients (using split mouth technique) before bonding, after 48 hrs of bonding using tooth brush only, and after 2 weeks of using fluoridated toothpaste. Stainless steel bracket was bonded on right first premolar while the left one was bonded with sapphire bracket. The calculation of the Streptococcus Mutans count was done usin

Biodiesel is an environmentally friendly fuel and a good substitution for the fossil fuel. However, the purity of this fuel is a major concern that challenges researchers. In this study, a calcium oxide based catalyst has been prepared from local waste eggshells by the calcination method and tested in production biodiesel. The eggshells were powdered and calcined at different temperatures (700, 750, 800, 850 and 900 °C) and periods of time (1, 2, 3, 4 and 5 hr.). The effect of calcination temperature and calcination time on the structure and activity of the solid catalyst were examined by X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM), and Brunaure-Emmett-Teller (BET). The optimum catalyst performance was obtained at 900 °C

In this research, design of advanced material for sunlight conversion requires focused research to obtain efficient photocatalytic system. Nanostructured ZnO was synthesized using spin coating technique. The structural, morphological and optical properties of annealed nanostructured ZnO thin film at 390 Co for 3 hours were characterized by x-ray diffraction, atomic force microscope AFM and UV-VIS spectrophotometer. Nanostructured ZnO was applied for removal Methylene Blue (MB) dye from water using sunlight induced photocatalytic process. Overall degradation of MB/ZnO was achieved after 120 minutes of sunlight irradiation while it needs more time for MB alone. The reaction rate constant fit pseudo first order for MB/ZnO degradation was 0.