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.

Rheumatoid arthritis and periodontitis use analogous effector destructive procedures, in that the inflammatory cells and pro-inflammatory cytokines that drive chronic bone erosion in RA and chronic periodontal destruction in Periodontitis are alike. Periodontitis (PD) has appeared as a hazard factor in a number of health situations as rheumatoid arthritis (RA). To determine the effect of anti-tumor necrosis factor alpha biological treatment (methotrexate and Enbrel or infliximab) on periodontal status of patients having rheumatoid arthritis with periodontitis in comparison to those having periodontitis without rheumatoid arthritis and control healthy subjects and to determine the serum levels of anti-cyclic citrullinated peptide (ACCP) in t

A general velocity profile for a laminar flow over a flat plate with zero incidence is obtained by employing a new boundary condition to the other available boundary conditions. The general velocity profile is mathematically simple and nearest to the exact solution. Also other related values, boundary layer thickness, displacement thickness, momentum thickness and coefficient of friction are nearest to the exact solution compared with other corresponding values for other researchers.

The removal of commercial orange G dye from its aqueous solution by adsorption on tobacco leaves (TL) was studied in respect to different factor that affected the adsorption process. These factors including the tobacco leaves does, period of orange G adsorption, pH, and initial orange G dye concentration .Different types of isotherm models were used to describe the orange G dye adsorption onto the tobacco leaves. The experimental results were compared using Langmuir, and frundlich adsorption isotherm, the constants for these two isotherm models was determined. The results fitted frundlich model with value of correlation coefficient equal to (0.981). The capacity of adsorption for the orange G dye was carried out using various kinetic models

Male reproductive health is intricately regulated by molecular and physiological processes, with the aryl hydrocarbon receptor (AhR) playing a crucial role. AhR is activated by various ligands and influences the onset and progression of diseases. The aim of this study was to evaluate the role of AhR on spermatogenesis in adult male rats were affected by resveratrol (RES) and CH223191, an AhR antagonist. The study include forty rats were randomly divided into four equal groups: Control group, DMSO group, RES group and AhR‾ group, the rats received respective treatments intraperitoneally twice weekly for 60 days, and various parameters related to male reproductive health were evaluated. The AhR that activation by the RES treatment w

The present study aims to establish an empirical correlation between biochemical oxygen demand (BOD5) and chemical oxygen demand (COD) of the sewage flowing in Al-Diwaniyah wastewater treatment plant. The strength of the wastewater entering the plant varied from medium to high. High concentrations of BOD5 and COD in the effluent were obtained due to the poor performance of the plant. This was observed from the BOD5 /COD ratios that did not confirm with the typical ratios for the treated sewage. Regression equations for BOD5 and COD removal percentages were suggested which can be used to evaluate rapid effluent assessment after the treatment processes or optimal process control to improve the performance of wastewater treatment plants.