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.

Background: The use of the cone beam computed tomography for analysing the position of the greater palatine foramen in relation to various anatomical landmarks is crucial in dentistry. The aims of the current study, firstly is to determine the greater palatine foramen position in relation to various anatomical landmarks by using cone beam computed tomography and secondly is to make a comparison of the measurements according to side, gender, and age. Materials and methods: This prospective study included 60 Iraqi patients (28males and 32 females) who selected according to availability of Inclusion criteria, which include age range (21 - 60 years), with no dentofacial deformities or pathological lesion at the maxilla. All patients had inform

The current study aims to determine the prevalence of Trichomonas vaginalis and Candida spp., and also to identify Candida parapsilosis and some virulence genes. It was conducted in Bint Al-Hoda Hospital of Maternity and Children in Thi-Qar province, south of Iraq for the period from the beginning of January to the end of December 2020. Two hundred and fifty samples were collected from the female genital tract for women whose age ranged between 17-50 years. Microscopic, traditional and molecular tests were used in the sample examination. The results recorded 12 (4.8%) samples infected with T. vaginalis parasite, whereas 130 (52%) samples showed Candida yeast distributed as follows: 75 (30 %) <

This study aims to predict the organic pollution produced from the presence of some polycyclic aromatic hydrocarbons (PAHs) and determination it's concentrations (µg/L , ppb) in Tigris river water by a collection twenty-seven water samples from a selected three stations with nine sampling sites and three depths of water (5 cm , 2 m and 4 m) each site for 4.6 km distance of a geographic studied area which is located between the ( Al-Senak and AL-Sarrafiah bridges ) at Baghdad city – Iraq on May, 2012. The geographic location was determined with a Global Positioning System (GPS) and Geographic Information System (GIS) software program. The concentrations of fourteen components (PAHs) were performed using the reverse phase

This study aimed at comparing the performance of vertical, horizontal and hybrid subsurface flow systems in secondary treatment for the effluent wastewater from the primary basins at Al-Rustumia wastewater treatment plant, Baghdad, Iraq. The treatments were monitored for six weeks while the testsduration were from 4 to 12 September 2018 under continuous wastewater feeding for chemical oxygen demand (COD), total suspended solid (TSS),ammonia-nitrogen(NH₄-N) and phosphate (PO₄-P) in comparison with FAO and USEPA standards for effluent discharge to evaluate the suitability of treated water for irrigation purposes. Among the systems planted with Phragmites Australia, the hybrid subsurface flow system which cons

The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environme

             In general, researchers and statisticians in particular have been usually used non-parametric regression models when the parametric methods failed to fulfillment their aim to analyze the models  precisely. In this case the parametic methods are useless so they turn to non-parametric methods for its easiness in programming. Non-parametric methods can also used to assume the parametric regression model for subsequent use. Moreover, as an advantage of using non-parametric methods is to solve the problem of Multi-Colinearity between explanatory variables combined with nonlinear data. This problem can be solved by using kernel ridge regression which depend o

Background: The cells of periodontium contain many intracellular enzymes like (alkaline phosphatase ALP) that are released outside into the saliva and gingival crevicular fluid (GCF) after destruction of periodontal tissue. The aim of study was to determine the activity of this enzyme in saliva and its relation to the salivary flow rate, PH and clinical periodontal parameters in patients with chronic periodontitis. Subject, Materials and methods: Sample population consist of 75 individuals ;divided into four groups , the first group (15):control subject, the second group (20):mild chronic periodontitis, the third group(20) moderate chronic periodontitis and the fourth group (20) sever chronic periodontitis, Measurements of plaque index (PL

The analysis, behavior of two-phase flow incompressible fluid in T-juction is done by using "A Computational Fluid Dynamic (CFD) model" that application division of different in industries. The level set method was based in “Finite Element method”. In our search the behavior of two phase flow (oil and water) was studed. The two-phase flow is taken to simulate by using comsol software 4.3. The multivariable was studying such as velocity distribution, share rate, pressure and the fraction of volume at various times.  The velocity was employed at the inlet (0.2633, 0.1316, 0.0547 and 0.0283 m/s) for water and (0.1316 m/s) for oil, over and above the pressure set at outlet as a boundary condition. It was observed through the program