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.

Abstract

This study highlights the importance of Iraq in the analysis of foreign trade and economic growth for the period (1980 - 2013) is an attempt to determine the equilibrium relationship long term and short term between these two variables were used ARDL model to explain the economic relationship between the two variables.

To achieve the objectives of the research has been the standard model estimate after testing the stability of exports X data series, and imports M, and GDP current prices, and exchange rate EXR, and verify the existence of a joint integration relationship between these variables.

In order to achieve the objectives of the research it

The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent o

The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent of the

Oral squamous cell carcinoma (OSCC) is the most common malignant neoplasm of the oral mucosa. Human papillomavirus (HPV) virus cause a broad scope of diseases from benign to invasive tumors, types 16 and 18 classified as carcinogenic to humans. This study aimed to provide the first molecular characterization of HPV types in Iraq. Thirty-five unstimulated whole saliva samples were collected from histopathologically confirmed patients with oral cancer were enrolled in this study. Genomic DNA was extracted from exfoliating cells to amplify HPV-DNA using HPV-L1 gene sequence primers by polymerase chain reaction method (PCR), the viral genotyping was performed using direct sequencing method. HPV genotypes identified were deposited in Gen

Background: Many studies have been conducted to evaluate the effect of using a hot material in the root canal and its potential for causing damage to the tooth supporting structure. Materials and methods: thirty permanent premolars were obturated with thermoplasticized Gutta-Percha using three different obturation techniques: soft core, Thermafil, and obtura to evaluate the rise in temperature on the root surface using a multipurpose digital thermometer. Results: temperature increases was significantly greater for Obtura versus Soft core (p<0.003), not significant for Thermafil versus Soft core (p<0.087), and Thermafil versus Obtura (p<0.125). Conclusions: temperatures rise on the root surface were below the critical level and, therefore, s

Elevated Interleukin-13 (IL-13) may play an important role in the pathophysiology of COVID-19, yet, the attenuated response did not notice across all severe cases. Susceptibility to asthma in specific populations is associated with several SNPs of multifunctional cytokines, such as IL-13, IL-31 and IL-33. This prospective case-control study is designed to investigate the extent of genetic susceptibility in subsets of Iraqi patients with COVID-19 by targeting the variants of interleukin IL-13rs20541 polymorphism in relation to disease susceptibility and severity of clinical presentation. One hundred samples were obtained from the throat, nasopharyngeal and nasal swabs enrolled in this study. Eighty samples of the throat, nasopharyngeal and

Rheumatoid arthritis is a chronic inflammatory autoimmune disease its etiology is unknown. The classical autoimmune diseases, have adaptive immune genetic associations with autoantibodies and major histocompatibility complex (MHC) class II such as rheumatoid arthritis (RA), diabetes mellitus type two (DM II). Serum of99 males suffering from RA without DMII as group (G1), 45 males suffering from RA with DM II as group (G2) and 40 healthy males as group (G3) were enrolled in this study to estimation of alkaline phosphates (ALP), C-reactive protein (CRP) and Pentraxin-3(PTX). Results showed a highly significant increase in PTX3 levels in G1 and G2 compared to G3 and a significant decrease in G1comparing to G2. Results also revealed a significa