Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Background : Diabetes mellitus, also known as blood sugar, is a series of metabolic disorders described by high blood glucose levels (hyperglycemia), low blood glucose (hypoglycemia), or both, resulting from defects in insulin production, insulin action, or both. Numerous studies have shown that interleukin (IL-6) acts on skeletal muscle cells , liver cells, and pancreas cells to influence glucose balance and metabolism, which directly or indirectly contributes to the development of diabetes. Research in this area is crucial because diabetes is recognized as a major risk factor for many diseases like Diabetic retinopathy, Diabetic nephropathy, Diabetic Neuropathy , heart disease and others.  Patients and methods : In this study, we

The present research aims at revealing the advertising image semiotics in the American printed poster by following the image's significance and its transformations through the poster design trends and indicating its nature whether it is an explicit or implicit image. The limits of the research were the American printed poster during 2016-2018 period. The theoretical side was determined by two sections, the first: (the advertising image semiotics) and the second (design trends in the printed poster). The research procedures were represented by the research method adopted in the analysis of the sample models identified in four models taken from the research community which contains (24) models. The selection was made according to the trend

Accurate computation of the roughness coefficient is important in the studies of open channel flow. To measure and identify the hydraulic characteristics of the flow system, the model simulation is necessary to study and get the results of the hydraulic properties to specify Manning coefficient of the Euphrates River. In this study, the reach is extended along the Euphrates River from Haditha Dam to Ramadi Barrage with a distance of 169km. The HEC-RAS model was implemented to simulate the flow within the study reach. The geometry of the river was represented by more than two hundred cross-sections surveyed in 2013 and 2021. The model was calibrated using some observed discharges at the Heet gage station for records of th

A three species food web model involving a stage structure and cannibalism in the top predator species is proposed and studied. It is assumed that the prey species growth logistically in the absence of predator and the predation process occurred according to theLotka-Volterra functional response. The existence, uniqueness and bounded-ness of the solution of the model are investigated. The local and global stability conditions of all possible equilibrium points are established.The persistence conditions of the model are also determined. The local bifurcation near each of the equilibrium points is analyzed. The global dynamics of the model is investigated numerically and compared with the obtained analytical results. It is observed that the p

Monitoring lotic ecosystems is vital for addressing sustainability issues. The Al-Shamiyah River is the primary source of water for various daily activities in the Al-Shamiyah district. This study assessed the pollution levels of the river by measuring the concentration and distribution of heavy metals—specifically chromium, cadmium, manganese, copper, zinc, and lead—in both the river's water and sediments. The concentrations of heavy metals in the water ranged from 0.05 to 1.44µg/ L for copper (Cu), 1.57 to 7.25µg/ L for manganese (Mn), 0 to 1.7µg/ L for cadmium (Cd), 0.02 to 1.33µg/ L for lead (Pb), 0.08 to 2.74µg/ L for zinc (Zn), and 0.44 to 1.84µg/ L for chromium (Cr). In the particulate phase, the concentrations ranged from

forty-six patients with asthma were tested for the scrum levels of total sialic and diffrental the results reveled a significant increased in the scra of asthmatic patients