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

Abstract

This study cares for the economic living conditions in Mosul City. Its importance lies in the critical period that has been covered
(2002-2007), which was dominated by far–reaching events at political economic and social levels. Among the main results that have been revealed are the following: the rate of economic growth in the City has been the lowest among major urban centers in Iraq. Besides, real income per capita in the City has stayed stagnant during the period of the study. However, the inequality in distribution of income has decreased. The main bulk of the city's population rely on their income from wages and salari

Geotechnical engineers have always been concerned with the stabilization of slopes. For this purpose,
various methods such as retaining walls, piles, and geosynthetics may be used to increase the safety factor of slopes prone to failure. The application of stone columns may also be another potential alternative for slope stabilization. Such columns have normally been used for cohesive soil improvement. Most slope analysis and design is based on deterministic approach i.e a set of single valued design parameter are adopted and a set of single valued factor of safety (FOS) is determined. Usually the FOS is selected in view of the understanding and knowledge of the material parameters, the problem geometry, the method of analysis and the

     Municipal solid waste generation, management, and dumping are economic and ecological concerns that metropolitan areas, particularly those in developing nations, must address. This study intended to ascertain the impacts of solid waste on the quality of groundwater around trash dumps located inside and surrounding landfill sites in the city of Erbil. Samples of groundwater, as well as two samples of leachate, were collected from eight wells situated near landfills during the dry and rainy seasons of August 2021 and February 2022. Several physico-chemical parameters, including pH, EC, NO₂, NO₃, alkalinity, HCO₃, Na, Ca, Mg, Cl, SAR, total hardness, and heavy metals, were evaluated in the samples.

Zygnematales an order of green algae in Shaqlawa District Erbil, Kurdistan Region, Iraq, has been studied in eighteen sites, distributed between twelve springs and six along the streams within Shaqlawa district from September2019 to August2020. A total of 116 species belonging to 9 genera were identified. The most dominant genera included Spirogyra and Cosmarium (31, 30) taxa respectively. Out of them, 30 species were recorded for the first time in Iraq. Newly found genera included one species each for Cylindrocystis, Debarya, Hallasia and Staurastrum, nine species belonged to Mougeotia

This study has been focused on the detection of phenolic compound in aerial parts (stem and leaves)of the species belonging the genus Arabis L. A.Caucasica Willd, A.Sagittata (Bertol)DC, A.Aucheri Boiss, A.nova Vill of family cruciferou (Brassicaceae) which were collected during field trips of the districted of Iraq. Phenolic compounds have been identified by using High Performance Liquid Chromatography (HPLC). Nine standard compounds used for comparison five of them flavonoids ( Rutin, Quercetin, kaempferol, Luteolin and Apigenin) and the other phenolic acid ( Chlorogenic acid, Caffeic acid, Ferulic acid and Rosmarinic acid) , results showed that species vary in containing phenolic compound which can be counted as a taxonomic evidence s

The current study is designed to investigate the histological and immunohistochemical characteristics of the thyroid gland in adult male Sciurus anamalus. This study found that the thyroid gland of the Caucasian squirrel is located in the neck area, below the larynx, on both sides of the trachea. It has two lobes (right and left) with cylindrical shape. The histological studies revealed that the thyroid gland is surrounded by a capsule which consists of connective tissue and forming of two layers which are outer layer and inner layer, and a layer of adipose tissue appears overlapping the outer layer. The inner tissue of the gland consists of follicles with different shapes and sizes, and is lined with simple cuboidal epithelial tissue (foll

The current study is designed to investigate the histological and immunohistochemical characteristics of the thyroid gland in adult male Sciurus anamalus. This study found that the thyroid gland of the Caucasian squirrel is located in the neck area, below the larynx, on both sides of the trachea. It has two lobes (right and left) with cylindrical shape. The histological studies revealed that the thyroid gland is surrounded by a capsule which consists of connective tissue and forming of two layers which are outer layer and inner layer, and a layer of adipose tissue appears overlapping the outer layer. The inner tissue of the gland consists of follicles with different shapes and sizes, and is lined with simple cuboidal epithelial tissue (foll

The research aims to determine optimal urban planning and design indicators of the urban clusters form in hot arid zones through studying of three urban areas in Baghdad, analyzing their urban indicators which include floor area ratio (FAR), urban clusters height, building density or land coverage, green areas, paved areas, shading ratio and how they affect urban temperature. The research reached the conclusion that air outdoor temperature on urban areas affected primarily by shadows casted on the ground, the effect of shaded area equals (5) times the effect of paved areas and (3.7) times the effect of green areas, this means that increasing urban clusters height in hot arid zones could minimize air outdoor temperature, building