The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

This research delts with study seven species of seeds and wild varieties wild belonging to the genus Medicago L., these species are: M. constricta Dur., M. coronata (L.) Bartal., M. intertexta (L.) Mill., M. intertexta.var. ciliaris (L.) Hyen., M. laciniata (L.) Mill., M. lupulina L., M. minima (L.) Bartal. and M. sativa L., the research involved characteristics of shapes, dimensions, colors and the nature of the surface ornamentation of seeds and also the hilum site. the seeds forms ranged between crescent, reniform and ovate, in addition there was a clear difference in seeds dimensions in height and width, while, the color has been vary between light brown to brown and dark brown. The nature of the surface ornamentation was smooth, retic

The effect of electrolysis operating parameters on the removal efficiency of cadmium from a simulated wastewater was studied by adopting response surface methodology combined with Box–Behnken Design. As a new electrode design, spiral-wound woven wire mesh rotating cylinder electrode was used for cadmium removal. Current (240–400 mA), rotation speed (200–1000 rpm), initial cadmium concentration (200–600ppm), and cathode mesh number (30–60) were chosen as independent variables while the removal efficiency of cadmium was considered as a response function. The results revealed that the rotation speed has the major effect on the removal efficiency of cadmium. Regression analysis showed good fit of the experimental data to the second-or

Objectives: The study aimed to clarify the role of Al-Sayyid Al-Ajall and his family in the service of the Mongol Empire. They worked to develop its administrative and military institutions, benefiting from their extensive experience in administration, politics, economics, and urban affairs. Due to their capabilities, they received the patronage of Genghis Khan and subsequent generations, earning the confidence of the ruling Mongol authority. As a result, they were granted significant powers within the state.       Methods: The study relied on the analytical method to analyze historical texts, compare them with others, and discuss them accurately. Results: The study yielded several results, including the minister's keen interes

The government of Iraq states that despite the massive amounts invested in the power generating sector, the country has been plagued by power outages for more than three decades; One of the most common sources of the problem and significant impact on the waste of public funds in contractual processes. The Ministry of Planning issued the sectorial
specialized standard bidding documents (SSBD) of Design, Supply, and Installation of the Electromechanical Works (DSIoEW), which is primarily designed to support the Ministry of Electricity (MoE) by developing economic projects to improve the contractual process that led to raisings Iraqi electricity generation field. The research evaluates the impact of
applying the SSBD-DSIoEW for