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

          The research aims to determine the nature of the Iraqi market in terms of banking financial stability and the extent impact of the operational efficiency on it, Accordingly, chosen 15 relational banks were chosen as an intentional sample that could represent the Iraqi banking system for the period 2010-2020. The operational efficiency variable was measured according to the data envelope model, and banking financial stability used  CAMELS model which includes five indicators (capital adequacy, asset quality, management quality, profitability, and liquidity), so for testing the research hypotheses used the random regression model by adopting the S

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

     The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

The study aims to explore the effect of cognitive behavioral therapy on internet addiction among university students. The experimental method was used. The study population consisted of (100) university students (50 males, 50 females). The Research sample included (13) University students at Baghdad University addicted to the Internet (9 males, 4 females), divided into two groups:  a control group consisting of (6) individuals (4 males, 2 females) and an experimental sample consisting of (6) individuals (4 males, 2 females). The Scale of Internet Addiction by Young (1996), which was translated and modified into the Arabic language by (Moegel and Prism, 2016), was administered to the study sample. The sample was subjected to two sess

The aim of the research is to measure the relationship and effect of the application of total production maintenance TPM in the operational strategy, as it is considered one of the most important strategies for the process of restoring production losses because of inefficient equipment. Competitive edge in the global market by upgrading the operational strategies of OS in the application of TPM in those institutions that apply both H-OS-oriented and P-OS-oriented strategies where the strategy has been identified as a critical success factor. The aim of this study is to attempt to consider the application of comprehensive productive maintenance in industrial establishments