The real and imaginary part of complex dielectric constant for InAs(001) by adsorption of oxsagen atoms has been calculated, using numerical analysis method (non-linear least square fitting). As a result a mathematical model built-up and the final result show a fairly good agreement with other genuine published works.

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

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

This review examines how artificial intelligence (AI) including machine learning (ML), deep learning (DL), and the Internet of Things (IoT) is transforming operations across exploration, production, and refining in the Middle Eastern oil and gas sector. Using a systematic literature review approach, the study analyzes AI adoption in upstream, midstream, and downstream activities, with a focus on predictive maintenance, emission monitoring, and digital transformation. It identifies both opportunities and challenges in applying AI to achieve environmental and economic goals. Although adoption levels vary across the region, countries such as Saudi Arabia, the UAE, and Qatar are leading initiatives that align with global sustainability targets.