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 current research aims to identify the effect of the proposed strategy in accordance with realistic mathematics on the achievement and mathematical Interrelation of third Intermediate students. Two samples were tested from the middle third grade in a school affiliated with the General Directorate of Baghdad- Rusafa, the first for the academic year (2022-2021). The experimental group is (30) students taught according to the proposed strategy, and the control group is (30) students based on the traditional method. To achieve the research objective, the researchers developed a test for achievement consisting of (30) items and a test of sports interconnection composed of (20) items. The results of the stu

Background: Postoperative pain is one of the main complications following impacted mandibular third molar (IMTM) surgery. Objectives: The aim of this study was to assess the effect of the local application of bupivacaine on reducing early postoperative pain following IMTM surgery. Material and methods: A prospective, single-blinded, randomized controlled study was conducted on 40 patients who had undergone the surgical removal of an IMTM under local anesthesia. In the study group (n = 20), absorbable gelatin sponge (AGS) soaked in 3 mL of 0.5% plain bupivacaine hydrochloride was locally applied in the post-extraction socket. In the control group (n = 20), AGS soaked in 3 mL of normal saline was used. Pain intensity was assessed using a pa

This research revolves around the study of sports press coverage to the third African Youth Games that took place in Algeria from 19 to 28 July 2018. The games featured approximately 3000 athletes from 54 countries who competed in 27 sports. Five sports were qualified for the Youth Olympic Games in Argentina. The aim of this study was to analyze the content of the Algerian newspaper Ennahar El-Djadid by focusing on the discussions of various sports activities during the event. Thus, the descriptive approach and content analysis method were adopted for this research. They were used to highlight the newspaper's interest in this sports phenomenon. The chosen study samples were ten issue numbers of Ennahar El-Djadid newspaper

 A dynamic analysis method has been developed to investigate and characterize embedded delamination on the dynamic response of composite laminated structures. A nonlinear finite element model for geometrically large amplitude free vibration intact plate and delamination plate analysis is presented using higher order shear deformation theory where the nonlinearity was introduced  in the Green-Lagrange sense. The governing equation of the vibrated plate were derived using the Variational approach. The effect of different orthotropicity ratio, boundary condition and delamination size on the non-dimenational fundamental frequency and frequency ratios of plate for different stacking sequences are studied. Finally th

We extended the characterization of strict local minimizers of order two in ward,s
theorem for nonlinear problem to a certain class of nonsmooth semi-infinite problems with inequality constraints in the nonparametric constraint case.

A perturbed linear system with property of strong observability ensures that there is a sliding mode observer to estimate the unknown form inputs together with states estimation. In the case of the electro-hydraulic system with piston position measured output, the above property is not met. In this paper, the output and its derivatives estimation were used to build a dynamic structure that satisfy the condition of strongly observable. A high order sliding mode observer (HOSMO) was used to estimate both the resulting unknown perturbation term and the output derivatives. Thereafter with one signal from the whole system (piton position), the piston position make tracking to desire one with a simple linear output feedback controller after ca