This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

Background: The study aimed to investigate the effect of different techniques of en masse retraction on the vertical and sagittal position, axial inclination, rate of space closure, and type of movement of maxillary central incisor. Materials and methods: A typodont simulation system was used (CL II division 2 malocclusion). Three groups were used group 1(N=10, T-loop), group 2(N=10, Time-Saving loop), and group 3(N=10, Microimplant). Photographs were taken before and after retraction and measurements were made using Autodesk AutoCAD© software 2010. Kruskal-Wallis one-way analyses of variance and Mann-Whitney U test (p?0.05) were used. Results: The rate of space closure showed no significant difference among the three groups (p?0.05), whi

Secured multimedia data has grown in importance over the last few decades to safeguard multimedia content from unwanted users. Generally speaking, a number of methods have been employed to hide important visual data from eavesdroppers, one of which is chaotic encryption. This review article will examine chaotic encryption methods currently in use, highlighting their benefits and drawbacks in terms of their applicability for picture security.

This study aims to demonstrate the role of artificial intelligence and metaverse techniques, mainly logistical Regression, in reducing earnings management in Iraqi private banks. Synthetic intelligence approaches have shown the capability to detect irregularities in financial statements and mitigate the practice of earnings management. In contrast, many privately owned banks in Iraq historically relied on manual processes involving pen and paper for recording and posting financial information in their accounting records. However, the banking sector in Iraq has undergone technological advancements, leading to the Automation of most banking operations. Conventional audit techniques have become outdated due to factors such as the accuracy of d

An ultrasonic treatment was applied to the vacuum gas oil at intervals of 5 to 30 minutes, at 70°C.  In this work, the improvement of the important properties of Iraqi vacuum gas oil, such as carbon residue, was studied with several parameter conditions that affect vacuum efficiency, such as sonication time (5, 10, 15, 20, 25, and 30) min, power amplitude (10–50%). After ultrasonic treatment, the carbon residue of vacuum gas oil was evaluated using a Conradson carbon residue meter (ASTM D189). The experiment revealed that the oil's carbon residue had decreased by 16%. As a consequence of the experiment It was discovered that ultrasonic treatment might reduce the carbon residual and density of oil samples being studied. It also notice

In this paper, a new class of nonconvex sets and functions called strongly -convex sets and strongly -convex functions are introduced. This class is considered as a natural extension of strongly -convex sets and functions introduced in the literature. Some basic and differentiability properties related to strongly -convex functions are discussed. As an application to optimization problems, some optimality properties of constrained optimization problems are proved. In these optimization problems, either the objective function or the inequality constraints functions are strongly -convex. 

The research aims to detect the problems of educational reality faced by university professors and identify statistically significant differences in the academic problems of university instructors. It has adopted an analytical descriptive research approach to achieve research objectives and identifies the study community with professors of public and private universities. A random sample of 250 instructors was selected for the purpose of applying the questionnaire to them, knowing the academic problems encountered in the course of their work at universities, and adopting appropriate statistical means to process and analyze the data. The research concluded with a set of results, including that all fields (infrastructure, admission of