This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison
Abstract
The hydrometallurgical method was used to platinum and palladium leaching with aqua regia solution (3HCl: HNO3). The leaching experiments were designed to obtain the optimum conditions by using Taguchi method with 16 experiments at three different factors (time, temperature and solid to liquid ratio), and each factor has four different levels. In this study, leaching the powder sample of catalytic converter that contains platinum and palladium was conducted on the basis of the formation of chloro complexes platinum and palladium (PtCl62-, PdCl42-) with different concentrations in the acidic solution. The optimum condi
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In 2020 one of the researchers in this paper, in his first research, tried to find out the Modified Weighted Pareto Distribution of Type I by using the Azzalini method for weighted distributions, which contain three parameters, two of them for scale while the third for shape.This research compared the distribution with two other distributions from the same family; the Standard Pareto Distribution of Type I and the Generalized Pareto Distribution by using the Maximum likelihood estimator which was derived by the researchers for Modified Weighted Pareto Distribution of Type I, then the Mont Carlo method was used–that is one of the simulation manners for generating random samples data in different sizes ( n= 10,30,50), and in di
... Show MoreGram-positive enterococciare opportunistic and resistant to many antibiotics. This study aimed to investigate the presence of Enterococcus spp. in our community and whether these isolates are resistant to the macrolides class of antibiotics. Fifty isolates from 112 clinical samples were recognized as Enterococcus spp. and confirmed using Vitek-2 system. The current study found that 50/112 (44.6%) represented the total isolates, 38/50 (76%) of which were Enterococcus faecalis, while 12/50 (24%) were Enterococcus faecium, twenty (40%) isolates from root canals and 30 (60%) isolates from urine were isolated. The sensitivity of the enterococcal isolates to various macrolides (erythromycin, azithromycin and clarithromycin) antibiotics wa
... Show MoreExplainable Artificial Intelligence (XAI) techniques enable transparency and trust in automated visual inspection systems by making black-box machine learning models understandable. While XAI has been widely applied, prior reviews have not addressed the specific demands of industrial and medical inspection tasks. This paper reviews studies applying XAI techniques to visual inspection across industrial and medical domains. A systematic search was conducted in IEEE Xplore, Scopus, PubMed, arXiv, and Web of Science for studies published between 2014 and 2025, with inclusion criteria requiring the application of XAI in inspection tasks using public or domain-specific datasets. From an initial pool of studies, 75 were included and categorized in
... Show MoreTo assess the use of miniaturized percutaneous nephrolithotomy (mini-PCNL) for renal stones in children, as well as its safety and efficacy. Seventy-seven patients with more than 15 mm renal stones whose age was less than 15 years were enrolled in this prospective case-controlled study at Al-Ramadi Teaching Hospital, Ar Razi Private Hospital, and Ghazi Al-Hariri Hospital for Surgical Specialties, Anbar and Baghdad, Iraq. The study was conducted from January 2020 to January 2024. The group mentioned above served as group A, and it was compared to the control group (group B), which consisted of 70 adult patients aged 18–60 years. Patients in both groups underwent mini-PCNL. Gender, stone size and location, time of operation, stone-free rate
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