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
Air pollution is very important topic for those interested in studying the environment because of its importance and the damage caused by it to human, animal and plant life. This research addresses the concept of air pollution, its causes, and its danger, and sheds light on the influence of climate elements on environmental pollution and the effect of temperature, rain, humidity, wind direction and speed, and atmospheric pressure on the increase or decrease of air pollution. This research discusses the sources of air pollution, including natural ones, including dust, smoke resulting from fires, erupting volcanoes, and others, including those resulting from human uses such as the use of fuel and others. The research addressed the dam
... Show MoreNumeral recognition is considered an essential preliminary step for optical character recognition, document understanding, and others. Although several handwritten numeral recognition algorithms have been proposed so far, achieving adequate recognition accuracy and execution time remain challenging to date. In particular, recognition accuracy depends on the features extraction mechanism. As such, a fast and robust numeral recognition method is essential, which meets the desired accuracy by extracting the features efficiently while maintaining fast implementation time. Furthermore, to date most of the existing studies are focused on evaluating their methods based on clean environments, thus limiting understanding of their potential a
... Show MoreDo’a and Zikr al-Mā’thur (authentic supplications and remembrance of ALLAH ‘Azza wa Jalla) can be suggested to Muslims to help them deal with challenges or issues in life. Counselling cases affect a person’s feelings. Do’a and Zikr al-Mā’thur are often applied as a counselling intervention. Unfortunately, the authentic Do’a and Zikr al-Mā’thur are dispersed in many resources not visible to users, and the fact that not all online resources offer access to accurate Do’a and Zikr al-Mā’thur to users and the dubious Do’a and Zikr al-Mā’thur frequently credited to the Prophet (pbuh). The goal of this research is to develop an ontology
... Show MoreThe interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values
... Show MoreStatistical learning theory serves as the foundational bedrock of Machine learning (ML), which in turn represents the backbone of artificial intelligence, ushering in innovative solutions for real-world challenges. Its origins can be linked to the point where statistics and the field of computing meet, evolving into a distinct scientific discipline. Machine learning can be distinguished by its fundamental branches, encompassing supervised learning, unsupervised learning, semi-supervised learning, and reinforcement learning. Within this tapestry, supervised learning takes center stage, divided in two fundamental forms: classification and regression. Regression is tailored for continuous outcomes, while classification specializes in c
... Show MoreCefixime (CFX) was treated with sodium nitrite and hydrochloric acid for diazotization reaction followed by coupling with ?-Naphthol in alkaline medium to form, a yellow colored azo dye compound which exhibits maximum absorption (?max) at 412 nm where the concentration of (CFX) was determined spectrophotometrically. The optimum reaction conditions and other analytical parameters were evaluated. Beer’s law was obeyed in the concentration range of (1-20) ?g.mL-1 with a molar absorptivity of 34870.5 L.mol-1.cm-1. The limit of detection was found to be 0.1090 ?g.mL-1 and the Sandell's sensitivity value was 0.0130 ?g.cm-2. The proposed method could be successfully applied to
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