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
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.
Kriging, a geostatistical technique, has been used for many years to evaluate groundwater quality. The best estimation data for unsampled points were determined by using this method depending on measured variables for an area. The groundwater contaminants assessment worldwide was found through many kriging methods. The present paper shows a review of the most known methods of kriging that were used in estimating and mapping the groundwater quality. Indicator kriging, simple kriging, cokriging, ordinary kriging, disjunctive kriging and lognormal kriging are the most used techniques. In addition, the concept of the disjunctive kriging method was explained in this work to be easily understood.
Exploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Exploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Letters in Biomathematics · Jul 7, 2025Letters in Biomathematics · Jul 7, 2025 Show publication This paper, presents the application of the B-spline transform as an effective and precise technique for estimating key parameters i.e., drift, volatility, and jump intensity for Lévy processes. Lévy processes are powerful tools for representing phenomena with continuous trends with abrupt changes. The proposed approach is validated through a simulated biological case study on animal migration in which movements are mo
... Show MoreSince the emergence of the science of international relations as an independent academic scientific field, various theories and trends have appeared and have tried to understand and explain the international reality and give a clear picture of what is happening within the international system of interactions and influences and the search for tools for stability and peace in international relations. Among these theories is the feminist theory, which is a new intellectual trend on the level of international relations theories, which tried to give an explanation of what is happening in world politics and in international relations in particular. The main issue that feminist theory is concerned with is the lack of women’s subordination
... Show MoreIn this research, a novel synthesis of CaONPs has been developed via an environmentally friendly, green method. Garlic extract (Allium sativum) was used as a green-reducing and stabilizing agent for CaONPs. The average particle size of CaONPs was approximately 24.42 nm. The synthesized CaONPs were identified by using Fourier transform infrared (FT-IR) spectroscopy, U.V.-vis spectrum, X-ray diffraction (XRD), Field Emission-Scanning Electron Microscopy (FE-SEM), Transmission Electron Microscopy, transmission electron microscopy (TEM), Energy Dispersive X-ray spectroscopy (EDX), Atomic Force Microscopy (AFM), and zeta potential (Zp) analysis. The current study highlights the notable applications for CaONPs. First, an antimicrobial assay revea
... Show MoreIn this work, composite materials were prepared by mixing different concentrations of ferrites with polyacrylonitrile (PAN) polymer. Using the electrospinning technique, these composites were deposited on a p-type silicon wafer. The prepared samples demonstrated nanofibers in both pure PAN polymers and their composites with ferrite. Prior to examining the humidity sensing effectiveness with a percentage of relative humidity at a frequency of 10 kHz, based on ambient temperature and a relative humidity range of 50–100%, the composite nanofibers demonstrated stronger humidity sensing compared to the pure PAN nanofibers, which demonstrated a powerful resistance response. More precisely, the PAN@ferrite nanocomposite showed a broad adsorption
... Show MoreThe integration of arti cial intelligence (AI), whether through devices or software, has become a critical tool in analyzing and evaluating technical performance. AI signi cantly contributes to enhancing athletic performance by enabling accurate data analysis and supporting educators in developing effective training programs and interactive curricula. This study addresses a noticeable gap in the literature regarding the attitudes and inclinations of educators toward AI in physical education and sport sciences—a gap often attributed to limited awareness and lack of access to moderntechnologies.Theprimaryaimofthestudyistoexaminethetendenciesandperceptionsoffemaleinstructorsin physical education and sport sciences toward the use of AI
... Show MoreResearch objective: This research aims to unveil how to use the method of referral in understanding the Holy Quran.
The reason for choosing the research: The one that invited me to write on this topic is the importance of the referral method, so I liked the research in it, and unveiled this wonderful Qur’anic method, so that it helps to understand the intention of God Almighty in his dear book.
The research plan: The research was divided into three topics and a conclusion.
As for the first topic, it is divided into two requirements. The first requirement deals with the definition of referral language.
In the second re