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
This study aims to answer a significant problem of social sciences and philosophy: How do we construct an institutional reality such as diplomacy with an objective recognizable existence? The study assumes that the ability to build institutional reality is based on our biological capacity, as it takes different forms in all the institutions we construct. The study takes the theory of the American philosopher John Searle as an approach to examining the assumption. The study sums up important findings; cultures, although they share the biological capacity on which they produce institutional realities, differ in the form of the value standards on which the institutional realities are based. The study recommends the need of Arab social resea
... Show MoreRecently, numerous the generalizations of Hurwitz-Lerch zeta functions are investigated and introduced. In this paper, by using the extended generalized Hurwitz-Lerch zeta function, a new Salagean’s differential operator is studied. Based on this new operator, a new geometric class and yielded coefficient bounds, growth and distortion result, radii of convexity, star-likeness, close-to-convexity, as well as extreme points are discussed.
Some experiments need to know the extent of their usefulness to continue providing them or not. This is done through the fuzzy regression discontinuous model, where the Epanechnikov Kernel and Triangular Kernel were used to estimate the model by generating data from the Monte Carlo experiment and comparing the results obtained. It was found that the. Epanechnikov Kernel has a least mean squared error.
Mannich base is a versatile compound that can be easily modified to introduce different functional groups, allowing for the creation diverse selection of items with varying features. Additionally, the Mannich reaction is a valuable tool in organic synthesis, due to the fact it provides an effortless and efficient approach for synthesizing C-N bonds. Overall, The Mannich base and even its derivatives are essential in many aspects of chemistry and its complexes are in the pharmaceutical industry. Studies have revealed that it shows good anti-cancer, anti-mycobacterial, remarkable anti-HIV, anti-tubercular, anti-convulsant, anti-fungal, antiviral, antitumor, cytotoxic activities and in industrial applications such as in the creation of polymer
... Show MoreIn this research, cyclic compounds derived from 2- furfural mercaptan (oxazole, triazoles) were synthesized, and their biological efficacy was measured and compared with standard drugs. Also, their effectiveness as anti-oxidant was measured and compared with ascorbic acid as a standard substance. Some of the synthesized compounds were deduced with good efficacy. © 2021 Sami Publishing Company. All rights reserved
In this paper, the class of semi
Rare earth metal oxides (REMOs) have gained considerable attention in recent years owing to their distinctive properties and potential applications in electronic devices and catalysts. Particularly, cerium dioxide (CeO2), also known as ceria, has emerged as an interesting material in a wide variety of industrial, technological, and medical applications. Ceria can be synthesized with various morphologies, including rods, cubes, wires, tubes, and spheres. This comprehensive review offers valuable perceptions into the crystal structure, fundamental properties, and reaction mechanisms that govern the well-established surface-assisted reactions over ceria. The activity, selectivity, and stability of ceria, either as a stand-alone catalyst or as
... Show MoreAs they include both nucleophilic and electrophilic moieties on the same skeleton, enaminones are an important subclass of chemical compounds that contain conjugated NC=CC=O fragments. These active sites aid in the production of organic molecules containing linear or cyclic heteroatoms. Enaminones and the chemica1 compounds produced from them are both biologically active against the most dangerous bacteria. As a result, they have been utilized as starting materials for the synthesis of anti-inf1ammatory, antibacteria1, anticonvulsant, anticancer, anti-urease, anti-malaria1, optically luminescent, corrosion inhibition, and antitumor agents. Their synthesis has usually a terrific deal of interest and a plethora of synthetic paths have been na
... Show MoreThis studies p- CuO / n - Si hete-rojunction was deposited by high vacuum thermal evaporation of Copper subjected to thermal oxidation at 300 oC on silicon. Surface morphology properties of The optical properties concerning the transmission spectra were studies for prepared thin films. this structure have been studied. XRD anaylsis discover that the peak at (𝟏𝟏𝟏-) and (111) plane are take over for the crystal quality of the CuO films. The band gap of CuO films is found to be 1.54 eV. The average grain size of is measured from AFM analysis is around 14.70 nm. The responsivity photodetector after deposited CuO appear increasing in response