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, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data sets
The paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.
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 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
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 Morethe research goal is preparing a list of standard criteria and quality controls for information technology applications to serve the Holy Quran.
To achieve this goal, the researcher has built a list of criteria according to the following steps:
First - identify the key areas covered by the whole list which are:
1 – Standards of system building and implementing with the operating screens.
2 – Standards of display forms including audio and video presentation.
3 – Standards which are related to the program philosophy.
4 - Standards which are related to the program objectives.
... Show MoreA critical milestone in nano-biotechnology is establishing reliable and ecological friendly methods for fabricating metal oxide NPs. Because of their great biodegradable, electrical, mechanical, and optical qualities, zirconia NPs (ZrO2NPs) attract much interest among all zirconia NPs (ZrO2NPs). Zirconium oxide (ZrO2) has piqued the interest of researchers throughout the world, particularly since the development of methods for the manufacture of nano-sized particles. An extensive study into the creation of nanoparticles utilizing various synthetic techniques and their potential uses has been stimulated by their high luminous efficiency, wide bandgap, and high exciton binding energy. Zirconium dioxide nano
... Show MoreIn this paper, the class of semi
In 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