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
The current research studies the aesthetic framework for the dialectical development of the functions of the contemporary theater director in an aesthetic approach to the mechanisms of functional overlap between the dramaturgy and direction functions, and scenography and direction, the detection of the controversial structure of that overlap, and what can be summed up in the following question: (what are the aesthetic approaches of the dialectical development in the function of the contemporary theatre director?). The research is determined by a pivotal aim which is (knowing the aesthetic nature of the dialectical development in
This investigation aims to study some properties of lightweight aggregate concrete reinforced by mono or hybrid fibers of different sizes and types. In this research, the considered lightweight aggregate was Light Expanded Clay Aggregate while the adopted fibers included hooked, straight, polypropylene, and glass. Eleven lightweight concrete mixes were considered, These mixes comprised of; one plain concrete mix (without fibers), two reinforced concrete mixtures of mono fiber (hooked or straight fibers), six reinforced concrete mixtures of double hybrid fibers, and two reinforced concrete mixtures of triple hybrid fibers. Hardened concrete properties were investigated in this study. G
Cerium oxide CeO2, or ceria, has gained increasing interest owing to its excellent catalytic applications. Under the framework of density functional theory (DFT), this contribution demonstrates the effect that introducing the element nickel (Ni) into the ceria lattice has on its electronic, structural, and optical characteristics. Electronic density of states (DOSs) analysis shows that Ni integration leads to a shrinkage of Ce 4f states and improvement of Ni 3d states in the bottom of the conduction band. Furthermore, the calculated optical absorption spectra of an Ni-doped CeO2 system shifts towards longer visible light and infrared regions. Results indicate that Ni-doping a CeO2 system would result in a decrease of the band gap. Finally,
... Show MoreManganese-zinc ferrite MnxZn1-xFe2O4 (MnZnF) powder was prepared using the sol-gel method. The morphological, structural, and magnetic properties of MnZnF powder were studied using X-ray diffraction (XRD), atomic force microscopy (AFM), energy dispersive X-ray (EDX), field emission-scanning electron microscopes (FE-SEM), and vibrating sample magnetometers (VSM). The XRD results showed that the MnxZn1-xFe2O4 that was formed had a trigonal crystalline structure. AFM results showed that the average diameter of Manganese-Zinc Ferrite is 55.35 nm, indicating that the sample has a nanostructure dimension. The EDX spectrum revealed the presence of transition metals (Mn, Fe, Zn, and O) in Mang
... Show MoreA developed model has been put for the hypothesis of capturing moons in explaining the origin of Jupiter moons, and study the change of the orbital properties of these satellites as well as the distance from the planet. Jupiter moons were divided into two types according to their physical and orbital properties, they are the moons , which are formed from the same material as the planet, so it was named the original moons ,while the moons that have been captured from the surrounding space was renamed exotic moons . And the moons of exotic origin asteroid belt and the Kuiper belt in the region which is behind Neptune, the origin of each clique of moons is an asteroid fragmented after colliding previously with another body and
... Show MoreThis research discloses the synthesis of various polyester resins, the polyesters containing homoring aromatic and others heterocyclic were synthesized by the condensation polymerization of suitable monomers (which are containing variety function groups in different structures) with phthalic anhydride. The main objective is synthesis of new polyester with keeping a reasonable electrical insulating behavior. The structural of polymer was characterized by Fourier Transform infra-red spectroscopy FTIR and HNMR. The dielectric constant (real ε' and imaginary parts ε") and AC conductivity (σAC) for all the polyester samples are studied by varying the frequency (30, 50, 70, 90, 120, 300, 500Hz and 1KHZ) at 25⁰ C. Indeed, study of the electri
... Show MoreIn this work, Pure and Cu: doped titanium dioxide nano-powder was prepared through a solid-state method. the dopant concentration [Cu/TiO2 in atomic percentage (wt%)] is derived from 0 to 7 wt.%. structural properties of the samples performed with XRD revealed all nanopowders are of titanium dioxide having polycrystalline nature. Physical and Morphological studies were conducted using a scanning electronic microscope SEM test instrument to confirm the grain size and texture. The other properties of samples were examined using an optical microscope, Lee's Disc, Shore D hardness instrument, Fourier-transform infrared spectroscopy (FTIR), and Energy-dispersive X-ray spectroscopy (EDX). Results showed that the thermal conductivity
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