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
Platinum nanoparticles (PtNPs) exhibit promising biomedical properties, but concerns about biocompatibility and synthesis-related toxicity remain. This study aimed to develop eco-friendly PtNPs using aqueous broccoli extract as a natural reducing and stabilizing agent, and to assess their multifunctional biomedical potential. PtNPs were synthesized through sonochemical reduction of K₂PtCl₆ in broccoli extract, followed by purification and comprehensive physicochemical characterization. UV–Vis confirmed nanoparticle formation at 253 nm, while XRD and FTIR analyses verified the crystalline FCC structure and phytochemical capping. TEM revealed mainly spherical PtNPs with an average core size of 14.83 ± 7.67 nm. Conversely, DLS showe
... Show MoreThis research reviews the aesthetic variables that were founded according to (theatrical rehearsal) as one of the most important pillars on which the theatrical process is based, because of its necessity in developing theatrical art on several levels that helped the theatrical director in organizing his work, and this became clear through the research chapters represented in the first chapter (methodological framework) and the second chapter, which consisted of the first topic (the duality of watching / rehearsal) and the second topic (the applications of theatrical rehearsal in theatrical experiences), all the way to the third chapter (research procedures), which included the analysis of theatrical rehearsals (sharing on life), and the
... Show MoreThis study was carrid out to produce animal gelatin from chicken skin. Gelatin was prepared by the chemical method using HCl 2% and extraction at the temperature degree 70, 80, 90 c° and at the period of time 4, 6, 8 hours, calculated the yield, functional and sensory characteristics were measured at. The result also demonstrated that the produced gelatin have good functional properties in solubility, viscosity, gelling capacity, water absorpation, lipid binding, emulsification. viscosity was higher in gelatin prepared at 70 c° and period of extraction 8 hours and reached 1.0846 cp. Gelatin prepared were featured by highe gelling capacity at 1% for all extraction time periods. The produced gelatin was characterized by good sensory qual
... Show MoreThis search study the effect of particle size of graphite on the mechanical and thermal properties of epoxy composites, where graphite adopted with particle sizes (45,53,75) ?m, respectively, and the percentages by weight (0,1,3,5,7,9)% for each size of this three particle sizes.Mechanical properties represented by the bending (three-point bending) and through which the conclusion is bending stress and modulus of elasticity, thermal properties were either through thermal conductivity tests.The results showed that the ratio(1%) is the maximum value of bending stress at the three particle size and the (45 ?m) is the maximum.Thermal conductivity result show is the maximum value at ratio (1%) of particle size(53 ?m)
The electrical characteristics of polyvinyl alcohol PVA doped with different concentrations (0, 1, 2, 3 and 4wt%) of sodium iodide NaI powder were studied. The films are prepared using solution casting technique, in order to investigate the effect of sodium iodide NaI additions on the electrical properties of PVA host. The D.C conductivity measured by measuring the D.C electrical resistance using the Keithly Electrometer type 616C, and for different temperatures ranging from 30 – 70oC.
The dielectric properties measured by measuring the capacitor and the loss
... Show MoreThis contribution aims to investigate volume-dependent thermal and mechanical properties of the two most studied phases of molybdenum nitride (c-MoN and h-MoN) by means of the quasi-harmonic approximation approach (QHA) via first-principles calculations up to their melting point and a pressure of 12 GPa. Lattice constants, band gaps, and bulk modulus at 0 K match corresponding experimental measurements well. Calculated Bader’s charges indicate that Mo–N bonds exhibit a more ionic nature in the cubic MoN phase. Based on estimated Gibbs free energies, the cubic phase presents thermodynamic stability higher than that detected for hexagonl, with no phase transition observed in the selected T–P conditions as detected experimentall
... Show Morethe structrual and mechanical properties of thin Ni films of different thicknesses deposited on coring glass substrate using lonbeam sputtering(IBS) technique under vacuum torr have been studied the TEM and electron
Vanadium dioxide nanofilms are one of the most essential materials in electronic applications like smart windows. Therefore, studying and understanding the optical properties of such films is crucial to modify the parameters that control these properties. To this end, this work focuses on investigating the opacity as a function of the energy directed at the nanofilms with different thicknesses(1–100) nm. Effective mediator theories(EMTs), which are considered as the application of Bruggeman’s formalism and the Looyenga mixing rule, have been used to estimate the dielectric constant of VO2 nanofilms. The results show different opacity behaviors at different wavelength ranges(ultraviolet, visible, and infrared). The results depict that th
... Show MoreThin films of tin sulfide (SnS) were prepared by thermal evaporation technique on glass substrates, with thickness in the range of 100, 200 and 300nm and their physical properties were studied with appropriate techniques. The phase of the synthesized thin films was confirmed by X-ray diffraction analysis. Further, the crystallite size was calculated by Scherer formula and found to increase from 58 to 79 nm with increase of thickness. The obtained results were discussed in view of testing the suitability of SnS film as an absorber for the fabrication of low-cost and non toxic solar cell. For thickness, t=300nm, the films showed orthorhombic OR phase with a strong (111) preferred orientation. The films deposited with thickness < 200nm deviate
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