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 electrospun nanofibers membranes (ENMs) have gained great attention due to their superior performance. However, the low mechanical strength of ENMs, such as the rigidity and low strength, limits their applications in many aspects which need adequate strength, such as water filtration. This work investigates the impact of electrospinning parameters on the properties of ENMs fabricated from polyacrylonitrile (PAN) solved in N, N-Dimethylformamide (DMF). The studied electrospinning parameters were polymer concentration, solution flow rate, collector rotating speed, and the distance between the needle and collector. The fabricated ENMs were characterized using scanning electron microscopy (SEM) to understand the surface morphology and es
... Show MoreIn recent years, nano-modified asphalt has gained significant attraction from researchers in the design of asphalt pavement fields. The recently discovered Titanium dioxide nanoparticles (TiO2) are among the most exciting and promising nanomaterials. This study examines the effect of 1, 3, 5, and 7% of nano-TiO2 by weight of asphalt on some of its rheological and hardened properties. The experimental study included physical and rheological properties. The asphalt penetration, softening point, ductility, and rotational viscometer tests indicate that 5% nano-TiO2 is the ideal amount to be added to bitumen as a modifier. The
The electrical properties of pure NiO and NiO:Au Films which are
deposited on glass substrate with various dopant concentrations
(1wt.%, 2wt%, 3wt.% and 4wt.%) at room temperature 450 Co
annealing temperature will be presented. The results of the hall effect
showed that all the films were p-type. The Hall mobility decreases
while both carrier concentration and conductivity increases with the
increasing of annealing temperatures and doping percentage, Thus,
indicating the behavior of semiconductor, and also the D.C
conductivity from which the activation energy decrease with the
doping concentration increase and transport mechanism of the charge
carriers can be estimated.
Effect of the thermal annealing at 400oC for 2 hours and Argon laser radiation for half hour on the optical properties of AgAlS2 thin films, prepared on glass slides by chemical spray pyrolysis at 360oC with (0.18±0.05) μm thickness .The optical characteristics of the prepared thin films have been investigated by UV/Vis spectrophotometer in the wavelength range (300 – 1100)nm .The films have a direct allow electronic transition with optical energy (Eg) values decreased from (2.25) eV for untreated thin films to (2.10) eV for the annealed films and to (2.00) eV for the radiated films. The maximum value of the refractive index (n) for all thin films are given about (2.6). Also the extinction coefficient (K) and the real and imaginary d
... Show MoreHedging is a linguistic avoidance of full commitment or precision. It is the use of a vague language. The main objectives of this study are to
... Show MoreIn 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions , is a non-negative integer
Mixed ligand metal complexes of CrIII, FeIII,II, NiII and CuII have been synthesized using 5-chlorosalicylic acid (5-CSA) as a primary ligand and L-Valine (L-Val) as secondary ligand. The metal complexes have been characterized by elemental analysis, electrical conductance, magnetic susceptibility measurements and spectral studies. The electrical conductance studies of the complexes indicate their electrolytic nature. Magnetic susceptibility measurements revealed paramagnetic nature of the all complexes. Bonding