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
These days, the world is facing a global environmental and sustainability problem due to the increasing generation of large amounts of waste through construction and demolition work, which causes a serious problem for the environment. Therefore, this research was conducted to get rid of the waste disposal problems, including old glass and concrete, which were used as recycled fine aggregates. Seven different mixtures were prepared. The first mixture was with the used sand, which is glass sand, and it was adopted as a reference mixture (ORPC), and three mixtures were prepared for each of the recycled materials (waste concrete and glass) and partially replaced by glass sand in different proportions (25, 50, and 75) %. Some
... Show MoreThis paper aims to find new analytical closed-forms to the solutions of the nonhomogeneous functional differential equations of the nth order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability
Inthis investigation the epoxy was reinforced by orange peel and carbonized orange peel particles with percentages (5%, 10%, 15% and 20% by weight).Mechanical tests like:Tensile, flexural,Hardness, impact and compression were carried out on these natural epoxy composites. The results showed the tensile strength have a higher value by adding (15% by weight )of orange peel and carbonized orange peel particles to epoxy,while the value (10% by weight ) of addition is suitable to get improvement in the other mechanical properties as flexural strength, Hardness, impact and compressive strength. The epoxy / carbonized orange peel powder have the best valuesin all mechanical properties than t
This paper reports the effect of Mg doping on structural and optical properties of ZnO prepared by pulse laser deposition (PLD). The films deposited on glass substrate using Nd:YAG laser (1064 nm) as the light source. The structure and optical properties were characterized by X-ray diffraction (XRD) and transmittance measurements. The films grown have a polycrystalline wurtzite structure and high transmission in the UV-Vis (300-900) nm. The optical energy gap of ZnO:Mg thin films could be controlled between (3.2eV and 3.9eV). The refractive index of ZnO:Mg thin films decreases with Mg doping. The extinction coefficient and the complex dielectric constant were also investigate.
In this research, an enhancement in lubricating, rheological, and filtration properties of unweighted water-based mud is fundamentally investigated using XC polymer NPs with 0.2gm, 0.5gm, 1gm, 2gm, and 4gm concentrations. Bentonite, that had been used in the preparation of unweighted water-based mud, was characterized using XRF-1800 Sequential X-ray Fluorescence Spectrometer, XRD-6100/7000 X-ray Diffractometer, and Malvern Mastersizer 2000 particle size analyzer, respectively. Lubricating, rheology and filtration properties of unweighted water-based mud were measured at room temperature (35°C) using OFITE EP and Lubricity Tester, OFITE Model 900 Viscometer, and OFITE Low-Pressure Filter Press, respectively. XC Polymer N
... Show MoreThe optical transmission and UV-VIS absorption spectra have been recorded in the wavelength range (200-1100m) for different composition of polyaniline and polyvinyl Alcohol(PVA ) blends thin films. Polyaniline was prepared in acidic medium to enhancement the solubility and processibility, The optical energy gap (Eopt) refractive index and optical dielectric constant real and imaginary part have been evaluated. The effects of doping percentage of prepared polyaniline on these parameters was discussed and the non –linear behavior for all these parameters was investigated.
AlO-doped ZnO nanocrystalline thin films from with nano crystallite size in the range (19-15 nm) were fabricated by pulsed laser deposition technique. The reduction of crystallite size by increasing of doping ratio shift the bandgap to IR region the optical band gap decreases in a consistent manner, from 3.21to 2.1 eV by increasing AlO doping ratio from 0 to 7wt% but then returns to grow up to 3.21 eV by a further increase the doping ratio. The bandgap increment obtained for 9% AlO dopant concentration can be clarified in terms of the Burstein–Moss effect whereas the aluminum donor atom increased the carrier's concentration which in turn shifts the Fermi level and widened the bandgap (blue-shift). The engineering of the bandgap by low
... Show MoreA new metal complexes are made from the ligands derived from amoxicillin based Schiff's base coordinated with Pd(II) and Co(II) have been synthesized and characterized via different spectroscopic methods. FT-IR spectroscopy have shown a formation of tetrahedral and square planar geometry for Co(II) and Pd(II) complexes, respectively. Surface morphology was inspected via field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). The Brunauer–Emmett–Teller surface area of the metal complexes samples is about 6.63 to 8.71 m2/g, with pore diameters and volume of 0.030–0.0501 cm3/g and 18.39–22.98 nm, respectively. The quadrupo