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 present work studies the mechanical properties of SiO2 μPs, and NPs in St/PVA blends. The samples were prepared by casting method as PVA, St/PVA blends at different concentrations (30, 40, 50, and 60 %). DSC and TGA tests were carried out to the samples evolved. The result showed a single glass transition temperature (Tg) for all St /PVA blends that was attributed to the good miscibility of the blends involved. It was found that (Tg) decrease with starch ratio increase. It was seen that (PVA) of (Tg=105 oC); The glass transition temperature which was decrease with starch ratio that was attributed to glass transition relaxation process due to micro-Brownian motion of the main chain back bond. The endothermic peak at 200 oC was attrib
... Show MoreThe present work shows a theoretical results that have been used the functional Hybrid of three parameters Lee-Yang-Parr (B3LYP) of the quantum mechanical approach for density functional theory with (Spanish Initiative for Electronic Simulations with Thousands of Atoms) SIESTA code. All calculations were carried out employing the used method at the Gaussian 09 package of programs. It was reported the main point for research on dominance of the bandgap of elongated pi-conjugated molecules by using different chemical groups replacing hydrogen atom in the most molecules that used in this work. The side groups creates another factor that controls the value of the band gap. The dihedral angle between the two pheny
... Show MoreThis contribution investigates structural, electronic, and optical properties of cubic barium titanate (BaTiO3) perovskites using first-principles calculations of density functional theory (DFT). Generalized gradient approximations (GGA) alongside with PW91 functional have been implemented for the exchange–correlation potential. The obtained results display that BaTiO3 exhibits a band gap of 3.21 eV which agrees well with the previously experimental and theoretical literature. Interestingly, our results explore that when replacing Pd atom with Ba and Ti atoms at 0.125 content a clear decrease in the electronic band gap of 1.052 and 1.090 eV located within the visible range of electromagnetic wavelengths (EMW). Optical parameters such as a
... Show MoreBackground: Polyetheretherketone (PEEK) is a promising implant material due to its superior biomechanical strength. However, due to its hydrophobic nature and lack of cellular adhesion properties, it has poor integration with bone tissue. Methods: A fractional CO2 laser was used with various parameters for surface texturing of PEEK substrate to enhance its surface properties. An optical microscope and field-emission scanning electron microscope (FESEM) were used to examine the surface morphology of untextured and laser-textured samples. Energy dispersive X-ray spectroscopy (EDX) was performed to determine the effect of the laser on the microstructure of PEEK. Surface microroughness, atomic force microscopy (AFM), and wettability were invest
... Show MoreOne of the most important problems that faces the concrete industry in Iraq is the deterioration due to internal sulfate attack , since it reduces the compressive strength and increases the expansion of concrete. Consequently, the concrete structure may be damage .The effects of total and total effective sulfate contents on high strength concrete (HSC) have been studied in the present study. The research studied the effect of sulfate content in cement , sand and gravel , as well as comparing the total sulfate content with the total effective SO3 content. Materials used were divided into two groups of SO3 in cement ,three groups of SO3 in sand ,and two groups of SO3 in gravel. The results show that considering the total effective sulfate con
... Show MoreRecently, a great rise in the population and fast manufacturing processes were noticed. These processes release significant magnitudes of waste. These wastes occupied a notable ground region, generating big issues for the earth and the environment. To enhance the geotechnical properties of fine-grained soil, a sequence of research projects in the lab were conducted to analyze the impacts of adding sludge waste (SW). The tests were done on both natural and mixed soil with SW at various proportions (2%, 4%, 6%, 8%, and 10%) based on the dry mass of the soil used. The experiments conducted focused on consistency, compaction, and shear strength. With the addition of 10% of SW, the values of LL and PI decreased by 29.7% and 3
... Show MoreThe study concern with the preparation of three type of mixtures; which are prepared from different percentage of polyvenil Butyral, Di-n-butyl phathalate and paraffin wax pastillated. The solvent used is Xylolzul analyses. After washing, Drying and milling the kaolin Dukhla, as a matrix in this study, and by using sieving Tech. The range of particle size used is less than and less than as a mesh batch. The added percentage from prepared mixture were 5% and 10% to 95% and 90% of the matrix respectively. Then disk samples were prepared by using a compaction pressure with heating. After cooling and drying the samples were undergo heat treatment in the range of (1250 – 1350) oC. The measurement of shrinkage and Dielectric properties sho
... Show MoreThe current Iraqi standard specifications for roads and bridges allowed the prepared Job-Mix Formula for asphalt mixtures to witness some tolerances with regard to the following: coarse aggregate gradation by ± 6.0 %, fine aggregate gradation by ± 4.0 %, filler gradation by ± 2.0 %, asphalt cement content by ± 0.3 % and mixing temperature by ± 15 oC. The objective of this work is to evaluate the behavior of asphalt mixtures prepared by different aggregates gradations (12.5 mm nominal maximum size) that fabricated by several asphalt contents (40-50 grade) and various mixing temperature. All the tolerances specified in the specifications are taken into account, furthermore, the zones beyond these tolerances
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