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
Overlapped have been prepared from epoxy resin material added to carbon Nanotube and percentages weight (0.1, 0.05, 0.01) % Studied the mechanical properties of the composite (bending, tensile an d hardness) has been found that the Flexural and tensile modulus of the composites were higher than the pure epoxy resin this may be due to the high mechanical strength of carbon nano tube (CNT). The hardness of the epoxy carbon Nanotube composites increased and the reason is due to increased overlap and stacking between the additives and material basis, which reduces the movement of polymer molecules leading to increased resistance to scratching material and cutting, will become more resistance to plastic deformation.
The optical energy gap and optical constants such as the reflective index, dielectric constant have been evaluated due to The optical transmission and UV-VIS absorption spectra have been recorded in the wavelength (200 - 1100 nm) for PVA/PANI polymer blends and PVA/PANI/ZnO nanocomposites with different concentrations of ZnO (0.02, 0.05, 0.07, 0.1and 0.2) wt %. The results indicate that the materials have allowed direct transition. The reflection index and dielectric constant are increase with wavelength
A calculation have been carried out for determination some of the spectroscopic properties of Hydrogen Iodide HI molecules such as, the intensity of the absorption spectrum as a function of the variation of the temperature ranging from 10 to 1000 K. This study shows that the populations and hence intensity of the molecule increased as the temperature increased. Another determination of the maximum rotational quantum number Jmax of N2 , CO , BrF AgCl and HI molecules has been carried out.
The huge magnetic fields of neutron star cause the nuclei of the stellar surface to form a tightly bound condensed layer. In this research some characteristics of polar gap and magnetosphere enclosed the star according to Sturrock Model were illustrated, positrons move out along the open field lines, and electrons flow to the stellar surface as in the related to Sturrock model. The magnetic field within polar gap areas, which is defined by the Irvin Radius (RL) decreases due to the expansion of the polar, resulting from the physical motion of the accreted material. The values of height gap at different distances from the star were estimated. The obtained results improve the most energetic positrons those with E? Emax radiate away their ener
... Show MoreThe research’s main goal is to investigate the effects of using magnetic water in concrete mixes with regard to various mechanical properties such as compressive, flexural, and splitting tensile strength. The concrete mix investigated was designed to attain a specified cylinder compressive strength (30 MPa), with mix proportions of 1:1.8:2.68 cement to sand to crushed aggregate. The cement content was about 380 kg/m3, with a w/c ratio equal to 0.54, sand content of about 685 kg/m3, and gravel content of about 1,020 kg/m3. Magnetic water was prepared via passing ordinary water throughout a magnetic field with a magnetic intensity of 9,000 Gauss. The strength test
Improving the ability of asphalt pavement to survive the heavily repeated axle loads and weathering challenges in Iraq has been the subject of research for many years. The critical need for such data in the design and construction of more durable flexible pavement in bridge deck material is paramount. One of new possible steps is the epoxy asphalt concrete, which is classified as a superior asphalt concrete in roads and greatly imparts the level of design and construction. This paper describes a study on 40-50 penetration graded asphalt cement mixed with epoxy to produce asphalt concrete mixtures. The tests carried out are the Marshall properties, permanent deformation, flexural fatigue cracking and moisture damage. Epoxy asphalt mixes perf
... Show MoreGypseous soils are common in several regions in the world including Iraq, where more than 28.6% of its surface is covered with this type of soil. This soil, with high gypsum content, causes different problems for construction and strategic projects. As a result of water flow through the soil mass, the permeability and chemical arrangement of these soils varies with time due to the solubility and leaching of gypsum. In this study, the soil of 36% gypsum content, was taken from one location about 100 km southwest of Baghdad, where the samples were taken from depths (0.5 - 1) m below the natural ground and mixed with (3%, 6%, 9%) of Copolymer and Novolac polymer to improve the engineering properties that include: collapsibility, perm
... Show MoreOne of the major problems in modern construction is the accumulation of construction and demolition waste; this study thus examines the consumption of waste brick in concrete based on the use of blended nano brick powder as replacement for cement and as a fine aggregate. Seven concrete mixes were developed according to ACI 211.1 using recycled waste brick. Nano powder brick at 0, 5, and 10% was used as a replacement by cement weight, with other mixes featuring 10, 20, and 30% partial replacement by volume of river sand with brick. The experimental results for replacement of cement with nano brick powder showed an enhancement in mechanical properties (compressive, flexural, and tensile strength) at 7,
