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
Iron-Epoxy composite samples were prepared by added
different weight percentages (0, 5, 10, 15, and 20 wt %) from Iron
particles in the range of (30-40μm) as a particle size. The contents
were mixed carefully, and placed a circular dies with a diameter of
2.5 cm. Different mechanical tests (Shore D Hardness, Tensile
strength, and Impact strength ) were carried out for all samples. The
samples were immersed in water for ten weeks, and after two weeks
the samples were take-out and drying to conducting all mechanical
tests were repeated for all samples. The hardness values increased
when the Iron particle concentration increased while the Impact
strength is not affected by the increasing of Iron particles
c
The effect of Al dust particles on glow discharge regions, discharge
voltage, discharge current, plasma potential, floating potential,
electron density and electron temperature in planar magnetron
sputtering device has been studied experimentally. Four cylindrical
Langmuir probes were employed to measure plasma parameters at
different point on the radial axis of plasma column. The results
shows the present of Al dust causes to increase the discharge voltage
and reduce the discharge current. There are two electron groups in
the present and absent of Al dust particles. The radial profiles of
plasma parameters in the present of dust are non- uniform. The
floating potential of probe becomes more negatively while
Different additives are used in drilling fluids when the demanded properties cannot be gotten with clays. Drilling muds needs several additives and materials to give good characteristics. There are local alternatives more suitable for enhancing the rheology and filtration of drilling fluids. An experimental work had been conducted to assess the suitability of using potato starch to enhance rheological properties and filtration in drilling mud. This study investigated the potato starch as a viscosifier and fluid losses agent in drilling fluid. Results from this study proved that rheological properties of potato starch mud increased when pH of drilling fluid is increased. Potato starch could be used to enhance gel strength at low pH
... Show MoreResearch in Iraq has expanded in the field of material technology involving the properties of the lightweight concrete using natural aggregate. The use of the porcelinate aggregate in the production of structural light concrete has a wide objective
and requires a lot of research to become suitable for practical application. In this work metakaolin was used to improve compressive strength of lightweight porcelinate concrete which usually have a low compressive strength about 17 MPa . The effect of metakaolin on compressive, splitting tensile, flexure strengths and modulus of elasticity of lightweight porcelinate concrete have been investigated. Many experiments were carried out by replacing cement with different percentages of
met
The electrical properties of Poly (ethylene oxide)-MnCl2 Composites were studied by using the impedance technique. The study was carried out as a function of frequency in the range from 10 Hz to 13 MHz and MnCl2 salt concentration ranged from 0% to 20% by weight. It was found that the dielectric constants and the dielectric loss of the prepared films increase with the increase of the MnCl2 concentration; The A.C. conductivity increases with the increase of the applied frequency, and the MnCl2 content in the composite membrane. Relaxation processes were observed to take place for composites which have a high salt concentration. The observed relaxation and polarization effects of the composite are mainly attributed to the dielectric
... Show MoreThis study investigates the ionic conduction dependence on the size of alkaline cations in gel polymer electrolytes based on double iodide can enhance by incorporating a salt having a bulky cation.
... Show MoreEpoxy resin has many chemical features and mechanical properties, but it has a small elongation at break, low impact strength and crack propagation resistance, i.e. it exhibits a brittle behavior. In the current study, the influence of adding kaolin with variable particle size on the mechanical properties (flexural modulus E, toughness Gc, fracture toughness Kc, hardness HB, and Wear rate WR) of epoxy resin was evaluated. Composites of epoxy with varying concentrations (0, 10, 20, 30, 40 weights %) of kaolin were prepared by hand-out method. The composites showed improved (E, Gc, Kc, HB, and WR) properties with the addition of filler. Also, similar results were observed with the decrease in particle size. In addition, in this study, mult
... Show MoreA computational investigation is carried out in the field of charged particle optics with the aid of the numerical analysis methods. The work is concerned with the design of symmetrical double pole piece magnetic lens. The axial magnetic flux density distribution is determined by using exponential model, from which the paraxial-ray equation is solved to obtain the trajectory of particles that satisfy the suggested exponential model. From the knowledge of the first and second derivatives of axial potential distribution, the optical properties such as the focal length and aberration coefficients (radial distortion coefficient and spiral distortion coefficient) are determined. Finally, the pole piece profiles capable of pr
... Show MoreThin films of CdS:Cu were deposited onto glass substrate temperature 400 °c. The optieal properties have been studied for Cds doped with (1,3, 8) wt% of Cu before and after Gamma irradiation. It was found that the irradiation caused an ( Frenkel defects) where the atom is displaced from its original site leaving vacancy and forming on interstitial atom. It was found the irradiation caused an absorption edge shifting towards long wavelength as a result of the increasing of Cu concentration.