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
This study was undertaken to provide more insight on the optimum injection temperature used for the production of PE crates, thereby saving time and money, and improving part quality. The work included processing trails of HDPE crates in an injection
molding machine at five temperatures ranged from 220 to 300°C. Both Rheological and mechanical characterization was conducted in order to understand the effect of injection temperature on the properties of crates. Oven aging was also applied for (4 weeks) to evaluate the long-term thermal stability. The results revealed that producing the crates at a temperature range of (260-280 °C) gives the best rheological and mechanical result. The lowest drop in thermal stability has been observed
The study was conducted to detect the effect of addition of 0.03, 0.06 and0.10% potassium sorbate and 0.10, 0.15, 0.20 and 0.30% sodium propionate upon the sensory properties of laboratory made biscuit. The statistical analysis of the results revealed no significant differences (P<0.05) between the propionate treatment (A,B,C,D) and between the sorbate treatment (E,F,G) and the control (H) in most sensory properties of biscuit prior to storage. Upon six month storage of biscuit made with addition of different levels of sodium propionate 20-40C (room temperature) no significant differences (P<0.05) were shown on softness, flakiness and color in comparison with the control . No significant differences (P<0.05) were also
... Show MoreThis research of using Feldspar in the production self compacting concrete (SCC) ( 5,10,15 )% as partial replacement by weight of cement .In this research some of fresh properties of SCC ( slump flow used V-funnel test and filling ability used ( U- box test ) for concrete mixes and also some of the harden properties of SCC ( compressive and flexural tests ). The research results showed that negative effect of Feldspar on the fresh properties of self compacting concrete but the positive effect of Feldspar on the harden properties of self compacting concrete .
The influence of Diethyl phthalate (DEP) on the optical characteristics of polystyrene solutions in the range between 200 to 400 nm at solvents of different polarities; chloroform, cyclohexane, dichloromethane, and tetrahydrofuran have been recorded. The experimental results showed that the behavior of the photophysical processes of polymer solutions depends on the nature of its environment. The intensity of the absorption and fluorescence spectra depends on the interactions between solvent-solute molecules. The experimental results indicate that the maximum most absorbance bands occur around 262 nm, which depends on the concentration of the quencher. The results did not determine any change in the positions of the most absorption bands.
... Show MoreMagnesium aluminum silicate of glass ceramic having different amounts of magnesium fluoride in the range (0-13.2)%. Thermal expansion coefficient and micro hardness of the base glass and glass ceramic samples are seen to be interdependent but due to the multi – component system, the behaviour is seen to be somewhat complex, with an increase in Mg F2 content. The thermal expansion coefficient increase and micro harness decrease, numerical simulation of thermal expansion and hardness is useful in this study, L2 – regression is used to calculate the two parameters associated with each glass component, by comparing the measured parameters and the calculated parameters ,it is useful to use such a method to calculate the quantity
... Show MoreThe atomic properties have been studied for He-like ions (He atom, Li+, Be2+ and B3+ions). These properties included, the atomic form factor f(S), electron density at the nucleus , nuclear magnetic shielding constant and diamagnetic susceptibility ,which are very important in the study of physical properties of the atoms and ions. For these purpose two types of the wave functions applied are used, the Hartree-Fock (HF) waves function (uncorrelated) and the Configuration interaction (CI) wave function (correlated). All the results and the behaviors obtained in this work have been discussed, interpreted and compared with those previously obtained.
Study the effect of additives polymer polyvinyl alcohol (PVA) after solving in water by concentration 10% since represent a standard of PVA solution with added to cement – silica composite of ratio (1:2) with 5%, 10%, 15%, 20%, and 25% respectively to the standard quantity of water which using as a mortar of building. The results are demonstrate increasing on compression resistance with increase of PVA solution until 20%, and decreasing of thermal conductivity which represent a composite are increasing in thermal insulating. The results were recommended decreasing of water absorption with increase of PVA solution ratio as illustrated in this study.
The problem of soil contamination is increased recently due to increasing the industrial wastes such as petroleum hydrocarbon, organic solvents, and heavy metals as well as maximizing the use of agricultural fertilizers. During this period, wide development of data collection methods, using remote sensing techniques in the field of soil and environment applications appear and state the suitable technique for remediation. This study deals with the application of remote sensing techniques in geoenvironmental engineering through a field spectral reflectance measurements at nine spots of naturally hydrocarbons contaminated soil in Al-Daura Refinery Company site which is located to the south west of Baghdad using radiometer device to get stan
... Show MoreThe different parameters on mechanical and microstructural properties of aluminium alloy 6061-T6 Friction stir-welded (FSW) joints were investigated in the present study. Different welded specimens were produced by employing variable rotating speeds and welding speeds. Tensile strength of the produced joints was tested at room temperature and the the effecincy was assessed, it was 75% of the base metal at rotational speed 1500 rpm and weld speed 50 mm/min. Hardness of various zones of FSW welds are presented and analyzed by means of brinell hardness number . Besides to thess tests the bending properties investigat
... Show MoreBlends of Polymethyl methacrylate (PMMA)/polyvinyl alcohol (PVA) doped with 2% weight percentage of Sn were prepared with different blend ratios using casting technique. The measurements of A.C conductivity σa.c within the frequency range (25kHz – 5MHz) of undoped and Sn doped PMMA/PVA blends obeyed the relationship σ= Aws were the value of s within the range 0 > s > 1. The results showed that σa.c increases with the increase of frequency. The exponent s showed preceding increase with the increase of PVA content for PMMA/PVA blends doped with Sn. The dielectric constant, dielectric loss, A.C electrical conductivity are varied with the concentration of PVA in the blend and frequency of applied electrical field.