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 Study was achieved adjectives physical and chemical water wells in the district of
Samarra , where a study has 42 sample groundwater in different regions of the judiciary
randomly distributed all over the judiciary and examined in vitro.
The study showed that the quality of groundwater in the general area of study
Kipritateh punctuated Klordih water quality and other quality Bicarboonatih.
Varied the key components of groundwater in the study area in concentrations
between periods of rain and drought, especially because of the cation ion exchange processes
as well as mitigation as a result of filtering rain water and dominated the calcium ion,
followed by sodium.
As for the negative ions has dominated ion s
Thin filis have been prepared from the tin disulphide (SnS2 ), the pure and the doped with copper (SnS2:Cu) with a percentages (1,2,3,4)% by using ahemical spray pyrolysis techniqee on substrate of glass heated up to(603K)and sith thicknesses (0.7±0.02)?m ,after that the films were treated thermally with a low pressure (10-3mb) and at a temperature of (473K) for one hour. The influence of both doping with copper and the thermal treatment on some of the physical characteristics of the prepared films(structural and optical) was studied. The X-ray analysis showed that the prepared films were polycrystalline Hexagonal type. The optical study that included the absorptance and transmitance spectra in the weavelength range (300-900)nm
... Show MoreIn this study three inorganic nano additives, namely; CaCO3, Al2O3 and SiO2 were used to prepare nanocomposites of unsaturated polyester in order to modify their mechanical properties, i.e. tensile strength, elongation, impact and hardness. The results indicated that all the three additives were effective to improve the mechanical properties up to 4% by weight. The effectiveness of them follows the order : CaCO3 > Al2O3 > SiO2 This is due to their particle size in which CaCO3 (13nm), Al2O3 (20-30nm) and SiO2 (15-20nm).
Low- and medium-carbon structural steel components face random vibration and dynamic loads (like earthquakes) in many applications. Thus a modification to improve their mechanical properties, essentially damping properties, is required. The present study focuses on improving and developing these properties, significantly dampening properties, without losing the other mechanical properties. The specimens used in the present study are structural steel ribbed bar ISO 6935 subjected to heating temperatures of (850, 950, and 1050) ˚C, and cooling schemes of annealing, normalizing, sand, and quenching was selected. The damping properties of the specimens were measured experimentally with the area under the curve for the loadi
... Show MoreIn this paper the effect of thermal annealing on the structural and optical properties of Antimony Selenide (Sb2Se3) is investigated. Sb2Se3 powder is evaporated on clean amorphous glass substrates at room temperature under high vacuum pressure (4.5×10-6 mbar) to form thin films. The structural investigation was done with the aid of X-ray diffraction (XRD) and atomic force microscopy (AFM). The amorphous to polycrystalline transformation of these thin films was shown by X-ray diffraction analysis after thermal annealing. These films' morphology is explained. (UV-Vis ) spectra in ranges from 300 to 1100 nm was used to examine the optical properties of the films .The absorption coefficient and optical energy gap of the investigated films are
... Show MoreThe D.C electrical and thermoelectrically properties of randomly mixed isolator – electrolyte system as (Al/ PVC – LiF/Al) junction consisting of polyvinyl chloride (PVC)resin reinforced with Lithium Fluoride (LiF) powder were studied. A comparison is made the properties of (PVC) material with varying percentage of (LiF) powder (0%, 30%, 50%, 80%)to find out the effect of reinforcement of isolator material. The composites dissolving in 10ml form tettraHaedroflourn (THF) and Solution were the castled in Petri dish and Laved it dry in the air, The out coming Sample were disc - Like shape of a diameter of about 3cm and thickness reneged between (0.01- 0.018) cm . The composites dissolving in 10ml form tettraHaedroflourn (THF) a
... Show MoreA nanocrystalline thin films of PbS with different thickness (400, 600)nm have been prepared successfully by chemical bath deposition technique on glass and Si substrates. The structure and morphology of these films were studied by X-ray diffraction and atomic force microscope. It shows that the structure is polycrystalline and the average crystallite size has been measured. The electrical properties of these films have been studied, it was observed that D.C conductivity at room temperature increases with the increase of thickness, From Hall measurements the conductivity for all samples of PbS films is p-type. Carrier's concentration, mobility and drift velocity increases with increasing of thickness. Also p-PbS/n-Si heterojunction has been
... Show MoreThe building of the Babylonian theater is considered as one of the distinctive buildings where its foundations have remained steadfast in the face of geographical changes, social's erosion and groundwater that threatened almost all traces of Babylon despite the destruction of the outer structure of the building. The general directorate of antiques performed prospection for those foundations (the ground map), and then the building was completed by new bricks over the original scheme. It became clear when examining the building; its components and foundations, that the building is unique in comparison with the old buildings of the world throughout Iraq. There are similar buildings in other places like Jordan and North Africa such as
CdS and CdS:Sn thin films were successfully deposited on glass
substrates by spray pyrolysis method. The films were grown at
substrate temperatures 300 C°. The effects of Sn concentration on the
structural and optical properties were studied.
The XRD profiles showed that the films are polycrystalline with
hexagonal structure grown preferentially along the (002) axis. The
optical studies exhibit direct allowed transition. Energy band gap
vary from 3.2 to 2.7 eV.