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
In this work, yttrium oxide particles (powder) reinforced AL-Si matrix composites (Y2O3/Al-Si) and Chromium oxide particles reinforced AL-Si matrix composites (Cr2O3/AL-Si) were prepared by direct squeeze casting. The volume percentages of yttrium oxide used are (4, 8.1, 12.1, 16.1 vol %) and the volume percentages of the chromium oxide particles used are (3.1, 6.3, 9.4, 12.5 vol. %). The parameters affecting the preparation of Y2O3/Al-Si and Cr2O3/AL-Si composites by direct squeeze casting process were studied. The molten Al-Si alloy with yttrium oxide particles or with chromium oxide particles was stirred again using an electrical stirrer at speed 500 rpm and the molten alloy was poured into the squeeze die cavity. Th
... Show MoreIn this research we studied the structural and optical properties of (CdTe) thin films which have been prepared by thermal evaporation deposition method on the glass substrate at R.T with thickness (450  25) nm., as a function of doping ratio with copper element in (1,3,5) % rate .The structure measurement by X-ray diffraction (XRD) analyses shows that the single phase of (CdTe) with polycrystalline structure with a preferred orientation [111]. The optical measurement shows that the (CdTe) films have a direct energy gap, and they decrease with the increase of doping ratio reaching to 5% . The optical constants are investigated and calculated, such as absorpti
... Show MoreThe 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
Lead-free ferroelectric nano ceramics of BaZrxTi1-xO3 (x=0.1, 0.2 and 0.3) were prepared by means of microwave assisted chemical route. The structural, dielectric and electrical properties were examined. The crystalline structure of the specimens was studied by X-ray diffraction patterns. All the samples showed pure single phase of perovskite structure with space group of I4/mcm. X-ray diffraction data illustrated that there is no secondary phases exist. Structural and electrical properties of barium titanate ceramics are influenced significantly by small additions of Zr. The electrical conductivity showed higher values at x=0.2 and decreased at higher Zr content. The Hall charge mobility is found
... Show MorePetrophysical properties of Mishrif Formation at Amara oil field is determined
from interpretation of open log data of (Am-1, 2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12
and13) wells. These properties include the total, the effected and the secondary
porosity, as well as the moveable and the residual oil saturation in the invaded and
uninvaded zones. According to petrophysical properties it is possible to divided
Mishrif Formation which has thickness of a proximately 400 m, into seven main
reservoir units (MA, MB11, MB12, MB13, MB21, MC1, MC2) . MA is divided into
four secondary reservoir units , MB11 is divided into five secondary reservoir units ,
MB12 is divided into two secondary reservoir units , MB13 is divided into
The 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
In this research the effect of cooling rate and mold type on mechanical properties of the eutectic
and hypoeutectic (Al-Si) alloys has been studied. The alloys used in this research work were (Al- 12.6%Si
alloy) and (Al- 7%Si alloy).The two alloys have been melted and poured in two types of molds with
different cooling rates. One of them was a sand mold and the other was metal mold. Mechanical tests
(hardness, tensile test and impact test) were carried out on the specimens. Also the metallographic
examination was performed.
It has been found that the values of hardness for the alloys(Al-12.6%Si and Al-7%Si) which poured in
metal mold is greater than the values of hardness for the same alloy when it poured in a heated
The superconductor compound (YBa2Cu2.8Zn0.2O7+δ) is prepared by solid state reaction (SSR), Sol-gel (SG) and laser Pulse deposition (PLD) methods. We used the X-ray diffraction technique, which shows an orthorhombic crystalline system for all the samples, and increase in the high-phase (Y-123) and decrease in low-phase and vary in proportion according to the method of preparation with the emergence of some impurities. The behavior of the samples in terms of electrical resistance and critical temperature was investigated all samples showed superconducting behavior. The properties of the dielectric (real dielectric constant, imaginary dielectric constant, loss tangent, alternating electrical conductivity) were s
... Show Morestructural and electrical of CuIn (Sex Te1-x)2
The research included anatomical study of nine wild species of the genus
Athionema R.BR. from BrassicaceA family in Iraq, and these species are:
A.arabicum (L.), A.carneum (Banks et sol.),A. cordifolium (DC.), A.fimbriatum
(Boiss.),A. froedinii (Rech. F.), A. speciosum (Boiss. et Huet), A. syriacum
(Boiss.),A. grandiflorum (Boiss. et Hoh.) , A.trinervium (D.C.).The research
covered the anatomical characteristic of the leaf Epidermis as well as leaves
venation, also transvers sections for leaves were studied ,and revealed that some
anatomical characteristics have taxonomic importance in distinguishing the species.
This research also showed the presence of important variations in internal charecters
for leaves an