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
Oilwell cementing operations are crucial for drilling and completion, preserving the well's productive life. However, weak and permeable formations pose a high risk of cement slurry loss, leading to failure. Lightweight cement, like foamed cement, is used to avoid these difficulties. This study is focused on creating a range of foamed slurry densities and examining the effect of gas concentration on their rheological properties. The foaming agent and foam stabilizer are tested, and the optimal concentration is determined to be 2% and 0.12%, respectively, by the weight of the cement.
Furthermore, the construction of samples of foam cement with different densities (0.8, 1.0, 1.2, 1.4, and 1.6) g/cc is performed to f
... Show MoreAntimony (Sb) films are fabricated by depositing (Sb) on glass substrates at room
temperature by the method of vacuum evaporation with thickness (0.25 and 0.51m),
with rate of deposition equal to (2.77Å/sec), the two samples are annealed in a
vacuum for one hour at 473K. The optical constants which are represented by the
refractive index (n), extinction coefficient (k) were determined from transmittance
spectram in the near Infrared(2500-3500 )nm regions. The tests have been shown
that the optical energy gap increases with increasing of annealing temperature for
the two samples.
The zeolite's textural properties have a significant effect on zeolite's effectiveness in the different industrial processes. This research aimed to study the textual properties of the NaX and FeX zeolites using the nitrogen adsorption-desorption technique at a constant low temperature. According to the International Union of Pure and Applied Chemistry, the adsorption-desorption isotherm showed that the studied materials were mixed kinds I/II isotherms and H3 type hysteresis. The Brunauer-Emmett-Teller isotherm was the best model to describe the nitrogen adsorption-desorption better than the Langmuir and Freundlich isotherms. The obtained adsorption capacity and Brunauer-Emmett-Teller surface area values for NaX were greater than FeX. Ac
... Show MoreIn this work, the emission spectra and atomic structure of the aluminum target had been studied theoretically using Cowan code. Cowan code was used to calculate the transitions of electrons between atomic configuration interactions using the mathematical method called (Hartree-Fock). The aluminum target can give a good emission spectrum in the XUV region at 10 nm with oscillator strength of 1.82.
The hydrodynamic properties of laser produced plasma (LPP) were investigated for the purpose of creating a light source working in the EUV region. Such a light source is very important for lithography (semiconductor manufacturing). The improved MEDUSA (Med103) code can calculate the plasma hydrodynamic properties (velocity, electron density,
The refractive indices, nD densities 𝜌, and viscosities of binary mixtures of sulfolane + n -butanol + sec- butanol + iso- butanol + tert – butanol + n-propanol and iso- propanol were measured at 298.15K. Form experimental data, excess molar volum VE , excess molar refractivity ∆nD, excess molar viscosity E and excess molar Gibbs free energy of activation of viscous flow G *E were calculated. From n-propanol – sulfolane and iso- propanol sulfolane mixtures showed negative ∆nD, n-butanol – sulfolane, sec-butanal – sulfolane, iso-butanol – sulfolane and tert- butanol sulfolane , nD was positive over the whole mole fraction rang , while VE , E and G *E show a negative deviation. The
... Show MoreStudy the effect of doping V2O5 on polymers poly vinyl alcohol ( PVA), poly vinyl pyrrolidone (PVP) on the optical and structural properties for film prepared by using Casting method at thickness( 300±20)nm ,All the materials dissolved in distilled water by magnetic mixer for one hour .The optical parameters measured by using UV-VIS spectrometer ,and the structural parameters measured by X-ray diffraction .when measured the energy gap found that the value was decreases from 4.6 eV to 2.98 eV with doping .The refractive index ,extinction coefficient ,absorption coefficient ,real and imaginary dielectric constants of (PVA/PVP) are increasing with doping by V2O5 and wit
... Show MoreAn extracellular β-galactosidase from the thermophilic fungus Rhizomucor
Pusillus IB8 has been purified via several steps included precipitation by ammonium
sulphate at 80 % saturation, DEAE- Cellulose Ion exchange chromatography and gel filteration on sepharose CL-6B column. The Final purification folds and the yield of the enzyme were 42.5 and 24.8 % respectively. The purified β-galactosidase has an optimum pH for its activity between 4.5 to 5, while the optimum pH for enzyme stability was between 5 to 5.5. Futhermore, it was found that the optimum temperature for its activity was 60 C°. The purified enzyme retained approximatly 98% of its original activity when incubated at 60 C° for 60 min. However, 25 % of its activity was
Polyaniline membranes of aniline were produced using an electrochemical method in a cell consisting of two poles. The effect of the vaccination was observed on the color of membranes of polyaniline, where analysis as of blue to olive green paints. The sanction of PANI was done by FT-IR and Raman techniques. The crystallinity of the models was studied by X-ray diffraction technique. The different electronic transitions of the PANI were determined by UV-VIS spectroscopy. The electrical conductivity of the manufactured samples was measured by using the four-probe technique at room temperature. Morphological studies have been determined by Atomic force microscopy (AFM). The structural studies have been measured by (SEM).