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
Titanium dioxide (TiO2) Nano powder has been synthesized by hydrothermal method. The reaction took place between titanium tetrachloride (TiCI4) and mixture solution consisted of deionized water and ethanol, in the ratio (3:7) respectively. Structure and surface morphology of TiO2 Nano powder at different annealing temperatures in the range 200-800°C for 120 min were characterized by X-ray diffraction (XRD), Atomic Force Microscope (AFM), Scanning Electron Microscopy (SEM), FT-IR and UV/visible spectroscopy measurements. The results show that with an increase in annealing temperature, the value of the intensity of (110) peak for rutile phase increases while the value of the full-width at half maximum (FWHM) decreases, and the band gap de
... Show Moreواحدة من أكثر مواد السيراميك الهيكلية الواعدة هي كربيد السيليكون(SiC) ، حيث له خصائص حرارية وكهروميكانيكية ممتازة. هذه الخصائص مفيدة ل CMC لتعزيز أداء المركب خاصة عند إضافات النانو المتكاملة. في هذا البحث, تم تصنيع مركب SiC من SiC بثلاثة تركيزات مع ZnO و Si. تم اختبار الخواص المغناطيسية لجميع المخاليط باستخدام مراقبة العينة الاهتزازية (VSM). تم تلبيد العينات الخضراء في فرن التلبيد عند 1600 درجة مئوية في بيئة النيتروجي
... Show MorePolyaniline (PANI) polymer was successfully prepared by the chemical oxidation method at 0 oC. Polyaniline-nano grapheme (GN) powder nanocomposites were prepared by the addition of GN with different weight ratios (0.1, 1, 5, and 10 g wt. %) during the polymerization of PANI. It was found that the polymerization reaction of poly-aniline was exothermic. The effect of adding nano-graphene powder during polymerization process on the time and temperature of the reaction was studied. The resulting polymer was diagnosed using several methods, including Fourier transform infrared spectroscopy (FT-IR) and UV-VIS spectrophotometry. The results of FTIR demonstrated a shift to higher wave numbers in the peaks of nanocomposites, due
... Show MoreCdSe alloy has been prepared successfully from its high purity elements. Thin films of this alloy with different thicknesses (300,700)nm have been grown on glass substrates at room temperature under very low pressure (10-5)Torr with rate of deposition (1.7)nm/sec by thermal evaporation technique, after that these thin films have been heat treated under low pressure (10-2)Torr at (473,673)K for one hour. X-ray patterns showed that both CdSe alloy and thin films are polycrystalline and have the hexagonal structure with preferential orientation in the [100] and [002] direction respectively. The optical measurements indicated that CdSe thin films have allowed direct optical energy band gap, and it increases from (1.77- 1.84) eV and from
... Show MoreIn this work, an organic semiconductor of copper (II) phthalocyanine (CuPc) and Tris(8-hydroxyquinoline) aluminum (III) (Alq3) were entirely dissolved in chloroform with various mixing ratios (1:0,0.75:0.25,0.5:0.5,0.25:0.75,0:1) (w/w) to make thin films. They were deposited on a pre-cleaned glass using a spin-coating process and heat-treated at 473 K in vacuum. X-ray diffraction and a scanning electron microscope were used to investigate the films. XRD analysis reveals that CuPc/Alq3 composites have a polymorphic structure, with the exception of Alq3's amorphous structure, the crystallinity increases after annealing, but decreases when the concentration of Alq3 is increased. The quantity of (CuPc) rod-like structure and (Alq3) grain-lik
... Show MoreThis work concerns the thermal and sound insulation as well as the mechanical properties of polymer matrix composite reinforced with glass fibers. These fibers may have dangerous effect during handling, for example the glass fibers might cause some damage to the eyes, lungs and even skin. For this reason the present work, investigates the behavior of polymer composite reinforced with natural fibers (Plant fibers) as replacement to glass fibers. Unsaturated Polyester resin was used as matrix material reinforced with two types of fibers, one of them is artificial (Glass fibers) and the other type is natural (Jute, Fronds Palm and Reed Fibers) by hand lay-up technique. All fibers are untreated with any chemical solvent. The Percentage of mi
... Show MoreCdSe alloy has been prepared successfully from its high purity elements. Thin films of this alloy with different thicknesses (300,700)nm have been grown on glass substrates at room temperature under very low pressure (10-5)Torr with rate of deposition (1.7)nm/sec by thermal evaporation technique, after that these thin films have been heat treated under low pressure (10-2)Torr at (473,673)K for one hour. X-ray patterns showed that both CdSe alloy and thin films are polycrystalline and have the hexagonal structure with preferential orientation in the [100] and [002] direction respectively. The optical measurements indicated that CdSe thin films have allowed direct optical energy band gap, and it increases from (1.771.84) eV and from (1.6-1
... Show MoreThe synthesis , characterization and mesomorphic behaviour of new Nacyl , thiourea and imidazole derivatives which derived from corresponding Schiff bases are reported. All the synthesized compounds which contain flexible methylene group in the centre of the molecule did not show any liquid crystalline properties . The derivatives of N- acyl [III]e and thiourea [VI]e which contain biphenyl and all compounds with one phenyl in the centre of the molecule display liquid crystalline behaviour .While the imidazoles did not show any liquid crystalline properties except [V]b [V]e with biphenyl in the centre of the molecule . All th
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