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
Configured binary polymer blends of epoxy and Polyurethane was chosen varying proportions of these materials led to the production of homogeneous mixtures of Althermust Althermust and descent was poured polyurethane models required in the form of 4 mm thick plates
The aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra without identity can be embedded into fuzzy normed algebra with identity and is an ideal in is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.
Alloy of (HgTe) has been prepared succesful in evacuated qurtz ampoule at pressure 4×10-5torr, and melting temperature equal to 823K for five days. Thin films of HgTe of thickness 1μm were deposited on NaCl crystal by thermal evaporation technique at room temperature under vacuum about 4×10-5torr as well as investiagtion in the optical porperties included (absorption coefficient , energy gap) of HgTe films and The optical measurements showed that HgTe film has direct energy gap equal to 0.05 eV. The optical constants (n, k, εr, εi) have been measured over will range (6-28)μm.
Thin films of iridium doped indium oxide (In2O3:Eu)with different doping ratio(0,3,5,7,and 9%) are prepared on glass and single crystal silicon wafer substrates using spray pyrolysis method. The goal of this research is to investigate the effect of doping ratio on of the structural, optical and sensing properties . The structure of the prepared thin films was characterized at room temperature using X-ray diffraction. The results showed that all the undoped and doped (In2O3:Eu)samples are polycrystalline in structure and nearly stoichiometric. UV-visible spectrophotometer in the wavelength range (200-1100nm)was used to determine the optical energy gap and optical constants. The optical transmittance of 83% and the optical band gap of 5.2eV
... Show MoreInterest has largely centered on the use of plant fibers to reinforce plastics, because these fibers are abundant and cheap. Carrot fibers (Curran) have been extracted from carrot, left over from carrot juice manufacture. The fibers of two sizes fine (50<µm) and coarse (100-150 µm) have been mixed with epoxy in four levels of loading (10, 20, 30, 40 wt %) respectively. Impact test, shore d hardness test and three point bending test of epoxy and carrot fiber-epoxy composites samples have been determined. The impact strength values of samples prepared with fine and coarse fibers increased as compared with pure epoxy sample. Hardness values increased, and the Young’s modulus values decreased with fiber content of both sizes.
This contribution investigates the effect of the addition of the Hubbard U parameter on the electronic structural and mechanical properties of cubic (C-type) lanthanide sesquioxides (Ln2O3). Calculated Bader's charges confirm the ionic character of Lnsingle bondO bonds in the C-type Ln2O3. Estimated structural parameters (i.e., lattice constants) coincide with analogous experimental values. The calculated band gaps energies at the Ueff of 5 eV for these compounds exhibit a non-metallic character and Ueff of 6.5 eV reproduces the analogous experimental band gap of cerium sesquioxide Ce2O3. We have thoroughly investigated the effect of the O/Ce ratios and the effect of hafnium (Hf) and zirconium (Zr) dopants on the reduction energies of C
... Show MoreThe optical transmission and absorption spectra in UV-VIS were recorded in the wavelength range 350-800 nm for different glass compositions in the system: (CuO)x (PbO)50-x (Bi2O3)50 (x=2.5, 5.0, 7.5, 10.0, 12.5, 15.0, 20.0). Absorption coefficient {α (λ)}, optical energy gap (Eopt), refractive index (n), optical dielectric constant (ε`), Urbach energy (Ee), constant B and ratio of carrier concentration to the effective mass (N/m) have been reported. The effects of compositions of glasses on these parameters have been discussed. It has been indicated that a small compositional modification of the glasses lead to an important change in all the optical properties including non-linear behavior. The optical parameters were found to b
... Show MoreBurnishing improves fatigue strength, surface hardness and decrease surface roughness of metal because this process transforms tensile residual stresses into compressive residual stresses. Roller burnishing tool is used in the present work on low carbon steel (AISI 1008) specimens. In this work, different experiments were used to study the influence of feed parameter and speed parameter in burnishing process on fatigue strength, surface roughness and surface hardness of low carbon steel (AISI 1008) specimens. The first parameter used is feed values which were (0.6, 0.8, and 1) mm at constant speed (370) rpm, while the second parameter used is speed at values (540, 800 and 1200) rpm and at constant feed (1) mm. The results of the fatigue
... Show MoreThe Sonic Scanner is a multifunctional instrument designed to log wells, assess elastic characteristics, and support reservoir characterisation. Furthermore, it facilitates comprehension of rock mechanics, gas detection, and well positioning, while also furnishing data for geomechanical computations and sand management. The present work involved the application of the Sonic Scanner for both basic and advanced processing of oil-well-penetrating carbonate media. The study aimed to characterize the compressional, shear, Stoneley slowness, rock mechanical properties, and Shear anisotropy analysis of the formation. Except for intervals where significant washouts are encountered, the data quality of the Monopole, Dipole, and Stoneley modes is gen
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