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 Silver1Indium1Selenide (AgInSe2) (AIS) thin1films of (3001±20) nm thickness have been1prepared2from the compound alloys2using thermal evaporation2 technique onto the glass2substrate at room temperature, with a deposition rate2(3±0.1) nm2sec-1.
The2structural, optical and electrical3properties have been studied3at different annealing3temperatures (Ta=450, 550 and 650) K.
The amount3or (concentration) of the elements3(Ag, In, Se) in the prepared alloy3was verified using an
... Show MoreA new hetrocyclic liquid crystal compounds containing 1,3,4-oxadiazole with different substituted in para position (Bromo, Chloro, Nitro and Methyl) were synthesized and characterized by melting points, FTIR Spectroscopy and 1HNMR spectroscopy for [Cl-SR6] and [NO2-SR6] compounds. The liquid crystalline properties of the synthesized compounds were studied by using hot-stage polarizing optical microscopy (POM), so they determined the transition enthalpies and entropies by using differential scanning calorimetery (DSC). All of the compounds show mesomorphic properties. The compounds [Br-SR6], [Cl-SR6] and [NO2SR6] exhibit an enantiotropic dimorphism smectic (Sm) phase, while the compounds [MeSR6] showed nematic (N) phase thro
... Show MoreCerium oxide (CeO2), or ceria, has gained increasing interest owing to its excellent catalytic applications. Under the framework of density functional theory (DFT), this contribution demonstrates the eect that introducing the element nickel (Ni) into the ceria lattice has on its electronic, structural, and optical characteristics. Electronic density of states (DOSs) analysis shows that Ni integration leads to a shrinkage of Ce 4f states and improvement of Ni 3d states in the bottom of the conduction band. Furthermore, the calculated optical absorption spectra of an Ni-doped CeO2 system shifts towards longer visible light and infrared regions. Results indicate that Ni-doping a CeO2 system would result in a decrease of the band gap. Finally,
... Show MoreThe durability of asphalt pavement is associated with the properties and performance of the binder. This work-study intended to understand the impact of blending Styrene-Butadiene-Styrene (SBS) to conventional asphalt concrete mixtures and calculating the Optimum Asphalt Content (OAC) for conventional mixture also; compare the performance between SBS modified with the conventional mixture. Two different kinds of asphalt penetration grades, A.C. (40-50) and A.C. (60-70), were improved with 2.5 and 3.5% SBS polymer, respectively. Marshall properties were determined in this work. Optimum Asphalt Content (OAC) was 4.93 and 5.1% by weight of mixture for A.C. (40-50) and (60-70), respectively. Marshall properties results show an increasem
... Show MoreThe silicon carbide/carbon fiber (SiC/CF) hybrid fillers were introduced to improve the electrical and thermal conductivities of the epoxy resin composites. Results of Fourier transform infrared spectroscopy revealed that the peaks at 3532 and 2850 cm−1 relate to carboxylic acid O–H stretching and aldehyde C–H stretching appearing deeper with an increased volume fraction of SiC. Scanning electron microscopic image shows a better interface bonding between the fiber and the matrix when the volume fraction of SiC particles are increased. As frequency increases from 102 Hz to 106 Hz, dielectric constants decrease slightly. Dissipation factor (tan δ) values keep low a
... Show MoreLos nombres propios nombran a un ser o a un objeto, distinguiéndolo de los demás seres de su misma clase, se escriben siempre con letra mayúscula a principio de palabra. Los lingüistas hacen mayor hincapié en las divergencias de referencia, entre nombres propios y nombres comunes. Así, suele decirse que el sustantivo propio no tiene como referente ningún concepto. El asunto de la traducción de los nombres propios parecería una cuestión de gusto personal del traductor pero vemos también que en algunas épocas es más frecuente traducirlos, y en otras, por el contrario, se prefiere dejar esos nombres en su forma original, tal vez con algunas adaptaciones ortográficas. Parecería entonces cuestión de modas. Pero, eviden
... Show MoreThe current research studies the aesthetic framework for the dialectical development of the functions of the contemporary theater director in an aesthetic approach to the mechanisms of functional overlap between the dramaturgy and direction functions, and scenography and direction, the detection of the controversial structure of that overlap, and what can be summed up in the following question: (what are the aesthetic approaches of the dialectical development in the function of the contemporary theatre director?). The research is determined by a pivotal aim which is (knowing the aesthetic nature of the dialectical development in
The 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
... Show More