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
An optical system including quantum dot cylindrical Fresnel lens (CFL) has been designed by using Zemax optical designing program. Quantum dot cylindrical Fresnel lens has a relatively small thickness compared to conventional lenses and high absorbance. It contains grooves in the form of parallel lines, and each groove represents an individual lens that works to change the path of light falling on it to a single focal line. (CFL) is characterized by its small focal length despite its large area and small thickness, due to the nature of its design that gives this feature, which is applied in many optical systems (imaging and non- imaging system). In this paper, the visual properties of the (CFL) were studied as it is one of the impor
... Show MoreAlginate from Large brown seaweeds act as natural polymer has been investigated as polymer and has been added to concrete in different percentages ( 0% , 0.5% , 1% and 1.5% ) by the cement weight and the study show the effect of using alginate biopolymer admixtures on some of the fresh properties of the concrete (slump & the density fresh) also in the hardened state ( Compressive strength , Splitting tensile strength and Flexural strength ) at 28 days. The mix proportion was (1:2.26:2.26) (cement: sand: gravel) respectively and at constant w/c equal to 0.47. The results indicate that the use of alginate as a percent of the cement weight possess a positive effect on fresh properties of co
... Show MoreCohesive soils present difficulties in construction projects because it usually contains expansive clay minerals. However, the engineering properties of cohesive soils can be stabilized by using various techniques. The research aims to elaborate on the influences of using hydrated lime on the consistency, compaction, and shear strength properties of clayey soil samples from Sulaimnai city, northern Iraq. The proportions of added hydrated lime are 0%, 2.5%, 5%, 7.5% and 10% to the natural soil sample. The results yielded considerable effects of hydrated lime on the engineering properties of the treated soil sample and enhancement its strength. The soil's liquid limit, plasticity index, and optimum moisture content were de
... Show MoreSeveral schottky diodes were fabricated from polyaniline/ Carbon nanotube (single and multiwalled) composites. These composites were synthesized with different concentration and two carbon nanotubes types, Single and Multi-Walled Carbon Nanotubes (SWCNT & MWCNT). Aluminum and silver paste were chosen as schottky and ohmic contact respectively. physical and electrical were used to studied these composite by using Atomic Force Microscopy (AFM) and electrical measurements. The Root Mean Square RMS surface roughness of the composite samples was found to be around 4nm. The currentvoltage characteristic were measurements for all samples in the bias range ±15V at room temperature. The results shows the increasing in carbon nanotubes concentration
... Show MoreAt a temperature of 300 K, a prepared thin film of Ag doped with different ratios of CdO (0.1, 0.3, 0.5) % were observed using pulse laser deposition (PLD). The laser, an Nd:YAG in ?=1064 nm, used a pulse, constant energy of 600 mJ ,with a repetition rate of 6 Hz and 400 pulses. The effect of CdO on the structural and optical properties of these films was studied. The structural tests showed that these films are of a polycrystalline structure with a preferred orientation in the (002) direction for Ag. The grain size is positively correlated with the concentration of CdO. The optical properties of the Ag :CdO thin film we observed included transmittance, absorption coefficient, and the energy gap in the wavelength range of 300-1100
... Show MoreDental casts come into direct contact with impression materials and other items that are contaminated by saliva and blood from a patient's mouth, leaving the casts susceptible to cross-contamination. The disinfectant solutions of the impression materials cause various adverse reactions. Therefore, disinfection of dental casts may be effective in preventing cross infection. This study was carried out to evaluate the surface hardness, dimensional accuracy, reproduction of details and surface porosity of type III, type IV and type IV extra hard dental stone after immersion in and spray by using SOLO and Sodium hypochlorite disinfectant solutions. Materials and methods: 240 Stone samples were prepared in rubber rings, A total of 60 test block w
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