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 existing investigation explains the consequence of irradiation of red laser on the optic properties of (CoO2) films. The film was equipped by the utilization of semi-computerized spray pyrolysis technique (SCSPT), it is the first time that this technique is used in the preparation and irradiation using a laser in this technique. From the XRD analysis, the crystalline existence with trigonal crystal system was when the received films were processed by continuous red laser (700 nm) with power (>1000mW)for different laser irradiation time using different number of times a laser scan (0, 6, 9, 12, 15 and 18 times) with total irradiation time(0,30,45,60,75,90 mi
Most dental supplies don't seem to be much of a barrier against germ infiltration. Therefore, the filling must be done with perfect caution and high antimicrobial effectiveness. When dental erosion occurs due to germs that lead to caries, a dental filling is used, creating a small microscopic space between the dental filling and the root end infiltration. This allowed the tooth to be penetrated for the second time, which was the research problem. Adding two compounds to antibacterial fillers (zinc polycarboxylate cement) made them work better: Firstly, was zinc oxide (ZnO) that was made chemically, and secondly, was green ZnO nanoparticles that were made from orange peels and mixed with ZPCC in different amounts. The study was conducte
... Show MoreObjective(s): In the present study, glycerin is used as a substitute for tin-foil and cold mold seal (Alginate mould seal)
in the process of curing heat and cold-cure acrylic resin denture base against stone and plaster.
Methodology: 60 specimens were prepared from heat-cure acrylic resin and cold-cure acrylic resin denture base. The
study includes 12 groups of specimens depending on the type of processing, investment material and type of
separating medium that are used in curing process. Each group of them contains 5 specimens for each test.
Some of physical properties of the processed acrylic denture base that (water sorption and solubility) have been
compared with those processed using tin-foil and tin-foil substitut
In this paper, a compression system with high synthetic architect is introduced, it is based on wavelet transform, polynomial representation and quadtree coding. The bio-orthogonal (tap 9/7) wavelet transform is used to decompose the image signal, and 2D polynomial representation is utilized to prune the existing high scale variation of image signal. Quantization with quadtree coding are followed by shift coding are applied to compress the detail band and the residue part of approximation subband. The test results indicate that the introduced system is simple and fast and it leads to better compression gain in comparison with the case of using first order polynomial approximation.
Analysis the economic and financial phenomena and other requires to build the appropriate model, which represents the causal relations between factors. The operation building of the model depends on Imaging conditions and factors surrounding an in mathematical formula and the Researchers target to build that formula appropriately. Classical linear regression models are an important statistical tool, but used in a limited way, where is assumed that the relationship between the variables illustrations and response variables identifiable. To expand the representation of relationships between variables that represent the phenomenon under discussion we used Varying Coefficient Models
... Show MoreLet be any group with identity element (e) . A subgroup intersection graph of a subset is the Graph with V ( ) = - e and two separate peaks c and d contiguous for c and d if and only if , Where is a Periodic subset of resulting from . We find some topological indicators in this paper and Multi-border (Hosoya and Schultz) of , where , is aprime number.
The compound Fe0.5CoxMg0.95-xO where (x= 0.025, 0.05, 0.075, 0.1) was prepared via the sol-gel technique. The crystalline nature of magnesium oxide was studied by X-ray powder diffraction (XRD) analysis, and the size of the sample crystals, ranging between (16.91-19.62nm), increased, while the lattice constant within the band (0.5337-0.4738 nm) decreased with increasing the cobalt concentration. The morphology of the specimens was studied by scanning electron microscopy (SEM) which shows images forming spherical granules in addition to the presence of interconnected chips. The presence of the elements involved in the super
The current work concerns preparing cobalt manganese ferrite (Co0.2Mn0.8Fe2O4) and decorating it with polyaniline (PAni) for supercapacitor applications. The X-ray diffraction findings (XRD) manifested a broad peak of PAni and a cubic structure of cobalt manganese ferrite with crystal sizes between 21 nm. The pictures were taken with a field emission scanning electron microscope (FE-SEM), which evidenced that the PAni has nanofibers (NFs) structures, grain size 33 – 55 nm, according to the method of preparation, where the hydrothermal method was used. The magnetic measurements (VSM) that were conducted at room temperature showed that the samples had definite magnetic properties. Additionally, it was noted that the saturation magnetizatio
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