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
Background In recent years, there has been a notable increase in the level of attention devoted to exploring capabilities of nanoparticles, specifically gold nanoparticles AuNPs, within context of modern times. AuNPs possess distinct biophysical properties, as a novel avenue as an antibacterial agent targeting Streptococcus Mutans and Candida Albicans. The aim of this study to create a nano-platform that has the potential to be environmentally sustainable, in addition to exhibiting exceptional antimicrobial properties against Streptococcus Mutans as well as Candida Albicans. Methods this study involved utilization of
Two series of 1,3,4-oxadiazole derivatives at the sixth position of the 2,4-di-
Dye-sensitized solar cells (DSSC) create imitation photosynthesis by using chemical reactions to produce electricity from sunlight. DSSC has been pursued in numerous studies due to its capability to achieve efficiencies of up to 15% with artificial photosensitizer in diffuse light. However, artificial photosensitizers present a limitation because of the complex processing of metal compound. Therefore, various types of sensitizers were developed and synthesized to surpass the artificial sensitizer performances such as natural sensitizers from bio-based materials including plants, due to simple processing techniques and low environmental impact. Thus, this study examines the potential and properties of natural sensitizers from the was
... Show MoreThis research was aimed to determine the petrophysical properties (porosity, permeability and fluid saturation) of a reservoir. Petrophysical properties of the Shuiaba Formation at Y field are determined from the interpretation of open hole log data of six wells. Depending on these properties, it is possible to divide the Shuiaba Formation which has thickness of a proximately 180-195m, into three lithological units: A is upper unit (thickness about 8 to 15 m) involving of moderately dolomitized limestones; B is a middle unit (thickness about 52 to 56 m) which is composed of dolomitic limestone, and C is lower unit ( >110 m thick) which consists of shale-rich and dolomitic limestones. The results showed that the average formation water
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