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 necessity of addressing global economic prosperity has garnered significant attention from recent studies and policymakers. This article analyses the effects of the digital economy, business synergies, and trade policies on the economic prosperity of China and India. The study examines the impact of political support on the digital economy, business synergies, trade policies, and global economic prosperity in China and India. The study collects data from prominent economists in India and China using questionnaires. The article utilised the SPSS-AMOS software to analyse the relationship between variables. The results showed that the digital economy, business synergies, and trade policies are positively linked to global economic prosperit
... Show MoreThe aim of the work is the synthesis and characterization of the tridentate Schiff base (HL) containing (N and O) as donor atoms type (ONO). The ligand is: (HL) phenyl 2-(2-hydroxybenzylidenamino)benzoate . This ligand was prepared by the reaction of (phenyl 2-aminobenzoate) with salicylaldehyde under reflux in ethanol and few drops of glacial acetic acid which gave the ligand (HL). The prepared ligand was characterized by (FT IR,UV–Vis) spectroscopy, Elemental analysis of carbon, hydrogen and nitrogen (C.H.N.) and melting point. The ligand was reacted with some metal ions under reflux in ethanol with (1 metal :2 ligand )mole ratio which gave complexes of the general formula: [M(L)2]Cl , M = Cr III La III and , Pr III Products were found
... Show MoreThe objective Effect of Internal and External Environment and its Psychological & Practical Reflection on the Political Decision-Making Process
Background: Pulpotomy is an accepted treatment for the management of cariously exposed pulps in symptom free primary molars to achieve one of the most important goals for Pedodontists, which is the retention of the pulpally involved deciduous teeth healthy until the time of normal exfoliation. The purpose of this study was to evaluate the relative success of pulpotec, formocresol and Mineral Trioxide Aggregate (MTA) in cariously exposed primary molar teeth, using clinical and radiographical examinations. Materials and methods: Thirty nine children with 45 primary molars requiring pulpotomy were selected in this study, 15 teeth treated by each type of pulpotomy medicament. Clinical and radiographical follow up for the patients was performed
... Show MoreThis study was designed to investigate the hypoglycemic and hypolipidemic activity of aqueous green tea (GT) extract in normal and alloxan-induced diabetic rats. Forty adult male albino rats weighing 180-200 g were divided into four groups of 10 rats each: The first group was served as control; the second group was treated with GT (250 mg/kg b.w); the third group was affected by inducing experimental diabetes by intraperitonial injection of alloxan (150 mg/kg b.w); and the fourth group was affected by inducing diabetes and treated with GT (250 mg/kg b.w). Level of blood glucose and lipid profile [total cholesterol (TC), triglycerides (TG), high-density lipoprotein cholesterol (HDL-C), low density lipoprotein cholesterol (LDL-C) and ve
... Show MoreSome metal ions (Mn+2, Co+2, Ni+2, Cu+2,Zn+2 and Cd+2) complexes of quodridentats Schiff base derived from (2-hydroxy benzaldehyde and 4,4'-methylenedianiline as primary ligand and 3-picoline (3-pic) secondary ligand have been synthesized and characterized on the basis of their 1H ,13C-NMR, FT-IR, UV-Vis spectroscopy, conductivity measurements, elemental analysis, and magnetic moments, metal to ligands ratio in all complexes has been found to be (1:1:2) (M:Schiff base:3-pic), Schiff base behaves as neutral tetra dentate ligand with (N2,O2) system from the results obtained, the following general formula has suggested for the prepared complexes [M+2(2-mbd)(3-pic)2] and octahedral stereochemistry, Where M+2 = (Mn , Co , Ni , Cu , Zn and Cd), 2
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