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
Abstract
In this manuscript, a simple new method for the green synthesis of platinum nanoparticles (Pt NPs) utilizing F. carica Fig extract as reducing agent for antimicrobial activities was reported. Simultaneously, the microstructural and morphological features of the synthesized Pt NPs were thoroughly investigated. In particular, the attained Pt NPs exhibited spherical shape with diameter range of 5-30 nm and root mean square of 9.48 nm using Transmission Electron Microscopy (TEM) and Atomic Force Microscopy (AFM), respectively. Additionally, the final product (Pt NPs) was screened as antifungal and antibacterial agent against Candida and Aspergillus species as well as Gram-positive Staphyllococcus aureus and G
... Show MoreTwo new nonsymmetrical mesogenic homologous series of terminal substituent ether (series [Vn]) and carboxy (series [VIn]) incorporating azobenzene and 1,3,4-oxadiazole group were synthesized. Both series have been All compounds thus isolated were purified and characterized by elemental analysis, Fourier Transform Infrared Spectroscopy, 1H NMR, along with thermal analysis and texture observation using Differential Scanning Calorimetry (DSC) and Polarizing Optical Microscopy (POM), respectively. All compounds of the first series exhibited liquid crystalline properties. The homologues [V1]-[V3] display a nematic mesophase, the compounds [V4]-[V7] exhibit a dimorphism behavior, nematic (N) and smectic A (SmA) mesophases, the compounds [V8] and
... Show MoreThe demand for expatriate labor to Iraq increased after 2003 as a result of the openness that Iraq experienced, but this expatriate labor, which was requested at an increasing rate, has had economic, social, and political effects on the Iraqi economy in general, and the Iraqi labor market in particular. This is due to the high rates of unemployment, as most of these expatriate workers cause competition to local labor, and thus cause repercussions on the Iraqi economy as a whole, except for those expatriate workers coming with companies working in the oil sector. Iraq's GDP
Artichoke (Cynara scolymus L.) is a nutritious vegetable that grown all over the world. It is a promising herbal plant, rich in bioactive components. It is considered as medicinal plant due to its nutritional and phytochemical composition, especially high proportion of phenolic compounds. The primary aim of this study was to achieve chemical profile analyses of artichoke for different phytochemcials, especially Scolymoside and Cynaroside. Methanolic crude was extracted from Artichoke leaves by rotary evaporator and separated by column chromatography. The fractions monitored by Thin Layer Chromatography (TLC), and identified in High-Pressure Liquid Chroma
... Show MoreThe project has been described the design and construction of a reliable optical testing platform used for evaluate the reflectivity of metal surfaces treated with special paintings required for laser beam attenuation. The platform comprises an Nd-YAG laser system which has been designed and fabricated with specifications to be compatible with their corresponding in laser range finder transmitters used for various applications. The reflectivity of various attenuating paintings, at different detection angles, has been observed. Moreover, the variation of the reflected energy with painting type and metal type to be painted has been studied experimentally. Results illustrated the existence of a definite angle, at which the reflectivity was max
... Show MoreThe effect of air injection device on the performance of airlift pump used for water pumping has been studied numerically and experimentally. An airlift pump of dimensions 42mm diameter and 2200 mm length with conventional and modified air injection device was considered. A modification on conventional injection device (normal air-jacket type) was carried out by changing injection angle from 90 (for conventional) to 22.5 (for modified). Continuity and Navier-Stokes equations in turbulent regime with an appropriate two-phase flow model (VOF) and turbulent model ( ) in two dimensions axisymmetry flow were formulated and solved by using the known package FLUENT version (14.5). The numerical and experimental investiga
... Show MoreThe removal of heavy metal ions from wastewater by sorptive flotation using Amberlite IR120 as a resin, and flotation column, was investigated. A combined two-stage process is proposed as an alternative of the heavy metals removal from aqueous solutions. The first stage is the sorption of heavy metals onto Amberlite IR120 followed by dispersed-air flotation. The sorption of metal ions on the resin, depending on contact time, pH, resin dosage, and initial metal concentration was studied in batch method .Various parameters such as pH, air flow rate, and surfactant concentration were investigated in the flotation stage. Sodium lauryl sulfate (SLS) and Hexadecyltrimethyl ammonium bromide (HTAB) were used as anionic and cationic surfactant re
... Show MoreAspirin and clopidogrel are considered the most important oral platelets aggregation inhibitors. So it is widely used for treatment and prophylaxis of cardiovascular and peripheral vascular diseases related to platelets aggregation .In this study aspirin and clopidogrel were formulated together as floating bilayer tablet system. Three different formulas of 75 mg aspirin were prepared by wet granulation method as immediate release layer; different disintegrants used to achieve rapid disintegration. Formula with crosscarmellose as disintegrant achieve rapid disintegration was selected for preparation of bilayer tablet.
Different formulas of 75 mg clopidogrel were prepared as sustained release floating layer by wet granulation (effe
... Show MoreThispaperpresentsthesynthesisandstudyofsomenewmixed-liagnd complexescontainingtowaminoacids[Alanine(Ala)andphenylalanine(phe)]withsome metals .Theresultsproductswerefoundtobesolidcrystallinecomplexeswhichhave been characterized by using (FT-IR,UV-Vis) spectra , melting point, elemental analysis (C.H.N) , molar conductivity and solubiltyThe proposed structure of the complexes using program , chem office 3D(2000) .The general formula have been given for the prepared complexes :[M(A-H)(phe-H)]M(II): Hg , Mn ,Co , Ni , Cu ) , Zn , Cd(II) .Ala = Alanine acid = C3H7NO2Phe = phenylalanine = C9H11NO2