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
this paper contains preparation of Active carbon surface (AC) from pro so millet grain husks and Loading and activating by Iron oxide and hydrogen peroxide sequentially to obtain surface (ACIPE). The changes of previous processes on Active carbon surface were diagnosed by Fourier transform infrared spectroscopy (FTIR) and Scanning electron microscopy ( SEM ). These surfaces (AC and ACIPE ) were using as adsorbent for removing of congo red dye from aqueous solutions under certain conditions through batch system. More than one kinetic model was applied to congo red dye adsorption process and it was found that the most kinetic model applied to it is a model ( pseudo second order model).
The apricot plant was washed, dried, and powdered after harvesting to produce a fine powder that was used in water treatment. created an alcoholic extract from the apricot plant using ethanol, which was then analysed using GC-MS, Fourier transform infrared spectroscopy, and ultraviolet-visible spectroscopy to identify the active components. Zinc nanoparticles were created using an alcoholic extract. FTIR, UV-Vis, SEM, EDX, and TEM are used to characterize zinc nanoparticles. Using a continuous processing procedure, zinc nanoparticles with apricot extract and powder were employed to clean polluted water. Firstly, 2 g of zinc nanoparticles were used with 20 ml of polluted water, and the results were Tetra 44% and Levo 32%; after
... Show MoreThis research set out to provide a faster, easier, and more efficient process for nanoparticle (NP) synthesis of aluminum oxide NPs preparation by microwave irradiation, using plant extracts separately and in the same way (tea, coffee, rosemary), which is an easy-to-use and inexpensive method. The structural properties were investigated by X-ray diffractometer analysis technique (XRD). The X-ray analysis shows the structure has a polycrystalline nature with a hexagonal phase. The optical properties were studied using ultraviolet visible (UV-Vis) spectrometer, where the energy gap was determined. The surface morphology properties of the prepared aluminum NPs were examined by atomic force microscope (AFM). The Fourier transform infra
... Show MoreEbastine (EBS) is a poorly water-soluble antihistaminic drug; it belongs to the class II group according to the biopharmaceutical classification system (BCS). The aim of the present work was to enhance the solubility, dissolution rate and micromeritic properties of the drug, by formulating it as spherical crystal agglomerates by Quasi Emulsion Solvent Diffusion (QESD) method.
Spherical crystal agglomerates (SCAs) were prepared in presence of three solvents dichloromethane (DCM), water and chloroform as a good solvent, poor solvent and bridging solvent respectively. Agglomeration of EBS involved the use of some hydrophilic polymers like polyethylene glycol 4000 (PEG 4000), polyvinyl pyrrolidine K30 (PVP K30), D-?-tocopheryl
... Show MoreIn this study, the modified size-strain plot (SSP) method was used to analyze the x-ray diffraction lines pattern of diffraction lines (1 0 1), (1 2 1), (2 0 2), (0 4 2), (2 4 2) for the calcium titanate(CaTiO3) nanoparticles, and to calculate lattice strain, crystallite size, stress, and energy density, using three models: uniform (USDM). With a lattice strain of (2.147201889), a stress of (0.267452615X10), and an energy density of (2.900651X10-3 KJ/m3), the crystallite was 32.29477611 nm in size, and to calculate lattice strain of Scherrer (4.1644598X10−3), and (1.509066023X10−6 KJ/m3), a stress of(6.403949183X10−4MPa) and (26.019894 nm).
Nowadays nanoparticles are used in many fields of life all over the world, and there are numerous ways to obtain them: chemical, physical and biological processes. In recent times, the biological method for the synthesis of nanoparticles associated with using plant extract is widely spread. Optimal conditions for synthesis of silver nanoparticles using aqueous seeds extract of Myristica fragrance were highlighted in this research, such as type of plant extract, weight of extracted plant material, volume ratio of plant extract to AgNO3 and temperature of reaction. The study proved that the optimal status for AgNPs synthesis by using 10 g of M. fragrance seeds powder were added to 100 mL boiled distilled water, then homogenized and filt
... Show MoreGypseous soil covers approximately 30% of Iraqi lands and is widely used in geotechnical and construction engineering as it is. The demand for residential complexes has increased, so one of the significant challenges in studying gypsum soil due to its unique behavior is understanding its interaction with foundations, such as strip and square footing. This is because there is a lack of experiments that provide total displacement diagrams or failure envelopes, which are well-considered for non-problematic soil. The aim is to address a comprehensive understanding of the micromechanical properties of dry, saturated, and treated gypseous sandy soils and to analyze the interaction of strip base with this type of soil using particle image
... Show MoreBackground: Lymphomas are a group of diseases caused by malignant lymphocytes that accumulate in lymph nodes and cause the characteristic clinical features of lymphadenopathy. Intercellular adhesion molecule-1 (ICAM-1) (CD54) is a transmembrane glycoprotein belonging to the immunoglobulin superfamily of adhesion molecules. Cortactin was first identified as one of the major substrates for src kinase. because it localized to Cortical actin structures, The aims of this study was to evaluate and compare the immunohistochemical of ICAM-1 expression as cell adhesion molecule marker and Cortactin expression as invasive marker. Material and Methods: This study was performed on (68) formalin-fixed, paraffin-embedded blocks, histopathologically diagn
... Show MoreIn general, the importance of cluster analysis is that one can evaluate elements by clustering multiple homogeneous data; the main objective of this analysis is to collect the elements of a single, homogeneous group into different divisions, depending on many variables. This method of analysis is used to reduce data, generate hypotheses and test them, as well as predict and match models. The research aims to evaluate the fuzzy cluster analysis, which is a special case of cluster analysis, as well as to compare the two methods—classical and fuzzy cluster analysis. The research topic has been allocated to the government and private hospitals. The sampling for this research was comprised of 288 patients being treated in 10 hospitals. As t
... Show MoreThis paper deals with constructing mixed probability distribution from exponential with scale parameter (β) and also Gamma distribution with (2,β), and the mixed proportions are ( .first of all, the probability density function (p.d.f) and also cumulative distribution function (c.d.f) and also the reliability function are obtained. The parameters of mixed distribution, ( ,β) are estimated by three different methods, which are maximum likelihood, and Moments method,as well proposed method (Differential Least Square Method)(DLSM).The comparison is done using simulation procedure, and all the results are explained in tables.