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Two efficient methods for solving Schlömilch’s integral equation
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Purpose

In this paper, the exact solutions of the Schlömilch’s integral equation and its linear and non-linear generalized formulas with application are solved by using two efficient iterative methods. The Schlömilch’s integral equations have many applications in atmospheric, terrestrial physics and ionospheric problems. They describe the density profile of electrons from the ionospheric for awry occurrence of the quasi-transverse approximations. The paper aims to discuss these issues.

Design/methodology/approach

First, the authors apply a regularization method combined with the standard homotopy analysis method to find the exact solutions for all forms of the Schlömilch’s integral equation. Second, the authors implement the regularization method with the variational iteration method for the same purpose. The effectiveness of the regularization-Homotopy method and the regularization-variational method is shown by using them for several illustrative examples, which have been solved by other authors using the so-called regularization-Adomian method.

Findings

The implementation of the two methods demonstrates the usefulness in finding exact solutions.

Practical implications

The authors have applied the developed methodology to the solution of the Rayleigh equation, which is an important equation in fluid dynamics and has a variety of applications in different fields of science and engineering. These include the analysis of batch distillation in chemistry, scattering of electromagnetic waves in physics, isotopic data in contaminant hydrogeology and others.

Originality/value

In this paper, two reliable methods have been implemented to solve several examples, where those examples represent the main types of the Schlömilch’s integral models. Each method has been accompanied with the use of the regularization method. This process constructs an efficient dealing to get the exact solutions of the linear and non-linear Schlömilch’s integral equation which is easy to implement. In addition to that, the accompanied regularization method with each of the two used methods proved its efficiency in handling many problems especially ill-posed problems, such as the Fredholm integral equation of the first kind.

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Publication Date
Sat Oct 28 2017
Journal Name
The Emirates Journal For Engineering Research (ejer), Issn: 1022-9892
The theory of sustainable integral design: Integration in the sustainability of the Marshes in southern Iraq
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Publication Date
Wed Jun 30 2021
Journal Name
Iraqi Journal Of Market Research And Consumer Protection
ELECTROCHEMICAL PREPARATION OF A MOLECULAR IMPRINTED POLYMER ELECTRODE FOR ESTEMATION OF ASPIRIN USING TWO DIFFERENT FUNCTIONAL MONOMERS.: ELECTROCHEMICAL PREPARATION OF A MOLECULAR IMPRINTED POLYMER ELECTRODE FOR ESTEMATION OF ASPIRIN USING TWO DIFFERENT FUNCTIONAL MONOMERS.
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For aspirin estimated, a molecularly imprinted polymer MIP-ASP electrodes were generated by electro-polymerization process, the electrodes were prepared by combining the template (aspirin) with (vinyl acetate (VA), 1-vinylimidizole (VIZ) as a functional monomer and N, N-methylene bisacrylamide (MBAA) as crosslinkers using benzoyl peroxide (BPO) as an initiator. The efficiency of the membrane electrodes was analyzed by differential pulse voltammetry (DPV). Four electrodes were synthesized using two different plasticizers, di-butyl sebacate (DBS), di-octyl phthalate (DOP) in PVC matrix. Scanning electron microscopy (SEM) was used to describe the generated MIP, studying the electrodes properties, the slope, detection limit, and life

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Publication Date
Mon Sep 09 2024
Journal Name
مداد الاداب
Lexical Stylistic Analysis of Two ‎Extracts from Tale of Two Cities: ‎A Contrastive Study
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Since the time it emerged, stylistics, as a field of knowledge which ‎combines both linguistics and literature, acquired a special status in the ‎linguistic arena. Its significance in complementing the meaning ‎delivered by linguistic means has been proven and acknowledged ‎through numerous stylistic analytic attempts of different literary works ‎and in different languages. The question put forward in this paper is ‎whether or not the stylistic analysis can work as effectively on translated ‎texts as it does on the original ones without having the results reached ‎by the analysis distorting the meaning of the original text. An attempt to ‎investigate this question is made herein by conducting a lexical stylistic ‎analysi

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Publication Date
Thu Jan 01 2009
Journal Name
J. Of University Of Anbar For Pure Science
Estimation of the Normalized Difference Vegetation Index (NDVI) Variation for Selected Regions in Iraq for two Years 1990 & 2001
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The Normalized Difference Vegetation Index (NDVI) is commonly used as a measure of land surface greenness based on the assumption that NDVI value is positively proportional to the amount of green vegetation in an image pixel area. The Normalized Difference Vegetation Index data set of Landsat based on the remote sensing information is used to estimate the area of plant cover in region west of Baghdad during 1990-2001. The results show that in the period of 1990 and 2001 the plant area in region of Baghdad increased from (44760.25) hectare to (75410.67) hectare. The vegetation area increased during the period 1990-2001, and decreases the exposed area.

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Publication Date
Sat Dec 03 2022
Journal Name
Iraqi Journal Of Science
Detection of Spectral Reflective Changes for Temporal Resolution of Land Cover (LC) for Two Different Seasons in central Iraq
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The purpose of the study is the city of Baghdad, the capital of Iraq, was chosen to study the spectral reflection of the land cover and to determine the changes taking place in the areas of the main features of the city using the temporal resolution of multispectral bands of the satellite Landsat 5 and 8 for MSS and OLI sensors respectively belonging to NASA and for the period 1999-2021, and calculating the increase and decrease in the basic features of Baghdad. The main conclusions of the study were, This study from 1999 to 2021 and in two different seasons: the Spring of the growing season and Summer the dry season. When using the supervised classification method to determine the differences, the results showed remarkable changes. Where h

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Publication Date
Sat Dec 01 2018
Journal Name
Al-khwarizmi Engineering Journal
Design and Implementation of an Automatic Control for Two Axis Tracking System for Applications of Concentrated Solar Thermal Power
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The present work presents design and implementation of an automated two-axis solar tracking system using local materials with minimum cost, light weight and reliable structure. The tracking system consists of two parts, mechanical units (fixed and moving parts) and control units (four LDR sensors and Arduino UNO microcontroller to control two DC servomotors). The tracking system was fitted and assembled together with a parabolic trough solar concentrator (PTSC) system to move it according to information come from the sensors so as to keep the PTSC always perpendicular to sun rays. The experimental tests have been done on the PTSC system to investigate its thermal performance in two cases, with tracking system (case 1) and without trackin

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Publication Date
Fri Sep 30 2022
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of Some Methods for Estimating the Survival Function and Failure Rate for the Exponentiated Expanded Power Function Distribution
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     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

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Publication Date
Fri Sep 30 2022
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of Some Methods for Estimating the Survival Function and Failure Rate for the Exponentiated Expanded Power Function Distribution
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       We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD) to estimate the parameters an

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Publication Date
Mon Oct 01 2012
Journal Name
Computers & Mathematics With Applications
Boundary element formulations for the numerical solution of two-dimensional diffusion problems with variable coefficients
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Publication Date
Fri Mar 15 2019
Journal Name
Journal Of The College Of Education For Women
Exploring the Effectiveness of two Scales for Measuring Cultural Intelligence of the Preparatory School Students
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The present study aims at exploring tow cultural intelligence scales of preparatory school students. It also aims at finding out the statistically significant differences according to gender and specification. Accordingly, the present study seeks to answer the following questions:

  1. Is there cultural intelligence of the preparatory school students?
  2. Is there any statistically significant differences according to gender and specification variables?
  3. Is there a scale more effective than cultural intelligence scales?

The stratified random sampling method is used to for selecting the sample of (216) students of scientific and humanistic specifications from

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