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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
Thu Nov 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
The Quality of University Education at the Middle Technical University in The Light of the Application of National Ranking project for the Quality of Iraqi Universities
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The research aims to identify ways of upgrading the quality level of university education at the Middle Technical University in light of its application for the National Ranking project for the quality of Iraqi universities in order to obtain advanced grades among the Iraqi universities , Which is qualified to enter the Ranking of universities worldwide, through displaying the mechanism of the Application of  National Ranking project for the quality of Iraqi universities in the Middle Technical University and its formations consisting of (5) technical colleges and (11) technical institute.

        The results of the application showed several observations: The most

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Publication Date
Mon Oct 01 2018
Journal Name
Journal Of Educational And Psychological Researches
The factors that affecting in the recruitment of a teaching staff for the Massive Open Online Courses (MOOCs) in university teaching at the University of Khartoum.
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This research aimed at identifying the factors that affecting in the recruitment of a teaching staff for the Massive Open Online Courses (MOOCs) in university teaching at the University of Khartoum. The descriptive method was followed. The questionnaire was used as a tool for data collection,, which was distributed directly to a sample of (181) respondent of the teaching staff members of the senate at University of Khartoum from those who were attend at the senate meeting No. (409) which was held on 22 August 2016 Of (272). The researcher followed for the distribution the chance method, where each questionnaire was distributed to each of a teaching staff from different faculties at the University of Khartoum, according to his willingness

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Publication Date
Tue Apr 14 2020
Journal Name
Modern Sport
The Effect of Using the Bybee Strategy(5ES) according to Brain Control Patterns in Learning a Kinetic Series on Floor exercises in Artistic Gymnastics for men
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The aim of this study to identify patterns of cerebral control (right and left) for second grade students in the collage of physical education and sports science of the University of Baghdad, as well as identify the definition of theThe Effect of Using the Bybee Strategy(5ES) according to Brain Control Patterns in Learning a Kinetic Series on Floor exercises in Artistic Gymnastics for menمجلة الرياضة المعاصرةالمجلد 19 العدد 1 عام 2020effect using the (Bybee) strategy (5ES) according to brain control patterns inlearning a Kinetic series on floor exercises In artistic gymnastics for men, andidentify the best combination between the four research groups learn, use Finderexperimental method research sample consi

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Publication Date
Sat Mar 01 2014
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Obstacles to the adoption of business commercial books to determine taxable income and ways to address them: An applied research at The General Commission for Taxes
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The research aims to shed light on the obstacles that hinder the use of taxpayers' commercial books covered by provisions of the amended commercial book-keeping system No. 2 of 1985 and ways to address these obstacles. On this basis, the main null hypothesis was formulated that there is no statistically significant relationship between the obstacles to the adoption of the commercial books and taxable income.

The research data were collected on the base of three applied case studies of registered taxpayers in the General Commission of Taxes, GCT, together with the use of a questionnaire distributed to a sample of taxpayers ( companies ). The collected data were analyzed, the result  were presented  and the hypothesis was

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Publication Date
Tue Nov 09 2021
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Adopting the green value chain to achieve sustainable competitive advantage: study to views of a sample from Ur General Company for Engineering Industries in Dhi Qar
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       In light of the developments and intense competition that the world has witnessed, the need to search for a sustainable and continuous competitive advantage for economic units has emerged, as the economic units must not lose sight of their interest in the activities they perform to achieve that advantage, and it can be said that the goal of the research is to identify the theoretical dimensions of the green value chain represented by: (Green research and development, green design, green manufacturing, green marketing, green services) and the dimensions of the sustainable competitive advantage represented by (quality, creativity, innovation, cost, response to the customer), as well as identifyi

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Publication Date
Sat Oct 03 2026
Journal Name
Journal Of Physical Education
An Analysis of some motor variables of butterfly stroke and their relationship to success in the 50-meter butterfly race for national team swimmers (candidate category)
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Publication Date
Sat Dec 31 2016
Journal Name
Al-kindy College Medical Journal
Dorsal plication during penile orthoplasty with and without neurovascular bundle mobilizationA comparative clinical trial conducted At Ghazy Al-Hariri teaching hospital for surgical specialties (2013 –2015)
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Background: Dorsal plication on each side of the penis at the 2 and 10-o’clock positions had been a mainstay for correction of ventral penile curvature. However, because only the 12-o’clock position proved to be a nerve-free zone, dorsal plication at the 12-o’clock position can be advocated.

Objectives: To evaluate tunica albuginea plication with and without neurovascular bundle mobilization in patients with ventral penile curvature. Type of the study: A prospective study.

Methods: A 34 patients with a mean age of (4.8 ± 0.54) years, Who still

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Publication Date
Wed Jul 01 2015
Journal Name
Journal Of Educational And Psychological Researches
The impact of discrete realization strategy in the development of reflective thinking among students of Qur'an and Islamic education departments for the course of Islamic jurisprudence
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The paper aims to identify the impact of discrete realization strategy in the development of reflective thinking among students: (males/females) of Qur'an and Islamic education departments for the course of Islamic jurisprudence according to the variability of sex. The researcher used the experimental approach and adopted an experimental determination with a set part of the two groups (experimental and controlled). He selected the sample deliberately which consists of (147) students spread over four classes (experimental males/ experimental females/ controlled males/ controlled females), and it took last for an academic year of (2010-2011). He, then, prepared a post test to measure the reflective thinking with his five skills (skill of o

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Publication Date
Fri Dec 01 2017
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The Roleof Time Management in Stages Claims Settlement of Insurance from Fire: Research Exploratory in General Iraqi Insurance Company and Private Al hamra Company for Insurance
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The insurance activity in the various countries of the world are important indicators of the strength of the country's economy, he came to study the stages compensation insurance settlement against fire and the importance of investing time risk in achieving the payment of compensation speed, and the implications for the continuation of the insured to carry out insurance with the insurance company, whether working within the public sector or the private sector. Hence the research problem in how quickly insurance companies to pay compensation as soon as possible and the return of the insured to carry out its work and make up for what he died from loss. Intentional sample was selected from branches and divisions and Their assistants manager

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Publication Date
Fri May 15 2009
Journal Name
Journal Of Planner And Development
Study of Change in Regional Land Use Using Remote Sensing Technology and Geographic Information Systems / Study Area (Hawr Al Huweiza) for the Years 1973-1990-2004
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his project try to explain the using ability of spatial techniques for land cover change detection on regional level with the time parameter and did select for explain these abilities study case (Hewaizah marsh ) . this area apply to many big changes with the time. These changes made action on characters and behaviors of this area as well as all activities in it . This Project concerting to recognize the Using importance of remote sensing and GIS Methodology in data collecting for the changes of land use and the methodology for the analyses and getting the results for the next using as a base data for development and drawing the plans as well as in regional planning .This project focus on practical

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