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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
Fri Jul 21 2023
Journal Name
Journal Of Engineering
The designed housing projects as an alternative for the informal building and their impact in addressing the heterogeneity of the urban escape in the built residential areas
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The phenomenon of informal building Spread recently in Iraqi residential areas, in general, and in Baghdad, in particular, due to the urgent housing need, on the one hand, and lack of commitment to building controls, on the other hand, to highlight the phenomenon of uncommitted building to controls and housing governing legislation in Iraq, leading to heterogeneity in both building densities and plot areas, and disorder in the urban fabric and urban escape of those areas. Research problem identified as the absence of a clear vision about the General aspects of the phenomenon of informal building in residential street scene, and the role of designed housing projects as a substitute for informal building in built residential areas. The des

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Publication Date
Sun Apr 23 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Comparative study for Effect of the Using of Aged Garlic Extract and Row Garlic extract added to drinking water as Immune Modulators of Broiler Infected with Gomboro
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   This study included the effect of Aged garlic extract (AgE) and Row garlic extract (RgE)as immune modulators for treating or redusing the infection of boiler by Gomboro.       This is made of measuring the stress index and serum antibodies levels against Gomboro virous( GV) estimated by HI,the study also detected the effect of each extract as antioxidents in broiler by estimation of peroxynitrite in serum . 300 chicks infected with Gumboro diseas brought at day ( 21 ) old and divided into three groups , the first group A was given the ( RgE ) at level of 5% with drinking water , the group B was given 5% of  ( AgE ) and group C is left as control group and wasn't given anything.  &

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Publication Date
Mon Jan 09 2023
Journal Name
College Of Islamic Sciences
The door of speaking souls From the book explaining the features of the origins of religion For Sheikh Abdul Rahman bin Abdullah Al-Khonji study and investigation
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Praise be to God who created the soul, perfected it, and inspired it with its immorality and piety. He says in His Noble Book: ﭤ Fajr: 27-30 Glory be to You, O God! O Lord, on whom I have chosen for You as a beloved from myself and the soul of the two worlds, may our master Muhammad be sacrificed for him, who enlightened the horizons with his introduction to enlightenment. It soon ends with the end of pleasure, which is the opposite of the pleasure of thought and meaning, as it is permanent and continuous, and from here we see that the Messenger of God, may God’s prayers and peace be upon him, urges us in various places to seek knowledge and fortify the soul and thought in a way that raises one’s status and protects him from the st

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Publication Date
Wed Aug 17 2022
Journal Name
Al–bahith Al–a'alami
Lawyers’ Use of the Website of the Supreme Judicial Council and the Gratifications Obtained from It Drawn Research Submitted for the Study of the Higher Professional Diploma
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The field study of this paper focused on the motives for lawyers to use the website
of the Supreme Judicial Council, and the gratifications achieved as a result of its use.
This study sought to achieve a number of goals, including:
1. Monitoring the patterns of lawyers’ use of the website of the Supreme Judicial Council.
2. Determining the forms that lawyers use to interact on the website of the Supreme
Judicial Council.
This study is a descriptive in kind as the researcher relied on the ‘survey method’ in
its study of the external audience (lawyers) using the questionnaire and scale toolThe questionnaire was distributed among a deliberately chosen sample, consisting of
(160) lawyers who used the website of

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Publication Date
Sat Jan 11 2025
Journal Name
Al–bahith Al–a'alami
The extent of Concern of the University Press in Students’ Issues (Journal of the University of Technology as a Model) for the Period from 2009 to 2012
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The university press is an essential pillar in building an academic community to achieve its objectives in the service of society. Since the university press is a means of university media, which is issued by the departments or units of media in Iraqi universities as academic governmental-institutions, so it highlights the activities of the university and link them to its internal society in the first place as the university press is a mirror of the university and its voice is sincerely expressed. This research comes to know the extent of interest of the university press in various student issues.

In order to identify the problem of the research, the method of content analysis was adopted within the survey method

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Publication Date
Sat Jan 11 2025
Journal Name
Revista Iberoamericana De Psicología Del Ejercicio Y El Deporte, Issn 1886-8576, Vol. 17, Nº. 6, 2022, Págs. 391-395
A study of mental perception and sports confidence and their relationship to the motivation of sports achievement for the players of the Iraqi premier league football clubs
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Autorías: Nuha Mohsin Dhahi, Ahmed Thare Hani, Muwafaq Obayes Khudhair. Localización: Revista iberoamericana de psicología del ejercicio y el deporte. Nº. 6, 2022. Artículo de Revista en Dialnet.

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Scopus
Publication Date
Wed Mar 23 2022
Journal Name
Journal Of Educational And Psychological Researches
The Problems of Teaching Computer Material Concerning Fourth Grade Students’ Point of View of in the Department of Computer College of Education for Women / University of Baghdad
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The aim of the research is to identify the problems of teaching computer material concerning fourth grade students’ point of view in the computer department in the College of Education for Women by identifying the statistically significant differences between the answers of female students to problems in the field of school administration and in the field of teaching computer subject included the sample of research On (39) of (50) students and (78%) From the fourth grade students in the department of computer who had achieved the theoretical part in the first semester and the assembly application in the second semester in the schools of Baghdad city for the aca

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Publication Date
Sat Jul 13 2019
Journal Name
Journal Of Northern Europe Academy For Studies & Research Denmark
The relationship between motor response speed and performance of the volleyball smash skill for students at the University of Baghdad - College of Physical Education and Sports Sciences
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NEACADEMY's JOURNALS

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Publication Date
Sun Jun 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Evaluation of Inhibitory Efficiency for Some Aqueous and Alcoholic Extracts of Cumin, Fenugreek, Sweet Fennel and Black Cumin in Growth of Escherichia Coli and Staphylococcus Aureus Bacteria
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  A factorial experiment was conducted at the laboratories of the College of Agriculture – Kerbala University during 2016. The aim was inhibitory efficiency for some aqueous and alcoholic extracts of Cumin, Fenugreek, Sweet Fennel and Black cumin in growth of Escherichia coli and Staphylococcus aureus bacteria. Results of Lab the extracts alcoholic, Concentrations 10, and 20 μg/ml giving to the highest percentage of inhibition from water extracts for both types of bacteria. Alcoholic extract of cumin highest percentage inhibition and concentration reached 23 and 26 mm, respectively, for the bacterium Staphylococcus aureus, while the bacteria Escherichia coli giving the alcoholic extract of the concentration of 20 μg/ml

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Publication Date
Tue Aug 01 2017
Journal Name
Journal Of Economics And Administrative Sciences
Evaluating the performance of Inspector General office of the Ministry of health in accordance with normative people and people results for the European excellence model EFQM 2013
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Current research sought to evaluate the performance and results of employees in accordance with normative to people and people result for the European model of excellence EFQM 2013 quality management Foundation in the Inspector General's Office/Ministry of health, so as to pursue a modern and advanced management methods in evaluating performance and the performance of the Office's relationship with a citizen's life, since it takes him beyond the accepted service capabilities today, but it became budget duties between dealers servicing responsibilities and future planning, financial control, competitiveness, human resources needs and maintaining quality and continuous improvement and development as well as The primary role of the

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