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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 Dec 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Organizational commitment and its role in enhancing the performance of employees : exploratory search of the views of a sample of managers and employees of the General Company for Dairy Products
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Expected to The organizational commitment by employees increases their loyalty towards their organization and thus contribute to enhancing their performance , therefore this study aimed to discover the relationship and the impact between the organizational commitment (emotional commitment, standard commitment, continuous commitment) and the performance of employees in the company researched, additional to know the available organizational commitment levels of employees in the company researched and its impact on the performance of employees, Research was conducted at the General Company for products in the dairy to achieve the goals of research has been developed questionnaire conation (22 ) items to collect data from the study s

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Publication Date
Sun Jun 01 2014
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Suggested Model for The Work of the Certified Fraud Examiner & His Role in Reducing The Incidents of Fraud and Corruption: An Applied Study in The Federal Board of Supreme Audit
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Is hardly day expire without hearing the news either Abuse Managementthe accounting standards or the existence of serious misstatements by someauditors.Which caused the demanding of many companies in the recent republication of the financial statements and the re-announcement of its financialresults. Such acts raise questioning about the role that should be played by theauditors, prompting agencies responsible for setting auditing standards to takeTo throw increasingly responsibility on the auditors in order to interest risksfraud The Risks of Fraud in their review of the financial statements.also The Public Company Accounting Oversight Board in the U.S.called about the need of owning the Certified Public Accountants those whoaudits for

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Publication Date
Sat Aug 20 2022
Journal Name
Journal Of Legal Sciences
The legal regulation of the distribution of parliamentary seats in Iraq under the law (45) for the year 2013 amended and its effects on the value of the parliamentary seat
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   The search came under the title "The Legal division of the distribution of seats in Iraq under Law No. (45) for the year 2013 and its effects on the value of the seat of Parliament)" as part of the response to the requirements of the current circumstances that are going through Iraq, after the experience of each of the electoral experiments that we are waging every four Nawat to elect a new house of representatives that cries out for amending the distribution systems of parliamentary seats, so that some have imagined that the devil is behind all the darkness of the crises in society, and that it is inevitable to believe that the distribution systems of the parliamentary seats is a legal ploy to confiscate the will of the peo

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Publication Date
Sun Oct 22 2023
Journal Name
Iraqi Journal Of Science
New Approach for the On-Line Spectrophotometric Determination of Vanadium (V) In Different River Water via the Use of a Homemade Ayah 6SX1-T-2D Solar-Continuous Flow Injection Analyser
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A new simple sensitive and selective spectrophotometric method has been developed for the analysis of vanadium(V) in three randomly chosen samples from river water at different locations by continuous flow injection analysis. The method based on the oxidation of pyrogallol by vanadium(V) in acidic solution to form color species and the same species was determined using homemade Ayah 6SX1-T-2D solar cell analyser . Chemical and physical parameters were investigated using the high intensity of snow white light emitted diode as a source. The linear dynamic range for the instrument response versus vanadium(V) concentration was 1-200 mg.L-1 with correlation coefficient r = 0.9920. The limit of detection (S/N=3) was 70 ng/ sample from the step

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Publication Date
Sat Dec 01 2018
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The contribution of the tax authorities to increase the tax revenues: An applied research on a sample of the supporting bodies in the health sector for the period 1998-2008
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the research was exposed to a study the importance of the role of the supportive entities in providing the useful information to the tax administration and their ability to extend the level of the tax base of taxpayers, through the improvement of the tax payers determination and their tax settle for the purpose of increasing the tax revenue, and shed light on the legal evidence through which these entities become officially assigned to perform a supplementary task to the General Committee for Taxes GCT, to help it to perform its task efficiently, and to study the reasons of the weak cooperation of the supportive entities and their reluctance to provide useful information which leads to limiting the tax base.

The research data hav

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Publication Date
Fri Jan 01 2021
Journal Name
Journal Of Economics And Administrative Sciences
Crisis management according to the strategic leadership - the interactive role of decision support systems. (An exploratory study at the Ministry of Industry and Minerals / the State Company for Steel Industries)
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The researcher aims to Diagnose the reality of research variables, strategic leadership and decision support systems, and their impact on crisis management in the General Company for Steel Industries because of their important role in preventing crises and reducing their occurrence for the research company in particular and other companies in general affiliated with the Ministry of Industry and Minerals, as well as clarifying theoretical concepts of research variables As it included the answer to questions related to the research problem, including (Is there an impact of the strategic leadership in managing crises if decision support systems are used), and the researcher adopted the descriptive and analytical approach in its comp

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Publication Date
Thu Dec 26 2024
Journal Name
Al–bahith Al–a'alami
The Responsibility of the Iraqi Journalism in Promoting Political Culture in Society: (An Analytical Study in Newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 - 31/ 3/ 2013)
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This study comes as: The responsibility of the Iraqi newspapers in promoting  the political culture inside society, an analytical study in newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 to 31/ 3/ 2013 to spot light on the extent to which the three mentioned newspapers are compliance with the promotion  of the political culture inside society which is seen as one of the essential requirements for the success and promotion of the democratic process inside society.

The study aims to: finding out the extent to which these newspapers are compliance with their responsibility in the promoting the political culture inside society; knowing the nature of their role in pr

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Publication Date
Wed Mar 23 2022
Journal Name
Journal Of Educational And Psychological Researches
The Actual Use of Instructional Technology in Teaching History Subject in the Colleges of Education for Humanities from the of the College Staff Members' Perspectives and their Attitudes Towards Them
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The study aims at knowing the actual uses of instructional technology in teaching history subject in the colleges of education for humanities from the college staff members' perspectives and their attitudes towards it. The sample of the study consisted of (24) instructors from the Colleges of Education for the Humanities, the College of Basic Education- Haditha and the College of Education for Women, the study used the descriptive method, and the questionnaire was consisted of (50) items, and the psychometric properties of the instrument of the study were extracted. The researchers used the appropriate statistical means to analyze the data, and the results of the study showed the following: the teaching staff attitudes towards the use of

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Publication Date
Wed Mar 30 2022
Journal Name
Journal Of Economics And Administrative Sciences
The Influence of Organizational Power on the Achievement of Entrepreneurship for Business Organizations An Analytical Study of the Views of a Sample of Managers in the Iraqi Ministry of Education
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This research aims to study the influence of organizational power on the achievement of entrepreneurship for business organizations. It is an analytical study of the views of a sample of managers in the Iraqi Ministry of Education. The research highlights the contribution that can be made from the knowledge of the theory of business organizations in achieving organizational success. The organizational power of the organization contributes to achieving entrepreneurship in the business environment and achieving a competitive position in the work environment. The research dealt with two variables: the first is the independent variable, the organizational power in its dimensions (Expend Power, Structural Power, Prestige Power). And t

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Publication Date
Fri Jun 14 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Myxobolus Infections of the Cyprinid Fishes from Lesser Zab and Greater Zab Rivers, North of Iraq with the Record of Seven Species of Myxobolus for the First Time in Iraq
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 A total of 1453 freshwater fishes, belonging to 14 species of the
family Cyprinidae was collected from Lesser Zab and Greater Zab
rivers in north of Iraq during the period from November 2000 to the
end of November 2001. The inspection of skin, gills and different
internal organs revealed the infection of these fishes with a total of 14
species of Myxobolus which included seven species that represented
their first record in Iraq. These species included M. bulbocordis from
both Barbus sharpeyi and Chondrostoma regium; M. karuni from B
grypus; M. mesopotamiae from B. luteus; M. molnári from B
esocinus; M. pcrsicus from both B. grypus and Cyprinion macrostomum;
M.  Shaagani from both B. b

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