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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 Nov 22 2014
Journal Name
Indian Journal Of Physics
Comparison between shell model and self-consistent mean field calculations for ground charge density distributions and elastic form factors of 12C and 16O nuclei
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Publication Date
Tue Dec 01 2020
Journal Name
Journal Of Economics And Administrative Sciences
Deposit insurance system and its role in financial security for the period (2010-2018) Study the experiences of Selected countries with reference to Iraq
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Founding a System to secure deposits and protecting the depositors is considered one of the important and exchanged subjects out there in the banking system/field in Iraq at the current time, and the reason behind the exchange and spread of this subject is due to the financial crisis of which the banking sector is suffering from and the stumbling of many banks, those factors have had led to the insecurity of the depositors and their mistrust towards banks, thus, it is necessary to create a system to secure deposits in which depositors would be compensated for the losses caused by the banks' failures. in addition, it could be a countermeasure system which maintains the banking stability, protects the rights of depositors and gains

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Crossref
Publication Date
Sat Oct 20 2018
Journal Name
Journal Of Economics And Administrative Sciences
Fluctuations of global crude oil prices and their effect on inflation and economic growth in Iraq " A standard study for the period 1988– 2015
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Abstract

That Iraq's dependence on the revenues of the oil product in financing its development programs and growth rates , Making the economy affected by external forces represented by fluctuations in crude oil prices in the global market, Which is directly reflected on the performance and efficiency of the Iraqi economy.

The study adopted its objectives to analyze the time series for the period (1988 - 2015) through the use of standard and statistical methods, Four standard models were estimated to reach those targets, Where the results of the stability test showed instability of most variables at their original level, But to achieve stability when taking the first differences, While the result

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Crossref
Publication Date
Fri Sep 30 2022
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Ijarah and lease ending with ownership and its implications for the bank's profits: A case study in the Emirates Islamic Bank and Emirates NBD
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The formula of Ijarah and Ijarah ending with ownership is one of the investment formulas in Islamic banks, so this research has shed light on it in order to benefit from the experiences of the research sample banks, This research aims to find a reliable way for Iraqi Islamic banks, namely (leasing and leasing ending with ownership) in order to invest their money without usurious interests, The problem of the research emerges through the lack of awareness of the Iraqi Islamic banks to work with different Islamic financing formulas and their inability to invest their money through the adoption of their administrations for different formulas, including the leasing, and this is reflected in the decrease and fluctuation of its profits, Theref

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Publication Date
Tue Oct 01 2019
Journal Name
Karbala Journal Of Physical Education Sciences
Effect of use a designed device to develop some biochemical variables for rear vault dismount with one-half twist on parallel bars in gymnastics
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The research included five sections containing the first section on the introduction o research and its importance and was addressed to the importance of the game of gymnastic and skilled parallel bars effectiveness and the importance of biochemical variables, either the research problem that there is a difference in learning this skill and difficulty in learning may be one of the most important reasons are falling and injury Has a negative impact on the performance and lack of sense of movement of is one of the obstacles in the completion of the skill and the goal of research to design a device that helps in the development of biochemical changes to skill of rear vault dismount with one-half twist on parallel bars in gymnastics . And the n

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Publication Date
Sun Dec 01 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Effect of existing deposit facilities on the quality of bank liquidity: Applied research in the Central Bank of Iraq for the period (2010 - 2017)
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The research aims at showing the effectiveness of the existing deposit facilities in the liquidity of the Iraqi banking system for the period 2010/2017. The problem of research indicates that the Iraqi banking system enjoys high liquidity levels exceeding the standard rate set by the Central Bank of Iraq amounting to 30% For an appropriate level of liquidity remains a major challenge to the management of the bank because it is a trade-off between profitability and liquidity, and also indicates the existence of funds disabled and not available for credit and investment opportunities, and based on the research hypothesis:

The existence of a significant effect of the deposit facilities existing in the liquidity of the Iraqi banking

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Publication Date
Mon Aug 25 2025
Journal Name
Iraq Acadmic Journals
The effect of an educational program using the Polya strategy on probing thinking and the application of some defensive formations in handball for students
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Browse Iraqi academic journals and research papers

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Publication Date
Tue Mar 31 2026
Journal Name
Tikrit Journal Of Administrative And Economic Sciences
IT Infrastructure Readiness for Business according to the International Standard ISO/IEC 2025: 27031at Earthlink, the Internet Service Provider in Iraq: A case study
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Abstract: The research aims to assess the level of readiness of the Information and Communication Technology (ICT) infrastructure for business continuity at Earthlink Telecommunications and Internet Services Company in Iraq, in light of the requirements of the international standard ISO/IEC 27031:2025. The research adopts a case study approach as an appropriate methodological framework for understanding and analyzing the organizational and technical complexity inherent in telecommunications sector organizations. To achieve the research objectives, a set of integrated data collection tools was employed, including field interviews with technical and administrative staff, a review of organizational documents and approved policies, as well as d

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Publication Date
Tue Jan 02 2018
Journal Name
Journal Of Educational And Psychological Researches
The awareness degree of teacher students in Arabic language department and their supervisors at Al-aqsa University for their future role in knowledge age
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The study aimed to identify the awareness degree of teacher students in the department of Arabic language and their supervisors at Al-aqsa University for their future roles in the age of knowledge. To achieve this objective, descriptive- analytical approach was used. The instruments of this study were two questionnaires: first one consist of (20) item for teacher students, and the second consist of (27) item for educational supervisors which covered three roles: professional, technological, and humanitarian. The sample was (120) student selected randomly, and (39) supervisors of Arabic language. The result revealed that the mean of degree awareness of teacher students and their supervisors of future role are (3.857), (3.472) respectively

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Publication Date
Wed Jul 24 2024
Journal Name
مداد الآداب
Navigating the Evolving Tourism Landscape: Examining the Challenges and Opportunities for TripAdvisor and Travelocity in the Era of AI:A Comparative Analysis of Innovation Strategies
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The tourism industry has undergone exponential transformation, reshaped by online travel agencies (OTAs), shifting consumer preferences, and technological advancements. Established OTAs like TripAdvisor and Travelocity face pressures to adapt their strategies to capitalize on these disruptive landscape changes. This research involves a comparative analysis examining the key challenges confronting TripAdvisor and Travelocity, with a focus on opportunities to leverage artificial intelligence (AI) in enhancing personalization and the traveler experience. The study utilizes publicly available data on the companies and academic literature on AI innovation diffusion. Findings reveal that while TripAdvisor has actively developed AI-based trip plan

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