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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
Mon Apr 24 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Theoretical Calculation of The Binding And Excitation Energies For 𝐍𝐢 𝟐𝟖 𝟓𝟖 30 Using Shell Model And Perturbation Theory
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    A theoretical calculation of the binding and excitation energies have been used at low – lying energies based on shell model and quantum theory. In this model, we evaluated the energies under assume Ni 28 56 30 as inert core with two nucleon extra, nucleons in the  2P3/2 ,  1f 5/2  and 2P1/2  configuration. Modified Surface Delta Interaction (MSDI) and Reid's Potential (RP) theory for two body matrix elements are evaluated by using a Matlab program to calculate the energies of experimental and Reid single particle energies. Our results of the theoretical calculation have been compared with the experimental results, which show no good agreement with the experiment but have a good agreement wit

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Publication Date
Sun Jan 12 2025
Journal Name
Al–bahith Al–a'alami
The Semiology of Narrative Construction in Television Advertising to an Announce "God Will not Forget us" about the Covid-19 Pandemic for Zain Mobile Telecommunication Company
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This research paper tries to show the significance of the narrative structure in the television advertisement and its connotations. The researchers chose the annual advertisement of Zain Mobile Telecommunication Company for the year 2020, which shed light on the global Corona pandemic crisis. The idea of the advertisement won wide approval as it focused on the suffering that everyone is witnessing like medical and security personnel in particular, and family relationships consequences.
In addition to the positive global interaction with the message presented by the Company in these exceptional circumstances. The advertisement, which lasted for 2.35 minutes, exceeded 13 million views in a short period of time. This prompted us to choos

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Publication Date
Mon Nov 30 2020
Journal Name
Journal Of Economics And Administrative Sciences
The Use of Auto-Regressive Distributed Lag Method in Investigating The Impact of Interest Rate on Foreign Direct Investment in Yemen for the Period 1990-2018
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 Foreign direct investment has seen increasing interest worldwide, especially in developing economies. However, statistics have shown that Yemen received fluctuating FDI inflows during the period under study. Against this background, this research seeks to determine the relationship and impact of interest rates on FDI flows. The study also found other determinants that greatly affected FDI inflows in Yemen for the period 1990-2018. Study data collected from the World Bank and International Monetary Fund databases. It also ensured that the time series were made balanced and interconnected, and then the Auto Regressive Distributed Lag method used in the analysis. The results showed that the interest rates and

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Publication Date
Mon Feb 13 2023
Journal Name
Journal Of Educational And Psychological Researches
Evaluation of Activities and Evaluation Questions Implied in the Content of the Computer Textbook for the Fifth Preparatory Grade According to Creative Thinking and Developing Suggestions
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The current research aims to evaluate the activities and evaluation questions implied in the content of the computer textbook for the fifth preparatory grade according to the creative thinking and developing suggestions through answering the following question: what is the percentage of creative thinking skills in the content of the computer textbook for the fifth Preparatory grade students issued by the Iraqi Ministry of Education/ Directorate General of the curriculum in the academic year (2019-2020)? The researchers followed the descriptive-analytical approach.  The research community was determined by the content of the computer textbook for the fifth preparatory grade. As for the research sample, it was limited to all activitie

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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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Crossref
Publication Date
Wed May 25 2022
Journal Name
Iraqi Journal Of Science
Effects of the Changes in the Neutron Number of Isotonic Nuclei on the Tow-Component Partial Level Density Formula Corrected for Pairing in Pre-Equilibrium Reactions
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Ericson’s formula describes the partial level density (PLD) of pre-equilibrium reactions and corrections. PLD with pairing correction can be calculated using four methods, namely, pairing, improved pairing, exact Pauli and back shift energy corrections. The variations in the PLD values of each of the four formulas of strontium (88Sr), Yttrium (89Y) and Zirconium (90Zr) isotones have been examined. Results shows that the PLD values that use pairing and improved pairing corrections do not vary for different isotones. However, a small change in PLD values is observed when exact Pauli correction and back shift energy were utilised. The change in the PLD values using back shift energy correction is bigg

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Scopus Crossref
Publication Date
Wed Jun 30 2021
Journal Name
Journal Of Economics And Administrative Sciences
The role of Iraqi trade policies in stimulating productive sectors to grow for the period (2003-2019) (an analytical study in light of the Malaysian experience)
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The research deals with analyzing the influencing role of trade policies in the growth and development of productive economic sectors and their contribution to GDP and its reflection on workforce employment. Studies have proven the success of the Malaysian experience in stimulating the productive economic sectors to grow and their contribution to the gross domestic product with an increase in the growth of local markets and access to international markets for national products. The research also deals with the ineffectiveness of Iraqi trade policies after 2003 in stimulating the productive economic sectors (agricultural and industrial) on economic growth, as most of the increase in Iraqi GDP growth throughout the study period was

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Crossref
Publication Date
Tue Mar 30 2021
Journal Name
Journal Of Economics And Administrative Sciences
The Effect of Organizational Creativity in Enhancing Knowledge Management Processes: survey study for a sample of academic staff members at the Technical College of management / Baghdad)
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In many organizations, employees who have high mental skills are the main source of organizational creativity. When a firm does not put creativity as a goal, cannot stand solid against the competition. Nowadays, knowledge is the path to discover the innovation and creativity aspects, This can assist the firm to stand face to face with competition in the market. The importance of this research comes from detecting and knowing the relation between creativity and knowledge to know and detect the influence of organizational creativity on backing the management of knowledge and determine the final results. The problem of research is to trace the role of organizational creativity on knowledge management processes in order to enable the

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Crossref
Publication Date
Mon Oct 25 2021
Journal Name
Iraqi Journal Of Science
Synthesis, Characterization and Kinetic Studies of Chelate Polymer Derived from 3-Nonyl Benzene and its Use for the Removal of Some Heavy Metals from Aqueous Solutions
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    A new chelate polymer (2-5-hydroxy-3-methyl-2- (3-nonyl benzene) imino) methyl) benzyl) 4-6-dimethyphenol] (K4) was prepared by using the condensation reaction method and identified by several techniques, including FT-IR, NMR, and atomic absorption spectroscopy, as well as TG-DTA thermal analysis. The kinetic equilibrium for the sorption of lead and cadmium ions on the chelate polymer surface was also investigated. The results showed that the sorption of both ions followed the pseudo-first-order and pseudo-second-order kinetic equilibrium. The rate constant values of pseudo-first-order reaction  were equal to 0.062 and 0.057 min-1  , while the values of pseudo-second-order were 0.0103 and 0.053 L.m

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Publication Date
Mon Jan 01 2024
Journal Name
Iraqi Journal Of Hematology
Provisional diagnosis of clinically significant hemoglobinopathies and decision on suitability for marriage as part of the premarital screening program in Iraq: Iraqi Society of Hematology Guidelines
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