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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
Tue Nov 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Money supply and the factors that affect it together with role central Bank of Iraq in controlling it Applicatory research of the Iraqi central bank for the period (2003- 2014)
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ABSTRACT

This research deals with the two item namely, the monetary policy central Bank of Iraqi and money supply . that contribute in up the problem of the paper that is concerned with the fact that to what extent the effectiveness of monetary policy conducted by the central Bank of Iraqi is valid in controlling money supply as well as the possibility of applying it in practical environment restricted to the scope of financial in stitiutions particularly in research population represented by central Bank of Iraqi .

For the purpose of a practical contribution for monetary and financial institutions . To achieve this , A hypothesis has been carried out and it suggested that the mon

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Publication Date
Sat Jun 03 2023
Journal Name
Iraqi Journal Of Science
New mode for the on-line determination of oxonium ion in different strong acids using CFIA via the use of homemade linear array Ayah 5Sx4-ST- 5D solar CFI analyser
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New mode for the on-line determination of oxonium ion in different strong acids using CFIA via the use of homemade linear array Ayah 5Sx4-ST- 5D solar CFI analyser

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Publication Date
Tue Jun 15 2021
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Effects of Exclusive Breast Feeding for First Six Months of life on Children Weight, Height and Head Circumference in Sulaimani City, Kurdistan-Iraq and Compare with Other Types of Feeding
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Breastfeeding (BF) serves as a complete nutritional source for the first six months of infant’s life. Breast milk contains all essential nutrients that necessary for the physiological growth and development of infants. The aim of this study was to compare the physiological growth of infants including weight, height and head circumference who were exclusively breastfed for 6 months and those who were given bottle-fed or mixed fed and to find a percentage of exclusive breastfeeding among mothers who contributed in this study in Sulaimani city. This study was carried out in Sulaimani city/ Kurdistan region of Iraq and the cases were enrolled between the first of October 2018 and first of October 2019. The infants’ weight, height and hea

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Publication Date
Tue Apr 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
Relationship between Emotional Intelligence and Decision Making Styles And their effect on Performance Excellence the university" An exploratory search for a sample of the administrative leaderships in the Mustansiriya University"
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   Addressed this research the impact of intelligence emotional dimensions of the main(self awareness, and self-management, and social awareness, and relationship management) in the performance excellence the university(performance optimization, and strategic development) this is by middling the styles decision making which are (rational and intuitive, and dependent, and spontaneous, and avoidant), and Go search of an intellectual dilemma raise fundamental questions revolve around the search was to answer those questions through a theoretical framework for search variables first and test models of the relationship and second through the impact six hypotheses President.The objective of the research to make sure the contr

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Publication Date
Wed Mar 30 2022
Journal Name
Journal Of Educational And Psychological Researches
The extent to which the content of social and national studies courses is included With interactive thinking maps for the stages of public education in the Kingdom of Saudi Arabia
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The present study aimed to identify the extent to which the content of social and national studies courses was included in interactive thinking maps in the educational stages in the Kingdom of Saudi Arabia, and to achieve the goal of the study, the researcher used the descriptive and analytical approach, and the study tool used consisted of a content analysis card; Where it included a list of the types of thinking maps, where the study sample consisted of all social and national studies courses at the elementary and intermediate levels, and it is (12) books for the student in its first and second parts, and after verifying the validity and reliability of the tool, it was applied to the study sample, and the study reached conclusions, inc

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Application of the Canadian Water Quality Index (CCME-WQI) for Aquatic Life to Assess the Effect of Tharthar Water upon the Quality of the Tigris Water, Northern Baghdad City,Iraq
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The present study aims to assess the effect of the Tharthar Canal as an outlet canal that feeds back from the Tharthar Lake on the quality of the Tigris water. Utilizing a Canadian Water Quality Index (CCME-WQI) for the protection of aquatic life Water samples were obtained every month from January to December of 2020. Six different sites were selected: four along the Tigris River and two on the Tharthar Canal. Seven ecological parameters were used to assess water quality depending on importance and availability: water temperature, Water Temperature, Turbidity, Dissolved Oxygen (DO), Total Dissolved Solids (TDS), pH, Nitrate (NO3-) and Phosphate ( . The study demonstrated that the water quality of the Tharthr canal ranked as a

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Publication Date
Thu Jun 01 2017
Journal Name
Journal Of Economics And Administrative Sciences
Customers emotional blackmail and reduce it the new product- study of the opinions of a sample of customers who deal with peak economy for household items in najaf al Ashraf
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The challenges facing today's multi-customer and this is due to the multiplicity of products and speed in launching new products so search came to reveal the  reveal the of the new product classification standards through a relationship (good products, low interest products, useful products and products desired) and the customer emotionally blackmail through deportation (fear, obligation and guilt). dentified the problem of the research in several questions focused on the nature of the relationship between the variables of research, and for that outline supposedly to search it expresses the head of one hypothesis and branched out of which four hypotheses subset, but in order to ensure the validity of the ass

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Crossref
Publication Date
Wed May 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Detection for The Production of Siderophore in Burkholderia cepacia Isolated From the Rhizosphers of Some Plants and studing the Effect of the Bacterial Filtrate and Extract on Some Pathogenic Fungi
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bstract         This study was performed to isolate and identify the Burkholderia cepacia from rhizosphers of different plants and study their ability to produce Siderophore, the study was also aimed to assess the antifungal activity of the bacterial filtrate and extracts of the isolates against some pathogenic fungi.     The isolate which showed higher inhibitory effects was selected for extraction of some active metabolites produced by it, and evaluate the activity in vitro, via inhibition of the growth of the fungi using different concentrations of extract (50, 100, 200 )µL/ml , The results showed that out of  (250) samples of soil , (8) isolates (3.2%) gave positive

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Publication Date
Sat Sep 30 2023
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Audit of accounting disclosure for potential liabilities and contingent obligations In light of the Corona pandemic and its reflection on the auditor's opinion: Applied research in the National Insurance Company
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Abstract:

                The research aims to identify how to audit potential liabilities and contingent liabilities in light of the pandemic and its reflection on the auditor's report. The research problem is represented by the complexity of the process of checking potential liabilities and contingent liabilities in insurance companies, which was negatively reflected in the auditor's neutral technical opinion. The researchers hypothesize that auditing potential liabilities and contingent liabilities in light of the Corona pandemic is positively reflected in the auditor's report. The research concludes that the process of checking potential liabilities and contingent liabilities is

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Publication Date
Fri Dec 31 2010
Journal Name
Journal Of Legal Sciences
The moment of concluding the contract according to the United Nations Convention on Contracts for the International Sale of Goods (1980) (A comparative study with some Arab and foreign legislations)
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There are two ways that the contract might be formed with (contracting between persons who are attended and contracting between absence persons).the need for determining the precise moment of the contract , is so clear because there is a specify period separate between the declaration of acceptance and the knowledge with it .and it is clear from the four theories known for jurisprudence (theory of the declaration of the acceptance, theory of exporting the acceptance , theory of the arrival of the acceptance , theory of the knowledge with the acceptance ) . It is difficult to promote one theory on another one if we look at each one and the justification of its supporters and what the opponents of each theory expose. Legal background and diff

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