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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
Wed Sep 02 2020
Journal Name
Indonesian Journal Of Chemistry
Synthesis, Characterization and Biological Efficacies from Some New Dinuclear Metal Complexes for Base 3-(3,4-Dihydroxy-phenyl)-2-[(2-hydroxy-3-methylperoxy-benzylidene)-amino]-2-methyl Propionic Acid
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The reaction of methyldopa with o-vanillin in refluxing ethanol afforded Schiff base and characterized through physical analysis with a number of spectra also the study of biological activity. The geometry of the Schiff base was identified through using (C.H.N) analysis, Mass, 1H-NMR, FT-IR, UV-Vis spectroscopy. Metal complexes of Cr3+, Mn2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Hg2+ with Schiff base have been prepared in the molar ratio 2:1 (Metal:L), (L = Schiff base ligand) except Hg2+ at molar ratio 1:1 (Hg:L). The prepared complexes were characterized by using Mass, FT-IR and UV-Vis spectral studies, on other than magnetic properties and flame atomic absorption, conductivity measurements. According to the results a dinuclear octahedral geo

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Publication Date
Fri Jan 10 2025
Journal Name
College Of Basic Education Researches Journal
Identify the effect of exercise of the arm is the practice in the development of accurate performance skill transmission (short and long) arm of practice for students badminton
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Publication Date
Tue Jan 01 2019
Journal Name
International Journal Of Supply Chain Management
The effect of internal training and auditing of auditors on supply chain management: An empirical study in listed companies of Iraqi stock exchange for the period 2012-2015
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Scopus (30)
Scopus
Publication Date
Sun Jun 30 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Proposed model for the work of audit committees in the public sector and its interaction with the Federal Board of Supreme Audit to reduce the incidents of fraud
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This growing interest of the international scientific specialized commissions is due to the role that the audit committee can play, as one of companies’ governance tools, to increase the accuracy and transparency of the financial information disclosed by the companies, through its oversight role on the process of preparing financial reports, its supervision on the internal audit function within the companies, and supporting its independency, as well as coordinating the efforts between the internal control unites and the external auditor represented by the (Board of Supreme Audit) to clear the observations and irregularities in order to reduce the fraud cases.

This research was built on an applied sample of audit committee works

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Publication Date
Thu Mar 30 2023
Journal Name
Iraqi Journal Of Science
New mode for the on –line determination of metoclopramide hydrochloride in pure and pharmaceutical preparations via the use of homemade Ayah 6SX1-T-2D Solar cell CFI Analyser
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A newly developed analytical method characterized by its speed and sensitivity for the determination of metoclopramide hydrochloride (MCP-HCl) in pure and pharmaceutical preparations via absorbance measurement by Ayah 6SX1-T-2D Solar cell-CFI Analyser. The method is based on the oxidation of the drug with Ce(IV)sulfate in acidic medium to form a red color species which determined using homemade Ayah 6SX1-T-2D Solar cell . Chemical and physical parameters were studied and optimized. The calibration graph was linear in the range of 0.05- 16 mMol.LP-1Pwith correlation coefficient r = 0.9855. The limit of detection(S/N = 3) 0.332 μg/sample from the step wise dilution for the minimum concentration in the linear dynamic ranged of the calibrat

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Publication Date
Wed Nov 16 2022
Journal Name
Res Militaris
The contents of the publications of the campaign (Together to defeat Corona) for the United Nations Development Program in Iraq to prevent infection with the Covid 19 virus
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The study deals with an analysis of the contents of the publications of the campaign (Together to defeat Corona), which was established by the United Nations Development Program in Iraq in the face of the Covid 19 virus.The research problem raises a main question:What are the implications of the campaign (Together to defeat Corona) of the United Nations Development Program (Iraq office) in addressing the Covid-19 virus in Iraq?From this main question, several sub-questions emerged, which were answered by this study in its chapters and investigations, including regarding the contents of advertisements, photos and videos for the publications of the (Together to Defeat Corona) campaign for the United Nations Iraq Office on their Facebook pageA

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Scopus
Publication Date
Fri Mar 01 2013
Journal Name
Journal Of Economics And Administrative Sciences
Balancing the Multi Assembly line Using Ranked Positional Weight and COMSOAL Algorithms: Case Study at the Sewing line Factory (7) /the General Company for Leather Industries (GCLI/ Baghdad)
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      The problem of multi assembly line balancing appears as one of the most prominent and complex type of problem. The research problem of this dissertation is concerned with choosing the suitable method that includes the nature of the processes of the multi assembly type of the sewing line at factory no. (7). The State Company for Leather Manufacturing. The sewing line currently suffers from idle times at work stations which resulted in low production levels that do not meet the production plans. The authors have devised a flexible simulation model which uses the uniform distribution to generate task time for each shoe type produced by the factory. The simulation of the multi assembly line was based on assigni

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Crossref
Publication Date
Fri Jan 10 2025
Journal Name
Journal Of Studies And Researches Of Sport Education
Design and rationing test compound to assess the performance of the attack straight in terms of power characteristic speed And vital capacity for young players duel weapon Blinds
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Publication Date
Sun Mar 01 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Implement some basic health accreditation standards Issued by the Health Care Accreditation Council (HCAC) for auditing the Performance of Hospitals: Applied research at the Education Children Protection Hospital
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The health care provided by health institutions and all kinds suffers from many problems, and since the health services provided are related to human life, it is necessary to shed light on this activity and identify the causes of these problems. This research aims to Definition of health institutions (hospitals) Performance audit of these institutions according to the latest indicators, which are the standards of health accreditation for hospitals, specifically the basic standards issued by the Health Care Accreditation Council (HCAC) to reach the level of performance and Knowledge of Constraints that lead to in an acceptable manner consistent with the approved standards. In theoretical and practical study, a number of conclusions were r

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Crossref
Publication Date
Fri Dec 30 2022
Journal Name
Iraqi Journal Of Science
Climate parameters analysis as an indication of climate Changes for Diwaniya, Nasiriya, Kut and Karbala meteorological stations - Central and southern Iraq: Karbala climate condition as a case study
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       The climate parameters (rainfall, number of rainy days and temperature) data for about seventy years from 1941 – 2009 for three Iraqi meteorological stations (Diwaniya, Nasiriya, and Kut) were investigated and gave good evidence of climate change. As well as  the climatic water balance and the climatic conditions were determined at Karbala meteorological station for the years (1982-2015). The annual precipitation for Karbala station-reflect declination from 105 mm for the period 1982-1990 to about 71 mm for the years 2011- 2015 confirms the effect of global climate change. Analyzing Karbala climate parameters reflects that the total annual rainfall is (89 mm), evaporation is (2984 mm), while the mean monthly relative humi

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