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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
Fri Dec 01 2017
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The Roleof Time Management in Stages Claims Settlement of Insurance from Fire: Research Exploratory in General Iraqi Insurance Company and Private Al hamra Company for Insurance
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The insurance activity in the various countries of the world are important indicators of the strength of the country's economy, he came to study the stages compensation insurance settlement against fire and the importance of investing time risk in achieving the payment of compensation speed, and the implications for the continuation of the insured to carry out insurance with the insurance company, whether working within the public sector or the private sector. Hence the research problem in how quickly insurance companies to pay compensation as soon as possible and the return of the insured to carry out its work and make up for what he died from loss. Intentional sample was selected from branches and divisions and Their assistants manager

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Publication Date
Sat Dec 31 2016
Journal Name
Al-kindy College Medical Journal
Dorsal plication during penile orthoplasty with and without neurovascular bundle mobilizationA comparative clinical trial conducted At Ghazy Al-Hariri teaching hospital for surgical specialties (2013 –2015)
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Background: Dorsal plication on each side of the penis at the 2 and 10-o’clock positions had been a mainstay for correction of ventral penile curvature. However, because only the 12-o’clock position proved to be a nerve-free zone, dorsal plication at the 12-o’clock position can be advocated.

Objectives: To evaluate tunica albuginea plication with and without neurovascular bundle mobilization in patients with ventral penile curvature. Type of the study: A prospective study.

Methods: A 34 patients with a mean age of (4.8 ± 0.54) years, Who still

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Publication Date
Tue Jan 01 2019
Journal Name
Journal Of Human Sport And Exercise - 2019 - Spring Conferences Of Sports Science
Effect of taking some of dietary supplements according to special forces exercises to develop some physical abilities, speed and accuracy smash shot for badminton young players
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Set dietary program for some of dietary supplements and training for badminton young players, and identifying effect of taking some of the dietary supplementary for badminton young players. The research population :( badminton young players group (Arminian club). For age group (16-18) years the sample is divided in to two experimental groups within each group (6) players, and two for the exploratory experiment which was within the research sample, they were divided in to two groups, the first group take some of the dietary supplements (multivitamin creating) .the set exercises by the researchers in the main part of the training unit and the second group (amino acids, vitamins) and the set exercises by the researcher. The scientific approach

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Publication Date
Wed Nov 01 2023
Journal Name
Ecological Engineering & Environmental Technology
Synthesis of Mn-Co-Ni Composite Electrode by Anodic and Cathodic Electrodeposition for Indirect Electro-oxidation of Phenol – Optimization of the Removal by Response Surface Methodology
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In the present work, Response Surface Methodology (RSM) was utilized to optimize process variables and find the best circumstances for indirect electrochemical oxidation of mimicked wastewater to remove phenol contaminants using prepared ternary composite electrode. The electrodeposition process is used for the synthesis of a ternary composite electrode of Mn, Co, and Ni oxides. The selected concentrations of metal salts of these elements were 0.05, 0.1, and 1.5 M, with constant molar ratio, current density, and electrolysis time of 1:1:1, 25 mA/cm2, and 2 h. Interestedly, the gathered Mn-Co-Ni oxides were deposited at both the anode and cathode. X-ray diffraction (XRD) and scanning electron microscopy (SEM) facilitated the qualitative char

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Publication Date
Sun Mar 04 2012
Journal Name
Baghdad Science Journal
The effect of crude alcoholic extracted for the Seeds and Leaves of Apium graveolens Var dulce. In the level of some female hormones in albino Mice.
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The quantitative determination of the estrogen E2, Progestron P4 & follicle stimulating hormones FSH in the serums of Albino mice used in the experiments & treated by crude alcoholic extracted 95% of the seeds & leaves of Apium graveolens was a significant increase in the concentration of estrogen of different kinds of the extracted in comparison with the values of the coefficient of the control group, that is the study recorded a significant increase of the concentration of estrogen; it was the highest in the mice which was administrated by the methanolic extracted 95%, then it was less in the mouse which was administrated by the ethanolic extracted., and it was the least in the mice which were administrated by the crude ethanolic-methano

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Publication Date
Thu Aug 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
The cognitive complexity of the leaders and their impact on the organizational flexibility of field research at the company's headquarters for the distribution of petroleum products
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The present research aims to test the effect of cognitive complexity as an independent variable in organizational agility as a responsive variable among the leaders working at the headquarters of the Iraqi Petroleum Products Distribution Company.

 To conclude a number of recommendations that contribute in the organizational agility in the company, and due to the importance of this research in public organizations and its notable role in community organizations. The research was carried out on a random sample of 101 individuals out of a total of 308, which represents the high leaders in the company (general managers, head of departments, and division officials). A questionnaire was used as information

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Publication Date
Wed Jul 17 2019
Journal Name
Iraqi Journal Of Science
Using Geographic Information System (GIS) to estimate the volume of water for Al Dammam unconfined Aquifer within Al Salman basin, Al- Muthana Governorate, South West Iraq
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The groundwater represents the main source of water in the study area due to lack of surface water. The Dammam unconfined aquifer represents the main aquifer in the study area and Southern desert because of the regional extent, the quantity and quality of water. Many groundwater wells have been drilled in the study area to coverage the huge demand of water for agricultural purposes. The Geographic Information System (GIS) was used to estimate the volume of water which calculated (25.6964 × 109 m3) within the study area , automate calculation of the area of Al Salman basin using digital elevation models, derive the thickness maps of Al
Dammam unconfined aquifer from Key holes (KH) and Bore holes (

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Publication Date
Sat Jul 01 2017
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Prevalence, risk factors and association of renal artery stenosis with coronary artery disease in patients undergoing coronary angiography in Ibn-Al Bitar center for cardiac surgery
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Background:-Atherosclerosis is a systemic disease that often affects multiple vascular distributions in a single patient. The increased prevalence of renal artery stenosis in association with coronary artery disease has been well documented.
Objectives:-To examine in detail the prevalence of renal artery stenosis in patients undergoing cardiac catheterization for suspected coronary artery disease.
Patients &methods:-Between April 2010 and February 2011, two hundred patients underwent coronary and renal angiography at the same session in Ibn Al-bitar Hospital for Cardiac Surgery. Clinical and procedural data for patients undergoing renal angiography were prospectively collected and entered into database specially designed for th

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Publication Date
Sun Jun 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
The Effect of Strategic Intelligence on the Process of Green Manufacturing An Explorative Study for the Managers Opinions of Sample of Mineral water factories at Dahuk
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         The studying trying to determine the role of  Strategic Intelligence on the Process of Green Manufacturing  of  Sample of Mineral water factories at Dahuk city.  The study submit a theoretical frame of Strategic Intelligence and Green Manufacturing, a supposed sample, had been set to reverye   the nature of the relations and effect in the study  Varity, the study  depend on group of the main and branch concurring with the relations and effect between the Strategic Intelligence and Green Manufacturing to answer the following questions about research to problems:

 What are the relationships and effects between stra

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Publication Date
Sat Jun 30 2018
Journal Name
College Of Islamic Sciences
Inform the people of the Enlightenment including what was said in detail In photography For Mohammed Hashim bin Ahmed footy famous Balva Hashim (Tel: 1349 e)
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Inform the people of the Enlightenment including what was said in detail
In photography
For Mohammed Hashim bin Ahmed footy famous Balva Hashim (Tel: 1349 e)

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