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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 Dec 25 2019
Journal Name
Journal Of Engineering
Comparison of Different DEM Generation Methods based on Open Source Datasets
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Digital Elevation Model (DEM) is one of the developed techniques for relief representation.  The definition of a DEM construction is the modeling technique of earth surface from existing data. DEM plays a role as one of the fundamental information requirement that has been generally utilized in GIS data structures. The main aim of this research is to present a methodology for assessing DEMs generation methods. The DEMs data will be extracted from open source data e.g. Google Earth. The tested data will be compared with data produced from formal institutions such as General Directorate of Surveying. The study area has been chosen in south of Iraq (Al-Gharraf / Dhi Qar governorate. The methods of DEMs creation are kriging, IDW (inver

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Publication Date
Mon Apr 01 2019
Journal Name
Arpn Journal Of Engineering And Applied Sciences
Assessment of vegetable cover in south Iraq by remote sensing methods
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The vegetable cover plays an important role in the environment and Earth resource sciences. In south Iraq, the region is classified as arid or semiarid area due to the low precipitations and high temperature among the year. In this paper, the Landat-8 satellite imagery will be used to study and estimate the vegetable area in south Iraq. For this purpose many vegetation indices will be examined to estimate and extract the area of vegetation contain in and image. Also, the weathering parameters must be investigated to find the relationship between these parameters and the arability of vegetation cover crowing in the specific area. The remote sensing packages and Matlab written subroutines may be use to evaluate the results.

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Scopus
Publication Date
Sat Feb 01 2020
Journal Name
Journal Of Economics And Administrative Sciences
Properties of Kumaraswamy binary Distribution and compare methods of estimating parameters
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The recent development in statistics has made statistical distributions the focus of researchers in the process of compensating for some distribution parameters with fixed values and obtaining a new distribution, in this study, the distribution of Kumaraswamy was studied from the constant distributions of the two parameters. The characteristics of the distribution were discussed through the presentation of the probability density function (p.d.f), the cumulative distribution function (c.d.f.), the ratio of r, the reliability function and the hazard function. The parameters of the Kumaraswamy distribution were estimated using MLE, ME, LSEE by using the simulation method for different sampling sizes and using preli

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Publication Date
Thu Oct 01 2015
Journal Name
Journal Of Educational And Psychological Researches
Recent trends of Arabic language teaching methods in contemporary education environment
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Arabic language the timeless language of the Qur'an ((I made it read Arabic you may understand)) (Al-Zukhruf No 3). It is a way to express his thoughts and feelings and capable of giving constant absorbed the needs of the times and meet the General requirements and interactive needs of life to achieve social and intellectual aspects.    

The aim of current research to identify what teaching the contemporary trends in teaching, what the nature of knowledge and teaching methods, how do you rate the modern Arabic language teaching methods, the criteria for evaluating the effectiveness of teaching where the researcher has reached some recommendations: 1. establish the basics of environmental ed

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Publication Date
Wed Feb 29 2012
Journal Name
Al-khwarizmi Engineering Journal
Effect of Laser Cutting Methods on Hole Deviation and Surface Integrity
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In the present work usedNd:YAG laser systems of different output characteristic were employed to study the drilling process of material used in scientific and industrial fields. This material include Manganese hard steel. Our study went into the affecting parameters in drilling of Manganese hard steel by laser. Drilling process is achieved through material absorption of part of the incident laser beam. It is the resultant of interfering both, laser beam and material properties and the focusing conditions of the beam. The results as shown that the increase in the laser pulse energy over the used level has raised the hole diameter, depth and increased the hole taper. In addition to that a hole taper was affected by the laser energy, the fo

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Publication Date
Mon Feb 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of Partial Least Squares and Principal Components Methods by Simulation
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Abstract                                                                                              

The methods of the Principal Components and Partial Least Squares can be regard very important methods  in the regression analysis, whe

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Publication Date
Mon Jun 07 2021
Journal Name
Jurnal Teknologi
MODELS, DETECTION METHODS, AND CHALLENGES IN DC ARC FAULT: A REVIEW
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The power generation of solar photovoltaic (PV) technology is being implemented in every nation worldwide due to its environmentally clean characteristics. Therefore, PV technology is significantly growing in the present applications and usage of PV power systems. Despite the strength of the PV arrays in power systems, the arrays remain susceptible to certain faults. An effective supply requires economic returns, the security of the equipment and humans, precise fault identification, diagnosis, and interruption tools. Meanwhile, the faults in unidentified arc lead to serious fire hazards to commercial, residential, and utility-scale PV systems. To ensure secure and dependable distribution of electricity, the detection of such ha

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Publication Date
Thu Feb 24 2022
Journal Name
Journal Of Educational And Psychological Researches
The Teaching Methods Used Calendar When Arabic Language Teachers in Middle
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This research aims to evaluate the teaching methods used by intermediate Arabic language teachers. To achieve the goal, the researcher followed the descriptive-analytical approach. The research sample was limited to Arabic language teachers at intermediate school for the academic year (2017-2018) the researcher chose a random sample included (155) teachers which form a (40%) Of the original community at Baghdad/ Rusafa1th. The researcher has developed standards of teaching methods which are (7) standards with (39) paragraphs included three alternatives. The results showed the need to pay attention to the use of various modern teaching methods. Moreover, the researcher suggested making an evaluation of the teaching methods used by Arabic

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Publication Date
Sat Oct 03 2009
Journal Name
Proceeding Of 3rd Scientific Conference Of The College Of Science
Research Address: New Multispectral Image Classification Methods Based on Scatterplot Technique
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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Study the Prevalence of Helicobacter pylori Infection by Different Diagnostic Methods
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A total of 41 patients with gastro duodenal symptoms (show signs of inflammation with or without duodenal ulcer) . 21 males (51.2%) and 20 female (48.8%) with an average age 0f  (20 – 80) years old under  going gastrointestinal endoscopy at Baghdad teaching hospital in internal disease clinical laboratory , between (February – June)  2009 . Biopsies specimen of antrum , gastric fundus ,& duodenal bulb were examined by the following methods (rapid urease test , Giemsa stain section to detect bacteria , & Haematoxilin and Eosin stained section for pathological study which are considered the gold standard methods , sera or plasma from these patients were tested by immunochromotography (ICM),serological m

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