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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.

Crossref
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Publication Date
Wed Jan 01 2020
Journal Name
Journal Of International Dental And Medical Research
Evaluation of selection criteria for patients indicated for fixed orthodontic appliance treatment
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Scopus (2)
Scopus
Publication Date
Tue Aug 15 2023
Journal Name
Al-academy
The shapes of adjacent structures for informing the stage show for children
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This research talked about the importance of adjacent structures for informing the stage show for children. The researcher began from the importance of adjacent structures for informing the show to introduce the various and different proofs, on the level of creativity and artistic shape of the accomplishment over it’s shifts that contribute to formation the show and it's intellectual, artistic, technical and cognitive Marks that contribute in dynamism the interactive show and contact the idea that connect with the design and directional vision for the beauty and cognitive. Lead to the eager operation in attention, sensitive and attractive the child. The research consist of four chapters: The first chapter include methodological framewo

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Crossref
Publication Date
Sat Jan 13 2018
Journal Name
Journal Of Engineering
Producing Coordinate Time Series for Iraq's CORS Site for Detection Geophysical Phenomena
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Global Navigation Satellite Systems (GNSS) have become an integral part of wide range of applications. One of these applications of GNSS is implementation of the cellular phone to locate the position of users and this technology has been employed in social media applications. Moreover, GNSS have been effectively employed in transportation, GIS, mobile satellite communications, and etc. On the other hand, the geomatics sciences use the GNSS for many practical and scientific applications such as surveying and mapping and monitoring, etc.

In this study, the GNSS raw data of ISER CORS, which is located in the North of Iraq, are processed and analyzed to build up coordinate time series for the purpose of detection the

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Publication Date
Wed Oct 01 2014
Journal Name
Journal Of Physical Education
Limiting standards for some defending tests against shooting for basketball juniors players
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The changes that happen in training progress especially in skill side demands tests researchers found poorness for patterns to special tests in defending skills against shooting although applying these tests on other samples without considering the age , so the problem of research came controlling the tests of defense against shooting that serve juniors players and match the original society to serve the basketball game . The research sample chosen for juniors players for Baghdad clubs in season (2011-2012) the sample numbered (82) players represented (7) clubs that their percentage (82%) , after gaining the data processed statically and we reached to conclusion that : defending tests against shooting applied first time in Iraq in Iraq envi

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Publication Date
Sat Sep 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
Production Function Analyze For Almansoor General Company For Engineering Industries In Iraq
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The production function forms one of the techniques used in evaluation the  production the process for any establishment or company, and to explain the importance of contribution of element from the independent variable and it's affect on the dependent variable. Then knowing the elements which are significant or non-significant on the dependent variable.

    So the importance of this study come from estimating the Cobb-Douglas production function for Al- Mansoor General Company for Engineering industries in Iraq during the period (1989-2001)

     To explain the importance which effects the independent variable such as
(N

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Crossref
Publication Date
Tue Sep 20 2022
Journal Name
Journal Of The College Of Basic Education
Building challenge test for basic skills in soccer for students -third stage
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The skill scale in most of sport activity monitoring a lot of dynamic behaviours conducted with playing situations that help the excerpt's in sport field to evaluate and put right solutions ,soccer one of games that studies in third stage in college and take skills ,dribbling , passing, shooting these skills helps to execute the plans in game ,the researchers notice that there is no test measure the skills of the game in the beginning of the first semester especially in the method of soccer in physical education college and the problem of the research were by answering the question that is there test connect between one or more that one of skill to measure the ability of students to execute the plans in soccer and the conclusion was the bui

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Publication Date
Sun Mar 29 2020
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Water Injection for Oil Recovery in Mishrif Formation for Amarah Oil Field
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The water injection of the most important technologies to increase oil production from petroleum reservoirs. In this research, we developed a model for oil tank using the software RUBIS for reservoir simulation. This model was used to make comparison in the production of oil and the reservoir pressure for two case studies where the water was not injected in the first case study but adding new vertical wells while, later, it was injected in the second case study. It represents the results of this work that if the water is not injected, the reservoir model that has been upgraded can produce only 2.9% of the original oil in the tank. This case study also represents a drop in reservoir pressure, which was not enough to support oil production

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Crossref (6)
Crossref
Publication Date
Sun Jan 01 2023
Journal Name
In Press
Man’s Search for Meaning
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Publication Date
Wed Jan 01 2020
Journal Name
Materials Science And Engineering
Gravel Sampling for Testing
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Abstract<p>Sampling is the selection of a representative portion of a material, and it’s as important as testing. The minimum weight of gravel field or lab sample depends on the nominal maximum particle size. The weight of the sample will always be greater than that portion required for testing. The approximate precision desired for the testing will control the weight of the gravel sample. In this study, gravel sample has been simulated by using multilinear approximated function for Fuller’s curve on the logarithmic scale. Gravel particles are divided into classes according to their medium diameter and each class was simulated separately. A stochastic analysis, by using 100 realizations in s</p> ... Show More
Scopus (2)
Scopus Crossref
Publication Date
Sun Sep 30 2012
Journal Name
College Of Islamic Sciences
Subject matter  for speakers
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Praise be to God, Lord of the worlds, and prayers and peace be upon our master Muhammad and upon his family and companions as a whole.
    The topic of attention was drawn to the attention of the speakers, as it made me ponder it carefully, and my goal in that is to know the reason for the interest of the speakers and their care for it, and to clarify from their books the purpose of making this topic one of the advanced investigations with them.

     The idea of ​​writing a paper on the subject of consideration was not absent from my thinking, because I saw the attention of speakers on this issue, as they made it one of the first issues that they deal with studying in their work

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