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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
Mon Apr 01 2013
Journal Name
مجلة كلية بغداد للعلوم الاقتصادية الجامعة العدد الخاص بمؤتمر الكلية
A propose method for hiding image into image
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Publication Date
Mon Dec 11 2017
Journal Name
Al-khwarizmi Engineering Journal
Proposed Hybrid Sparse Adaptive Algorithms for System Identification
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Abstract 

For sparse system identification,recent suggested algorithms are  -norm Least Mean Square (  -LMS), Zero-Attracting LMS (ZA-LMS), Reweighted Zero-Attracting LMS (RZA-LMS), and p-norm LMS (p-LMS) algorithms, that have modified the cost function of the conventional LMS algorithm by adding a constraint of coefficients sparsity. And so, the proposed algorithms are named  -ZA-LMS, 

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Publication Date
Tue Apr 14 2015
Journal Name
Journal Of Physical Education
Criteria for Some Agility Tests in Young Basketball
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The problem of the research lies in choosing agility tests suitable to the test taker to observe the relative changes in some players. In addition to that, there are a lot of agility tests that lack special test models that coordinate gender and age. This means the youth basketball player on one hand and time and distance in applying the tests on the other. The importance of the research lies in designing agility tests for youth basketball players to achieve variations in tests a matter that will benefit coaches in their training. The subjects of the research were (30) youth basketball players from the specialized school of the National Center that sponsor gifted basketball players in Baghdad for the season 2014 – 2015. The data was colle

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Publication Date
Thu Aug 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Some NONPARAMETRIC ESTIMATORS FOR RIGHT CENSORED SURVIVAL DATA
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The using of the parametric models and the subsequent estimation methods require the presence of many of the primary conditions to be met by those models to represent the population under study adequately, these prompting researchers to search for more flexible parametric models and these models were nonparametric, many researchers, are interested in the study of the function of permanence and its estimation methods, one of these non-parametric methods.

For work of purpose statistical inference parameters around the statistical distribution for life times which censored data , on the experimental section of this thesis has been the comparison of non-parametric methods of permanence function, the existence

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Publication Date
Sun Mar 30 2014
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Design of Horizontal Well Program for Ajeel Field
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Horizontal wells are of great interest to the petroleum industry today because they provide an attractive means for improving both production rate and recovery efficiency. The great improvements in drilling technology make it possible to drill horizontal wells with complex trajectories and extended for significant depths.
The aim of this paper is to present the design aspects of horizontal well. Well design aspects include selection of bit and casing sizes, detection of setting depths and drilling fluid density, casing, hydraulics, well profile, and construction of drillstring simulator. An Iraqi oil field (Ajeel field) is selected for designing horizontal well to increase the productivity. Short radius horizontal well is suggested fo

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Publication Date
Thu Jan 01 2009
Journal Name
Journal Of The College Of Languages (jcl)
Graphic Novels : A Privilege For Teachers and Students
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There are many ways to communicate a story, one can tell it, sing it, act it, write it, film it and can draw it. Each form of storytelling has its unique characteristics that separate it from the other forms. These distinguishing characteristics of each form does not indicate the superiority of one form over the other, on the contrary, it indicates the human ability to be creative on many levels. As students of literature, only the written form of a story is taken into account. One reason for the negligence of other forms of storytelling might be that singing and filming a story is not related to literature. But there has been a form of storytelling that uses words along with pictures which eventually became a genre of novels called grap

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Publication Date
Tue Mar 31 2015
Journal Name
Al-khwarizmi Engineering Journal
Profiles and Geotechnical Properties for some Basra Soils
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 Abstract

Basra province is known for its logistic location for trading activity and oil industry. By geological point of view, Basra areas are believed to consist mainly of alternation of (clay, silty clay, clayey silt, silt and sand) type of soil. Any development of industry in this area should be affected by the occurrence of the clay soil. That is why the investigation to the soil is more than necessary. In this case, a vast testing program was carried out by the author to evaluate the various formations constituting the of some Basra soils. An attempt to characterize and discuss the nature, minerals, engineering behavior and field properties of soil samples extracted from more than one thousand and one

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Publication Date
Wed Jan 01 2020
Journal Name
University Of Plymouth
Intrinsic Control Strategies for Herpesvirus-based Vaccine Vectors
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Publication Date
Fri Apr 12 2024
Journal Name
Revista Latinoamericana De Hipertension
Most common risk factors distribution for cervical cancer
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Scopus
Publication Date
Mon Feb 19 2018
Journal Name
Al-academy
Dynamic Knowledge Athenaeum for Parametricism in Interior Design
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Over the last few years, the interior designer has been given the ability to access many innovative tools for new forms of unprecedented diversity and efficiency. Some design experts have described the new parametric procedures they are introducing to create new interior projects as a radical transformation that carries all the elements of a qualitative shift in interior design. The best of these parametric procedures is the technical capabilities offered by us to create new forms that are different from what has been discussed in everything that has been produced by designers and architects since modernity and even before it to the present time, which returns our design products through a series of computer programs that perform the pro

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