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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
Sun Dec 09 2018
Journal Name
Baghdad Science Journal
Conjugated Polymer (MEH-PPV:MWCNTs) Organic Nanocomposite for Photodetector Application
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Fabrication of a photodetector consists of the conjugated polymer "MEH-PPV"- poly (2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenlenevinylene) and MEH-PPV:MWCNT nanocomposite thin film. The volume ratio investigated was 0.75:0.25. MEH-PPV was dissolved in chloroform solvent and doped with MWCNTs. The spin coating method was used to achieve a facile and low cost photodetector. The absorption spectrum decreases by adding the CNTs. The PL spectrum detected recombination curve results by doping the polymer with CNTs, and AFM measurement showed an increase of roughness average from (0.168 to 2.43nm) of "MEH-PPV" and "MEH-PPV:CNTs", respectively. The doping ratio 0.25, which has a higher photoresponsivity, was evaluated at 1.70 A/W and 2.14 A/W of th

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Publication Date
Tue Mar 10 2020
Journal Name
Journal Of Inverse And Ill-posed Problems
Direct and inverse source problems for degenerate parabolic equations
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Abstract<p>Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-pose</p> ... Show More
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Scopus (27)
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Publication Date
Mon Oct 02 2023
Journal Name
Journal Of Interdisciplinary Mathematics
Score for the groups SL(2,121) and SL(2,169)
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A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

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Publication Date
Thu Sep 15 2022
Journal Name
Al-academy
Production mechanisms and their implications for Iraqi theater techniques
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Theatrical production mechanisms were determined according to the extents of the theatrical performance, the directing plan, and the ideas that the theatrical performance seeks to convey to the audience. Accordingly, theatrical production mechanisms differ between one theatrical performance and another according to the requirements of each of them and the surrounding circumstances that accompany the production of theatrical performance, and in order to search for production mechanisms and their repercussions on the show. Theatrical The current research was divided into four chapters, namely (Chapter One - Methodology), which identified the research problem in the following question: What are the production mechanisms and their implicatio

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Publication Date
Tue Dec 01 2020
Journal Name
Al-khwarizmi Engineering Journal
Cloud Manufacturing framework for controlling and monitoring of machines
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Due to the development that occurs in the technologies of information system many techniques was introduced and played important role in the connection between machines and peoples through internet, also it used to control and monitor of machines, these technologies called cloud computing and Internet of Things. With the replacement of computing resources with manufacturing resources cloud computing named converted into cloud manufacturing.

In this research cloud computing was used in the field of manufacturing to automate the process of selecting G-Code that Computer Numerical Control machine work it, this process was applied by the using of this machine with Radio Frequency Identification and a AWS Cloud services and some of py

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Publication Date
Fri Jan 01 2021
Journal Name
Research Methods In Modern Urban Transportation Systems And Networks
Factors Affecting the Choice of Transportation for School Trips
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Publication Date
Tue Apr 21 2020
Journal Name
University Of Thi-qar Journal Of Science (university Of Thi-qar Journal Of Science (utsci) The 4th Scientific Conference Of Science College/ University Of Thi_qari) The 4th Scientific Conference Of Science College/ University Of Thi_qar
Enhancement of Nano Catalyst for an Alkaline Fuel Cells
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Publication Date
Mon Mar 31 2025
Journal Name
Iraqi Statisticians Journal
Hypothesis Testing for Non-Normal Multiple Compact Regression Model
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Generalized multivariate transmuted Bessel distribution belongs to the family of probability distributions with a symmetric heavy tail. It is considered a mixed continuous probability distribution. It is the result of mixing the multivariate Gaussian mixture distribution with the generalized inverse normal distribution. On this basis, the paper will study a multiple compact regression model when the random error follows a generalized multivariate transmuted Bessel distribution. Assuming that the shape parameters are known, the parameters of the multiple compact regression model will be estimated using the maximum likelihood method and Bayesian approach depending on non-informative prior information. In addition, the Bayes factor was used

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Publication Date
Fri Apr 01 2016
Journal Name
Journal Of Engineering
Estimation of Mass Transfer Coefficient for Copper Electrowinning Process
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Mass transfer was examined at a stationary rectangular copper electrode (cathode) by using the reduction of cupric ions as the electrochemical reaction. The influence of electrolyte temperature (25, 45, and 65 oC), and cupric ions concentration (4, 8, and 12 mM) on mass transfer coefficient were investigated by using limiting current technique. The mass transfer coefficient and hence the Sherwood number was correlated as Sh =

 

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Publication Date
Sun Oct 15 2023
Journal Name
Journal Of Yarmouk
Artificial Intelligence Techniques for Colon Cancer Detection: A Review
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