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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 Apr 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Solving a three dimensional transportation problem using linear programming
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Transport is a problem and one of the most important mathematical methods that help in making the right decision for the transfer of goods from sources of supply to demand centers and the lowest possible costs, In this research, the mathematical model of the three-dimensional transport problem in which the transport of goods is not homogeneous was constructed. The simplex programming method was used to solve the problem of transporting the three food products (rice, oil, paste) from warehouses to the student areas in Baghdad, This model proved its efficiency in reducing the total transport costs of the three products. After the model was solved in (Winqsb) program, the results showed that the total cost of transportation is (269,

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Publication Date
Sat Jan 01 2022
Journal Name
1st Samarra International Conference For Pure And Applied Sciences (sicps2021): Sicps2021
Solving the created ordinary differential equations from Lomax distribution
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Publication Date
Mon Feb 04 2019
Journal Name
Journal Of The College Of Education For Women
Creative skills in solving environmental problems among kindergarten children
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Acquires this research importance of addressing the subject (environmental problems) with
age group task, a category that children pre-school, and also reflected the importance of
research, because the (environmental problems) constitute a major threat to the continuation
of human life, particularly the children, so the environment is Bmchkladtha within
kindergarten programs represent the basis of a hub of learning where the axis, where the
kindergarten took into account included in the programs in order to help the development of
environmental awareness among children and get them used to the sound practices and
behaviors since childhood .
The research also detected problem-solving skills creative with kids Riyad

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Publication Date
Sat Jan 01 2011
Journal Name
Journal Of The College Of Basic Education
Solving Job-Shop Scheduling Problem Using Genetic Algorithm Approach
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Publication Date
Sun Mar 02 2008
Journal Name
Baghdad Science Journal
Orthogonal Functions Solving Linear functional Differential EquationsUsing Chebyshev Polynomial
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A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

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Publication Date
Sat Dec 31 2022
Journal Name
Journal Of Economics And Administrative Sciences
Improving Customer Value Through the Integral of Techniques Quality Function Deployment and Value Engineering
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Health service institutions suffer from challenges resulting from the great changes that our world is witnessing today.  This has affected the value that these institutions add to the patient.

This research aims to identify the effect of integrating each of the techniques of QFD and value engineering for the health services provided to the patient to improve the value for him and thus obtain his satisfaction, which is reflected in the reputation of the surveyed hospitals. To achieve this, the descriptive analytical method was used, and a questionnaire was designed to collect the necessary data, which represents a measure of this research. The questionnaire was distri

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Publication Date
Wed Apr 01 2015
Journal Name
Mathematical Methods In The Applied Sciences
An inverse problem of finding the time-dependent diffusion coefficient from an integral condition
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Publication Date
Tue Dec 05 2023
Journal Name
Baghdad Science Journal
Enhancing Smart Cities with IoT and Cloud Computing: A Study on Integrating Wireless Ad Hoc Networks for Efficient Communication
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Smart cities have recently undergone a fundamental evolution that has greatly increased their potentials. In reality, recent advances in the Internet of Things (IoT) have created new opportunities by solving a number of critical issues that are allowing innovations for smart cities as well as the creation and computerization of cutting-edge services and applications for the many city partners. In order to further the development of smart cities toward compelling sharing and connection, this study will explore the information innovation in smart cities in light of the Internet of Things (IoT) and cloud computing (CC). IoT data is first collected in the context of smart cities. The data that is gathered is uniform. The Internet of Things,

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Publication Date
Thu Feb 06 2020
Journal Name
Scientific Reports
Waste foundry sand/MgFe-layered double hydroxides composite material for efficient removal of Congo red dye from aqueous solution
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Abstract<p>We aimed to obtain magnesium/iron (Mg/Fe)-layered double hydroxides (LDHs) nanoparticles-immobilized on waste foundry sand-a byproduct of the metal casting industry. XRD and FT-IR tests were applied to characterize the prepared sorbent. The results revealed that a new peak reflected LDHs nanoparticles. In addition, SEM-EDS mapping confirmed that the coating process was appropriate. Sorption tests for the interaction of this sorbent with an aqueous solution contaminated with Congo red dye revealed the efficacy of this material where the maximum adsorption capacity reached approximately 9127.08 mg/g. The pseudo-first-order and pseudo-second-order kinetic models helped to describe the sorption measure</p> ... Show More
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Publication Date
Sat Dec 01 2018
Journal Name
Journal Of Molecular Liquids
Synthesis of bimetallic gold-pallidum loaded on carbon as efficient catalysts for the oxidation of benzyl alcohol into benzaldehyde
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