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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
Fri Nov 01 2013
Journal Name
Journal Of Cosmetics, Dermatological Sciences And Applications
Podophyllin (10%) Ointment: A New Therapeutic Modality for Psoriasis
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KE Sharquie, AA Noaimi, WK Al-Janabi, Journal of Cosmetics, Dermatological Sciences and Applications, 2013

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Publication Date
Wed Feb 29 2012
Journal Name
Al-khwarizmi Engineering Journal
Design a Fault Tolerance for Real Time Distributed System
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This paper designed a fault tolerance for soft real time distributed system (FTRTDS). This system is designed to be independently on specific mechanisms and facilities of the underlying real time distributed system. It is designed to be distributed on all the computers in the distributed system and controlled by a central unit.

Besides gathering information about a target program spontaneously, it provides information about the target operating system and the target hardware in order to diagnose the fault before occurring, so it can handle the situation before it comes on. And it provides a distributed system with the reactive capability of reconfiguring and reinitializing after the occurrence of a failure.

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Publication Date
Tue Feb 28 2023
Journal Name
Periodicals Of Engineering And Natural Sciences (pen)
Modeling the trend of Iraqi GDP for 1970-2020
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The study of economic growth indicators is of fundamental importance in estimating the effectiveness of economic development plans, as well as the great role it plays in determining appropriate economic policies in order to optimally use the factors that lead to the dynamics of growth in Iraq, especially during a certain period of time. The gross domestic product (GDP) at current prices), which is considered a part of the national accounts, which is considered as an integrated dynamic of statistics that produces in front of policy makers the possibility of determining whether the economy is witnessing a state of expansion or evaluating economic activity and its efficiency in order to reach the size of the overall economy. The research aims

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Publication Date
Sun Jun 01 2014
Journal Name
مجلة كلية مدينة العلم الجامعة
Palynological study for nine cultivated species of Asteraceae family
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The current research included palynological study for nine ornamental cultivated species of Asteraceae family. The study included measurement the dimensions of pollen grains and there shape in polar view and equatorial view, sculpturing,colpi length and width, spines length and number of spines rows between colpiand exine thickness, the study showed variations in pollen grains characters forthe studied taxa

Publication Date
Mon Jan 01 2024
Journal Name
Aip Conference Proceedings
Quality measurement for openstreetmap buildings outlines in Baghdad/Iraq
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OpenStreetMap (OSM) is the world’s biggest publicly licensed geographic data collection. Because OSM is rapidly being used in a wide range of applications, researchers have focused their efforts on determining its quality. The OSM buildings data quality is still ambiguous, due to the limitations, and a few researchers have evaluated the OSM buildings data quality through difficulties where the authoritative data are not obtainable. The focus of this research is to analyze and assess the accuracy of OSM buildings including completeness, and positional accuracy methods. Two different study areas in Baghdad city-Iraq have been investigated: Al-Rasheed and Al-Karrada. The process of the (OSM) data evaluation involved identifying the correspon

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Publication Date
Thu Jan 05 2023
Journal Name
Mathematical Theory And Modeling
(Tc) Technique for Finding Optimal Solution To Transportation Problem
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Given the importance of increasing economic openness transport companies’ face various issues arising at present time, this required importing different types of goods with different means of transport. Therefore, these companies pay great attention to reducing total costs of transporting commodities by using numbers means of transport methods from their sources to the destinations. The majority of private companies do not acquire the knowledge of using operations research methods, especially transport models, through which the total costs can be reduced, resulting in the importance and need to solve such a problem. This research presents a proposed method for the sum of Total Costs (Tc) of rows and columns, in order to arrive at the init

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Publication Date
Sun Dec 31 2023
Journal Name
Journal Of Pioneering Medical Science
Nurses' Perception Toward Therapeutic Strategies for Children with Pneumonia
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Background: Pneumonia is the common lower respiratory tract infection among pediatrics, especially under five; it is a common cause of under-five children morbidity and mortality. Objectives of study: To identify nurses' perceptions toward therapeutic strategies for children with pneumonia and to find the association between their perceptions and their demographic variables. Methods: A Convenient sample of 46 nurses in Baghdad city from three hospitals) Kadhimiya Hospital for Children, Central Teaching Hospital of Pediatrics, and Child Welfare Teaching Hospital) included in the study to identify their perceptions regarding pneumonia in children. Results: The results of the study present that most of the nurses' participants in the a

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Publication Date
Wed Dec 13 2017
Journal Name
Al-khwarizmi Engineering Journal
Weldability of New Material Sandwich Steel for Automotive Applications
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Todays, World is faced an energy crisis because of a continuous increasing the consumption of fuels due to intension demand for all types of vehicles. This study is one of the efforts dealing with reduce the weight of vehicles by using a new material of sandwich steel, which consists of two skin steel sheets with core of a polymer material. Resistance spot welding (RSW) can be easily implemented on metals; however a cupper shunt tool was designed to perform the resistance welding of sandwich steel with DP800 cover sheets to resolve a non-conductivity problem of a polymer core. Numerical simulations with SORPAS®3D were employed to test the weldability of this new material and supported by many practical experiments. In conclus

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Publication Date
Sat Aug 01 2015
Journal Name
International Journal Of Advanced Research In Computer Science And Software Engineering
Partial Encryption for Colored Images Based on Face Detection
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Publication Date
Tue Jan 01 2008
Journal Name
2008 15th Asia-pacific Software Engineering Conference
G2Way A Backtracking Strategy for Pairwise Test Data Generation
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