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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
Wed Dec 01 2021
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of Some Non-Parametric Quality Control Methods
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    Multivariate Non-Parametric control charts were used to monitoring the data that generated by using the simulation, whether they are within control limits or not. Since that non-parametric methods do not require any assumptions about the distribution of the data.  This research aims to apply the multivariate non-parametric quality control methods, which are Multivariate Wilcoxon Signed-Rank ( ) , kernel principal component analysis (KPCA) and k-nearest neighbor ( −

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Publication Date
Tue Aug 31 2021
Journal Name
International Journal Of Nonlinear Analysis And Applications
Face mask detection methods and techniques: A review
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Corona virus sickness has become a big public health issue in 2019. Because of its contact-transparent characteristics, it is rapidly spreading. The use of a face mask is among the most efficient methods for preventing the transmission of the Covid-19 virus. Wearing the face mask alone can cut the chance of catching the virus by over 70\%. Consequently, World Health Organization (WHO) advised wearing masks in crowded places as precautionary measures. Because of the incorrect use of facial masks, illnesses have spread rapidly in some locations. To solve this challenge, we needed a reliable mask monitoring system. Numerous government entities are attempting to make wearing a face mask mandatory; this process can be facilitated by using face m

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Publication Date
Tue Jun 23 2020
Journal Name
Baghdad Science Journal
Content Based Image Retrieval (CBIR) by Statistical Methods
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            An image retrieval system is a computer system for browsing, looking and recovering pictures from a huge database of advanced pictures. The objective of Content-Based Image Retrieval (CBIR) methods is essentially to extract, from large (image) databases, a specified number of images similar in visual and semantic content to a so-called query image. The researchers were developing a new mechanism to retrieval systems which is mainly based on two procedures. The first procedure relies on extract the statistical feature of both original, traditional image by using the histogram and statistical characteristics (mean, standard deviation). The second procedure relies on the T-

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Publication Date
Mon Jan 01 2018
Journal Name
Asian Journal Of Ournal Of Chemistry
Extraction of Ocimum basillicum Oil by Solvents Methods
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The extraction of Basil oil from Iraqi Ocimum basillicum leaves using n-hexane and petroleum ether as organic solvents were studied and compared. The concentration of oil has been determined in a variety of extraction temperatures and agitation speed. The solvent to solid ratio effect has been studied in order to evaluate the concentration of Ocimum basillicum oil. The optimum experimental conditions for the oil extraction were established as follows: n-hexane as organic solvent, 60 °C extraction temperature, 300 rpm agitation speed and 40:1mL:g amount of solvent to solid ratio.

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Publication Date
Tue Jan 21 2025
Journal Name
Periodicals Of Engineering And Natural Sciences (pen)
A comparison between the hierarchical clustering methods for postgraduate students in Iraqi universities for the year 2019-2020 using the cophenetic and delta correlation coefficients
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The educational sector is one of the important sectors in the world, and it is considered one of the means of community development. In addition, it is one of the means of making the country’s renaissance and devel-opment because it represents the factory of thinking minds that make change. There is no doubt that this sector is the same as any other sector. The deficit in the studied scientific planning has been prolonged, which led to its deterioration, and the problems of education remain diverse and inherited from previous time periods, where the hierarchical cluster analysis was used on postgraduate students in universities in Iraq, except for Kurdistan region, and the number of universities that were included in the study was

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Publication Date
Wed Jun 04 2025
Journal Name
Kufa Journal For Agricultural Sciences – 2025:17(2) : 56- 65
Efficacy of different Conidial concentrations, fungal Filtrations and silver nanoparticles Mycosynthesis using two isolates of Metarhizium anisoplae against Two Stored-grain Insects
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Publication Date
Tue Dec 15 2020
Journal Name
Journal Of Baghdad College Of Dentistry
Impact of two non-nutritive sucking patterns on the development of anterior open bite in children of two kindergartens in Baghdad city
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Background: Non-nutritive sucking habit (NNSH) is the main environmental causative factor that disturbs normal orofacial development. In spite of the harmful effect of pacifier as a NNSH, mothers aware from the other types of NNSH like thumb sucking far more than pacifier use. Open bite is one of the most challenging malocclusions in orthodontics due to the high prevalence of relapse after treatment, so preventing the causative factor of its occurrence is essential at early age of child life. This study aims to assess the impact of two non-nutritive patterns on the development of anterior open bite in primary dentition and to compare which of these habits mostly affect open bite development. Materials and Methods: The sample consisted of

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Publication Date
Thu Nov 17 2016
Journal Name
Plos One
Efficient and Stable Routing Algorithm Based on User Mobility and Node Density in Urban Vehicular Network
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Vehicular ad hoc networks (VANETs) are considered an emerging technology in the industrial and educational fields. This technology is essential in the deployment of the intelligent transportation system, which is targeted to improve safety and efficiency of traffic. The implementation of VANETs can be effectively executed by transmitting data among vehicles with the use of multiple hops. However, the intrinsic characteristics of VANETs, such as its dynamic network topology and intermittent connectivity, limit data delivery. One particular challenge of this network is the possibility that the contributing node may only remain in the network for a limited time. Hence, to prevent data loss from that node, the information must reach the destina

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Scopus (36)
Crossref (30)
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Publication Date
Fri Mar 01 2013
Journal Name
Journal Of Economics And Administrative Sciences
The construction of Investment Portfolios in the Iraq Stock Exchange: Market Timing Vs. an Efficient Selection
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Abstract

         Uncertainty, the deeply-rooted fact that surrounding the investment environment, especially the stock market which just prices have taken a specific trend until they moved to another one for its up or down. This means that the volatility characteristic of financial market requires the rational investor an argument led towards the adoption of planned acts to gain greater benefit in the goal of wealth maximizing. There is no possibility to achieve this goal without the burden of uncertainty and the risk of systematic fluctuations of investment returns in the financial market after the facts of  efficient diversification have pro

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Publication Date
Sat Jan 01 2022
Journal Name
Indonesian Journal Of Electrical Engineering And Computer Science (ijeecs)
A new smart approach of an efficient energy consumption management by using a machine-learning technique
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Many consumers of electric power have excesses in their electric power consumptions that exceed the permissible limit by the electrical power distribution stations, and then we proposed a validation approach that works intelligently by applying machine learning (ML) technology to teach electrical consumers how to properly consume without wasting energy expended. The validation approach is one of a large combination of intelligent processes related to energy consumption which is called the efficient energy consumption management (EECM) approaches, and it connected with the internet of things (IoT) technology to be linked to Google Firebase Cloud where a utility center used to check whether the consumption of the efficient energy is s

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