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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 Aug 01 2021
Journal Name
Sensors And Actuators B: Chemical
Sensitive and simple colorimetric methods for visual detection and quantitative determination of semicarbazide in flour products using colorimetric reagents
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After baking the flour, azodicarbonamide, an approved food additive, can be converted into carcinogenic semicarbazide hydrochloride (SEM) and biurea in flour products. Thus, determine SEM in commercial bread products is become mandatory and need to be performed. Therefore, two accurate, precision, simple and economics colorimetric methods have been developed for the visual detection and quantitative determination of SEM in commercial flour products. The 1st method is based on the formation of a blue-coloured product with λmax at 690 nm as a result of a reaction between the SEM and potassium ferrocyanide in an acidic medium (pH 6.0). In the 2nd method, a brownish-green colored product is formed due to the reaction between the SEM and phosph

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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
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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Publication Date
Mon Mar 01 2021
Journal Name
Solar Energy
Efficient thermal management of the photovoltaic/phase change material system with innovative exterior metal-foam layer
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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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Publication Date
Mon Jan 01 2024
Journal Name
The Scientific World Journal
Efficient Removal of Brilliant Green Dye Using Mesoporous Attapulgite Clay: Investigating Adsorption Kinetics, Isotherms, and Mechanisms
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The study involved the effectiveness of Iraqi attapulgite (IQATP) clay as an environmentally friendly material that easily adsorbs brilliant green (BG) dye from water systems and is identified by various complementary methods (e.g., FTIR, SEM‐EDS, XRD, ICP‐OES, pHpzc, and BET), where the result reported that the IQATP specific surface area is 29.15 m2/g. A systematic analysis was selected to evaluate the impact of different effective adsorption performance variables on BG dye decontamination. These variables included IQATP dosage (0.02–0.8 g/L), solution pH (3.05–8.15), contact time (ranging from 2 to 25 min), and initial BG dye concentration from 20 to 80 mg/L. The parameter

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Publication Date
Sun Sep 30 2007
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Dynamics of a single Condensing Two-Phase Bubble
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The dynamics of a single condensing two-phase bubble of two different dispersed-continuous systems were studied. The systems were, CCl4 - water and CCl4 - 100% glycerol. Cinephotography was used to determine the change in height, diameter and time. These results were used to determine the experimental rise velocity of the bubble, which was compared with a theoretical one based on some equations used. It was found that the velocity of the first system remained almost constant, while it decreased gradually for the second system.

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Publication Date
Sat Jul 01 2000
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
BLOOD PARASITES OF TWO BEE-EATERS iN IRAQ
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Examination of 241 specimens of two bee-eater species, Merops apiaster and Merops
superciliosus persicus reveal recording of Haemoproteus meropis (Zagar, 1945) emend.
Bennett, 1978 and H. manwelli Bennett, 1978 for the first time in Iraq. A new species
Haemoproteus hudaidensis sp. nov. is described. Microfilariae are also infected the two host
species. The results are discussed with the pertinent literature and the necessary comparision
of morphometric measurements of the recorded parasites with that previously reported is
provided along with a taxonomic key including the newly described haemoproteid.

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Publication Date
Sat Jun 30 2007
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Drag Forces under Longitudinal Interaction of Two Particle
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Direct measurements of drag force on two interacting particles  arranged in the longitudinal direction for particle Reynolds numbers varying from J O to 103 are conducted using a micro-force measurement system. The effect of the interparticle distance and Reynolds number on the drag forces  is examined. An empirical equation is obtained to describe the effect of the interparticle distance (l/d) on the dimensionless drag.

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Publication Date
Wed Aug 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Comparing parameters and Reliability of two-parameters exponential
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One of the most important problems in the statistical inference is estimating parameters and Reliability parameter and also interval estimation , and testing hypothesis . estimating two parameters of exponential distribution and also reliability parameter in a stress-strength model.

This parameter deals with estimating the scale parameter and the Location parameter µ , of two exponential distribution   ,using moments estimator and maximum likelihood estimator , also we estimate the parameter R=pr(x>y), where x,y are two- parameter independent exponential random variables .

Statistical properties of this distribution and its properti

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