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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 Jun 05 2016
Journal Name
Baghdad Science Journal
Flame Atomic Emission and Colorimetric Methods for the Determination of Cephalexin Monohydrate in Pharmaceutical Preparations
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We propose two simple, rapid, and convenient spectrophotometric methods which are described for the determination of cephalexin in bulk and its pharmaceutical preparations. They are based on the measurement of the flame atomic emission of potassium ion (in the first method) and colorimetric determination of the green colored solution at 610 nm formed after the reaction of cephalexin with potassium permanganate as an oxidant agent (in the second method) in basic medium. The working conditions of the methods are investigated and optimized. Beer's law plot shows a good correlation in the concentration range of 5-40?g ml-1. The detection limits are 2.573,2.814 ?g ml-1 for the flame emission photometric method and 1.844,2.016 ?g ml-1 for colo

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Publication Date
Sat Oct 28 2023
Journal Name
Baghdad Science Journal
Indirect Flow Injection Spectrophotometric and Chromatographic Methods for the Determination of Mebendazole in Pharmaceutical Formulations
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Chromatographic and spectrophotometric methods for the estimation of mebendazole in
pharmaceutical products were developed. The flow injection method was based on the oxidation of
mebendazole by a known excess of sodium hypochlorite at pH=9.5. The excess sodium hypochlorite is then
reacted with chloranilic acid (CAA) to bleach out its color. The absorbance of the excess CAA was recorded
at 530 nm. The method is fast, simple, selective, and sensitive. The chromatographic method was carried out
on a Varian C18 column. The mobile phase was a mixture of acetonitrile (ACN), methanol (MeOH), water
and triethylamine (TEA), (56% ACN, 20% MeOH, 23.5% H2O, 0.5% TEA, v/v), adjusted to pH = 3.0 with
1.0 M hy

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Publication Date
Mon Oct 03 2022
Journal Name
International Journal Of Nonlinear Analysis And Applications
Use of learning methods for gender and age classification based on front shot face images
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Publication Date
Fri Jan 01 2021
Journal Name
Journal Of Economics And Administrative Sciences
Comparison Between Maximum Likelihood and Bayesian Methods For Estimating The Gamma Regression With Practical Application
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In this paper, we will illustrate a gamma regression model assuming that the dependent variable (Y) is a gamma distribution and that it's mean ( ) is related through a linear predictor with link function which is identity link function g(μ) = μ. It also contains the shape parameter which is not constant and depends on the linear predictor and with link function which is the log link and we will estimate the parameters of gamma regression by using two estimation methods which are The Maximum Likelihood and the Bayesian and a comparison between these methods by using the standard comparison of average squares of error (MSE), where the two methods were applied to real da

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Publication Date
Sun Jan 01 2023
Journal Name
Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees22fr
Investigate the structural properties of Tl1-xHgxSr2Ca2Cu3O8+δ compound by using Scherrer modified equation
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Publication Date
Thu Jan 01 2015
Journal Name
Journal Of Chemical,biological And Physical Sciences
Study the Electron Drift Velocity in Carbon Dioxide Gas Obtained From Boltzmann Equation Analysis‏
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Publication Date
Sun Dec 31 2017
Journal Name
Al-khwarizmi Engineering Journal
Solving the Inverse Kinematic Equations of Elastic Robot Arm Utilizing Neural Network
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The inverse kinematic equation for a robot is very important to the control robot’s motion and position. The solving of this equation is complex for the rigid robot due to the dependency of this equation on the joint configuration and structure of robot link. In light robot arms, where the flexibility exists, the solving of this problem is more complicated than the rigid link robot because the deformation variables (elongation and bending) are present in the forward kinematic equation. The finding of an inverse kinematic equation needs to obtain the relation between the joint angles and both of the end-effector position and deformations variables. In this work, a neural network has been proposed to solve the problem of inverse kinemati

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Crossref
Publication Date
Sun Jul 09 2023
Journal Name
Journal Of Engineering
Solving Time-Cost Tradeoff Problem with Resource Constraint Using Fuzzy Mathematical Model
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Scheduling considered being one of the most fundamental and essential bases of the project management. Several methods are used for project scheduling such as CPM, PERT and GERT. Since too many uncertainties are involved in methods for estimating the duration and cost of activities, these methods lack the capability of modeling practical projects. Although schedules can be developed for construction projects at early stage, there is always a possibility for unexpected material or technical shortages during construction stage. The objective of this research is to build a fuzzy mathematical model including time cost tradeoff and resource constraints analysis to be applied concurrently. The proposed model has been formulated using fuzzy the

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Crossref
Publication Date
Mon Jun 01 2009
Journal Name
Journal Of Engineering
Dowel Action Between Two Concretes
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Publication Date
Tue Jun 30 2020
Journal Name
Iraqi Journal Of Market Research And Consumer Protection
BUILD AN EFFICIENT INVESTMENT PORTFOLIO USING THE WILLIAM RATIO (EMPIRICAL STUDY) IN IRAQ STOCK EXCHANGE: BUILD AN EFFICIENT INVESTMENT PORTFOLIO USING THE WILLIAM RATIO (EMPIRICAL STUDY) IN IRAQ STOCK EXCHANGE
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ABSTRACT

            This study aimed to choose top stocks through technical analysis tools specially the indicator called (ratio of William index), and test the ability of technical analysis tools in building a portfolio of shares efficient in comparison with the market portfolio. These one technical tools were used for building one portfolios in 21 companies on specific preview conditions and choose 10 companies for the period from (March 2015) to (June 2017). Applied results of the research showed that Portfolio yield for companies selected according to the ratio of William index indicator (0.0406) that

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