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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 May 01 2016
Journal Name
Iraqi Journal Of Science
Efficient text in image hiding method based on LSB method principle
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The steganography (text in image hiding) methods still considered important issues to the researchers at the present time. The steganography methods were varied in its hiding styles from a simple to complex techniques that are resistant to potential attacks. In current research the attack on the host's secret text problem didn’t considered, but an improved text hiding within the image have highly confidential was proposed and implemented companied with a strong password method, so as to ensure no change will be made in the pixel values of the host image after text hiding. The phrase “highly confidential” denoted to the low suspicious it has been performed may be found in the covered image. The Experimental results show that the covere

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Publication Date
Fri Aug 15 2025
Journal Name
Baghdad Science Journal
Hydrothermal synthesis of high surface area mesoporous silica as an efficient adsorbent for removal of crystal violet dye from aqueous solution
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Publication Date
Sun Sep 01 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The effect of accounting disclosure in the efficient performance of the tax authority: Applied research in the General Commission for Taxes
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               Starting with a problem of the weakness of accounting disclosure in some companies administration when preparing and presenting the financial reports which are submitted to the Tax authority. This problem impacts on Tax authority performance (The effect on the quality of the performance of the tax authority), because of the lack of conviction for the information contained in those reports, and the  failure to achieve accurate results in tax authority performance that leads to a negative impact on determining taxable income and affect tax revenue, as well as negative impact on  determining taxable income and affect tax revenue, as well as negati

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Crossref
Publication Date
Sun Mar 04 2012
Journal Name
Baghdad Science Journal
Double Stage Cumulative Shrunken Bayes Estimator for the variance of Normal distribution for equal volume of two sample
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In this article we study the variance estimator for the normal distribution when the mean is un known depend of the cumulative function between unbiased estimator and Bays estimator for the variance of normal distribution which is used include Double Stage Shrunken estimator to obtain higher efficiency for the variance estimator of normal distribution when the mean is unknown by using small volume equal volume of two sample .

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Crossref
Publication Date
Sat Jun 01 2013
Journal Name
Journal Of Economics And Administrative Sciences
Comparison between some well- Known methods to estimate the parameter of the proposed method of measurement and the reliability of the distribution function with two parameters Rally by simulation
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Abstract

            Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t

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Publication Date
Thu Dec 21 2017
Journal Name
International Journal Of Engineering & Technology
Determination of liquefaction potential for two selected sites in Kerbala city- middle of Iraq
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Geotechnical characterization of the sites has been investigated with the collection of borehole data from different sources. Using the data, grain size distribution curves have been developed to understand the particle size distribution of the alluvium present. These curves were further used for preliminary assessment of liquefiable areas. From geotechnical characterization, it has been observed that the soil profile in the two sites is dominated by sand and silty sand.Seed and Idriss (1971) approachhas been usedevaluatethe liquefaction potentialbydeterminationof the relation between the maximum ground acceleration (a max/g) valuesdue to an earthquake and the relative density of a sand deposit in the field. The results reveal that

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Scopus (6)
Crossref (2)
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Publication Date
Tue Apr 02 2024
Journal Name
Engineering, Technology & Applied Science Research
Two Proposed Models for Face Recognition: Achieving High Accuracy and Speed with Artificial Intelligence
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In light of the development in computer science and modern technologies, the impersonation crime rate has increased. Consequently, face recognition technology and biometric systems have been employed for security purposes in a variety of applications including human-computer interaction, surveillance systems, etc. Building an advanced sophisticated model to tackle impersonation-related crimes is essential. This study proposes classification Machine Learning (ML) and Deep Learning (DL) models, utilizing Viola-Jones, Linear Discriminant Analysis (LDA), Mutual Information (MI), and Analysis of Variance (ANOVA) techniques. The two proposed facial classification systems are J48 with LDA feature extraction method as input, and a one-dimen

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Scopus (14)
Crossref (12)
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Publication Date
Sat Jan 01 2011
Journal Name
Journal Of Engineering
TWO-PARAMETER GAMMA DISTRIBUTION AND LOG NORMAL DISTRIBUTION FOR DERIVATION OF SYNTHETIC UNIT HYDROGRAPH
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Most available methods for unit hydrographs (SUH) derivation involve manual, subjective fitting of
a hydrograph through a few data points. The use of probability distributions for the derivation of synthetic
hydrographs had received much attention because of its similarity with unit hydrograph properties. In this
paper, the use of two flexible probability distributions is presented. For each distribution the unknown
parameters were derived in terms of the time to peak(tp), and the peak discharge(Qp). A simple Matlab
program is prepared for calculating these parameters and their validity was checked using comparison
with field data. Application to field data shows that the gamma and lognormal distributions had fit well.<

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Crossref (1)
Crossref
Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
An Approximate solution for two points oundary value problem corresponding to some optimal control
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this paper presents a novel method for solving nonlinear optimal conrol problems of regular type via its equivalent two points boundary value problems using the non-classical

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Publication Date
Thu Nov 08 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Effect of using two packing Technic on Hardness of two dental acrylic resin
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Objective: the aim of this study is to invest age and determine the effect of using (2) packing
technique (conventional and new tension technique) on hardness of (2) types of heat cure acrylic
resin which are (Ivoclar and Qual dental type).
Methodology : this study was intended the using of two types of heat cure acrylic (IVoclar and
Qual dental type) which are used in construction of complete denture which packed in two different
packing technique (conventional and new tension technique) and accomplished by using a total of
(40) specimens in diameter of ( 2mm thickness, 2 cm length and 1 cm width) . This specimens were
sectioned and subdivide into (4) group each (10) specimens for one group , then signed as (A, Al B

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