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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 May 17 2023
Journal Name
Journal Of Engineering
Comparison of the Combining Methods Used In Space Diversity
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The basic concept of diversity; where two or more inputs at the receiver are used to get uncorrelated signals. The aim of this paper is an attempt to compare some possible combinations of diversity reception and MLSE detection techniques. Various diversity combining techniques can be distinguished: Equal Gain Combining (EGC), Maximal Ratio Combining (MRC), Selection Combining and Selection Switching Combining (SS).The simulation results shows that the MRC give better performance than the other types of combining (about 1 dB compare with EGC and 2.5~3 dB compare with selection and selection switching combining).

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Publication Date
Sat Jun 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of some methods for estimating the parameters of the binary logistic regression model using the genetic algorithm with practical application
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Abstract

   Suffering the human because of pressure normal life of exposure to several types of heart disease as a result of due to different factors. Therefore, and in order to find out the case of a death whether or not, are to be modeled using binary logistic regression model

    In this research used, one of the most important models of nonlinear regression models extensive use in the modeling of applications statistical, in terms of heart disease which is the binary logistic regression model. and then estimating the parameters of this model using the statistical estimation methods, another problem will be appears in estimating its parameters, as well as when the numbe

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Publication Date
Sun Nov 01 2015
Journal Name
Karbala International Journal Of Modern Science
Batch and flow injection spectrophotometric methods for the determination of barbituric acid in aqueous samples via oxidative coupling with 4-aminoantipyrine
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A batch and flow injection (FI) spectrophotometric methods are described for the determination of barbituric acid in aqueous and urine samples. The method is based on the oxidative coupling reaction of barbituric acid with 4-aminoantipyrine and potassium iodate to form purple water soluble stable product at λ 510 nm. Good linearity for both methods was obtained ranging from 2 to 60 μg mL−1, 5–100 μg mL−1 for batch and FI techniques, respectively. The limit of detection (signal/noise = 3) of 0.45 μg mL−1 for batch method and 0.48 μg mL−1 for FI analysis was obtained. The proposed methods were applied successfully for the determination of barbituric acid in tap water, river water, and urine samples with good recoveries of 99.92

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Publication Date
Sun Dec 01 2019
Journal Name
2019 First International Conference Of Computer And Applied Sciences (cas)
A Comparison for Some of the estimation methods of the Parallel Stress-Strength model In the case of Inverse Rayleigh Distribution
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Publication Date
Sun Jun 30 2024
Journal Name
International Journal Of Intelligent Engineering And Systems
Enhancement of the Blood Glucose Level for Diabetic Patients Based on an Adaptive Auto-Tuned PID Controller via Meta-Heuristic Methods
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Publication Date
Wed Feb 01 2023
Journal Name
Petroleum Science And Technology
Lithofacies and electrofacies models for Mishrif Formation in West Qurna oilfield, Southern Iraq by deterministic and stochastic methods (comparison and analyzing)
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Publication Date
Thu Aug 04 2022
Journal Name
Sport Tk-revista Euroamericana De Ciencias Del Deporte
The reality of motivational administrative methods for academic decision-makers in the faculties of physical education and sports sciences of Baghdad
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The purpose of this study was to know the reality of motivational administrative methods for academic decision-makers in the faculties of physical education and sports sciences in Baghdad from the perspective of faculty members. To solve the nature of the current problem, the two researchers used the descriptive approach of the survey method. The two researchers determined their research community by limiting the sample to all faculty members in the faculties of physical education and sports sciences in Baghdad (Al-Mustansiriya University, Al-Jadriya Univeristy & Al-Waziriyah University). Their number reached 314 faculty members and the two researchers determined their research community by 90%, so the research sam

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Publication Date
Mon Nov 01 2010
Journal Name
Iraqi Journal Of Physics
Correction of Spherical Aberration of an Immersion Lens Operating Under Space Charge Effect Described by a 2nd Order Equation
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The present work represents a theoretical study for the correction of spherical aberration of an immersion lens of axial symmetry operating under the effect of space charge, represented by a second order function and preassigned magnification conditions in a focusing of high current ion beams. The space charge depends strongly on the value of the ionic beam current which is found to be very effective and represents an important factor effecting the value of spherical aberration .The distribution of the space charge was measured from knowing it's density .It is effect on the trajectory of the ion beam was studied. To obtain the trajectories of the charged particles which satisfy the preassined potential the axial electrostatic potential w

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Publication Date
Thu Dec 01 2022
Journal Name
Iraqi Journal Of Statistical Sciences
Use the robust RFCH method with a polychoric correlation matrix in structural equation modeling When you are ordinal data
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Publication Date
Wed Mar 30 2022
Journal Name
Journal Of Educational And Psychological Researches
Evaluating Educational Programs in Combating Indecent Behaviors Among University Students Using Structural Equation Modeling (Field study: Northern Border University)
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The study aimed to evaluate educational programs efficiency in applying the best educational practices to educate students from the dangers of indecent behaviors, in line with higher education policy and the appropriateness of educational program dimensions to spread awareness among students to not fall into the indecent behaviors clutches. The study adopted the inductive exploratory approach through structural equation modeling and the descriptive analysis of the collected data from randomly selected sample (n=385) from educational academics at Northern Border University in the Saudi Arabia using a specially designed survey tool to meet study purposes to evaluate dimensions of teaching methods, evaluation tools, training courses, course

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