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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
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
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
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
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
Mon Oct 01 2018
Journal Name
Journal Of Educational And Psychological Researches
The ability of solving a mathematical problem and its relation to system thinking among fifth preparatory students
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The research seeks to examine the ability of fifth preparatory students in solving a mathematical problem in relation to system thinking. To this end, the researcher chose (140) fifth preparatory students from four-different secondary schools in Kirkuk city for the academic year (2016-2017). Two tests were adopted to collect study data: a test of (5) items about skills in solving math problem designed by (Al-raihan, 2006); and a test of system thinking skills designed by the researcher himself consisted of (14) items. It was divided into four skills (analyzing the main system to subsystems, eliminating all inner gaps of system, identifying the inner connection of system, and reorganizing the system). The findings indicated a good ability

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Publication Date
Sat May 02 2026
Journal Name
Modern Sport
Information Processing Styles, Problem Solving, and Their Relationship with Metamotivation and Perceived Control among Postgraduate Female Students
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The demands of professional, scientific, and academic life have made it necessary to identify the various difficulties faced by postgraduate female students, which lead to problems that hinder their achievement of the required goals. This necessitates directing efforts toward finding solutions to confront and solve problems through appropriate cognitive behavior. Therefore, this study aimed to identify information processing styles and problem-solving and their relationship with metamotivation and perceived control among postgraduate female students (PhD/Master's). To achieve this aim, the descriptive approach using the survey method was adopted due to its suitability to the nature of the research problem. The population was defined

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Publication Date
Wed Sep 15 2021
Journal Name
Al-academy
Applying the substance-field model mechanism to problem solving in industrial product design: محمد علي حسين القيسي
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  Problem solving methods and mechanisms contribute to facilitating human life by providing tools to solve simple and complex daily problems. These mechanisms have been essential tools for professional designers and design students in solving design problems.
This research dealt with one of those mechanisms, which is the (the substance-field model model), as it has been mentioning that this mechanism is characterized by the difficulty of its application, which formed the main research problem. In home gardens (the sub-problem of research), an analysis of this problem was applied and then a solution was found to address it. The researcher used the 3dsmax program to implement the proposed design.
The most important research res

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Publication Date
Tue Feb 01 2022
Journal Name
Baghdad Science Journal
Solving Whitham-Broer-Kaup-Like Equations Numerically by using Hybrid Differential Transform Method and Finite Differences Method
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This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

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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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