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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 Jan 01 2023
Journal Name
Computers, Materials & Continua
An Efficient Method for Heat Recovery Process and燭emperature燨ptimization
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Publication Date
Sat Apr 01 2023
Journal Name
Baghdad Science Journal
Iraqi porcelanite Rocks for Efficient Removal of Safranin Dye from Aqueous Solution
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This research includes a study of the ability of Iraqi porcelanite rocks powder to remove the basic Safranine dye from its aqueous process by adsorption. The experiments were carried out at 298Kelvin in order to determine the effect of the starting concentration for Safranin dye, mixing time, pH, and the effect of ionic Strength. The good conditions were perfect for safranine dye adsorption was performed when0.0200g from that adsorbed particles and the removal max percentage  was found  be 96.86%  at 9 mg/L , 20 minutes adsorption time and at PH=8 and in 298 K. The isothermal equilibrum stoichiometric adsorption confirmed, the process data were examined by Langmuir, Freundlich and Temkin adsorption equations at different temperatures

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Publication Date
Thu Apr 20 2023
Journal Name
Fire
An Efficient Wildfire Detection System for AI-Embedded Applications Using Satellite Imagery
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Wildfire risk has globally increased during the past few years due to several factors. An efficient and fast response to wildfires is extremely important to reduce the damaging effect on humans and wildlife. This work introduces a methodology for designing an efficient machine learning system to detect wildfires using satellite imagery. A convolutional neural network (CNN) model is optimized to reduce the required computational resources. Due to the limitations of images containing fire and seasonal variations, an image augmentation process is used to develop adequate training samples for the change in the forest’s visual features and the seasonal wind direction at the study area during the fire season. The selected CNN model (Mob

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Publication Date
Thu Jan 01 2026
Journal Name
Aip Conference Proceedings
Using gravitational search algorithm for solving optimization problems based on hypervolume indicator
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Extended utilization of adaptive algorithms, Evaluative Algorithms (EAs), to address these issues offers a way to handle massive multi-objective optimization, even if the algorithmic method for handling combinations of objectives (CO) has been accessible for quite some time. Combining the idea of superiority with the Hypervolume (HV) tag approach, the GSA algorithm utilizes various target effects to explain several algorithms depending on the Hypervolume (HV) spacing. The Multi-objective Gravitational Search Algorithm with Hypervolume (MOGSA/HV). Since rapid convergence could result from GSA foundation work, Hypervolume rewrites the multi-objective problem (MOP) as a sequence of Tchebycheff solutions, improving it. Since the one in charge h

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Publication Date
Mon Jul 27 2026
Journal Name
Journal Of University Of Anbar For Pure Science
Comparison of Methods for The Determination of Beta-Lactam Drugs Using Different Analytical Methods
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Given the increasing global use of antibiotics, it has become necessary to examine and recognize their significance. An antibiotic formulation may contain one or more active components, depending on the antibiotic’s type and formulation. Antibiotics act exclusively against bacterial diseases and are ineffective against viral infections such as the common cold and influenza. The purpose of this review is to analyze the existing literature on the determination of antibiotics and to present the methods used for estimating specific antibiotics, including cephalexin, cloxacillin, piperacillin, nafcillin, and cefamandole, in medicinal preparations and biological fluids, such as blood and urine, from humans and animals. Verifying the quality of

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Publication Date
Tue Oct 22 2024
Journal Name
Iraqi Statisticians Journal
Inferential Methods for the Dagum Regression Model
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The Dagum Regression Model, introduced to address limitations in traditional econometric models, provides enhanced flexibility for analyzing data characterized by heavy tails and asymmetry, which is common in income and wealth distributions. This paper develops and applies the Dagum model, demonstrating its advantages over other distributions such as the Log-Normal and Gamma distributions. The model's parameters are estimated using Maximum Likelihood Estimation (MLE) and the Method of Moments (MoM). A simulation study evaluates both methods' performance across various sample sizes, showing that MoM tends to offer more robust and precise estimates, particularly in small samples. These findings provide valuable insights into the ana

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Publication Date
Wed Apr 30 2025
Journal Name
Iraqi Journal Of Science
Calculating the Variation of the Universal Parameter (Variable) Using Kepler's Equation for Different Orbits
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Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions

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Publication Date
Mon Aug 01 2022
Journal Name
Baghdad Science Journal
An Analytic Solution for Riccati Matrix Delay Differential Equation using Coupled Homotopy-Adomian Approach
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An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

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Publication Date
Mon Dec 30 2024
Journal Name
Wasit Journal For Pure Sciences
A New Class of Higher Derivatives for Harmonic Univalent Functions Established using a Generalized Fractional Integral Operator
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A new class of higher derivatives  for harmonic univalent functions defined by a generalized fractional integral operator inside an open unit disk E is the aim of this paper.

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Publication Date
Sun Mar 05 2017
Journal Name
Baghdad Science Journal
An efficient of Sansevieriatrifasciataplantas biosorbent for the treatment of metal contaminated industrial effluents
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Sansevieriatrifasciata was studied as a potential biosorbent for chromium, copper and nickel removal in batch process from electroplating and tannery effluents. Different parameters influencing the biosorption process such as pH, contact time, and amount of biosorbent were optimized while using the 80 mm sized particles of the biosorbent. As high as 91.3 % Ni and 92.7 % Cu were removed at pH of 6 and 4.5 respectively, while optimum Cr removal of 91.34 % from electroplating and 94.6 % from tannery effluents was found at pH 6.0 and 4.0 respectively. Pseudo second order model was found to best fit the kinetic data for all the metals as evidenced by their greater R2 values. FTIR characterization of biosorbent revealed the presence of carboxyl a

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