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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 Sep 01 2024
Journal Name
Journal Of Energy Storage
Nanofluid-assisted enhanced sealing security for efficient geological hydrogen storage in Saudi Arabian basalt
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The modification of hydrophobic rock surfaces to the water-wet state via nanofluid treatment has shown promise in enhancing their geological storage capabilities and the efficiency of carbon dioxide (CO2) and hydrogen (H2) containment. Despite this, the specific influence of silica (SiO2) nanoparticles on the interactions between H2, brine, and rock within basaltic formations remains underexplored. The present study focuses on the effect of SiO2 nanoparticles on the wettability of Saudi Arabian basalt (SAB) under downhole conditions (323 K and pressures ranging from 1 to 20 MPa) by using the tilted plate technique to measure the contact angles between H2/brine and the rock surfaces. The findings reveal that the SAB's hydrophobicity intensif

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Publication Date
Fri Dec 31 2021
Journal Name
International Journal Of Intelligent Engineering And Systems
Performance Analysis for Hybrid Massive MIMO FSO/RF Links Based on Efficient Channel Codes
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Scopus (2)
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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
Fri Aug 31 2012
Journal Name
Al-khwarizmi Engineering Journal
Sub–Nyquist Frequency Efficient Audio Compression
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This paper presents the application of a framework of fast and efficient compressive sampling based on the concept of random sampling of sparse Audio signal. It provides four important features. (i) It is universal with a variety of sparse signals. (ii) The number of measurements required for exact reconstruction is nearly optimal and much less then the sampling frequency and below the Nyquist frequency. (iii) It has very low complexity and fast computation. (iv) It is developed on the provable mathematical model from which we are able to quantify trade-offs among streaming capability, computation/memory requirement and quality of reconstruction of the audio signal. Compressed sensing CS is an attractive compression scheme due to its uni

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Publication Date
Thu Feb 01 2007
Journal Name
No
On Solvability of an Operator Equation-
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Publication Date
Wed Aug 01 2007
Journal Name
University Of Baghdad, College Of Education For Pure Science (ibn Al-haitham), Department Of Mathematical
Thesis.On Solvability of an Operator Equation-
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Publication Date
Sat Mar 01 2008
Journal Name
The Third International Conference On Mathematical Sciences
On Solvability of an Operator Equation
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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
Sat Dec 01 2012
Journal Name
Journal Of Engineering
Different Resolution Merging Methods For Environmental Areas Extraction
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The usage of remote sensing techniques in managing and monitoring the environmental areas is increasing due to the improvement of the sensors used in the observation satellites around the earth. Resolution merge process is used to combine high resolution one band image with another one that have low resolution multi bands image to produce one image that is high in both spatial and spectral resolution. In this work different merging methods were tested to evaluate their enhancement capabilities to extract different environmental areas; Principle component analysis (PCA), Brovey, modified (Intensity, Hue ,Saturation) method and High Pass Filter methods were tested and subjected to visual and statistical comparison for evaluation. Both visu

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