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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 May 19 2012
Journal Name
Wireless Personal Communications
Stable-Aware Evolutionary Routing Protocol for Wireless Sensor Networks
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Publication Date
Wed Jul 31 2024
Journal Name
Iraqi Geological Journal
Correlating Capillary Pressure and Resistivity Index for Carbonate Reservoir
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Capillary pressure is a significant parameter in characterizing and modeling petroleum reservoirs. However, costly laboratory measurements may not be sufficiently available in some cases. The problem amplifies for carbonate reservoirs because relatively enormous capillary pressure curves are required for reservoir study due to heterogeneity. In this work, the laboratory measurements of capillary pressure and formation resistivity index were correlated as both parameters are functions of saturation. Forty-one core samples from an Iraqi carbonate reservoir were used to develop the correlation according to the hydraulic flow units concept. Flow zone indicator (FZI) and Pore Geometry and Structure (PGS) approaches were used to identify

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Publication Date
Mon Jun 01 2015
Journal Name
Journal Of Engineering
Laboratory Preparation of Simulated Sludge for Anaerobic Digestion Experimentation
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Health and environmental factors as well as operational difficulties are major challenges facing the development of an anaerobic digestion process. Some of these problems relate to the use of sludge collected from primary and secondary clarifier units in wastewater treatment plants for laboratory purposes.

The present study addresses the preparation of sludge for laboratory purposes by using a mixture that consists of the digested sludge, which is less pathogenic, compared to the collected sludge from the primary or secondary clarifier, and food wastes. The sludge has been tested experimentally for 19 and 32 days under mesophilic conditions. The results show a steady methane production rate from the anaerobic dig

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Publication Date
Tue Jun 01 2021
Journal Name
Journal Of Interdisciplinary Mathematics
Enforcement for the partition (7, 7, 4; 0, 0)
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Scopus (17)
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Publication Date
Mon Jun 30 2025
Journal Name
Ingénierie Des Systèmes D Information
Comparative Analysis of Four Programming Languages for Machine Learning
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Publication Date
Wed Feb 29 2012
Journal Name
Al-khwarizmi Engineering Journal
Design a Fault Tolerance for Real Time Distributed System
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This paper designed a fault tolerance for soft real time distributed system (FTRTDS). This system is designed to be independently on specific mechanisms and facilities of the underlying real time distributed system. It is designed to be distributed on all the computers in the distributed system and controlled by a central unit.

Besides gathering information about a target program spontaneously, it provides information about the target operating system and the target hardware in order to diagnose the fault before occurring, so it can handle the situation before it comes on. And it provides a distributed system with the reactive capability of reconfiguring and reinitializing after the occurrence of a failure.

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Publication Date
Sat Dec 10 2022
Journal Name
Al-rafidain Journal Of Medical Sciences ( Issn: 2789-3219 )
Actual Benefits of Zinc for Cardiovascular Diseases: Mini Review
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The leading causes of death, particularly among the elderly, are cardiovascular illnesses, which are frequently linked to altered lifestyle patterns. Numerous academic studies on health and disease have stressed the role of micronutrients like zinc. Furthermore, both healthy and unwell patients are increasingly consuming dietary supplements that contain micronutrients for wellbeing. Cardiovascular disease can be brought on by trace element deficiencies, particularly zinc insufficiency. This study's goal is to analyze current theories regarding the benefits of zinc supplementation for people with cardiovascular problems. We used reliable websites like Google Scholar, PubMed, and Research Gate to find the most recent papers. Preprints

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Publication Date
Wed May 10 2023
Journal Name
Journal Of Engineering
Cross Dipole Antennas Solution for Angle of Arrival Estimation
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The Multiple Signal Classification (MUSIC) algorithm is the most popular algorithm to estimate the Angle of Arrival (AOA) of the received signals. The analysis of this algorithm (MUSIC) with typical array antenna element ( ) shows that there are two false direction indication in the plan
aligned with the axis of the array. In this paper a suggested modification on array system is proposed by using two perpendiculars crossed dipole array antenna in spite of one array antenna. The suggested modification does not affect the AOA estimation algorithm. The simulation and results shows that the proposed solution overcomes the MUSIC problem without any effect on the performance of the system.

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Publication Date
Fri Aug 01 2025
Journal Name
Radio Science
Integrating Drones With Digital Twins for Aerial Remote Sensing
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Abstract<p>Drones are highly autonomous, remote‐controlled platforms capable of performing a variety of tasks in diverse environments. A digital twin (DT) is a virtual replica of a physical system. The integration of DT with drones gives the opportunity to manipulate the drone during a mission. In this paper, the architecture of DT is presented in order to explain how the physical environment can be represented. The techniques via which drones are collecting the necessary information for DT are compared as a next step to introduce the main methods that have been applied in DT progress by drones. The findings of this research indicated that the process of incorporating DTs into drones will result in the advanc</p> ... Show More
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Publication Date
Mon Aug 28 2023
Journal Name
Cureus
The Enigma of the Impervious Nobel Prize for Neurosurgeons
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