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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
Mon Apr 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Result for the group SL(2,172)
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Publication Date
Sun Apr 01 2012
Journal Name
Journal Of Educational And Psychological Researches
Perceived Self-efficacy for university students
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Research was: 1- known as self-efficacy when students perceived the university. 2- know the significance of statistical differences in perceived self-efficacy according to gender and specialty. Formed the research sample of (300) students were chosen from the original research community by way of random (150) male specialization and scientific and humanitarian (150) females specialized scientific and humanitarian. The search tool to prepare the yard tool to measure perceived self-efficacy based on measurements and previous literature on the subject of perceived self-efficacy. The researcher using a number of means, statistical, including test Altaúa and analysis of variance of bilateral and results showed the enjoyment of the research s

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Publication Date
Mon Sep 01 2014
Journal Name
Proceedings Of Ieee East-west Design & Test Symposium (ewdts 2014)
Qubit method for diagnosing digital systems
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Manufacturing electrolysis cell for hydrogen production
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Deep Bayesian for Opinion-target identification
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The use of deep learning.

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Publication Date
Mon Mar 07 2022
Journal Name
Journal Of Educational And Psychological Researches
Future thinking skills for university students
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The study aimed to identify the future thinking skills of university students and which of these skills are prevalent. The sample of the study consisted of (400) male and female students from the university students. In order to achieve the goals of the research, the researcher built a measure of future thinking skills based on Torrance theory (2003). Psychometric properties of the standards were extracted, which are represented by honesty and consistency and the application of the measures to the research sample. The researchers found that Future thinking skills of university students, and that the skill of future planning is the most common skill among the research sample.

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Score for the group 𝓢𝓛(2,38)
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Publication Date
Fri Mar 30 2007
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Computer Aided Design for Spray Driers
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The aim of this work is to develop an axi-symmetric two dimensional model based on a coupled simplified computational fluid dynamics (CFD) and Lagrangian method to predict the air flow patterns and drying of particles.  Then using this predictive tool to design more efficient spray dryers. The approach to this is to model what particles experience in the drying chamber with respect to air temperature and humidity. These histories can be obtained by combining the particles trajectories with the air temperature/humidity pattern in the spray dryer. Results are presented and discussed in terms of the air velocity, temperature, and humidity profiles within the chambers and compared for drying of a 42.5% solids solution in a spray chamber

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Publication Date
Thu Dec 01 2011
Journal Name
Iraqi Journal Of Physics
Multilayer Perceptron for analyzing satellite data
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Different ANN architectures of MLP have been trained by BP and used to analyze Landsat TM images. Two different approaches have been applied for training: an ordinary approach (for one hidden layer M-H1-L & two hidden layers M-H1-H2-L) and one-against-all strategy (for one hidden layer (M-H1-1)xL, & two hidden layers (M-H1-H2-1)xL). Classification accuracy up to 90% has been achieved using one-against-all strategy with two hidden layers architecture. The performance of one-against-all approach is slightly better than the ordinary approach

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Publication Date
Sat Apr 21 2012
Journal Name
Arabian Journal For Science And Engineering
A Procedure for Analysing Reinforced Embankments
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