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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
Tue Dec 01 2015
Journal Name
Journal Of Economics And Administrative Sciences
A Comparison Between Some Estimator Methods of Linear Regression Model With Auto-Correlated Errors With Application Data for the Wheat in Iraq
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This research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),

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Publication Date
Tue Jan 01 2019
Journal Name
Energy Procedia
The relationship of Nuclear Decay Methods (alpha and beta) Particles with the Nuclear Deformation for Nuclei inUranium-238 and Thorium -232 Series
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Publication Date
Sun Mar 06 2016
Journal Name
Baghdad Science Journal
Comparison Between Conventional and Microwave Methods For Extraction Pectin and Degree of Esterification from Orange (Citrus sinesis) and Grapefruit (Citrus paradisi) Peels
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In this study Microwave and conventional methods have been used to extract and estimate pectin and its degree of esterification from dried grapefruit and orange peels. Acidified solution water with nitric acid in pH (1.5) was used. In conventional method, different temperature degrees for extraction pectin from grape fruit and orange(85 ,90 , 95 and 100?C) for 1 h were used The results showed grapefruit peels contained 12.82, 17.05, 18.47, 15.89% respectively, while the corresponding values were 5.96, 6.74, 7.41 and 8.00 %, respectively in orange peels. In microwave method, times were 90, 100, 110 and 120 seconds. Grapefruit peels contain 13.86, 16.57, 18.69, and 17.87%, respectively, while the corresponding values were of 6.53, 6.68, 7.2

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Publication Date
Sun Jan 10 2016
Journal Name
British Journal Of Applied Science & Technology
Illumination - Invariant Facial Components Extraction Using Adaptive Contrast Enhancement Methods
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The process of accurate localization of the basic components of human faces (i.e., eyebrows, eyes, nose, mouth, etc.) from images is an important step in face processing techniques like face tracking, facial expression recognition or face recognition. However, it is a challenging task due to the variations in scale, orientation, pose, facial expressions, partial occlusions and lighting conditions. In the current paper, a scheme includes the method of three-hierarchal stages for facial components extraction is presented; it works regardless of illumination variance. Adaptive linear contrast enhancement methods like gamma correction and contrast stretching are used to simulate the variance in light condition among images. As testing material

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Publication Date
Mon Mar 23 2020
Journal Name
Journal Of Engineering
Drag Reduction Using Passive Methods on KIA PRIDE Car Model
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An experimental study on a KIA pride (SAIPA 131) car model with scale of 1:14 in the wind tunnel was made beside the real car tests. Some of the modifications to passive flow control which are (vortex generator, spoiler and slice diffuser) were added to the car to reduce the drag force which its undesirable characteristic that increase fuel consumption and exhaust toxic gases. Two types of calculations were used to determine the drag force acting on the car body. Firstly, is by the integrating the values of pressure recorded along the pressure taps (for the wind tunnel and the real car testing), secondly, is by using one component balance device (wind tunnel testing) to measure the force. The results show that, the avera

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Publication Date
Fri Nov 30 2007
Journal Name
Alustath Journal For Human And Social Sciences
Plagiarism in Theses and Dissertations: Methods of Detecting and Avoiding
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The present study aims at identifying the styles, procedures of Iraqi universities to avoid plagiarism and evaluate these steps, also to evaluate the form prepared by the Directory of Scientific Supervision and Evaluation, Ministry of Higher Education and Scientific Research. The study uses documentary style, 150 teachers in the following colleges (Education Ibn Rushd, Languages and Arts) in university of Baghdad whom already used the aforementioned list were the sample of the study and they asked to give their opinions about the list.The study consists of five sections, first one deals with general view, second explains plagiarism and its types, shapes and reasons,third tackles with ways of detecting plagiarism, its programs, consequences

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Publication Date
Sat Jun 01 2024
Journal Name
Ecological Engineering & Environmental Technology
Employing Phytoremediation Methods to Extract Heavy Metals from Polluted Soils
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The phytoremediation technique has become very efficient for treating soil contaminated with heavy metals. In this study, a pot experiment was conducted where the Dodonaea plant (known as hops) was grown, and soil previously contaminated with metals (Zn, Ni, Cd) was added at concentrations 100, 50, 0 mg·kg-1 for Ni and Zn, and at concentrations of 0, 5, 10 mg·kg-1 for cadmium. Irrigation was done within the limits of the field capacity of the soil. Cadmium, nickel and zinc was estimated in the soil to find out the capacity of plants to the absorption of heavy and contaminated metals by using bioconcentration factors (BCFs), bioaccumulation coefficient (BAC) and translocation factor (TF). Additionally, BCF values of both Ni and Zn were l

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Publication Date
Tue Feb 18 2025
Journal Name
International Journal Of Scientific Research In Science, Engineering And Technology
A Comprehensive Review on Cryptography Algorithms: Methods and Comparative Analysis
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The evolution of cryptography has been crucial to preservation subtle information in the digital age. From early cipher algorithms implemented in earliest societies to recent cryptography methods, cryptography has developed alongside developments in computing field. The growing in cyber threats and the increase of comprehensive digital communications have highlighted the significance of selecting effective and robust cryptographic techniques. This article reviews various cryptography algorithms, containing symmetric key and asymmetric key cryptography, via evaluating them according to security asset, complexity, and execution speed. The main outcomes demonstrate the growing trust on elliptic curve cryptography outstanding its capabi

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Publication Date
Sun Jan 10 2016
Journal Name
British Journal Of Applied Science & Technology
The Effect of Classification Methods on Facial Emotion Recognition ‎Accuracy
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The interests toward developing accurate automatic face emotion recognition methodologies are growing vastly, and it is still one of an ever growing research field in the region of computer vision, artificial intelligent and automation. However, there is a challenge to build an automated system which equals human ability to recognize facial emotion because of the lack of an effective facial feature descriptor and the difficulty of choosing proper classification method. In this paper, a geometric based feature vector has been proposed. For the classification purpose, three different types of classification methods are tested: statistical, artificial neural network (NN) and Support Vector Machine (SVM). A modified K-Means clustering algorithm

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Publication Date
Thu Mar 01 2018
Journal Name
Journal Of Engineering
Permeability Estimation by Using the Modified and Conventional FZI Methods
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There many methods for estimation of permeability. In this Paper, permeability has been estimated by two methods. The conventional and modified methods are used to calculate flow zone indicator (FZI). The hydraulic flow unit (HU) was identified by FZI technique. This technique is effective in predicting the permeability in un-cored intervals/wells. HU is related with FZI and rock quality index (RQI). All available cores from 7 wells (Su -4, Su -5, Su -7, Su -8, Su -9, Su -12, and Su -14) were used to be database for HU classification. The plot of probability cumulative of FZI is used. The plot of core-derived probability FZI for both modified and conventional method which indicates 4 Hu (A, B, C and D) for Nahr Umr forma

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