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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 Jun 02 2019
Journal Name
Baghdad Science Journal
Comparative Histological Study of the Stomach in Two Species of Iraqi Vertebrates (Magpie Pica pica L. and Small Asian Mongoose Herpestes javanicus E.)
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          A histological study showed the wall of the stomach in Pica pica and Herpestes javanicus consists of four layers: mucosa, submucosa, muscularis externa and serosa. Also, the present study showed many  differences in the histological structures of the stomach for each in both types. The stomach of P. pica consists of two portions: the proventiculus and gizzard, while the stomach of H. javanicus consists of three portions: cardiac, fundic and pyloric regions. The mucosa layer formed short gastric folds, named plicae. In the proventiculus of P. pica, sulcus is found between each two plicae, but the folds called gastric pits in the gizzard, which are full with koilin. Lamina properia in both types contained gastric g

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Publication Date
Thu Dec 15 2022
Journal Name
Al-academy
Strategies of brain-based learning theory and its impact on the achievement of students of the Department of Art Education in Teaching Methods
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The aim of the current research is to reveal the effect of using brain-based learning theory strategies on the achievement of Art Education students in the subject of Teaching Methods. The experimental design with two equal experimental and control groups was used. The experimental design with two independent and equal groups was used, and the total of the research sample was (60) male and female students, (30) male and female students represented the experimental group, and (30) male and female students represented the control group. The researcher prepared the research tool represented by the cognitive achievement test consisting of (20) questions, and it was characterized by honesty and reliability, and the experiment lasted (6) weeks

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Publication Date
Thu Dec 19 2019
Journal Name
Opicon
The Role of Total Quality in Increasing the Productivity of Wheat and Barley Crops and Reducing Costs Using Modern Irrigation Methods in Iraq
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Most of the world is seeking attention to the agricultural sector, which occupies a distinguished economic center, including Iraq, it is no wonder that the focus is on this sector, especially in developing countries. Descriptive analysis of the sample tables of wheat and barley crops in Iraq showed that adherence to the principles and rules of total quality, including modern irrigation methods (irrigated) has a significant impact in increasing productivity, reducing costs and improving quality compared to traditional irrigation methods, so it became necessary to take agricultural economic units All procedures and means that will help in the application of the rules of total quality to promote the reality of wheat and barley cultivation in I

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Publication Date
Wed Aug 07 2019
Journal Name
Iraqi National Journal Of Nursing Specialties
Effect of Non-Pharmacological Pain Management Methods on Reduction the Duration of Labor Stages in Primigravida Women at AL-Elwyia Maternity Teaching Hospital
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Objectives: To evaluate the effect of non-pharmacological pain relief methods on duration of labor stage.
Methodology: A quasi-experimental study design was conducted during the period of (4th July 2018 through 24th October 2018) on non-probability of (60) women (30) of them were a control group and (30) were the study group whom admitted to Al-Elwyia Maternity Teaching Hospital suffering from labor pain. A questionnaire was used as a tool of data collection Descriptive& Inferential statistical analyses were used to analyze the data.
Result: The highest percentages of study and control groups were in age group (< 20) years old, primary schools graduates, housewife, from "urban area", within low category of socioeconomic scal

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Publication Date
Sun Jun 30 2019
Journal Name
Iraqi National Journal Of Nursing Specialties
Effect of Non-Pharmacological Pain Management Methods on Reduction the Duration of Labor Stages in Primigravida Women at AL-Elwyia Maternity Teaching Hospital
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Objectives: To evaluate the effect of non-pharmacological pain relief methods on duration of labor stage.Methodology: A quasi-experimental study design was conducted during the period of (4th July 2018 through 24th October 2018) on non-probability of (60) women (30) of them were a control group and (30) were the study group whom admitted to Al-Elwyia Maternity Teaching Hospital suffering from labor pain. A questionnaire was used as a tool of data collection Descriptive& Inferential statistical analyses were used to analyze the data.Result: The highest percentages of study and control groups were in age group (< 20) years old, primary schools graduates, housewife, from "urban area", within low category of socioeconomic scale,

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Publication Date
Wed Nov 07 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
The Effect of Different Types of Separating Medium On Some Physical Properties of Processing Acrylic Denture-base with Two Investment Materials: A comparative Study
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Objective(s): In the present study, glycerin is used as a substitute for tin-foil and cold mold seal (Alginate mould seal)
in the process of curing heat and cold-cure acrylic resin denture base against stone and plaster.
Methodology: 60 specimens were prepared from heat-cure acrylic resin and cold-cure acrylic resin denture base. The
study includes 12 groups of specimens depending on the type of processing, investment material and type of
separating medium that are used in curing process. Each group of them contains 5 specimens for each test.
Some of physical properties of the processed acrylic denture base that (water sorption and solubility) have been
compared with those processed using tin-foil and tin-foil substitut

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Publication Date
Thu Feb 29 2024
Journal Name
Iraqi Journal Of Science
Tigecycline is the Most Effective against Multi-Drug Resistant Klebsiella pneumoniae Recovered from Burn Wound Infections in Two Hospitals in Al-Kut City, Iraq
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     Klebsiella pneumoniae is among the most frequent microorganisms isolated from infections of burn wounds. This cross-sectional study aimed to investigate the distribution of multi-drug resistant (MDR) K. pneumoniae in two burn hospitals and the antibiotic resistance profile in different burn regions of the same patient. It was performed in two hospitals (Al-Zahraa and Al-Karama) in Al-Kut, Iraq, between January and May 2022. Totally, 100 burn swabs were collected from 40 patients of both genders suffering from burn wound infections, with ages ranging between 3 and 50 years. Klebsiella pneumoniae were isolated and identified using conventional methods followed by VITEK®2 system and confirmed via polymerase chain reaction targeting t

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Publication Date
Thu Feb 16 2023
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Phytochemical Screening of Petroleum Ether Fractions by GC/MS and Isolation of Lupeol from Two Different Parts of Iraqi Leucaena leuco-cephala. (Conference Paper )#
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Abstract

This work is considered the first study for the components of the Iraqi Leucaena leucocephala plant, where the different phytochemical compounds that present in the aerial parts were identified by using the gas chromatography/mass spectrometry technique (GC/MS). The type of the components and their concentration will differ according to the part of the plant used and the method of extraction (hot and cold). This study made a comparison in lupeol concentration that was identified and isolated from petroleum ether fractions of Leucaena leucocephala by using Gas Chromatography/Mass Spectrometry (GC/MS), High-performance thin-layer chromatography (HPTLC), and Preparative High-Performance Li

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Publication Date
Thu Sep 01 2011
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The Correlation Of Economic Attractiveness Measurement Methods With Regulating Factors Of Capital Investment Appraisal In The Public Industrial Companies In Jordan: An Empirical Study
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The process of capital investment appraisal takes hold the attention of managers and accountants of the industrial companies. This process involves the use of multiple and diverse financial evaluation methods to measure the economic attractiveness of capital investment peojects. This multiplicity and diversity of financial evaluation metods have been the motive of this research to: investigate some organizational variables such as the desired objectives, identify managerial procedures which regulate the capital investment process, specify evaluation methods and examine the relationships between these variables and evaluation methods actually used by a sample of public industrial companies in Jordan.

    The data wa

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Publication Date
Thu Feb 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Use Simulation To Differentiate Between Some Modern Methods To the Model GM(1,1) To Find Missing Values And Estimate Parameters With A Practical Application
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Abstract

       The grey system model GM(1,1) is the model of the prediction of the time series and the basis of the grey theory. This research presents the methods for estimating parameters of the grey model GM(1,1) is the accumulative method (ACC), the exponential method (EXP), modified exponential method (Mod EXP) and the Particle Swarm Optimization method (PSO). These methods were compared based on the Mean square error (MSE) and the Mean Absolute percentage error (MAPE) as a basis comparator and the simulation method was adopted for the best of the four methods, The best method was obtained and then applied to real data. This data represents the consumption rate of two types of oils a he

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