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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 Mar 07 2010
Journal Name
Baghdad Science Journal
Calculate the one – expectation to electronic charge of atomic system contiun two electron
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The aim of this work is to calculate the one- electron expectation value of the electronic charge of atomic system Z=2,3….7 and we compare with He atom . the electronic density function D(r1) of He atom and like ions are evaluated . using Hartree –Fock wave.

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Publication Date
Thu Aug 31 2017
Journal Name
Pramana
Matter density distributions and elastic form factors of some two-neutron halo nuclei
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The Skyrme–Hartree–Fock (SHF) method with MSK7 Skyrme parameter has been used to investigate the ground-state properties for two-neutron halo nuclei 6He, 11Li, 12Be and 14Be. These ground-state properties include the proton, neutron and matter density distributions, the corresponding rms radii, the binding energy per nucleon and the charge form factors. These calculations clearly reveal the long tail characterizing the halo nuclei as a distinctive feature.

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Publication Date
Tue Apr 30 2024
Journal Name
Abdulraheem Assi Obaid
Effect of shading net, planting methods and bio-extract on production of muskmelon
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Publication Date
Thu Nov 14 2024
Journal Name
Journal Of Emergency Medicine, Trauma And Acute Care
Novel isolation and optimization of anti-MRSA bacteriophages using plaque-based biokinetic methods
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Background: MRSA (methicillin-resistant Staphylococcus aureus) is a global health problem. Many people are looking for new ways to combat MRSA, for example by using bacteriophages (phages). It has been extremely challenging to isolate a sufficient quantity of lytic anti-MRSA phages. Therefore, new techniques for separating, refining, and reworking anti-MRSA phages were sought in this study.

Methods: Of 437 S. aureus isolates, nine clinical MRSA isolates were obtained from three hospitals in Baghdad, Iraq and two ATCC MRSA strains were used to separate wild anti-MRS

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Publication Date
Wed Dec 12 2018
Journal Name
Iop Conference Series: Materials Science And Engineering
Extraction of Essential Oil from Iraqi Eucalyptus Camadulensis Leaves by Water Distillation Methods
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The extraction of Eucalyptus oil from Iraqi Eucalyptus Camadulensis leaves was studded using water distillation methods. The amount of Eucalyptus oil has been determined in a variety of extraction temperature and agitation speed. The effect of water to Eucalyptus leaves (solvent to solid) ratio and particle size of Eucalyptus leaves has been studied in order to evaluate the amount of Eucalyptus oil. The optimum experimental condition for the Eucalyptus oil extraction was established as follows: 100 C extraction temperature, 200 rpm agitation speed; 0.5 cm leave particle size and 6: 1 ml: g amount of water to eucalyptus leaves Ratio.

Publication Date
Fri Jul 01 2022
Journal Name
Biomedicine And Chemical Sciences
Identification of Pathogenic Fungi in Renal Transplant Patients by Conventional and Molecular Methods
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Opportunistic fungal infections due to the immune- compromised status of renal transplant patients are related to high rates of morbidity and mortality regardless of their minor incidence. Delayed in identification of invasive fungal infections (IFIs), will lead to delayed treatment and results in high mortality in those populations. The study aimed to assess the frequency of invasive fungal infection in kidney transplant recipients by conventional and molecular methods. This study included 100 kidney transplant recipients (KTR) (75 males, and 25 females), collected from the Centre of Kidney Diseases and Transplantation in the Medical City of Baghdad. Blood samples were collected during the period from June 2018 to April 2019. Twent

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Publication Date
Mon Apr 15 2013
Journal Name
Eng. & Tech. Journal,
Assessment the Impact of Different Hydrated Lime Addition Methods on Fatigue Life Characteristic
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The purpose of this study is to evaluate the effect of hydrated lime addition methods as filler replacement on fatigue performance of Hot Mix Asphalt (HMA). Three types of addition methods of hydrated lime were introduced namely dry HL on dry aggregate and saturated surface aggregate above 3% and slurry HL on dry aggregate, ordinary Lime stone powder was reduced by three HL percentage (1.0, 2.0 and 3.0 %). The effect of different methods were investigated on the fatigue properties of HMA using, third-point flexural fatigue bending Test. Pneumatic Repeated Load System (PRLS) was carried out to establish the effect of hydrated lime on the fatigue failure criteria and to select the proper hydrated lime application methods on fatigue behavior o

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Publication Date
Thu May 02 2019
Journal Name
Journal Of Planner And Development
ways to employ planning and architectural methods to rationalize the introduction of electricity
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the rationalization of energy consumption Require awareness in the possibility of bridging the local need severe shortage of electric power for daily requirements. The research aims to show that the engineers of various specializations and architects, including in particular can have an active role in about the importance of the role of energy in human life, and it’s best utilization without extravagance (which our religion forbids it). Here lies the problem of the research to find possible means and alternative methods to reduce (rationalization) electrical energy consumption in hot dry areas in general which need large energy for air conditioning because of the crucial climate of these regions that making access to the area o

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Publication Date
Wed Jun 30 2021
Journal Name
Journal Of Economics And Administrative Sciences
A Comparison between robust methods in canonical correlation by using empirical influence function
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       Canonical correlation analysis is one of the common methods for analyzing data and know the relationship between two sets of variables under study, as it depends on the process of analyzing the variance matrix or the correlation matrix. Researchers resort to the use of many methods to estimate canonical correlation (CC); some are biased for outliers, and others are resistant to those values; in addition, there are standards that check the efficiency of estimation methods.

In our research, we dealt with robust estimation methods that depend on the correlation matrix in the analysis process to obtain a robust canonical correlation coefficient, which is the method of Biwe

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Publication Date
Mon Feb 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Problematic of Non Performing Banking Loans in Iraq and the Methods of Treatment
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The banking system considered as one of the most important intermediate circle between creditor and debtors it is mean the most important funding rings in economic activity, whether finance takes the a consumer or investment form and therefore it is the main base to stimulate economic activity both on the demand side, both consumption and investment and therefore of the main motivating factors for economic growth.

The banking system depends in achieve its goals on the grants and loan recovery, or what is known credit process and according to what the importance referred to the role of the banking system, it is important to ensure the safety and efficiency of the mechanisms of banking device and safety is

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