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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
Wed Mar 29 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Investigation and Comparative Study Among Various Methods of Contraception Used in Erbil City
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The objective of this study was to investigate and compare among five different methods of contraception including combined oral contraceptive pills (COC), Depot medroxyprogesterone acetate (DMPA), copper Intrauterine contraceptive device (IUCD), vaginal spermicides and male condom used in Hawler City through estimate of their effect, relative failure rate, percentage of use, adherence and compliance and adverse effects of each contraceptive method. In order to reach to these aims, a retrospective study was conducted in Hawler City in Azadi Health Care Center over a period of 6 months from 22th November, 2010 to 15th May, 2011 during which data collection and subjects follow up for 3 months had been achieved. A conv

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Publication Date
Wed Jul 01 2015
Journal Name
Al–bahith Al–a'alami
The Role of Communication Methods in Changing the Values of the Urban Family
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This article discusses the change of values in urban family, because of various communication media and modern technologies as one of the most important factors affecting the changing family values in urban areas, this means becoming part of urban life. And focuses on the family in urban areas, for the privacy of the social, economic, demographic and cultural help to this effect, and because cities are the most friction and interaction with modern technologies.

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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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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
Fri Jun 30 2023
Journal Name
Iraqi National Journal Of Nursing Specialties
Evaluation of Women's knowledge about Family Planning Methods at Omer Sawi Teaching Hospital
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Objectives:This study aimed to identify women perception and experience regarding family planning(FP) methods

 Methodology:Descriptive cross-sectional hospital based study,was conducted at Omer Sawi teaching hospital,from august to September 2019.Sample of 320 women, were selected randomly after their agreement.Data were collected through interview questionnaire and analyzed using a statistical package for social sciences (SPSS)and descriptive and inferential statistical methods were used.With accepted P.< 0.05.for the correlation significant. 

Results:Age group between 21-25 years represent (53.1%),most common education levels were secondary school 56%.Majority of women had 2-5 children.Half of the wo

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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
Tue Feb 26 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Rationalization of Decision –Making and Performance evaluation methods through Employing Strategic Management Accounting
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This research dealt with the process of reducing costs through some strategic methods of management accounting targeted cost analysis unassembled and Alkeisen, where he focused this research through his theory on a review of some administrative accounting strategic technologies, while the second practical side through the application of targeted cost analysis unassembled and Alkeisen, acquired Search importance of focusing on the decisions to cut costs, through the use of some administrative accounting strategic methods and this we can unassembled analysis, continuous improvement, and the cost of quality) when applied quality, "in light of this has been reached to a set of conclusions that the most important of the  company's relian

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Publication Date
Thu Jan 30 2020
Journal Name
Neuroquantology
Electronic Transfers and (NLO) Properties Predicted by AB Initio Methods with Prove Experimentally
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Hartree-Fock (HF) method relies in the calculations of nonlinear optical properties (NLO) for benzoic acid molecule. Also, another theoretical study is conducted by using the TD-DFT Density Functional Theory through B3LYP/High Base Set 6-311++G (2d,2p) on Gaussian program09. Moreover, an experimental study has been done to obtain the electrons spectrum for benzoic acid with and without ethanol. While the experimental study is done by using UV/VIS. spectrophotometer. Energy gap values of electronic transition between HOMO and LUMO is obtained from theoretical and experimental results. Consequently, the theoretical result for determining the energy gap calculated from EHOMO-LUMO wasvery close to the results of UV / VIS. spectrum. A theoretica

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Publication Date
Thu Apr 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Brief Review: Some Interesting Methods of Synthesis Chromene Derivatives as Bioactive Molecules
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Chromene is considered a fused pyran ring with a benzene ring, which is found in many plants and is part of many important compounds such as anthocyanidins, anthocyanins, catechins, and flavanones. These compounds are included under the headings "flavonoids" and "isoflavonoids." These compounds are well known as bioactive molecules with wide medicinal uses. According to these pharmacokinetic characteristics, many researchers are giving more attention to this type of compound and its derivatives. Many chromene derivatives have been synthesized to study their biological effects for the treatment of many diseases. Furthermore, the researcher displayed wide interest in finding new methods for synthesizing chromene derivatives. These met

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Publication Date
Sat Oct 01 2022
Journal Name
Baghdad Science Journal
Assessment of surface water quality using statistical analysis methods: Orontes River (Case study)
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The study investigates the water quality of the Orontes River, which is considered one of the important water recourses in Syria, as it is used for drinking, irrigation, swimming and industrial needs. A database of 660 measurements for 13 parameters concentrations used, were taken from 11 monitoring points distributed along the Orontes River for a period of five years from 2015-2019, and to study the correlation between parameters and their impact on water quality, statistical analysis was applied using (SPSS) program. Cluster analysis was applied in order to classify the pollution areas along the river, and two groups were given: (low pollution - high pollution), where the areas were classified according to the sources of pollution to w

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