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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
Thu Oct 31 2019
Journal Name
Journal Of Engineering And Applied Sciences
Comparison of Estimate Methods of Multiple Linear Regression Model with Auto-Correlated Errors when the Error Distributed with General Logistic
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In this research, we studied the multiple linear regression models for two variables in the presence of the autocorrelation problem for the error term observations and when the error is distributed with general logistic distribution. The auto regression model is involved in the studying and analyzing of the relationship between the variables, and through this relationship, the forecasting is completed with the variables as values. A simulation technique is used for comparison methods depending

Scopus (1)
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Publication Date
Sat Jan 02 2021
Journal Name
Journal Of The College Of Languages (jcl)
Methods of computer word formation in the modern Russian language: Способы словообразования в сфере компьютерных неологизмов в современном русском языке
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This paper discusses the study of computer Russian language neologisms. Problems of studying computer terminology are constantly aggravated by the processes of computer technology that is introduced to all walks of life. The study identifies ways of word formation: the origin of the computer terms and the possibility of their usage in Russian language. The Internet is considered a worldwide tool of communication used extensively by students, housewives and professionals as well The Internet is a heterogeneous environment consisting of various hardware and software configurations that need to be configured to support the languages used. The development of Internet content and services is essential for expanding Internet usage. Some of the

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Crossref
Publication Date
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
A comparative study between conventional methods and Vidas UP Salmonella (SPT) to investigate salmonella species from local and imported meat
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The study was preformed for investigating of Salmonella from meat, and compared Vidas UP Salmonella (SPT) with the traditional methods of isolation for Salmonella , were examined 42 meat samples (Beef and Chicken) from the Local and Imported From local markets in the city of Baghdad from period December 2013 -February 2014 the samples were cultured on enrichment and differential media and examined samples Vidas, and confirmed of isolates by cultivation chromgenic agar, biochemical tests ,Api20 E systeme , In addition serological tests , and the serotypes determinate in the Central Public Health Laboratory / National Institute of Salmonella The results showed the contamination in imported meat was more than in the local meat 11.9% and 2

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Publication Date
Tue Mar 27 2018
Journal Name
Mustansiria Dental Journal
The Effect of Modified Carisolv Gel on Surface Roughness of two Different Types of Ceramic Materials Using Light Polarizing Microscope
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This in vitro study evaluated the influence of chemomechanical caries removal solution on the surface topography of metal-ceramic feldspar porcelain (MAJOR ceramic) and All-ceramic feldspar porcelain (Vita Alpha) using light polarizing microscope. Forty specimens of MAJOR ceramic and forty specimens of Vita Alpha ceramic of (12mm diameter & 3mm height) were prepared .All specimens were polished with silicon polishing burs, cleaned, autoglazed and stored in 37°C before exposure to Carisolv. Thirty specimens of each material randomly exposed to Carisolv gel for 5, 10 and 20 minutes respectively, other ten specimens were not, to act as control group. All specimens were subjected to surface roughness test by profilometer and evalua

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Publication Date
Sat Oct 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
ORGANIZATIONAL VALUES AND ITS IMPACT ON STRATEGIC PERFORMANCE A field study a comparison between Two Universities of Baghdad & Al-Nahrain
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ABSTRACT

     The researcher seeks to shed light on the relationship analysis and the impact between organizational values in all its dimensions (Administration Management, Mission, relationship management, environmental management) and strategic performance (financial perspective, customer perspective, the perspective of internal processes, learning and development) in the presidency of Two Universities of Baghdad & Al-Nahrain, it has been formulating three hypotheses for this purpose.

      The main research problem has been the following question: Is there a relationship and the impact of bet

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Publication Date
Wed Jan 01 2020
Journal Name
Plant Archives J.
Evaluation of the performance of triple, single crosses and their inbred in bred lines of maize under two plant population
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Scopus (2)
Scopus
Publication Date
Sun Jun 04 2017
Journal Name
Baghdad Science Journal
Evaluation of Air Pollution Tolerance Index (APTI) by two species of terrestrial plants in some stations within Babylon Province, Iraq
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This study deals with air pollution tolerance index (APTI) and anatomical variation in leaves of two species of terrestrial plants Ficus sp. and Conocarpus sp. that have bee commonly the separated along roadsides in many stations within Babylon province. APTI values of both species were less than 10 during study period which represented sensitivity of these plants to air pollution. There are Anatomical responses to pollution in the leaves of both studied species. Main adaptations included increased thickness of parenchyma cell walls with clear dark deposits in sections of Ficus sp. from sections of stations 2 and 4 which represent polluted stations. Conocarpus sp. main adaptation included stomata increased in density and decreased in size w

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Publication Date
Tue Jun 03 2025
Journal Name
Journal Of Umm Al-qura University For Applied Sciences
Application of Benesi–Hildebrand and Tauc approaches of new synthesized Schiff bases interacted with two types of electron acceptors modules
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This study has three parts, the first one is the synthesis of a novel Schiff bases by the condensation of guanine or 9-[{2-hydroxyethoxy}methyl]-9H-guanine with variety aldehydes to yield four different bases as follows: (E)-2-((4-nitrobenzylidene)amino)-1,9-dihydro-6H-purin-6-one (S1), (E)-2-((4-methoxybenzylidene)amino)-1,9-dihydro-6H-purin-6-one (S2), (E)-2-((2-hydroxybenzylidene) amino)-9-((2-hydroxy ethoxy)methyl)-1,9-dihydro-6H-purin-6-one (S3), and (E)-2-(((9-((2-hydroxy ethoxy)methyl)-6-oxo-6,9-dihydro-1H-purin-2-yl)imino)methyl)benzoic acid (S4). Then, spectroscopic analyses such as Elemental Analysis, UV/VIS, Mass spectra, FTIR, 1H,13C-NMR were made to recognize these bases. In the second part, the ability of synthesized bases to

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Publication Date
Wed Aug 31 2022
Journal Name
Al-kindy College Medical Journal
Efficiency and Safety of Desferioxamine Chelation Therapy in Paediatric Patients with Transfusion-Dependent Anaemia: Experience of two Centres from Sudan
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Background: Repeated blood transfusion   is   the main   therapeutic option for transfusion-dependent anaemias with consequent iron overload and organ damage .Therefore iron chelating agents are important protective measures for these patients. The aim of this study was  to investigate  the efficiency and safety of Desferroxamine  in paediatrics population subjected  to iron overload as a consequence  of repeated transfusion in a group of  Sudanese children  

Subjects & Methods: This was a descriptive cross-sectional hospital based study.  Conducted in two main paediatric reference hospitals   in, Su

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Crossref (1)
Crossref
Publication Date
Sat Jul 01 2023
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The market value between the two dilemmas of profit distribution and retention: an analytical study in the Iraqi stock market
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Abstract:

             The distribution or retention of profits is the third decision among financial management decisions in terms of priority, whether at the level of theory or practice, as the issue of distribution or retention is multi-party in terms of influence and impact, as determining the optimal percentage for each component is still the subject of intellectual debate because these decisions are linked to the future of the organization and several considerations, The research focus on the nature of the policies followed by the Iraqi banking sector As the sample chosen by the intentional sampling method was represented by the Commercial Bank of

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