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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 Feb 01 2022
Journal Name
Baghdad Science Journal
Impact of Culture Media Composition, Nutrients Stress and Gamma Radiation on Biomass and Lipid of the Green Microalga, Dictyochloropsis splendida as a Potential Feedstock for Biodiesel Production
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Biodiesel production from microalgae depends on the biomass and lipid production. Both biomass and lipid accumulation is controlled by several factors. The effect of various culture media (BG11, BBM, and Urea), nutrients stress [nitrogen (N), phosphorous (P), magnesium (Mg) and carbonate (CO3)] and gamma (γ) radiation on the growth and lipid accumulation of   Dictyochloropsis splendida were investigated. The highest biomass and lipid yield of D. splendida were achieved on BG11 medium. Cultivation of D. splendida in a medium containing 3000 mg L−1 N, or 160 mg L−1 P, or 113 mg L−1 Mg, or 20 mg L-1 CO3, led to enhanced growth rate. While u

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Publication Date
Fri Sep 24 2021
Journal Name
Journal Of The College Of Education For Women
Arabic Language Teachers’ Training Needs for Implementing Cognitive Trips Strategy when Teaching Arabic Language Courses in the Kingdom of Saudi Arabia: أمل ناصر الحربي, و وفاء العويضي
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The present work focuses on examining the strategy of cognitive trips and the Arabic language teachers’ training needs of such a strategy when teaching Arabic language courses in the Saudi Arabia Kingdom. To achieve the objective of the study, and check whether this strategy is used in lesson planning, lesson teaching, or lesson assessment, a descriptive approach and a questionnaire have been adopted. The researchers used a number of statistical tools, and chose a purposive sample, which consists of (58) Arabic language teachers from Saudi Arabia Kingdom. Results have shown that the training needs of Arabic language teachers for implemining the strategy of cognitive journeys while teaching Arabic language courses came in the following

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Publication Date
Tue Aug 03 2021
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Measurement and accounting disclosure for small and medium-sized enterprises according to the International Financial Reporting Standard (SMEs) and its reflection on the fairness of financial statements.
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The research aims to identify small and medium enterprises in accounting thought in terms of definition and concept, and this international financial reporting standard for small and medium-sized enterprises (SMEs) in the theoretical aspect. As for the practical aspect, the small and medium-sized enterprises standard has been applied to the financial statements of the company in question, the preparation of the opening entry on the date of the transition, the requirements of measurement and the accounting disclosure on the date following the application of the standard, and the preparation of the company's financial statements and the accompanying explanations according to the standard of small and medium-sized enterprises. The r

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Publication Date
Sat Jan 11 2025
Journal Name
Revista Iberoamericana De Psicología Del Ejercicio Y El Deporte, Issn 1886-8576, Vol. 17, Nº. 6, 2022, Págs. 402-404
The Effect Exercises Of Stretching Featured Strength On Special Flexibility, Insulin Hormone, And The Achievement Of The Snatch, Clean And Jerk Lifts For Advanced Lifters, Baghdad Clubs
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Autorías: Ghassan Adeeb Abdulhasan, Rasha Raed Hamid Hameed, Hussein Jabber Abood. Localización: Revista iberoamericana de psicología del ejercicio y el deporte. Nº. 6, 2022. Artículo de Revista en Dialnet.

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Scopus
Publication Date
Sat Jan 11 2025
Journal Name
Journal Of Physical Education
The Effect of Exercises Using Maximum Strength Assisting Training Apparatus On Some Working Muscles' Electric Activity During Bench Press For Physical Strength Athletes Of Baghdad Clubs
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Publication Date
Tue Nov 09 2021
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Strategic leadership and its role in achieving competitiveness in industrial establishments": "A field study in Bashir Al-Siksik & Co. for the manufacture of sanitary and plastic tools
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This study aims to know the role of strategic leadership to achieving competitiveness in industrial establishments by identifying the respondents’ perceptions about the level of availability of dimensions of leadership strategies (creativity and innovation, risk tolerance, available opportunities) in Bashir Al-Siksek & Partners Company for the manufacture of sanitary and plastic ware in Gaza strip

To achieve this, a questionnaire was developed and distributed to a sample of managers, auditors, accountants, and administrative employees in the study sample company. The questionnaire tool was distributed to 60 employees and employees, of which (52) were retrieved, or 86.6%, and (8) were excluded for la

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Publication Date
Sat Jan 11 2025
Journal Name
Journal Of Baghdad College Of Dentistry
A Clinical Method for Prediction of Alveolar Bone Mineral Density in the Area between the Second Premolar and First Molar in Iraqi Adults with Class I Occlusion
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Background: Orthodontic mini-implants are increasingly used in orthodontics and the bone density is a very important factor in stabilization and success of mini-implant. The aim of this study was to observe the relationship among maximum bite force (MBF); body mass index (BMI); face width, height and type; and bone density in an attempt to predict bone density from these variables to eliminate the need for CT scan which have a highly hazard on patient. Materials and Methods: Computed tomographic (CT) images were obtained for 70 patients (24 males and 46 females) with age range 18-30 years. The maxillary and mandibular buccal cortical and cancellous bone densities were measured between 2nd premolar and 1st molar at two levels from the alveol

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Publication Date
Mon Jan 01 2018
Journal Name
Al–bahith Al–a'alami
The Role of TV Programs in Spreading the Culture of Community for Peace: Studying the Attitudes of the Publics towards a Program entitled Mosamih Kareem on YouTube
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The fundamental problem in determining the role of television programs in broadcasting the culture of community for peace through studying almosamig kareem program by studying the topics addressed in this program. It is a descriptive study and it follows the approach survey method.  In this study, the spatial framework is limited to the program of almosamih kareem on YouTube, while the temporal framework is concerned with the episodes that are raised on YouTube from the second half of 2014 to 2015 of almosamih kareem program. The fundamental problem in determining the role of television programs in broadcasting the culture of community for peace through studying almosamig kareem program by studying the topics addressed in this

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Crossref
Publication Date
Tue Sep 28 2021
Journal Name
Journal Of The College Of Education For Women
Reasons for Lying in Kindergarten Children from the Kindergarten Teachers’ Point of View: A Comparative Study between Males and Females: سجلاء فائق هاشم , كلثوم عبد عون ردام
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Lying is considered a dangerous tendency among children if it has become a habit. It results in many social problems, such as child’s loss of confidence, lack of others’ respect to him, and his lack of respect to the desired values ​​of the society, such as honesty and trust. Consequently, he will be led to a deviation when he becomes old; especially if the child’s socially unaccepted behavior has not been directed. The research, thus, aims to examine the causes of lying in the most important stage of children’s life; that is, between (4-6) years. Such an aim helps to know about the individual reasons of lying among males and females from teachers’ perspectives. To meet the objective of the study, a number of (128) children

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Publication Date
Tue Jun 11 2019
Journal Name
Al-kindy College Medical Journal
Evaluation of Application of Nutritional Status Assessment for Children Under 5 years by Using IMCI Program in a Sample of Primary Health Care Centers in Baghdad City
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Background: World Health Organization (WHO) and United Nation International Children Fund (UNICEF) developed a strategy known as Integrated Management of Childhood Illness (IMCI); which aims to reduce less than five years children morbidity and mortality in developing countries.

Objective: To assess the completion of the IMCI format status in primary health care centers, Baghdad.

Methods:  A cross sectional study with analytic element was conducted during the period from 15th  of January till 15th  May 2016 in selected Primary health centers in Baghdad, Iraq. The sample consists of form of child files less than 2 months and form from 2

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