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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
Mon Jan 29 2024
Journal Name
Eximia
The cognitive and educational importance of the academic teacher for developing the applied skills of third-stage female students in the subject of teaching methods from their point of view
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The research aimed to prepare a measure of the importance of enlightenment, academic education, and applied skills for third-stage female students, including teaching methods from their point of view/College of Education and Sports Sciences/University of Baghdad/Al-Jadriyah. The researchers used descriptive description in the comprehensive research procedures, an appropriate methodology in achieving the research objectives, sufficient for interpretations, how important is the academic teacher’s knowledge of teaching methods for student learning, what are the roles that the learners have acquired from the academic teacher. The scale of importance and horror consists of 15 items. The research population includes female students of t

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Publication Date
Mon Jan 29 2024
Journal Name
Eximia
The cognitive and educational importance of the academic teacher for developing the applied skills of third-stage female students in the subject of teaching methods from their point of view
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The research aimed to prepare a measure of the importance of enlightenment, academic education, and applied skills for third-stage female students, including teaching methods from their point of view/College of Education and Sports Sciences/University of Baghdad/Al-Jadriyah. The researchers used descriptive description in the comprehensive research procedures, an appropriate methodology in achieving the research objectives, sufficient for interpretations, how important is the academic teacher’s knowledge of teaching methods for student learning, what are the roles that the learners have acquired from the academic teacher. The scale of importance and horror consists of 15 items. The research population includes female students of t

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Publication Date
Wed Jun 30 2021
Journal Name
Modern Sport
The impact of the question network strategy in accordance with mental capacity in the strength of cognitive control in the subject of teaching methods of sports education for undergraduate students
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The study aimed at identifying the mental capacity of the research sample and classifying them for the purposes of the study, preparing the scale of cognitive control of the subject of teaching methods of sports education, preparing educational units by establishing the question network for the subject of the teaching methods of sports education, and adopting the experimental method by experimental design workers (2×2) for the two groups The limits of the research community are represented by third-stage students of the Department of Physical Education and Sports Science in the morning study of the College of Knowledge, the Community University, which continues in the regular working hours of the year (2019-2020) adult Their number

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Publication Date
Sun Mar 01 2009
Journal Name
Journal Of Economics And Administrative Sciences
Study of direct marketing methods and identificationThe suitability of each of them for application in the Iraqi marketAn analytical study of the views of a sample of wholesalers in Baghdad
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Study of Direct Marketing techniques and determining the scope of the suitability of each of them in the application in the Iraqi market - An analytical and explorative study for sample of views for wholesaler in Baghdad. The essential idea of the research is to go into the most important concepts which have been mentioned in the direct marketing and determining its current and most important techniques and knowing the scope of applying these techniques in Baghdad main markets (Karrada, Jamilah, shorja, Baya area, zeyouna and new Baghdad) and which of those techniques most applicable in these markets. The research took a sample of (100) wholesalers who practice the activities of selling nutritional items, auto and outs spare part

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Publication Date
Wed Oct 10 2018
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
TWO NEW RECORDS OF DWARF SNAKES OF THE GENUS EIRENIS JAN, (REPTTILIA, COLUBRIDAE) IN IRAQI KURDISTAN (NORTH AND NORTHEASTERN OF IRAQ) WITH ANNOTATED CHECKLIST, FOR THE GENUS EIRENIS IN IRAQ
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    Two dwarf snakes were discovered, Eirenis thospitis Schmidtler & Lanza from Sereen mountain, north east of Arbil  and E. rothii Jan from Saffin mountain North of Arbil  city  North of Iraqi Kurdistan. Supported by description and important notes on variation. In addition summarized list for 9 species of the genus Eirenis Jan in Iraq is also presented.  

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Publication Date
Sat Oct 01 2022
Journal Name
Al–bahith Al–a'alami
METHODS OF MEASURING THE LEVEL OF COMMUNICATION EFFICIENCY IN NEWS HEADLINES: (Drawn from the doctoral thesis)
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Measuring the level of communicative competence in news headlines and the level of stylistic and semantic processing in its formulation requires creating a quantitative scale based on the bases on building the scales and their standards. As judging by scientific of journalism studies lies in the possibility of quantifying the journalistic knowledge, i.e. the ability of this knowledge to shift from qualitative language to its equivalent in the language of numbers.

News headlines and editorial processing are one of the journalistic knowledges that should be studied, analyzed stylistically and semantically; their conclusions drawn and expressed in numbers. Press knowledge is divided into two types:<

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Publication Date
Fri Oct 28 2022
Journal Name
Political Sciences Journal
The Difficulties of Teaching Political Science Research Methods: A Comparative Study between Western and Arab Universities
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This research aims to identify the reality of teaching political science research methods curriculum, to observe practices, and differences in teaching and learning between the Arab and Western universities. Moreover, it focuses on the difficulties that face students' acquisition of the course skills. The research uses the course model of some Western and Arab universities as case study.

This research shows that the curriculum do not reach yet the final form as other political science curriculums, and its upcoming changes will reflect the needs of stakeholders. The best method to teach this curriculum is to use applied learning in groups, learning by doing, and finally problem-based learning approach. Using optimal assessment deep

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Publication Date
Wed Oct 17 2018
Journal Name
Journal Of Economics And Administrative Sciences
Comparison Between the Methods Estimate Nonparametric and Semiparametric Transfer Function Model in Time Series Using Simulation
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Publication Date
Sat Dec 01 2012
Journal Name
Annals Of Agricultural Sciences
Water use efficiency of potato (Solanum tuberosum L.) under different irrigation methods and potassium fertilizer rates
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Publication Date
Sat Aug 01 2020
Journal Name
Iop Conference Series: Materials Science And Engineering
Comparison of Single and Group Jet Grout Columns Settlement Based on Field Test and Theoretical Methods
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Abstract<p>The settlement evaluation for the jet grouted columns (JGC) in soft soils is a problematic matter, because it is influenced by the number of aspects such as soil type, effect mixture between soil and grouting materials, nozzle energy, jet grouting, water flow rate, rotation and lifting speed. Most methods of design the jet-grouting column based on experience. In this study, a prototype single and group jet grouting models (single, 1*2, and 2*2) with the total length and diameter were (2000 and 150 mm) respectively and clear spacing (3D) has been constructed in soft clay and subjected to vertical axial loads. Furthermore, different theoretical methods have been used for the estimation </p> ... Show More
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