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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 Feb 10 2019
Journal Name
Journal Of The College Of Education For Women
Features of wisdom and methods in the approach of Imam Hassan al-Askari (Peace Be upon Him)
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Wisdom is the separation and distinction between aim in the word and work and the lack thereof in accordance with the knowledge surrounding the arts of science, which reached a thorough understanding of things and put them in the quorum. In this research, I have tried to discern the characteristics of the wisdom of Imam Hassan al-Askari (peace be upon him) and to explain his methods and actions which are indicative of the various facets of wisdom required by the nature of the actions and behavior that he has to deal with. Or future mother.
The second topic was devoted to the style of Imam (p) and his wisdom in the situations that necessitated the diversity of methods of dealing such as the method of concealment and the method of refer

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Publication Date
Tue Dec 15 2020
Journal Name
Al-academy
Methods of Acting Performance and Watching Industry in Street Theatre- Play (Sold) - A Model: بهاء زهير كاظم
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  The audience is one of the important practical elements in the theatrical show and its importance is not confined to its static activity as a receiver element only, rather it went beyond that issue as an effective and influential element in the proceedings of the show and the process of meaning construction, that it gains an active role in the construction and production of the connotation that influences and is influenced by the actor, where the communication channels are open between the two sides, consequently a kind of watching and joint interaction happens between them. Thus, it has become necessary for the actor to create a suitable environment for the onlookers in order for it to be an essential part of the show system. The

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Publication Date
Tue Oct 23 2018
Journal Name
Journal Of Economics And Administrative Sciences
Processing of missing values in survey data using Principal Component Analysis and probabilistic Principal Component Analysis methods
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The idea of ​​carrying out research on incomplete data came from the circumstances of our dear country and the horrors of war, which resulted in the missing of many important data and in all aspects of economic, natural, health, scientific life, etc.,. The reasons for the missing are different, including what is outside the will of the concerned or be the will of the concerned, which is planned for that because of the cost or risk or because of the lack of possibilities for inspection. The missing data in this study were processed using Principal Component  Analysis and self-organizing map methods using simulation. The variables of child health and variables affecting children's health were taken into account: breastfeed

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Publication Date
Thu Oct 08 2026
Journal Name
Al–bahith Al–a'alami
New Methods and Old Issues: Theoretical and Methodological Approaches to Social Network Sites in the Arab Region
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This paper critically looks at the studies that investigated the Social Network Sites in the Arab region asking whether they made a practical addition to the field of information and communication sciences or not. The study tried to lift the ambiguity of the variety of names, as well as the most important theoretical and methodological approaches used by these studies highlighting its scientific limitations. The research discussed the most important concepts used by these studies such as Interactivity, Citizen Journalism, Public Sphere, and Social Capital and showed the problems of using them because each concept comes out of a specific view to these websites. The importation of these concepts from a cultural and social context to an Ara

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Publication Date
Thu Aug 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Development of methods of treatment of medical waste in the hospitals of Baghdad health Department / (Rusafa survey)
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Purpose: To contribute to the development of an appropriate program for the management of medical waste based on clear-cut principles in order to reach the overall goal of improving the public health and environment of the population in our country.

Design / Approach / Introduction: The research is based on the analytical descriptive approach as a method of study in the field of data collection using a check list and analysis of the data through the use of some statistical treatments.

 Results: The need is to establish a medical waste management in hospitals and follow international standards in all stages of waste management from sorting, collection, transportation and treat

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Publication Date
Wed Dec 18 2019
Journal Name
Baghdad Science Journal
Molecular and Immunological Methods to Confirm Toxiginicity (Microcystin Production) of Westiellopsis Prolifica Isolated from Tigris River – Iraq
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Several toxigenic cyanobacteria produce the cyanotoxin (microcystin). Being a health and environmental hazard, screening of water sources for the presence of microcystin is increasingly becoming a recommended environmental procedure in many countries of the world. This study was conducted to assess the ability of freshwater cyanobacterial species Westiellopsis prolifica to produce microcystins in Iraqi freshwaters via using molecular and immunological tools. The toxigenicity of W. prolifica was compared via laboratory experiments with other dominant bloom-forming cyanobacteria isolated from the Tigris River: Microcystis aeruginosa, Chroococcus turigidus, Nostoc carneum, and Lyngbya sp. signifi

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Publication Date
Wed Jan 01 2025
Journal Name
Educational Process International Journal
The Role of Digital Educational Content in Eliminating Traditional Methods in the Educational Process within Iraqi Universities
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Publication Date
Sat May 30 2026
Journal Name
Microbes And Infectious Diseases
Reveal by genotyping and phenotyping methods of some Metallo- Beta Lactamases genes among environmental Klebsiella pneumoniae isolates
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Background: Since carbapenems are currently the preferred treatment for severe infections brought on by multidrug-resistant bacteria which can create Extended-Spectrum β-Lactamases (ESBLs), it is extremely concerning that Gram-negative bacteria are becoming resistant to carbapenem. It has been demonstrated that Klebsiella pneumoniae produces a beta-lactamase that hydrolyses the β-lactam ring in antibiotics, making it one of the few bacteria which are currently exhibiting a high value of resistance because of changing in the organism's core genome. Methods: For the current study, 50 samples were gathered from different water sources, and based on morphological and biochemical testing, 10 isolates were determined to be K. pneumoniae. Accord

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Publication Date
Sat Oct 01 2022
Journal Name
Journal Of Applied Geophysics
Predicting dynamic shear wave slowness from well logs using machine learning methods in the Mishrif Reservoir, Iraq
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Publication Date
Fri Jan 01 2021
Journal Name
Basra Journal Of Science
Effects of Thicknesses of Two Different Gate Insulators on the Performance of Pentacene Based Organic Field Effect Transistor
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In this paper, a simulation of the electrical performance for Pentacene-based top-contact bottom-gate (TCBG) Organic Field-Effect Transistors (OFET) model with Polymethyl methacrylate (PMMA) and silicon nitride (Si3N4) as gate dielectrics was studied. The effects of gate dielectrics thickness on the device performance were investigated. The thickness of the two gate dielectric materials was in the range of 100-200nm to maintain a large current density and stable performance. MATLAB simulation demonstrated for model simulation results in terms of output and transfer characteristics for drain current and the transconductance. The layer thickness of 200nm may result in gate leakage current points to the requirement of optimizing the t

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