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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 Jun 30 2019
Journal Name
College Of Islamic Sciences
Two Poets Alandaluian Abu Al Makshi and His Douter Hasana
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Andalusian literature is a literature in itself that is influenced and influenced, and it did not come out of thin air. Muslim Arabs came from the East to this country for jihad and a desire to live, and they carried with them their beliefs, customs and traditions. They must blend in the new element and its environment, so interference, fusion, diversity and influence actually took place.
It seems to us that the Arabs in the era of the governors in Andalusia (92-138 AH) strived hard to preserve everything that is Eastern. Literature is an oriental model in the content of prose and poetry, but in the era of the Umayyad emirate, we will notice that the environment, the development of ages, and the mixing of civilizations have an effect

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Publication Date
Sat Jan 01 2022
Journal Name
Latin American Journal Of Solids And Structures
Peak Ground Acceleration Models Predictions Utilizing Two Metaheuristic Optimization Techniques
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Crossref (21)
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Publication Date
Sat Jan 01 2022
Journal Name
Latin American Journal Of Solids And Structures
Peak Ground Acceleration Models Predictions Utilizing Two Metaheuristic Optimization Techniques
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Publication Date
Mon Apr 01 2019
Journal Name
Journal Of Engineering
Two Stage Evaporative Cooling of Residential Building Using Geothermal Energy
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The weather of Iraq has longer summer season compared with other countries. The ambient temperature during this season reaches over 50 OC which makes the evaporative cooling system suitable for this climate. In present work, the two-stage evaporative cooling system is studied. The first stage is indirect evaporative cooling (IEC) represented by two heat exchangers with the groundwater flow rate (5 L/min). The second stage is direct evaporative cooling (DEC) which represents three pads with groundwater flow rates of (4.5 L/min). The experimental work was conducted in July, August, September, and October in Baghdad. Results showed that overall evaporative efficiency of the system (two coils with three pads each

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Publication Date
Fri Mar 01 2019
Journal Name
Al-khwarizmi Engineering Journal
MINIATURE TWO-FINGERED ROBOT HAND DRIVEN BY MUSCLE WIRES ACTUATORS
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In this research, a modified artificial hand with direct control has been designed using electrical artificial muscle wires that receive direct sensory impulses through human hand instead of using the mechanical action to open and close this artificial hand. Each finger is designed as a chain and its movements achieved through the conventional arrangement control of the electrical muscles wires. The results indicate that it is possible to design an artificial hand using electrical muscle wire for control it with high accuracy.

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Publication Date
Mon Feb 04 2019
Journal Name
Journal Of The College Of Education For Women
The Historical Value of Dickens’s A Tale of Two Cities
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In "historical" fiction, characters that never really existed, give expression to the impact of historical events on the people who really did live through them. The result is not history, as an accurate record of actual events, but fiction in which an earlier age is rendered through the personal joys and sufferings of characters. This paper
aims at investigating the historical realities presented in Dickens’s A Tale of Two Cities.

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Publication Date
Mon Jul 01 2019
Journal Name
Applied Mathematical Modelling
Potential flow of fluid from an elevated, two-dimensional source
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Publication Date
Sun Mar 04 2018
Journal Name
Baghdad Science Journal
Biodegradation of Anthracene Compound by Two Species of Filamentous Fungi
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Isolation and identification fungi of Emericella nidulans and Aspergillus flavus from a pinkish and yellowish artificial clay, by using potato dextrose agar (PDA). Results revealed that E. nidulans was the best for degrading anthracene (92.3%) with maximum biomass production (3.7gm/l), compared to A. flavus with the rate of degradation (89%) and biomass production of (1.2gm/l), when methylene blue was used as redox indicator after incubating in a shaker incubator 120rpm at 30Co for 8days. Results indicated that E. nidulans has a high ability of anthracene degradation with the rate of (84%), while A. flavus showed the lower level with (77%) by using HPLC.

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Publication Date
Sun Mar 13 2011
Journal Name
Baghdad Science Journal
Comparison study between two different Environment areas regarding diarrhea causes.
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This study Achieved to search form the infections by Cholera and Diarrhea in two different areas from the side of Cultural, Social, Economical and Environmental field in Baghdad governorate, during a period from 3/10 – 3/12/2007.these were in Obiady city and Palestine street. This study included groups of patients who went to the Kindy Hospital lab. The researcher use a sample of (300) persons of different ages with range (150) persons in each city from the study city, in this study show a great different in the percentage of infection by parasites, helminthes, viruses, bacteria and vibrio cholera in the two city according to age groups, reach upper percentage by infection in age (1-10) years in Obiady city with percent (57.5 %) wh

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Publication Date
Mon May 04 2009
Journal Name
Journal Of Al-nahrain University
Solution of two-dimensional fractional order volterra integro-differential equations
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In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

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