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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.

Crossref
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Publication Date
Sun Jul 01 2001
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
SURVEY ON THE PREVALENCE OF INTESTINAL PARASITES AMONG ORPHAN CHILDREN INHABIT TWO STATEHOMES IN BAGHDAD CITY
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230 stool samples were collected from 2 state homes for (males and females) to investigate
the infection of different intestinal parasites (pathogenic and non-pathogenic).
The infection rate was higher among males 15.7% than females 6%, these rates were
increased when concentration method was employed up to 54.8% for males and 8.7% for
females significantly.
Most infected orphans were found to harbor single parasite followed by double, triple
parasites.
The highest rate of infection was found among young age group (1-5) years old, while
the older age groups got lowest rates.
Of helminthes, the commonest parasite was Hymenolepis nana 5.7% and of protozoa, the
commonest intestinal parasite was Giardia lamblia

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Publication Date
Tue Oct 09 2018
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
THIRTY TWO ALGAE NEW RECORDS REPORTED IN PONDS AT GWER SUB-DISTRICT, ERBIL -KURDISTAN REGION, IRAQ
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    This study was carried out from February to October 2012 in six semi salty ponds in Gwer sub-district which is the first work in the area. A total of 32 species and 2 genera of algae where reported as the new records. Mostly the non diatoms are belonging to Cyanophyta, Chlorophyta, Euglenophyta, Cryptophyta, Chrysophyceae, while diatoms or Bacilariophyceae are belong to pennals- order.

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Publication Date
Sun May 08 2022
Journal Name
Al-kindy College Medical Journal
Two Decades in the Journey of Al-Kindy College Medical Journal: Key Barriers, Achievements, and Prospects
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Apart from graduating five-star doctors, a particular medical college has the mission to motivate and offer researchers the opportunity to publish high-quality researches on various health problems and disseminate updated medical knowledge to a wide range of local and international readers. This could be accomplished by establishing a medical journal and releasing issues regularly

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Crossref
Publication Date
Mon Feb 10 2025
Journal Name
Journal Of Optics
Implementing quantum key distribution based on coincidence detection captured from two different single photon detection modules
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Quantum key distribution (QKD) provides unconditional security in theory. However, practical QKD systems face challenges in maximizing the secure key rate and extending transmission distances. In this paper, we introduce a comparative study of the BB84 protocol using coincidence detection with two different quantum channels: a free space and underwater quantum channels. A simulated seawater was used as an example for underwater quantum channel. Different single photon detection modules were used on Bob’s side to capture the coincidence counts. Results showed that increasing the mean photon number generally leads to a higher rate of coincidence detection and therefore higher possibility of increasing the secure key rate. The secure key rat

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Publication Date
Tue Jan 28 2014
Journal Name
Journal Of Energy And Power Engineering
Comparison between Two Vertical Enclosures Filled With Porous Media under the Effect of Radiation and Magnetohydrodynamics
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Crossref
Publication Date
Wed Jan 01 2014
Journal Name
Journal Of Thi – Qar Science
Enhanced of the Two photon Absorption in Nanostructure Wide Band gap Semiconductor CdS using femtosecond Laser
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We observed strong nonlinear absorption in the CdS nanoparticles of dimension in the range 50-100 nm when irradiant with femtosecond pulsed laser at 800 nm and 120 GW/cm 2 irradiance intensity. The repetition rate and average power were 250 kHz and

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Publication Date
Sun Oct 01 2017
Journal Name
Journal Of Economics And Administrative Sciences
Analysis the context of Uncertainty (Nature and management) under two school of strategic thinking (theoretical perspective
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Purpose: studying and analyzing the nature of uncertainty as part of strategy formulation, through analyzing the uncertainty faced by managers in the modern business environment characterized by high complexity and dynamism, though developing of an idea about the uncertainty cases and how enable the mind to understand these cases.

Methodology: It was the use of inductive and analytical approach, in order to study the accumulation of knowledge towards development areas that could contribute to strengthening the strategy formulation.

Findings: Mentoring the future will not make the success for business organization but thought business organization ability to developing share mental

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Crossref
Publication Date
Sun Mar 07 2010
Journal Name
Baghdad Science Journal
Study of the Singlet and the Triplet States of Two ElectronSystems in the First Excited State
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A study of the singlet and triplet states of two electron systems in the first excited state was performed using a simple quantum mechanical model, which assigns the 1s,and 2s orbital with two different variational parameters. Our results agree with a high level calculation used by Snow and Bills.

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Crossref
Publication Date
Mon Mar 25 2019
Journal Name
Al-academy
Time in the Cinema...The Two Films (The Knife and The Deceived) -A Model: كريمة ناوي
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This study deals with the time property in the cinema through two films: (The Knife) directed by Khalid Hamada and (The Deceived) directed by Tawfiq Saleh. These two films were excerpted by the cinema from two novels of the Palestinian writer Ghassan Kanafani, the first is from the novel (What is Left for You) and the second is from the novel (Men in the Sun).  If the Palestinian novel has imposed its presence on the Arab creative scene through a group of novelists who took it upon themselves to communicate their cause to the world,   the Palestinian cinema has been far from being a purely Palestinian, because many of the cinematic works have been provided by Arab countries on the issue, while this cinema is still seeking

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Crossref
Publication Date
Tue Oct 08 2002
Journal Name
Iraqi Journal Of Laser
Study of Laser Propagation Parameters in the Underdense Plasma Region Using a Two Dimensional Simulation Code
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The propagation of laser beam in the underdense deuterium plasma has been studied via computer simulation using the fluid model. An appropriate computer code “HEATER” has been modified and is used for this purpose. The propagation is taken to be in a cylindrical symmetric medium. Different laser wavelengths (1 = 10.6 m, 2 = 1.06 m, and 3 = 0.53 m) with a Gaussian pulse type and 15 ns pulse widths have been considered. Absorption energy and laser flux have been calculated for different plasma and laser parameters. The absorbed laser energy showed maximum for  = 0.53 m. This high absorbitivity was inferred to the effect of the pondermotive force.

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