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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
Thu May 31 2018
Journal Name
International Journal Of Control And Automation
Power Flow Control of Iraqi International Super Grid with Two-Terminal HVDC Techniques Using PSS/E
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Publication Date
Mon Dec 25 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Impact of Two Doses of Vitamin K2 (Menaquinone-7) on Doxorubicin-Induced Hepatotoxicity in Rats
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The objective of this study was to evaluate the impact two doses of Menaquinones-7 on hepatotoxicity induced by doxorubicin in rats. Sixty adult rats of both sexes were used in this study; the animals were randomly enrolled into six groups of 10 animals each. Group I: negative control (rats administered distilled water); Group II: Menaquinones-7 at a dose of  16 µg/kg; Group III: Menaquinones-7 at a dose of 48 µg/kg; Group IV: positive control (Doxorubicin 15 mg/kg); Group V: Menaquinones-7 at a dose of 16 µg/kg administered prior to a single dose of Doxorubicin 15 mg/kg; Group VI: Menaquinones-7 at a dose of 48 µg/kg administered prior to a single dose of  Doxorubicin 15 mg/kg. On day twelve of the study, blood was

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Publication Date
Sun Apr 30 2023
Journal Name
Sabrao Journal Of Breeding And Genetics
STUDY OF THE GENETIC DIVERSITY OF SOME GENOTYPES OF MAIZE UNDER TWO LEVELS OF NITROGEN FERTILIZATION
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The present study aimed to determine the genetic divergence of seven maize genotypes (Al-Maha, Sumer, Al-Fajr, Baghdad, 5018, 4 × 1 single hybrid, and 4 × 2 single hybrid) under two varied levels of nitrogen fertilization (92 and 276 kg N ha-1). The experiment occurred in 2022 in a randomized complete block design (RCBD) with a split-plot arrangement and three replications at the College of Agricultural Engineering Sciences, University of Baghdad, Iraq. The nitrogen fertilization levels served as main plots, with the maize genotypes allocated as the subplots. The results revealed that genetic variance was higher than the environmental variance for most traits, and the coefficient of phenotypic variation was close to the genetic va

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Publication Date
Fri Jan 01 2016
Journal Name
Aip Conference Proceedings
Analysis of performance measures with single channel fuzzy queues under two class by using ranking method
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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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Publication Date
Sun Dec 31 2023
Journal Name
Biomedical And Pharmacology Journal
Extraction, Isolation and Structure Elucidation of Two Phenolic Acids from Aerial Parts of Celery and Coriander
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Celery and coriander are vastly applied in modern medicine and traditionally because various medicinal and nutritional benefits depend on their medicinal characteristics. The study aimed to detect, isolate and compare extracts contents of phenolic acids (caffeic and p-coumaric acids) in ethyl acetate fraction of fresh and dry aerial parts of coriander (Coriandrum sativum L.) and celery (Apium graveolens L.) of the Apiaceae family. The extraction of these constituents was carried out by maceration method using 70% ethanol and fractionation was done by using petroleum ether, and ethyl acetate. The existence of caffeic and p-coumaric acids in aerial part extracts of two plants was identified by thin-layer chromatography (TLC) and high-

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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 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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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Oral Medicine And Oral Surgery
Reliability of two difficulty indexes in predicting the surgical extraction difficulty of impacted mandibular third molars
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Introduction: The aim of this study was to compare the reliability and the agreement of the Pederson and Pernambuco difficulty indexes in predicting the surgical extraction difficulty of the impacted mandibular third molars. Materials and methods: A prospective observational cohort study was conducted on 83 patients who had undergone surgical removal of impacted mandibular third molar. The difficulty of extraction was determined preoperatively according to the total scores obtained from the Pederson and Pernambuco difficulty indexes, the operative difficulty was determined by the surgical technique and the duration of extraction. The accuracy of prediction of the surgical difficulty and

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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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