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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 Dec 09 2018
Journal Name
Baghdad Science Journal
A Comparative Efficiency Study of Two Adsorbent Materials to Remove Eosin Y Dye from Aqueous Solutions
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This study was done to find a cheap, available and ecofriendly materials that can remove eosin y dye from aqueous solutions by adsorption in this study, two adsorbent materials were used, the shells of fresh water clam (Cabicula fluminea) and walnut shells. To make a comparison between the two adsorbents, five experiments were conducted. First, the effects of the contact time, here the nut shell removed the dye quickly, while the C. flumina need more contact time to remove the dye. Second, the effects of adsorbent weight were examined. The nut shell was very promising and for all used adsorbent weight, the R% ranged from 94.87 to 99.29. However C. fluminea was less effective in removing the dye with R% ranged from 47.59 to 55.39. The thi

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Publication Date
Sun Mar 18 2018
Journal Name
Mustansiria Dental Journal
The Effect of Pepsi Cola Beverage on Surface Roughness of Two Composite Resins (In Vitro study)
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An acidic environment causes surface changes of resin composites. Filler particlesize and filler distribution also have a direct effect on these surface changes. This invitro study evaluated the influence of Pepsi Cola drink on the surface roughness ofComposan LCM and Composan Ceram over time. Sixteen disc shaped specimens(10mm diameter, 2mm thickness) of each resin composite were fabricated, therebyforming two groups (n= 8). Surface roughness (Ra) was analyzed after 24 hrs beforeexposure to beverage. The specimens were submitted to a five minutes immersion inPepsi Cola three times daily interrupted by immersion in deionized distilled water (37C˚). Surface roughness measurements were done at 10, 30, and 60 days intervals. Datawere

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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
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
Fri Mar 15 2019
Journal Name
Al-khwarizmi Engineering Journal
Experimental and Theoretical Study of the Energy Flow of a Two Stages Four Generators Adsorption Chiller
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This work is concerned with a two stages four beds adsorption chiller utilizing activated carbon-methanol adsorption pair that operates on six separated processes. The four beds that act as thermal compressors are powered by a low grade thermal energy in the form of hot water at a temperature range of 65 to 83 °C.  As well as, the water pumps and control cycle consume insignificant electrical power. This adsorption chiller consists of three water cycles. The first water cycle is the driven hot water cycle. The second cycle is the cold water cycle to cool the carbon, which adsorbs the methanol. Finally, the chilled water cycle that is used to overcome the building load. The theoretical results showed that average cycle cooling power

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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
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
Sun Jun 30 2013
Journal Name
Journal Of Madenat Alelem
Effect of Essential Oils Extracted from the Peels of Two Species of Citrus on Some Fungi
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This study investigated the effect of essential oils extracted from peel of Citrus limon and Citrus reticulata on two species of fungui: Penicillium expansum and Fusarium proliferatum and also effect of two fungicides: Hymexazol and Benomyl against this fungi. Results showed that the essential oils of C. limon inhibited the radial growth of P. expansum and F. proliferatum at concentration 4.5 and 5%, respectively. However, the essential oil of C. reticulate inhibited this growth at concentration 5.5 and 6%, respectively. Moreover, the two fungicides inhibited radial growth of this fungi. In conclusion, there is a positive relationship between the increasing of concentration and the percentage of inhibiting of radial growth of fungi.

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Publication Date
Wed Jul 27 2011
Journal Name
Molecules
Antioxidant Capacities and Total Phenolic Contents Increase with Gamma Irradiation in Two Types of Malaysian Honey
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Two types of monofloral Malaysian honey (Gelam and Nenas) were analyzed to determine their antioxidant activities and total phenolic and flavonoid contents, with and without gamma irradiation. Our results showed that both types of honey can scavenge free radicals and exhibit high antioxidant-reducing power; however, Gelam honey exhibited higher antioxidant activity (p < 0.05) than Nenas honey, which is in good correlation (r = 0.9899) with its phenolic contents. Interestingly, we also noted that both irradiated honeys have higher antioxidant activities and total phenolic and flavonoid contents compared to nonirradiated honeys by Folin-Ciocalteu and UV-spectrophotometry methods, respectively. However, HPLC analysis for phenolic co

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Publication Date
Thu May 01 2025
Journal Name
Egyptian Journal Of Histology
Comparative morphological and histological study of liver in two Iraqi mammals (Felis catus) and (Sciurus anomalus)
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Introduction: The mammals digestive system demonstrates various structural and functional adaptations to their diverse offeeding habits, and the digestive system representing a function link between food-seeking activities and energy conservationby allocating energy to different events.Aim of the Work: This study was aimed to compare the histological structure of the liver in the domestic cat ( F. catus) andCaucasian squirrel (S. anomalus), which differ in their feeding pattern.Materials and Methods: In the present study, ten adult animals were used including five of F. catus and five of S. Caucasian,Samples were obtained from local market in Baghdad . Samples fixed using formalin (10%) to prepare all specimens for thehistological study. Th

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