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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
Sat Sep 12 2020
Journal Name
Al-kindy College Medical Journal
Spectrum of central nervous system infections in neurosciences hospital in two years : a retrospective study
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Background :Infectious disorders in general have high morbidity and mortality.. CNS infections include many disorders like bacterial meningitis, tuberculous and other subacute and chronic meningitis, viral meningitis, cerebral abscess, spinal cord infections, and others.
Objective: To assess our locality about prevalence of CNS infections , to have more awareness regarding CNS infections, and to try to find the proper way to reduce their prevalence and to treat them in appropriate way.
Method :We revised the records of all the cases of CNS infections excluding cases of spinal cord infections who were admitted in the wards of neuroscience hospital over the previous two years ( from July/2010 to June 2012 ),those were 132 cases.Seaso

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Publication Date
Tue Oct 06 2026
Journal Name
Journal Of Baghdad College Of Dentistry
In vivo plaque count of Streptococcus Mutans around orthodontic brackets bonded with two different adhesives
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Background: The prevention of the enamel demineralization at the periphery of the brackets is a significant challenge to orthodontic professionals. The aim of this clinical study was to compare the Streptococcus mutants count in the plaque surrounding two orthodontic adhesive types, Fuji Ortho LC and Enlight (Ormco). Materials and methods: A total of 13 patients (7 male and 6 female) needing fixed orthodontic appliance therapy were participated. A split mouth technique was followed with appliances bonded by two orthodontic adhesive types, Fuji Ortho LC and Enlight (Ormco). Saliva was collected before placement of appliances (T0) and again at three weeks (T1) and six weeks (T2) after placement of appliances. Plaque was collected from areas a

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Publication Date
Thu Feb 07 2019
Journal Name
Iraqi Journal Of Laser
Design and Comparative Study of a one and Two Stage Blumlein Circuit TEA Nitrogen Laser
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Two Prototypes of Transversely Excited at atmospheric pressure (TEA) Nitrogen laser systems (One Stage Blumlein Circuit and Two Stage Blumlein Circuit) were fabricated and operated. High voltage power supply with variable operating voltage (0-20 kv) and operating current (1-3A) was built and tested successfully. The gas flow rate of 15 L/ min and 10 L/ min for OSBC and TSBC was used. The performance of the fabricated systems was studied extensively reaching to the optimum operating conditions. The obtained laser output energy for the first system has linear relationship with the applied voltage. The maximum output energy was about (1.14 mJ) with (10.40) ns pulse duration and the half-wave divergence angle was about (0.1455 m rad). In the

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Publication Date
Fri Sep 30 2016
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Parameters Affecting the Thermodynamic Efficiency of PEM Single Cell and Stack of Cells (Two Cells)
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In this work, thermodynamic efficiency of individual cell and stack of cells (two cells) has been computed by studying the variation of voltage produced during an operation time of 30 min as a result of the affected parameters:- stoichiometric feed ratio, flow field design on single cell and feed distribution on stack of cells. The experiments were carried out by using two cells, one with serpentine flow field and the other with spiral flow field. These cells were fed with hydrogen and oxygen at low volumetric flow rates from 1 to 2 ml/sec and stoichiometric ratios of fuel (H2) to oxidant (O2) as 1:2, 1:1 and 2:1 respectively. The results showed that

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Publication Date
Fri Apr 01 2022
Journal Name
Baghdad Science Journal
Comparison of Protein Concentration in Red and White Muscles in Two Species of Bony Fish
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The current study deals with estimating the protein concentration and the effect of fish weight on protein concentration values in red and white muscles in two different regions ( R1 : Anterior region lies 2 cm behind the head and R2: posterior region lies 2cm from caudal fin  (in  two types of bony fish, namely common carp (Cyprinus carpio) and Nile tilapia (Oreochromis niloticus). Samples were collected from Karmat Ali river- north of Basrah between October 2019 and February 2020. The protein was extracted using protein extraction buffer, the current study show that the average of  protein concentration in red muscles of Nile tilapia ranged between  7.74-7.4 mg / ml  and ( 6.8-8.85 mg / ml) in R1 and R2 region re

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Publication Date
Fri Apr 04 2025
Journal Name
European Journal Of Dentistry
The Effectiveness of Conventional and Advanced Aligning Archwires: The Insights of Two Randomized Clinical Trials
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Abstract<p> Objectives This study aimed to compare the clinical effectiveness of four aligning archwires: Superelastic Nickel-Titanium (Superelastic-NiTi), SmartArch, Copper-Nickel-Titanium (Cu-NiTi), and Speed Tubular coaxial-Nickel-Titanium (Tubular coaxial-NiTi), regarding the alignment efficiency, associated perception of pain, and possibility of inducing root resorption.</p><p> Materials and Methods This study includes two randomized clinical trials run in parallel. Patients with 5 to 9 mm of mandibular anterior teeth crowding according to Little's irregularity index (LII) who needed fixed orthodontic appliances without extraction were randomly assigned to four groups of</p> ... Show More
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Publication Date
Thu Aug 07 2025
Journal Name
Scientific Reports
Evaluation of how laser photostimulation at two wavelengths alters the antimicrobial potential of Streptomycetes spp
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The purpose of this study was to isolate and identify additional products produced by direct laser irradiation, as well as to ascertain if laser irradiation may stimulate the synthesis of antibiotic compounds in a local Streptomycetes (Strept). Moreover, we postulate the mechanisms by which lasers function within living bacterial cells and suggest that sequential photochemical reactions may transpire following a designated period of irradiation. Thiophene was found as one of the most significant clinical products with antibacterial and anticancer properties. To accomplish these objectives, we selected two isolates: Streptomyces thinghirensis strain S10 (Strept thin), which inherently synthesizes an antibacterial agent, and Streptomyces lien

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Publication Date
Fri Sep 05 2025
Journal Name
مجلة مركز بابل للدراسات الإنسانية
Two Unpublished Economic Texts from The Reign of The King of Larsa Gun-gun-um
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. The Larsa dynasty was one of the contemporary Amorite dynasties that disputed sovereignty in the Old Babylonian era, along with other dynasties such as Isin - First Babylon - Eshnunna - Ashur - Mari - Uruk - Kish - Kisura - Kazalu and Manana. It can be considered the first of these dynasties, which were founded at the end of the era of the Third Ur Dynasty during the time of its last ruler, Ibi-Sin. It was founded by one of the sheikhs of the Amorite tribes. The rule of the Larsa dynasty lasted about 262 years, from 2025 BC to 1763 BC, during which 16 rulers and kings ruled, some of whom achieved wide fame and some of whom did not, depending on their strength and achievements, according to what has reached us through their date formulas

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Publication Date
Sun Jan 01 2023
Journal Name
Ibero- American Journal Of Exercise And Sports Psychology
THE EFFECT OF SPECIAL EXERCISES USING TWO DESIGNED DEVICES IN DEVELOPING SOME DEFENSIVE HANDBALL SKILLS
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Publication Date
Wed May 14 2025
Journal Name
Journal Of Applied Mathematics
Role of Wind and Fear on the Dynamic of a Prey and Two Competing Predators
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An essential tool for studying the web is its ability to show how energy moves through an ecosystem. Understanding and elucidating the relationship between species variety and their placement within the inclusive trophic dynamics is also beneficial. A food web ecological model with prey and two rival predators under fear and wind flow conditions is developed in this article. The boundedness and positivity of the system’s solution are established mathematically. The stability and existence constraints of the system’s equilibria are examined. The proposed system’s persistence limitations are established. Additionally, the bifurcation analysis of every potential equilibrium is examined using the Sotomayor theorem. To describe the

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