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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
Fri Dec 15 2023
Journal Name
Iraqi Journal Of Laser
The Reliability of Two Different Laser Wavelengths in Inducing Bone Healing Around Dental Implants: Comparative Clinical Trial
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Background/purpose: Dental implantology involves different treatments that have been used in conjunction with dental implant surgery to increase implant stability and bone regeneration process. Photobiomodulation( PBM) can be one of these techniques. The objective of this study was to evaluate the bone density around implants. Materials and methods: in this study, 10 individuals had 20 implants inserted in the posterior of their mandibles. each patient received two implants the left side served as the control whereas the right side served as the study group with a diode laser (same patients). measurements were made for each implant. Measurements were obtained using cone-

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Publication Date
Fri Nov 02 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Impact of Maternal Risk Factors on Birth Weight of Newborn in Two Maternity Hospitals in Baghdad City
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Objectives: A cross sectional analytic study was carried out to identify the maternal risk factors which
contribute to occurrence of low birth weight, and to determine the statistical significant differences between low
birth weight and maternal risk factors.
Methodology: A purposive sample of (400) woman was selected from AL-Elwyia Maternity Teaching Hospital
and Fatima Al-Zaharia Maternity and Pediatric Teaching Hospital. Data was collected through the interview of
mothers. Questionnaire format was designed and consisted seven parts, demographic variables, and reproductive
variables , Reproductive health variables, complications during the current pregnancy, the mother newborn
variables nutritional status for the m

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Publication Date
Sat Jul 08 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Estimation of Superoxide Dismutase, Matrix-metalloprotinase-9, and Interleukin -18 in Patients with Type Two Diabetes Mellitus
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Antioxidant status imbalance and inflammatory process are cooperative events involved in type 2 diabetes mellitus. This study aimed to investigate     superoxide dismutase as a potential biomarkers of antioxidant imbalance, matrix-metaloprotinase-9,   and interleukin -18  as biomarkers of inflammation in serum and to estimate  the effects of other confounding factors  gender, age and finally measuring the relation among the interested biomarkers.

This case - control study included 50 patients,   and   45 of  healthy subjects matched age –gender were also enrolled  in this study as a control group.    The   focused &nbsp

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Publication Date
Sun Sep 01 2019
Journal Name
Baghdad Science Journal
The Effect of MHD on a Longitudinal Flow of a Fractional Maxwell Fluid between Two Coaxial Cylinders
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      In this paper fractional Maxwell fluid equation has been solved. The solution is in the Mettag-Leffler form. For  the corresponding solutions for ordinary Maxwell fluid are obtained as limiting case of general solutions. Finally, the effects of different parameters on the velocity and shear stress profile are analyzed through plotting the velocity and shear stress profile.

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Publication Date
Fri Aug 30 2019
Journal Name
Environmental Engineering Research
Numerical modeling of two-dimensional simulation of groundwater protection from lead using different sorbents in permeable barriers
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This study is to investigate the possibility of using activated carbon prepared from Iraqi date-pits (ADP) which are produced from palm trees (Phoenix dactylifera L.) as low-cost reactive material in the permeable reactive barrier (PRB) for treating lead (Pb<sup>+2</sup>) from the contaminated groundwater, and then compare the results experimentally with other common reactive materials such as commercial activated carbon (CAC), zeolite pellets (ZP). Factors influencing sorption such as contact time, initial pH of the solution, sorbent dosage, agitation speed, and initial lead concentration has been studied. Two isotherm models were used for the description of sorption data (Langmuir and Freundlich). The maximum lead sorp

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Publication Date
Tue Jan 01 2019
Journal Name
Biochemical And Cellular Archives
Effect of gibberellins on growth and production of two cultivars of ranunculus plant under different environmental conditions
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Scopus
Publication Date
Thu Dec 22 2022
Journal Name
Chemistry &amp; Chemical Technology
Turbidimetric Determination of Mebeverine Hydrochloride in Pharmaceutical Formulations Using Two Consecutive Detection Zones under Continuous Flow Conditions
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A simple, low cost and rapid flow injection turbidimetric method was developed and validated for mebeverine hydrochloride (MBH) determination in pharmaceutical preparations. The developed method is based on forming of a white, turbid ion-pair product as a result of a reaction between the MBH and sodium persulfate in a closed flow injection system where the sodium persulfate is used as precipitation reagent. The turbidity of the formed complex was measured at the detection angle of 180° (attenuated detection) using NAG dual&Solo (0-180°) detector which contained dual detections zones (i.e., measuring cells 1 & 2). The increase in the turbidity of the complex was directly proportional to the increase of the MBH concentration

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Publication Date
Wed Jun 20 2018
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Synthesis, Characterization and Antimicrobial Evaluation with DFT Study of New Two-Amino-4-(4-Chlorophenyl) Thiazole Derivatives
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2-amino-4-(4-chloro phenyl)-1,3-thiazole (1) was synthesized by refluxing thiourea with para-chloro phenacyl bromide in absolute methanol. The condensation of amine compound (1)  with phenylisothiocyanate in the presence of pyridine will  produce 1-(4-(4-chlorophenyl)thiazol-2-yl)-3-phenylthiourea(2), which is  upon treatment with 2,4 dinitrophenyl hydrazine by conventional method, afforded 1- ( 4 - ( 4 – chlorophenyl ) thiazol – 2 – yl ) – 3 - phenylhydrazonamide,N' - ( 2 , 4 -dinitrophenyl) ,(3).The characterization of the titled compounds were performed utilizing FTIR spectroscopy, 1HNMR and CHNS elemental analysis, and by me

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Publication Date
Tue Dec 24 2024
Journal Name
Malaysian Journal Of Mathematical Sciences
Exploring the Role of Hunting Cooperation, and Fear in a Prey-Predator Model with Two Age Stages
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The aim of this study is to utilize the behavior of a mathematical model consisting of three-species with Lotka Volterra functional response with incorporating of fear and hunting cooperation factors with both juvenile and adult predators. The existence of equilibrium points of the system was discussed the conditions with variables. The behavior of model referred by local stability in nearness of any an equilibrium point and the conditions for the method of approximating the solution has been studied locally. We define a suitable Lyapunov function that covers every element of the nonlinear system and illustrate that it works. The effect of the death factor was observed in some periods, leading to non-stability. To confirm the theore

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Publication Date
Thu Sep 01 2016
Journal Name
Journal Of Engineering
Effect of Using Porcelanite as Partial Replacement of Fine Aggregate on Roller Compacted Concrete with Different Curing Methods
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Roller-Compacted Concrete is a no-slump concrete, with no reinforcing steel, no forms, no finishing and wet enough to support compaction by vibratory rollers. Due to the effect of curing on properties and durability of concrete, the main purpose of this research is to study the effect of various curing methods (air curing, 7 days water curing, and permanent water curing) and porcelanite (local material used as an Internal Curing agent) with different replacement percentages of fine aggregate (volumetric replacement) on some properties of Roller-Compacted Concrete and to explore the possibility of introducing practical Roller-Compacted Concrete for road pavement with minimum requirement of curing. Specimens were sawed fro

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