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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
Tue Apr 18 2023
Journal Name
Electronics
A Systematic Approach to Stable Grasping of a Two-Finger Robotic Hand Activated by Jamming of Granular Media
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A systematic approach is presented to achieve the stable grasping of objects through a two-finger robotic hand, in which each finger cavity was filled with granular media. The compaction of the latter, controlled by vacuum pressure, was used to adjust the structural and contact stiffness of the finger. The grasping stability was studied under the concurrent effect of an external torque and applied vacuum pressure. Stable grasping was defined as the no slippage condition between the grasped object and the two fingers. Three control schemes were adopted and applied experimentally to ensure the effectiveness of the grasping process. The results showed that stable and unstable grasping regions exist for each combination of applied torqu

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Publication Date
Mon Sep 20 2021
Journal Name
Journal Of Craniofacial Surgery
Presurgical Assessment of Anatomical Landmark Position Using Two Views of Cone Beam Computed Tomography: A Comparative Radiological Study
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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Phytochemical Study of some Flavonoids Present in the Fruits of Two Ammi L. Species Wildly Grown in Iraq
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Ammi species belong to the family Umbellifereae that provide a host of bioactive compounds (mainly coumarins and flavonoids) of important biological activities, like prevention and treatment of heart and vascular disease and some types of cancer. Literature survey revealed that there was no study concerning Ammi flavonoids in Iraq. Ammi majus and Ammi visnaga, which are wildly grown in Iraq, were chosen for this study. This study concerned with extraction, identification, isolation, and purification of some biologically important flavonols quercetin and kaempferol from the fruits of Ammi majus and Ammi visnaga. Extraction of these flavonols was carried out using 85% methanol and 90% e

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Publication Date
Sun Mar 01 2020
Journal Name
International Journal Of Modern Physics E
Investigation of halo structure of neutron rich 14B, 15C, 19C and 22N nuclei in the two body model
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The two body model of (Core+n) within the radial wave functions of the cosh potential has been used to investigate the ground state features such as the proton, neutron and matter densities, the root mean square (RMS) nuclear proton, neutron, charge and mass radii of unstable neutron-rich 14B, 15C, 19C and 22N nuclei. The calculated results show that the two body model with the radial wave functions of the cosh potential succeeds in reproducing neutron halo in these nuclei.

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Publication Date
Mon Feb 01 2021
Journal Name
Engenharia Agrícola
HYPERSPECTRAL SPECTROSCOPY TO DETECT DIFFERENT RESPONSES OF TWO SOYBEAN (GLYCINE MAX) CULTIVARS TO CHARCOAL ROT (MACROPHOMINA PHASEOLINA) TOXIN
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Publication Date
Sat Oct 01 2011
Journal Name
Iraqi Journal Of Physics
Two dimensional grating and efficiency enhancement of Si photovoltaic cells by surface texturing using UV femtosecond laser pulses
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A fast laser texturing technique has been utilized to produce micro/nano surface textures in Silicon by means of UV femtosecond laser. We have prepared good absorber surface for photovoltaic cells. The textured Silicon surface absorbs the incident light greater than the non-textured surface. The results show a photovoltaic current increase about 21.3% for photovoltaic cell with two-dimensional pattern as compared to the same cell without texturing.

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Publication Date
Sat Jul 01 2000
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
COMPARATIVE ECOLOY OF TWO SPECIES OF BIVALVE CORBICULA FL UMINEA AND CORBICULE FL UMINALIS IN SHATT AL-ARAB
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Some aspects of population dynamics of both corbicula species inhabiting intertidal zone of
shatt al-Arab are described. These informations are explained in accordance with the possible
occurrence of competition between the two related species.

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Publication Date
Tue Mar 20 2018
Journal Name
Mustansiria Dental Journal
A comparative Study in the Antibacterial effect of Eugenol as Hand Wash Material with two Types of Soap
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Hands have consistently been an important vehicle in the transmission of disease (1). Thus, thorough hand-washing remains the single most important factor in preventing infection specially in hospitals and labs.Twenty-nine non-clinical volunteers (do not work or come in contact with a clinical or hospital setting) that lacked visible skin injuries, eczema or apparent skin disease were used, those subjects were all tested by a material of each of the three used in the study weekly and laboratory tests were done pre- and post washing.All three material were effective , Eugenol extract as effective as the bar and lotion soap. And this was confirmed statistically.Eugenol has a great antibacterial action even in small concentration and t

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Publication Date
Mon Oct 01 2018
Journal Name
Journal Of Educational And Psychological Researches
The Effectiveness of Two Educational Models in Acquiring Historical Concepts and Orientation of Fourth Grade Students in History
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The study focuses on Kamez model and the Claus Meyer model of instructional design, which are models that provide the learner with educational experiences to suit the logical information of the learner and the variety of instructional models. Research Objective: The present research aims to identify Limitations of the study. The current research is determined by ((fourth grade preparatory students, the book of the date of the fourth preparatory course)) Chapter II includes Arabic and foreign studies on the model of Kemp and Claus Mayer in the acquisition of concepts and direction towards the material. Chapter III Experimental Design: The researcher adopted an experimental design with two experimental groups and a control group. The resea

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Publication Date
Tue Mar 10 2026
Journal Name
Revista Iberoamericana De Psicología Del Ejercicio Y El Deporte, Issn 1886-8576, Vol. 17, Nº. 5, 2022, Págs. 323-327
Comparison Of Some Kinematic Variables Of The Triple Jump Between The Two World Championships (IAAF) (2017) And (2018)
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Autorías: Mustafa Abdulamir Hussain, Ahmed Sebeaatea Almujamay, Riyadh khaleel khammas. Localización: Revista iberoamericana de psicología del ejercicio y el deporte. Nº. 5, 2022. Artículo de Revista en Dialnet.

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