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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 Jun 27 2019
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
TWO NEW RECORDS OF THE GENUS APHODIUS ILLIGE, 1798 (COLEOPTERA: APHODIIDAE) IN IRAQTWO NEW RECORDS OF THE GENUS APHODIUS ILLIGE, 1798 (COLEOPTERA: APHODIIDAE) IN IRAQ
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    In this study, the dung beetles Aphodius (Bodilus) ictericus (Laicharting, 1781) and Aphodius (Planolinellus) vittatus Say, 1825 which belongs to the family of Aphodiidae (Order: Coleoptera) are redscribed here as to being found for the first time in Iraq.

 

    The specimens were collected from different regions in the middle of Iraq; the main diagnostic characters and some morphological features of males were drawn and pictured.

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Publication Date
Mon Jan 01 2018
Journal Name
Journal Of Global Pharma Technology
Synthesis, Diagnosis and Microbiological Studies of Mn+2, Co+2, Ni+2, Cu+2 and Hg+2 Chelates of Two Schiff Bases Derived from OPhathaldehyde
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A new Schiffbase derivative ligands [H4L1] and [H2L2] have been produced by condensed ophathaldehyde with ethylene diamine and [N1, N1'E, N1, N1'E)-N1, N1'-(1, 2-phenylenebis (methan-1-yl- 1ylidene)) diethane-1, 2-diamine] with 2-benzoyl benzoic acid. Schiffbase ligands have been separated and categorized by 1H, 13 C-NMR, (CHN) elemental analysis, UV-visible, mass spectroscopy and FTIR methods. Ten new coordination complexes were prepared and structurally diagnosed: [M(L1)Cl2] and [M2(L2)Cl2] where M(II) = Mn (II), Co(II), Ni(II), Cu(II) and Hg(II). The complexes have been typified by FTIR, UV-visble atomic absorption, molar conductance elemental analysis, and magnetic susceptibility. The details of the ligand (H4L1) compounds are getting a

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Publication Date
Sun Dec 03 2017
Journal Name
Baghdad Science Journal
CFIA-Turbidimetric and Photometric Determination of Vitamin B9 (Folic acid) Using LEDs as a Source of Irradiation and Two Solar Cells as an Energy Transducer
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A specific, sensitive and simple method was used for the determination of: vitamin B9 (Folic acid) in pure and pharmaceutical formulations using continuous flow injection analysis. The method is based on formation of ion pair compound between folic acid and ammonium molybdate in an aqueous medium to obtain a gray precipitate complex, using homemade; Ayah-6SX1-ST-2D solar cell CFI Analyzer. Optimum parameters was studied to increase the sensitivity for developed method. The linear range for the calibration graph was 0.01-0.6 mMol.L-1 of vitamin B9 and LOD was 131.994 ng/sample with correlation coefficient ( r ) of 0.9810, RSD% was lower than 0.1%, (n=9) for the determination of vitamin B9 at concentration (0.07and 0.5) mMol.L-1 respectiv

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Publication Date
Wed May 12 2021
Journal Name
Annals Of The Romanian Society For Cell Biology
Contribution Ratio of Cognitive Learning Outcome in the Performance of the Two Skills of Mastering by Parallel Spherical Standing and Equilibrium on the Balance Beam
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The purpose of this paper is to identify the statistical indicators of the searched variables and identify the relationship between the cognitive learning outcome and the performance of the two mastering skills by parallel spherical standing and equilibrium on the balance beam. And the identification of the percentage of the cognitive learning outcome contribution to the performance of the two mastering skills by parallel spherical standing and the equilibrium on the balance beam. The two researchers used the descriptive approach in the survey method and the correlational relations, being the most appropriate to the nature of the research problem. The research community for the second stage students in the College of Physical Education and

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Publication Date
Thu Jun 25 2020
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Effects of Two Different Doses of Zinc Sulfate on Serum Troponin I 3 Enzyme Level and Cardiac Malondialdehyde Contents in Mitoxantrone-Induced Cardiotoxicity in Rats
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Abstract

   Mitoxantrone is an antitumor agent used in the treatment of breast and prostate cancer, acute leukemia, lymphoma, and also in the treatment of multiple sclerosis due to its immunosuppressive properties. The mitoxantrone's cardiotoxicity is irreversible, dose-dependent, and it may occur years after treatment. Zinc is considered as an essential mineral for cell division and the synthesis of DNA and protein; furthermore, such mineral has an important role in states of cardiovascular diseases; and may have protective effects in coronary artery disease and cardiomyopathy.

Objective: The current study is designed to investigate effects of two different doses of zinc sulfat

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Publication Date
Sat Feb 24 2024
Journal Name
Journal Of Studies And Researches Of Sport Education
The effect of the use of the Colb model according to the two forms (adaptive, ascending) in learning some of the technical skills of women
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The objective of the study was to identify the effect of the use of the Colb model for the students of the third stage in the College of Physical Education and Sports Sciences, University of Baghdad,As well as to identify the differences between the research groups in the remote tests in learning skills using the model Colb.The researcher used the experimental method and included the sample of the research on the students of the third stage in the College of Physical Education and Sports Science / University of Baghdad by drawing lots, the third division (j) was chosen to represent the experimental group,And the third division (c) to represent the control groupafter the distribution of the sample splitting measure according to the Colb mode

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Publication Date
Sat Jan 01 2022
Journal Name
Dental Hypotheses
Comparison of Microleakage of Composite and Glass Ionomer Restorations in Primary Molars Pretreated with Silver Diamine Fluoride at Two Time Intervals: An In Vitro study
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Publication Date
Thu Dec 31 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Electronic payment methods used for salary resettlement and its impact on improving the mental image of customers: an applied study of the opinions of a sample of (private) commercial banks 'customers contracting with the Ministry of Higher Education and Scientific Research to localize employees' salaries
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The research seeks to identify the contemporary events that face the use of electronic payment methods to localize the salaries of state employees and its impact in enhancing the mental image of customers, and to achieve this purpose from the fact that a questionnaire was designed and distributed to an optional sample of (31) individual customers (employees) dealing With the researched private banks, it has been analyzed and reached a number of conclusions and recommendations, the most prominent of which is the lack of modernity of electronic payment methods by customers, which is reflected in the mental image of customers and the achievement of their satisfaction, in the Emiratization project for salaries needs an advanced leade

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Publication Date
Sat Dec 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Comparison between the Methods of Ridge Regression and Liu Type to Estimate the Parameters of the Negative Binomial Regression Model Under Multicollinearity Problem by Using Simulation
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The problem of Multicollinearity is one of the most common problems, which deal to a large extent with the internal correlation between explanatory variables. This problem is especially Appear in economics and applied research, The problem of Multicollinearity has a negative effect on the regression model, such as oversized variance degree and estimation of parameters that are unstable when we use the Least Square Method ( OLS), Therefore, other methods were used to estimate the parameters of the negative binomial model, including the estimated Ridge Regression Method and the Liu type estimator, The negative binomial regression model is a nonline

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Publication Date
Sat Jun 25 2022
Journal Name
International Journal Of Drug Delivery Technology
Assessment of Serum Levels of the WNT Pathway Antagonist (Dickkopf-1) in a Sample of Type 2 Diabetic Patients with Retinopathy using Two Groups of Antidiabetics
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Objectives: Dickkopf-1 (DKK-1) is WNT/b-catenin pathway antagonist which plays a detrimental role in the development of diabetic retinopathy (DR). This research aimed to assess serum DKK-1 levels in diabetic patients who have and have not developed DR and, compare them with the control subjects finding out whether we can use it as an indicator for DR early diagnosis and to find out which one of the widely used two groups of antidiabetic treatments had the greater effect on this biomarker and hence on the progression of DR. Methods: The study participants were divided into two subgroups: First, 70 patients (36 male, 34 female) with type 2 diabetes mellitus, among them 35 patients diagnosed with DR and 35 with no evidence of DR, and s

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