Preferred Language
Articles
/
3Bb8zIcBVTCNdQwCJGHd
Two efficient methods for solving Schlömilch’s integral equation
...Show More Authors
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.

Crossref
View Publication
Publication Date
Wed Aug 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
A Comparative Study of Some Methods of Estimating Robust Variance Covariance Matrix of the Parameters Estimated by (OLS) in Cross-Sectional Data
...Show More Authors

 

Abstract

The Classical Normal Linear Regression Model Based on Several hypotheses, one of them is Heteroscedasticity as it is known that the wing of least squares method (OLS), under the existence of these two problems make the estimators, lose their desirable properties, in addition the statistical inference becomes unaccepted table. According that we put tow alternative,  the first one is  (Generalized Least Square) Which is denoted by (GLS), and the second alternative is to (Robust covariance matrix estimation) the estimated parameters method(OLS), and that the way (GLS) method neat and certified, if the capabilities (Efficient) and the statistical inference Thread on the basis of an acceptable

... Show More
View Publication Preview PDF
Crossref
Publication Date
Tue Jul 01 2025
Journal Name
Journal Of Studies In Humanities And Educational Sciences
The Effect of the Needham Constructivist Model on the Achievement of Third Year Biology Department Students in the Subject of Teaching Methods
...Show More Authors

The current research aims to know the effect of Needham's constructivist model on the achievement of third-year students in the Life Sciences Department in the teaching methods subject. To achieve the research objectives, the experimental method was followed for the experimental and control groups with dimensional measurement of the achievement variable of the teaching methods subject. The research sample included (62) students in the third year of the Life Sciences Department, distributed into two equal groups in the variables (self-assessment of learning methods - chronological age in years - intelligence level - previous information). To measure the level of students' achievement, an achievement test was constructed consisting of (40) te

... Show More
Preview PDF
Publication Date
Tue Jun 01 2021
Journal Name
Journal Of The College Of Languages (jcl)
The methods used to translate medical terms between Arabic and Spanish: Los métodos utilizados para traducir términos médicos entre árabe y español
...Show More Authors

         The present paper deals with medical terms translation and its relationship with the medical text of Arabic and Spanish. Medical translation is the process of transferring texts related to the field of health and medicine to achieve an accurate effective translation from the source language text to the equivalent target language text. The most prominent medical translations are from English to Arabic as most of the syllabuses in Arab countries are taught in English.

       Translation is an innovative work intended to render the original text in the source language into the target language with the highest level of linguistic and intellec

... Show More
View Publication Preview PDF
Crossref
Publication Date
Sat Nov 30 2019
Journal Name
Journal Of Engineering And Applied Sciences
The use of Resource Consumption Accounting and Balanced Scorecard Methods as an Integrated Framework in Correcting the Economic Unit Performance: Applied Study
...Show More Authors

View Publication
Scopus (3)
Scopus Crossref
Publication Date
Sat Oct 28 2023
Journal Name
Baghdad Science Journal
Qualitative and Quantitative Determination of Dapagliflozin Propanediol Monohydrate and Its Related Substances and Degradation Products Using LC-MS and Preparative Chromatography Methods
...Show More Authors

Dapagliflozin is a novel sodium-glucose cotransporter type 2 inhibitor. This work aims to develop a new
validated sensitive RP-HPLC coupled with a mass detector method for the determination of dapagliflozin, its
alpha isomer, and starting material in the presence of dapagliflozin major degradation products and an internal
standard (empagliflozin). The separation was achieved on BDS Hypersil column (length of 250mm, internal
diameter of 4.6 mm and 5-μm particle size) at a temperature of 35℃. Water and acetonitrile were used as
mobile phase A and B by gradient mode at a flow rate of 1 mL/min. A wavelength of 224nm was selected to
perform detection using a photo diode array detector. The method met the

... Show More
View Publication Preview PDF
Scopus (8)
Crossref (1)
Scopus Crossref
Publication Date
Sat Dec 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
The use of two indicators of market value-added and return on capital invested in measuring the performance of the Iraqi banking sector
...Show More Authors

For a long time, the intensification of profit represented a major goal for the company management ,but this goal confirmed a series of restrictions such the constriction on short period, the time rather than on long and medium strategic goal, the relationships with customers ,the supplies, employees , This goal is replaced by another one (intensification of the company's value) ,and the fortune of the share holders itself ,for the purpose  of creating value, the company must generate  great outcomes to cover the operating expense and to insure the a suitable compensation to the invested capital (the market value added) is  the indication used to estimate the company ability to create value –added the development

... Show More
View Publication Preview PDF
Crossref
Publication Date
Sun Mar 13 2011
Journal Name
Baghdad Science Journal
Effect of cultar, potassium and salinity of irrigation water on some characteristics of vegetative growth of two cultivars of apricot (Prunus armeniaca L.)
...Show More Authors

This experiment was conducted in the orchard of the Department of Horticulture,college of Agriculture,Baghdad University during the growing season of 2007 To study the effects of spray with three concentration of cultar(0,500,1000 mg.L-1) ,tow concentration of K2SO4(0,5g.L-1), and salinity of irrigation water with three concentration (1,2,3dS.m-1) on some characteristics of vegetative growth of two cultivars of apricot trees (Labib1 and Zienni).The age of trees was four years .The tree grafted on original of seed apricot . Afactorial trail was carry out according to randomized complete block design with arrangement of split-split with three replications. Salinity of irrigation water took main plot, potassium took sub plot and cultar took s

... Show More
View Publication Preview PDF
Crossref
Publication Date
Mon Jun 15 2020
Journal Name
Journal Of Baghdad College Of Dentistry
Evaluation of dental enamel color after fixed orthodontic therapy using two types of protectors to prevent white spot lesions (A prospective clinical study)
...Show More Authors

Background: The aim of this study is to evaluate the color change ∆E of the dental enamel following treatment with 2 kinds of protector (icon infiltrant, clinpro varnish) before fixed orthodontic treatment to avoid the possible white spot lesions. Materials and Methods: Fifty four subjects treated with fixed appliances were divided into 3 groups: the 1st group was control, while the 2nd and 3rd groups were treated with icon infiltrant and clinpro varnish before bonding procedure, respectively. Color parameters (L,a,b) were recorded for the middle and gingival thirds before and after bonding procedure to get the ∆E of each group. Results: One-way ANOVA test showed a non-significant difference in ∆E between the 3 groups a

... Show More
View Publication Preview PDF
Scopus Crossref
Publication Date
Wed Jan 01 2025
Journal Name
Smart Innovation, Systems And Technologies
The Effect of Two Training Approaches with (Hanging–Heavy) Ropes in Developing Some Physical Abilities and Accuracy of Shooting—In Front of Handball
...Show More Authors

View Publication
Scopus Crossref
Publication Date
Sun Jan 01 2023
Journal Name
Brazilian Dental Science
Effect of adhesive primer application on shear bond strength of self-adhesive cement to tooth structure and two different CAD/CAM milled blocks
...Show More Authors

View Publication
Scopus (4)
Crossref (1)
Scopus Crossref