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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 Jun 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
The Effect of the Stability of Some Commodity Activities in Iraq on the Estimation of the Statistical Data Models for the Period (1988-2000)
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There is an assumption implicit but fundamental theory behind the decline by the time series used in the estimate, namely that the time series has a sleep feature Stationary or the language of Engle Gernger chains are integrated level zero, which indicated by I (0). It is well known, for example, tables of t-statistic is designed primarily to deal with the results of the regression that uses static strings. This assumption has been previously treated as an axiom the mid-seventies, where researchers are conducting studies of applied without taking into account the properties of time series used prior to the assessment, was to accept the results of these tests Bmanueh and delivery capabilities based on the applicability of the theo

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Publication Date
Sun Mar 10 2024
Journal Name
Journal Of Sport And Health Research
The effectiveness of a rehabilitation program with aqueous media on the egree of pain and balance for those suffering from sacroiliitis in football players
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Abstract in English  The aim of this study is to identify the effectiveness of rehabilitation exercises in conjunction with aquatic therapy for those suffering from sacroiliitis in football players. The researcher used the experimental approach, using the experimental design (pre-measurement, post-measurement). Similar to the objectives and procedures of the research, the researcher assumed the following: the existence of significant differences. Statistics between pre- and post-measurements in variables in favor of post-measurement for the following variables (degree of pain and level of balance). The experimental approach was used with a pre- and post-measurement design on one group of football players with sacroiliitis, nu

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Publication Date
Sat Feb 01 2020
Journal Name
Journal Of Economics And Administrative Sciences
Effect of applying the CAMEL model to profitability of banks )An applied study on a number of Iraqi banks for the period 2010-2016(
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The evaluation of banks plays an important role in maintaining the interests of customers with the bank as well as providing continuous supervision and control by the Central Bank. The Central Bank of Iraq conducted an assessment of the Iraqi banks through the implementation of the CAMEL model during a certain period. This evaluation did not continue. The research provides continuity to the Central Bank's assessment and as a step to continue the evaluation process for all banks through the use of the CAMEL model. ROA and ROE by using the regression model for four Iraqi banks registered in the Iraqi market for securities during the period 2010-2016. The results showed that the capital and profitability indicators have a significan

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Publication Date
Wed Dec 30 2020
Journal Name
Al-kindy College Medical Journal
Effectiveness of conventional phototherapy, intensive phototherapy and exchange transfusion in treating neonatal jaundice at Fatima Al-Zahra Hospital for maternity and children in Baghdad
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Background: Neonatal hyperbilirubinemia is a common disease in neonates especially in early days of birth that requires a good and successful treatment for reducing the severity and its complications that can produce important and irreversible effects.

Objectives: To evaluate the effectiveness of conventional phototherapy, intensive phototherapy and exchange transfusion on outcomes of neonatal jaundice at Fatima Al-Zahra Hospital for maternity and child care in Baghdad.

Patients & Methods: A retrospective study was carried out using medical records of neonates with diagnosis of unconjugated jaundice, admitted in the septic neonatal care unit of Fatima Al-Zahra hospital over 6 months period b

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Publication Date
Tue Sep 01 2009
Journal Name
Journal Of Economics And Administrative Sciences
Impact of budget on the basis of activities in the implementation of competitive strategiesApplied Study in the General Company for Electrical Industries - Tammuz Laboratory
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The Contemporary Business Environment is Surrounded by many quick and continues variable and changes which has an effect on the economic units. These variables and changes like the high competition which need many tools to help them to continue and achieve The critical success. So to achieve this they have many competitive strategies like cost leadership strategy, differentiation strategy and focus strategy.

Budget is regarded one of main tools to execute objectives polices and programs of the economic units, beside show how the economic units had execute the available economic resources.

Activity based on budgeting is regarded one of the modern technique in the m

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Publication Date
Mon Feb 18 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The Role of Insurance Awareness in marketing Insurance Services: An Explorative Research views of a Sample of Employees in the National Company for Insurance
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This research aims at shedding light on the concept of insurance awareness and clarifying its role on marketing insurance services of a sample of (100) employees in the National Company for Insurance. Questionnaire is used as a main instrument for collecting data and information from the sample. Their answers were analyzed by using arithmetic means, standard deviation, centesimal weight, and the correlation coefficient ( , F, t) tests .The research reached several conclusions of which:1.The sample member's response to insurance awareness and marketing insurance services factors was in the medium level.2.There was a positive relationship of a moral sign between insurance awareness and marketing insurance services, that correlation coeffic

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Crossref
Publication Date
Thu Aug 10 2023
Journal Name
Migration Letters
The Effectiveness of E-Training in Developing the Skills of Designing E-Courses for Teachers of Arabic in the Colleges of Education in Iraq
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This study aimed to examine the effects of electronic training to improve the skills of designing electronic courses for teachers of Arabic language in the colleges of education in Iraq. The descriptive approach is applied and the sample included 145 teachers of Arabic who were selected randomly from the colleges of education in Iraq. Moreover, the results reflected that e-training is effective in improving the skills related to designing online educational courses for teachers of Arabic in the colleges of education in Iraq. Besides, there was no difference between the mean of the respondents' responses to the total score of the tool on the role of electronic training to develop the skills related to electronic courses designing for teacher

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Publication Date
Fri May 10 2019
Journal Name
Research Journal Of Chemistry And Environment
Solid Phase Extraction of Theophylline in Aqueous Solutions by Modified Magnetic Iron Oxide Nanoparticles as an Extractor Material and Spectrophotometry Technique for the Determination
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new, simple and fast solid-phase extraction method for separation and preconcentration of trace theophylline in aqueous solutions was developed using magnetite nanoparticles (MIONPs) coated with aluminium oxide (AMIONPs) and modified with palmitate (P) as an extractor (P@AMIONPs). It has shown that the developed method has a fast absorbent rate of the theophylline at room temperature. The parameters that affect the absorbent of theophylline in the aqueous solutions have been investigated such as the amount of magnetite nanoparticle, pH, standing time and the volume, concentration of desorption solution. The linear range, limit of quantification (LOQ) and limit of detection (LOD) for the determination of theophylline were 0.05-2.450 μg mL-

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Publication Date
Thu Jun 20 2024
Journal Name
Acta Facultatis Medicae Naissensis
Clinical properties and seminal fluid analysis of patients with primary infertility consulting the urology outpatient clinic for the first time: A cross-sectional study
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Introduction/Aim. Seminal fluid analysis (SFA) plays a crucial role in helping infertility clinics diagnose the underlying reason of male infertility. The aim of the study was to investigate seminal fluid patterns of male partners of an infertile couple with apparently fertile female partners. Materials and methods. A cross-sectional study was conducted between January 2019 and December 2022. Patients were attending consultations for delayed conception for more than 12 months with apparently fertile female partner. Results. Four hundred fifty-three patients were included in the study. The distribution of patients according to age groups showed that 277 patients were young, aged 21 - 30 years (61%). Two hundred sixty-two (58%) patien

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Publication Date
Sat Oct 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Harnessing Innovative Solutions for Achieving Continuous Quality Improvement Requirements in Water Treatment Plants: A Case Study of Continuous Quality Improvement in Baghdad Water Authority.
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Abstract

This Research aims for harnessing critical and innovative thinking approaches besides innovative problem solving tools in pursuing continual quality improvement initiatives for the benefit of achieving operations results effectively in water treatment plants in Baghdad Water Authority. Case study has been used in fulfilling this research in the sadr city water treatment plant, which was chosen as a study sample as it facilitates describing and analyzing its current operational situation, collecting and analyzing its own data, in order to get its own desired improvement opportunity be done. Many statistical means and visual thinking promoting methods has been used to fulfill research task.

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