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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
Sun Dec 06 2015
Journal Name
Baghdad Science Journal
Bounded Solutions of the Second Order Differential Equation x ?+f(x) x ?+g(x)=u(t)
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In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

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Publication Date
Fri Mar 29 2024
Journal Name
Iraqi Journal Of Science
Determination of Timewise-Source Coefficient in Time-Fractional Reaction-Diffusion Equation from First Order Heat Moment
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     This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie

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Publication Date
Sat Jul 01 2017
Journal Name
Global Journal Of Bio-science And Biotechnology
Efficiency of different denture disinfection methods
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Dentures that are not cleaning and maintained properly may prone to contamination by different microbial pathogens that result in several oral conditions. This study was design to compare the antimicrobial effect of different denture cleansers oxalic, tartaric, citric acids and alkaline peroxide with microwave irradiation on the growth of Candida albicans and Staphylococcus aureus respectively. Microwave oven used to disinfect specimens of heat-activated acrylic resin and soft linear. Oxalic, citric, tartaric acids, and alkaline peroxide were also used. Microorganisms that tested were Candida albicans and Staphylococcus aureus separately. Treatment with microwave or tartaric acid could achieve sterilization of both hot cured acrylic resins

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Publication Date
Sat Feb 02 2019
Journal Name
Journal Of The College Of Education For Women
Simplification of new fashion design methods
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Simplification of new fashion design methods

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Publication Date
Thu Apr 04 2024
Journal Name
مجلة مركز بابل للدراسات الانسانية
The Rhetorical methods in Hebrew advertisements
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Advertisement is one of the Media most efficient persuasive communicative activities designed to marketing different ideas and products with the aim of influencing consumers' perception of goods and services. The present study sheds light on the most prominent rhetorical devices that constitute the persuasive structure of the Hebrew advertisements published in various media outlet. The study is conducted by means of analyzing the linguistic structure of the advertising texts and according to the analytic and descriptive approach to know the characteristics and the functions of the oratorical devices used in the advertising industry. The research elucidates that most of the advertisements are written in slang language, and this is due to th

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Publication Date
Tue Jun 01 2021
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of Hurst exponent estimation methods
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Publication Date
Fri Feb 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Bayesian methods to estimate sub - population
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The aim of the research is to estimate the hidden population. Here، the number of drug users in Baghdad was calculated for the male age group (15-60) years old ، based on the Bayesian models. These models are used to treat some of the bias in the Killworth method Accredited in many countries of the world.

Four models were used: random degree، Barrier effects، Transmission bias، the first model being random، an extension of the Killworth model، adding random effects such as variance and uncertainty Through the size of the personal network، and when expanded by adding the fact that the respondents have different tendencies، the mixture of non-random variables with random to produce

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Publication Date
Wed Jun 30 2021
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of Hurst exponent estimation methods
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Through recent years many researchers have developed methods to estimate the self-similarity and long memory parameter that is best known as the Hurst parameter. In this paper, we set a comparison between nine different methods. Most of them use the deviations slope to find an estimate for the Hurst parameter like Rescaled range (R/S), Aggregate Variance (AV), and Absolute moments (AM), and some depend on filtration technique like Discrete Variations (DV), Variance versus level using wavelets (VVL) and Second-order discrete derivative using wavelets (SODDW) were the comparison set by a simulation study to find the most efficient method through MASE. The results of simulation experiments were shown that the performance of the meth

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Publication Date
Wed Jul 01 2015
Journal Name
Al–bahith Al–a'alami
Methods of Arab TV Programs Production
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This research investigates the methods of producing Investigative Arabic Television Programs that are able to prove its existence during a short period of time as a form of Television programs on Arab satellite channels growing in number and varied in content. The research aims to present qualitative and quantitative descriptions of the methods used in tackling the topics discussed in the program, and knowing whether they satisfy the conditions and scientific foundations for the research, investigation, analysis, and interpretation. The researcher uses the survey method and uses the tool of content analysis including a set of methodological steps that seek to discover the implied meaning of the research sample represented by the program

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Publication Date
Mon May 01 2023
Journal Name
Periodicals Of Engineering And Natural Sciences
Solving the multi-criteria: total completion time, total late work, and maximum earliness problem
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Within this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an effic

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