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Direct Method for Variational Problems Using Boubaker Wavelets

The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, in 2021, the wavelet Boubaker (WB) polynomials were used for the first time to study their properties and applications in detail. They were also utilized for solving the Lane-Emden equation. The aim of this paper is to show the truncated Wavelet Boubaker polynomials for solving variation problems. In this research, the direct method using wavelets Boubaker was presented for solving variational problems. The method reduces the problem into a set of linear algebraic equations. The fundamental idea of this method for solving variation problems is to convert the problem of a function into one that involves a finite number of variables. Different numerical examples were given to demonstrate the applicability and validity of this method using the Matlab program. Also, the results of this technique were compared with the exact solution, and graphs were added to these examples to test the convergence of Wavelet Boubaker polynomials using this method.

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Publication Date
Thu May 01 1997
Journal Name
Polymer-plastics Technology And Engineering
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Publication Date
Sun Oct 01 2017
Journal Name
Journal Of The Association Of Arab Universities For Basic And Applied Sciences
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Publication Date
Tue Feb 28 2023
Journal Name
Iraqi Journal Of Science
Modified Iterative Method for Solving Sine - Gordon Equations

       The basic goal of this research is to utilize an analytical method which is called the Modified Iterative Method in order to gain an approximate analytic solution to the Sine-Gordon equation. The suggested method is the amalgamation of the iterative method and a well-known technique, namely the Adomian decomposition method. A method minimizes the computational size, averts round-off errors, transformation and linearization, or takes some restrictive assumptions. Several examples are chosen to show the importance and effectiveness of the proposed method. In addition, a modified iterative method gives faster and easier solutions than other methods. These solutions are accurate and in agreement with the series

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Publication Date
Fri Jul 21 2023
Journal Name
Journal Of Engineering
Development A Method For Production Of Carbon Nanotubes

In this work chemical vapor deposition method (CVD) for the production of carbon nanotubes (CNTs) have been improved by the addition of S. Steel mesh container (SSMC) inside which the catalyst (Fe/Al2O3) was placed. Scanning electron microscopy (SEM) investigation method used to study nanotubes produced, showed that high yield of two types of (CNTs) obtained, single wall carbon nanotube (SWCNTs) with diameter and length of less than 50nm and several micrometers respectively and nanocoil tubes with a diameter and length of less than 100nm and several micrometers respectively. The chemical analysis of (CNTs) reveals that the main component is carbon (94%) and a little amount of Al (0.32%), Fe (2.22%) the reminder is oxygen. It was also fou

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Publication Date
Wed Aug 01 2018
Journal Name
Engineering And Technology Journal
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Publication Date
Tue Apr 26 2011
Journal Name
Evolutionary Algorithms
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Publication Date
Mon Oct 01 2012
Journal Name
Computers & Mathematics With Applications
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Publication Date
Mon Jul 05 2010
Journal Name
Evolutionary Algorithms
Variants of Hybrid Genetic Algorithms for Optimizing Likelihood ARMA Model Function and Many of Problems

Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc

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Publication Date
Tue Jul 01 2008
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Prevalence and Risk Factors for Eye Problems among 20-65 Years Old Iraqi Diabetics Patients

Background: Diabetes is a chronic illness that requires continuing medical care to prevent acute complications and to reduce the risk of long-term complication. Eye
diseases are the most feared complication of diabetes. The main disorders include diabetic retinopathy, cataracts and glaucoma. Early detection of these conditions is
important to avoid risk of vision affection or even blindness.
Objectives: This study aimed to assess the prevalence and risk factors for eye problems among 20-65 years old diabetics' patients.
Methods: We studied 2540 diabetic patients selected from the Specialized Center for Endocrinology & Diabetes and the National Center for Treatment & Research of
Diabetes in Al-Mu

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Publication Date
Wed Aug 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Proposed Measure for Effect Size in Mediation Analysis with Solution to Some Mediation Process Problems

In this paper, the effect size measures was discussed, which are useful in many estimation processes for direct effect and its relation with indirect and total effects. In addition, an algorithm to calculate the suggested measure of effect size was suggested that represent the ratio of direct effect to the effect of the estimated parameter using the Regression equation of the dependent variable on the mediator variable without using the independent variable in the model. Where this an algorithm clear the possibility to use this regression equation in Mediation Analysis, where usually used the Mediator and independent variable together when the dependent variable regresses on them. Also this an algorithm to show how effect of the

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