Note on Triple Aboodh Transform and Its Application

Abstract— In this paper, we introduce the definition of triple Aboodh transform, some properties for the transform are presented. Furthermore, several theorems dealing with the properties of the triple Aboodh transform are proved. In addition, we use this transform to solve partial differential equations with integer and non-integer orders

First Aboodh Transform of Fractional Order and Its Properties

In this paper, we propose definitions of a fractional first Aboodh transform of order α, where α ϵ [0, 1], for a functions which are fractional differentiable. We then present some main properties of this transform. Furthermore, we prove some related theorems

The periodic solutions of the model of drop formation on a coated vertical fibre

7th International Conference on Management Science and Engineering Management, ICMSEM 2013 -- 7 November 2013 through 9 November 2013 -- Philadelphia, PA -- 102588Nonlinear differential equations and its systems are used to describe various processes in physics, biology, economics etc. There are a lot of methods to look for exact solutions of nonlinear differential equations: the inverse scattering transform, Hirota method, the Backlund transform, the truncated Painlev'e expansion. Here, we present a well known auxiliary equation method that produce new types of exact travelling wave solutions to nonlinear equations. In this paper, by means of symbolic computation, the new solutions of original auxiliary equation of first-order nonlinear ordinary differential equation with sixth-degree nonlinear term are presented to obtain novel exact solutions of the leading-order evolution equation which is the model of drop formation on a coated vertical fibre. © Springer-Verlag Berlin Heidelberg 2014

Dealing with learning concepts via support vector machines

7th International Conference on Management Science and Engineering Management, ICMSEM 2013 -- 7 November 2013 through 9 November 2013 -- Philadelphia, PA -- 102588Extracting learning concepts is one of the major problems of artificial intelligence on education. Essentially, the determination of learning concepts within an educational content has some differences as compared with keyword or technical term extraction process. However, the problem can still taught as a classification problem, notwithstanding. In this paper, we examine how to handle the extraction of learning concepts using support vector machines as a supervised learning algorithm, and we evaluate the performance of the proposed approach using f-measure. © Springer-Verlag Berlin Heidelberg 2014

Harmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable

The second-order harmonic balance method is used to construct three approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable. Two procedures are used to solve the nonlinear differential equation approximately. In the first the differential equation is rewritten in a form that does not contain the expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first one and the discrepancy between the approximate frequency and the exact one is lower than 1.28%.This work was supported by the "Ministerio de Educación y Ciencia", Spain, under project FIS2005-05881-C02-02, and by the "Generalitat Valenciana", Spain, under project ACOMP/2007/020

Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient.This work was supported by the “Ministerio de Educación y Ciencia”, Spain, under project FIS2005-05881-C02-02, and by the “Generalitat Valenciana”, Spain, under project ACOMP/2007/020