• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.71-82
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• 2023

In this article, we find the approximate solutions of Abel differential equation (ADE) with uncertainty using residual power series (RPS) method. This method helps to calculate the sequence of solutions of ADE. Finally, numerical illustrations demonstrate the applicability of the method.

• The Mathematical Education
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• v.29 no.1
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• pp.55-61
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• 1990

There are three objectives of this paper. First, we present an elegant and simple generalization of Abel's theorem (i .e. tile Abel summability (on the unit disk of the euclidean plane) is regular). Second, we consider the definition of Abel summability through lim (equation omitted) which immediately has clear connexctions with CeSARO summability and Cesaro sums (equation omitted). This approach examplifies some simple aspects of so-called Tauberian theorems of divergent series. Third, we present the applications of the previous results to find the limits of transition probabilities of homogeneous Marker chain. Finally, we explain why the original Abel's theorem which looks obvious is difficult to be proved, and can not be proved analytically.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.729-736
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• 2022

To help solving intractable nonlinear evolution equations (NLEEs) of waves in the field of fluid dynamics we develop an algorithm to find new high order solutions of the class of Abel, Bernoulli, Chini and Riccati equations of the form y' = ayⁿ + by + c, n > 1, with constant coefficients a, b, c. The role of this class of equations in NLEEs is explained in the introduction below. The basic algorithm to compute the coefficients of the power series solutions of the class, emerged long ago and is further developed in this paper. Practical application for hitherto unknown solutions is exemplified.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.499-511
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• 2013

In this article, Adomian decomposition method (ADM), variation iteration method(VIM) and homotopy analysis method (HAM) for solving integro-differential equation with singular kernel have been investigated. Also,we study the existence and uniqueness of solutions and the convergence of present methods. The accuracy of the proposed method are illustrated with solving some numerical examples.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.329-336
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• 2006

In the category of the group theoretic methods using invertible discrete group transformation, we give a useful relation between Emden-Fowler equations and nonlinear heat equation. In this paper, by means of appropriate transformations of discrete group analysis, the nonlinear hate equation transformed into the class of the Emden-Fowler equations. This approach shows that, under the group action, the solution of reference equation can be transformed into the solution of the transformed equation.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.27 no.7
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• pp.52-58
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• 2013

The two-dimensional finite difference time domain algorithm is used to numerically reconstruct the electron density profile in O-mode ultrashort pulse reflectometry. A Gaussian pulse is employed as the source of a probing electromagnetic wave. The Gaussian pulse duration is chosen in such a manner as to have its frequency spectrum cover the whole range of the plasma frequency. By using a number of numerical band-pass filters, it is possible to compute the time delays of the frequency components of the reflected signal from the plasma. The electron density profile is reconstructed by substituting the time delays into the Abel integral equation. As a result of simulation, the reconstructed electron density profile agrees well with the assumed profile.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.81-106
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• 2016

In this paper, we study the fractional iterates of the exponential function. This is an unresolved problem, not due to a lack of a known solution, but because there are an innite number of solutions, and there is no agreement as to which solution is "best." We will approach the problem by rst solving Abel's functional equation ${\alpha}(e^x)={\alpha}(x)+1$ by perturbing the exponential function so as to produce a real xed point, allowing a unique holomorphic solution. We then use this solution to nd a solution to the unperturbed problem. However, this solution will depend on the way we rst perturbed the exponential function. Thus, we then strive to remove the dependence of the perturbed function. Finally, we produce a solution that is in a sense more natural than other solutions.

• Explosives and Blasting
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• v.30 no.2
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• pp.43-51
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• 2012

The Demolition blasting has been applied for buildings and structures so far. In this study, however, a confined vessel blasting filled with water has been focused. A small amount of explosives were placed in a sealed vessel with water, perfect elastic body, supposed as a relay agent in it, and the blasting aspect was observed. Blasting pressure was standardized by Abel's equation of state. In result, if there was a relay agent in it, the pressure vessel was torn apart with smaller power than its tensile strength. If there was not, it needed 7.1~8.5 times as much power as the previous one, and the blasting pressure had not also affected the demolition and it had gone or vanished until it reached a certain point, In terms of pressure vessel made by steel, the elastic-plastic failure was took a place, and the first yield point happened along the welded area as a form of heating plastic failure we thought.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.401-416
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• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• Publications of The Korean Astronomical Society
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• v.26 no.1
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• pp.25-35
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• 2011

A diagnostic tool has been proposed to convert the observed surface distribution of hydrogen recombination line intensities into the radial distributions of the electron temperature and the density in HII regions. The observed line intensity is given by an integral of the volume emission coefficient along the line of sight, which comprises the Abel type integral equation for the volume emission coefficient. As the emission coefficient at a position is determined by the temperature and density of electrons at the position, the local emission coefficient resulted from the solution of the Abel equation gives the radial distribution of the temperature and the density. A test has been done on the feasibility of our diagnostic approach to probing of HII regions. From model calculations of an HII region of pure hydrogen, we have theoretically generated the observed surface brightness of hydrogen recombination line intensities and analyzed them by our diagnostic tool. The resulting temperatures and densities are then compared with the model values. For this case of uniform density, errors in the derived density are not large at all the positions. For the electron temperature, however, the largest errors appear at the central part of the HII region. The errors in the derived temperature decrease with the radial distance, and become negligible in the outer part of the model HII region.