• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.17-28
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• 2017

A combined form of the modified Laplace Adomian decomposition method (LADM) is developed for the analytic treatment of the nonlinear Volterra-Fredholm integro differential equations. This method is effectively used to handle nonlinear integro differential equations of the first and the second kind. Finally, some examples will be examined to support the proposed analysis.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.323-334
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• 2017

In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

• Journal of Korean Society for Quality Management
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• v.29 no.1
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• pp.11-23
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• 2001

This paper is concerned with suggesting a Bayesian method for variable selection in multinomial logit model. It is based upon an optimal rule suggested by use of Bayes rule which minimizes a risk induced by selecting the multinomial logit model. The rule is to find a subset of variables that maximizes the marginal likelihood of the model. We also propose a Laplace-Metropolis algorithm intended to suggest a simple method forestimating the marginal likelihood of the model. Based upon two examples, artificial data and empirical data examples, the Bayesian method is illustrated and its efficiency is examined.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.73-82
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• 2017

In this paper we aim to demonstrate how one can obtain so far unknown Laplace transforms for the generalized hypergeometric functions $_pF_p$ for p = 2, 3, 4, and 5 by employing known summation theorems available in the literature.

• International Journal of Reliability and Applications
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• v.3 no.4
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• pp.199-202
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• 2002

In this paper, we obtain an explicit formula of the Laplace transform of the forward recurrence time at finite time t > 0 in an alternating renewal process, by adopting a Markovian approach. As a consequence, we obtain the first two moments of the forward recurrence time.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1376
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• 2019

We investigate the valuation of participating life insurance policies with default risk under a geometric regime-switching jump-diffusion process. We derive explicit formula for the Laplace transform of the price of participating contracts by solving integro-differential system and then price them by inverting Laplace transforms.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.487-503
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• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.219-230
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• 2022

We examine the bi-rotational hypersurface x = x(u, v, w) with the third Laplace-Beltrami operator in the four dimensional Euclidean space 𝔼⁴. Giving the i-th curvatures of the hypersurface x, we obtain the third Laplace-Beltrami operator of the bi-rotational hypersurface satisfying ∆^IIIx =𝒜x for some 4 × 4 matrix 𝒜.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.83-93
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• 2023

We would like to consider Laplace transform of the form of fg, the form of product, and applies it to Burger's equation in general case. This topic has not yet been addressed, and the methodology of this article is done by considerations with respect to several approaches about the transform of the form of f g and the mean value theorem for integrals. This paper has meaning in that the integral transform method is applied to solving nonlinear equations.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.359-379
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• 2023

In the present paper, we study translation hypersurfaces in E⁴. In this context, firstly we obtain first, second and third Laplace-Beltrami (LB^I, LB^II and LB^III) operators of the translation hypersurfaces in E⁴. By solving second and third order nonlinear ordinary differential equations, we prove theorems that contain LB^I-minimal, LB^II-minimal and LB^III-minimal translation hypersurfaces in E⁴.