• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1419-1443
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• 2021

The asymmetric Laplace distribution arises as a limiting distribution of geometric summations of independent and identically distributed random variables with finite second moments. The main purpose of this paper is to study the weak limit theorems for geometric summations of independent (not necessarily identically distributed) random variables together with convergence rates to asymmetric Laplace distributions. Using Trotter-operator method, the orders of approximations of the distributions of geometric summations by the asymmetric Laplace distributions are established in term of the "large-𝒪" and "small-o" approximation estimates. The obtained results are extensions of some known ones.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.6
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• pp.1187-1196
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• 2019

Information security has become a major challenge with the advent of cloud and social networking sites. Conventional encryption algorithms might not be suitable for image encryption because of the large data size and high redundancy among the raw pixels of a digital image. In this paper, we generalize the encryption method for of color image proposed by Jeong et al. to color image encryption using parametric 3-dimensional chaotic cat map using Laplace expansion and C-MLCA. Through rigorous experiments, we demonstrate that the proposed new image encryption system provides high security and reliability.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1158-1168
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• 1994

For BEM analyses of the impact problems of dissimilar materials, the connected multi-region method using perfect bonded conditions on the interface boundaries was added to two-dimensional Laplace transformed-domain BEM program for a single region analysis. It was confirmed that the BEM results of impact problems of a single-region and multi-regions for a homogeneous isotropic material are agreed well. The two-dimensional Laplace transformed-domain BEM program combined with connected multi-region method was applied to analyse several impact problems of dissimilar materials. Also the feasibility of BEM impact analyses was investigated for dissimilar materials by the analysis of the BEM results for impact problems of dissimilar materials in terms of physical aspects. As for an application, the two-dimensional Laplace transformed BEM concerning impact problems of cracks at the interface of dissimilar materials and the determinating process of the dynamic stress intensity factors by extrapolation method are presented in this paper.

• East Asian mathematical journal
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• v.14 no.2
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• pp.311-316
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• 1998

We study some spectral properties of the Laplace-Beltrami operator on compact Riemannian manifolds.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.883-890
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• 1992

Analysis of dynamic or impact problems is very important in engineering fields such as airplanes and automobiles. In the present study, two-dimensional elastodynamic BEM program with Laplace transformation is developed to analyze dynamic or impact problems. Accuracy and efficiency of the BEM program are tested by making the comparision of impact analysis of some models with other's published results. The BEM developed is applied to the impact crack problem and the dynamic stress intensity factors of some impact cracks is obtained by the displacement extrapolation method. It is confirmed to be possible to analyze impact problems accurately with only a little elements in simple models. And also it is found to be careful to use the singular element usually using in static crack problems because that the elastodynamic fundamental solution usually using in static crack problems because that the elastodynamic fundamental solution has more sensitive singularity than the static fundamental solution and to determine the boundary conditions in dynamic problems.

• Korean Journal of Soil Science and Fertilizer
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• v.28 no.3
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• pp.233-240
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• 1995

Fick's diffusion equation was transformed into algebraic subsidiary equation with its initial and boundary conditions through Laplace transformation, and the subsidiary equation was transformed back on the basis of Burington's table of inverse transformations so that it became the solution of Fick's equation. The initial and boundary condition was for upward diffusion of salts into flooding water of constant depth from uniform polder soil of infinite depth containing constant concentration of salt. The derived solution was tested through comparison for its conformability with other solutions of simpler initial and boundary conditions. The importance of shallow transplanting of rice seedlings and salt removing by growing rice was mentioned on the basis of very slow desalting rate by diffusion calculated from the derived solutions.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.50 no.3
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• pp.292-300
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• 2014

The Laplace Transform solution is used as a mathematical model to analyse the thermal performance of the building constructed using different wall materials. The solution obtained from Laplace Transform is an analytical solution of an one dimensional, linear, partial differential equation for wall temperature profiles and room air temperatures. The main purpose of the study is showing the detail of obtaining solution process of the Laplace Transform. This study is conducted using weather data from two different locations in Korea: Seoul, Busan for both winter and summer conditions. A comparison is made for the cases of an on-off controller and a proportional controller. The weather data are processed to yield hourly average monthly values. Energy consumption load is well calculated from the solution. The result shows that there is an effect of mass on the thermal performance of heavily constructed house in mild weather conditions such as Busan. Building using proportional control experience a higher comfort level in a comparison of building using on-off control.

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.597-605
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• 2012

Evidence framework enables us to determine the tuning constant in a penalized likelihood formula. We apply the framework to the estimating parameters of normal mixtures. Evidence, which is a solely data-dependent measure, can be evaluated by Laplace approximation. According to a synthetic data simulation, we found that the proper values of the tuning constant can be systematically obtained.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.9-16
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• 1994

In this paper, a boundary integral equation for transient plate bending problem is proposed. Approach, using laplace transform is considered. The boundary integral equations with respect to deflection, normal slope, bending moment effective shear are presented and the effect of corner point is considered.