• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.385-395
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• 2005

A finite element scheme is considered for the viscous Cahn-Hilliard equation with the nonconstant gradient energy coefficient. The scheme inherits energy decay property and mass conservation as for the classical solution. We obtain the corresponding error estimate using the extended Lax-Richtmyer equivalence theorem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.235-242
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• 2012

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

• Bulletin of the Korean Chemical Society
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• v.34 no.11
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• pp.3425-3428
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• 2013

We solve the Klein-Gordon equation with the Morse empirical potential energy model. The bound state energy equation has been obtained in terms of the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the $X^1{\sum}^+$ state of ScI molecule have been computed by using the Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

• East Asian mathematical journal
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• v.32 no.1
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• pp.117-128
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• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.79-86
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• 2011

Suppose that (M,g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by $-K{\leq}0$ and (N, $\bar{g}$) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : $M{\times}[0,{\infty}){\rightarrow}N$ be the solution of a heat equation for harmonic map with a bounded image. We estimate the energy density of u.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.703-728
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• 2019

Considered herein is the orbital stability in the energy space $H^1({\mathbb{R}})$ of a decoupled sum of N peakons for a Camassa-Holm-type equation with quartic nonlinearity, which admits single peakon and multi-peakons. Based on our obtained result of the stability of a single peakon, then combining modulation argument with monotonicity of local energy $H^1$-norm, we get the stability of the sum of N peakons.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.255-277
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• 2024

In this paper, we introduce the notion of stress-energy tensor Q of the traceless Ricci tensor for Riemannian manifolds (Mⁿ, g), and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when (M, g) satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 1996.11a
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• pp.101-103
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• 1996

This Paper describes Peak load forecasting technique of pole transformers with correlation equation. While customers are demanding safe energy supply, current correlation equation that is used for load management of pole transformers has some problems. To get accurate correlation equation. several correlation equation were examined using past data and nu data collected using the measuring instrument developed for this study. It was recognized that the quadratic equation was the most accurate for peak load forecasting from working electrical energy.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.451-460
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• 1983

Computational four-equation turbulence model is developed and is applied to predict twodimensional unsteady thermal surface discharge into a reservoir. Turbulent stresses and heat fluxes in the momentum and energy equations are determined from transport equations for the turbulent kinetic energy (R), isotropic rate of kinetic energy dissipation (.epsilon.), mean square temperature variance (theta. over bar $^{2}$), and rate of destruction of the temperature variance (.epsilon. $_{\theta}$). Computational results by four-equation model are favorably compared with those obtained by an extended two-equation model. Added advantage of the four-equation model is that it yields quantitative information about the ratio between the velocity time scale and the thermal time scale and more detailed information about turbulent structure. Predicted time scale ratio is within experimental observations by others. Although the mean velocity and temperature fields are similarly predicted by both models, it is found that the four-equation model is preferably candidate for prediction of highly buoyant turbulent flows.

• The Journal of Engineering Geology
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• v.24 no.4
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• pp.575-581
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• 2014

The reliable measurement of geotechnical properties in cold regions should account for their fluctuations with temperature. The objective of this paper is to introduce a chemical model based on the Arrhenius equation that can predict the properties of materials as their temperature changes. The model can monitor phases and reaction rates as they change with temperature. It has been already applied in the fields of geology, construction, chemistry, materials engineering, and food science. The application of the Arrhenius equation requires a reliable estimate of the activation energy. Therefore, this study also demonstrates several methods for evaluating activation energy in different contexts through summaries and reviews of previous research related to the Arrhenius equation. This paper may be of wide use in obtaining temperature-dependent parameters in geotechnical engineering.