• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1509-1533
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• 2020

We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.895-903
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• 2009

The penalized partial likelihood based on restricted maximum likelihood method has been widely used for the inference of frailty models. However, the standard-error estimate for frailty parameter estimator can be downwardly biased. In this paper we show that such underestimation can be corrected by using hierarchical likelihood. In particular, the hierarchical likelihood gives a statistically efficient procedure for various random-effect models including frailty models. The proposed method is illustrated via a numerical example and simulation study. The simulation results demonstrate that the corrected standard-error estimate largely improves such bias.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1787-1799
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• 2017

In this paper, we prove basic a priori estimate for the ${\bar{\partial}}$-Neumann problem on an annulus between two pseudoconvex submanifolds of a Stein manifold. As a corollary of the result, we obtain the global regularity for the ${\bar{\partial}}$-problem on the annulus. This is a manifold version of the previous results on pseudoconvex domains.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.4
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• pp.64-70
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• 2013

Estimation approaches for casual relation model with high-order factors have strict restrictions or limits. In the case of ML (Maximum Likelihood), a strong assumption which data must show a normal distribution is required and factors of exponentiation is impossible due to the uncertainty of factors. To overcome this limitation many PLS (Partial Least Squares) approaches are introduced to estimate the structural equation model including high-order factors. However, it is possible to yield biased estimates if there are some differences in the number of measurement variables connected to each latent variable. In addition, any approach does not exist to deal with general cases not having any measurement variable of high-order factors. This study compare several approaches including the repeated measures approach which are used to estimate the casual relation model including high-order factors by using PLS (Partial Least Squares), and suggest the best estimation approach. In other words, the study proposes the best approach through the research on the existing studies related to the casual relation model including high-order factors by using PLS and approach comparison using a virtual model.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.909-914
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• 2021

In this short note we prove new differential Harnack inequalities interpolating those for the static surface and for the Ricci flow. In particular, for 0 ≤ 𝜀 ≤ 1, α ≥ 0, 𝛽 ≥ 0, 𝛾 ≤ 1 and u being a positive solution to $${\frac{{\partial}u}{{\partial}t}}={\Delta}u-{\alpha}u\;{\log}\;u+{\varepsilon}Ru+{\beta}u^{\gamma}$$ on closed surfaces under the flow ${\frac{\partial}{{\partial}t}}g_{ij}=-{\varepsilon}Rg_{ij}$ with R > 0, we prove that $${\frac{\partial}{{\partial}t}}{\log}\;u-{\mid}{\nabla}\;{\log}\;u{\mid}^2+{\alpha}\;{\log}\;u-{\beta}u^{{\gamma}-1}+\frac{1}{t}={\Delta}\;{\log}\;u+{\varepsilon}R+{\frac{1}{t}{}\geq}0$$.

• Journal of the Korean Mathematical Society
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• v.6 no.2
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• pp.55-73
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• 1969

• Journal of the Korean Mathematical Society
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• v.7 no.1
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• pp.1-5
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• 1970

• Proceedings of the KIEE Conference
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• 1994.07b
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• pp.1649-1651
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• 1994

This paper presents a new method for estimating partial discharge position using improved cross-correlation technique and neural networks in the power transformer. When ultrasonic signal is occurred by partial discharge, we detected these signals and calculated cross-correlation values with Hamming window. Also, we estimated partial discharge position using neural network with cross-correlation values. In the result of case study, we can estimate more accurately the partial discharge position than any other algorithms.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.631-644
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• 2021

In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds $$\frac{{\partial}u}{{\partial}t}={\Delta}u+a(x,t)u^p+b(x,t)u^q$$ where, 0 < p, q < 1 are real constants and a(x, t) and b(x, t) are functions which are C² in the x-variable and C¹ in the t-variable. We shall get an interesting Harnack inequality as an application.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1121-1136
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• 2005

Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $$U_t\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;U_x,\;U_{xx})\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(u,\;u_x),\;{\alpha}\;=\;0,\;1,\;2$$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.