• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.949-966
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• 2009

We proved in [10] that Friedrich's estimate [5] for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1579-1589
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• 2014

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ${\nabla}$ with skew torsion $T{\in}{\Lambda}^3M$ in the situation where the tangent bundle splits under the holonomy of ${\nabla}$ and the torsion of ${\nabla}$ is of 'split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.249-265
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• 2017

Interface problem here refers to a second order elliptic problem with a discontinuous coefficient for the second order derivatives. For the corresponding boundary value problem, the maximum principle still holds but Hopf's boundary point lemma may fail. We will give an optimal power type estimate that replaces Hopf's lemma at those boundary points, where this coefficient jumps.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.175-186
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• 2018

Let (M, J, ${\theta}$) be a complete pseudohermintian (2n+1)-manifold. In this paper, we derive the subgradient estimate for positive solutions to a nonlinear subelliptic equation ${\Delta}_bu+au{\log}u+bu=0$ on M, where $a{\leq}0$, b are two real constants.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.383-395
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• 1999

This study is concerned with the evaluation of predictive ability of classification models with ordered multiple categories. If categories can be ordered or ranked the spread of misclassification should be considered to evaluate the performance of the classification models using loss rate since the apparent error rate can not measure the spread of misclassification. Since loss rate is known to underestimate the true loss rate the bootstrap method were used to estimate the true loss rate. thus this study suggests the method to evaluate the predictive power of the classification models using loss rate and the bootstrap estimate of the true loss rate.

• Journal of the Optical Society of Korea
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• v.18 no.6
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• pp.672-678
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• 2014

We propose a method to estimate the 3-D shape of surfaces with specular reflection, using a model of the difference in appearance between images reflected from a flat surface and a curved surface. First, we analyze the geometry of spatial reflection from a specular surface and how reflected light varies due to a curved surface. This is used to estimate 3-D shape. The proposed method is shown to be effective in experiments using illumination from spatially distributed light sources and a camera capturing the reflected light from curved, specular surfaces.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.289-300
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• 2007

The stock return is changed by factors of inside and outside or is changed by factor of market system. But most studies have not considered the changes of stock return distribution when estimate the VaR. Such study may lead us to wrong conclusion. In this paper we calculate the VaR of price-to-earnings ratios by the distribution that have considered the change point and used transformation to satisfy normal distribution.

• Journal of information and communication convergence engineering
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• v.1 no.4
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• pp.189-193
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• 2003

A new algorithm is presented for adaptive notch filtering of narrow band or sine signals for embedded among broad band noise. The notch filter is implemented as a constrained infinite impulse response filter with a minimal number of parameters, Based on the recursive prediction error (RPE) method, the algorithm has the advantages of the fast convergence, accurate results and initial estimate of filter coefficient and its covariance is revealed. A convergence criterion is also developed. By using the information of the noise-to-signal power, the algorithm can self-adjust its initial filter coefficient estimate and its covariance to ensure convergence.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.35 no.11
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• pp.503-510
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• 1986

A new algorithm based on the concept of prediction error minimization is suggested to estimate the time varying delay in discrete processes. In spite of the existence of the stochastic noise, this algorithm can estimate time varying delay accurately. Computation time of this algorithm is far less than that of the previous extended parameter methods. With the use of this algorithm, generalized minimum variance control shows good control behavior in simulations.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.35 no.11
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• pp.519-528
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• 1986

By using a least-square input estimator and likelihood ratio technique, a tracking problem is presented. A Kalman tracking filter based on constant-velocity, straight-line model is used to track a target and the filtered estimate is updated using an input estimate when a maneuver is detected. Track residuals at each scan are sensed by a detector to guard against unexpected corrections of the filter. The simulation results show there are significant improvements using the scheme presented.