• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.355-379
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• 2024

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1661-1676
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• 2008

Norm estimates of the pre-Schwarzian derivatives are given for meromorphic functions in the outside of the unit circle. We deduce several univalence criteria for meromorphic functions from those estimates.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.495-503
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• 2002

We consider Holder estimates for ∂ in analytic polyhedra. In the case of dimension 2, it preserves exact Ho1der regularity, and it maps bounded (0,1)-forms into BMO with respect to volume measure.

• Journal of Integrative Natural Science
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• v.4 no.4
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• pp.289-293
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• 2011

In this paper we obtain some Sobolev estimates for the integral operator over singular curves (t, $t^m$) on $\mathbb{R}^2$ for $m{\geq}2$.

• Proceedings of the Korea Society for Simulation Conference
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• 1999.10a
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• pp.294-298
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• 1999

In this paper, through simulations, we find the second derivative SPA(Smoothed Perturbation Analysis) estimates of mean busy cycle with respect to a given parameter in a Markov renewal process which is generated by two exponential distributions. We compare these SPA estimates with the traditional SD(symetric difference) estimates.

• East Asian mathematical journal
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• v.39 no.3
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• pp.369-376
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• 2023

In this paper, we provide Sawyer type conditions on a pair of weights so that the dyadic paraproduct π_b is bounded from L²(u) into L²(v). The conditions can be obtained by checking the boundedness of the dyadic paraproduct on a collection of test functions.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.321-341
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• 2013

In this paper, we discuss the a posteriori error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear hyperbolic equations. The state and the co-state are discretized by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k(k{\geq}0)$. Using mixed elliptic reconstruction method, a posterior $L^{\infty}(L^2)$-error estimates for both the state and the control approximation are derived. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.41-57
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• 2000

In this paper, we consider first order generalized difference scheme for the two-point boundary value problem and one-dimensional second order parabolic type problem. The optimal error estimates in $L_p$ and $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) as well as some superconvergence estimates in $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) are obtained. The main results in this paper perfect the theory of GDM.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.7
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• pp.1677-1684
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• 1996

The theory of optimal stack filtering has been used in difference of estimates(DoE) approach to the detection of intensity edges in noisy image. In this approach, stack filters are applied to a noisy image to obtain local estimates of the dilated and eroded versions of the noise-free image. Thresholding the difference between these two estimates produces the estimated edge map. In this paper, the DoE approach is modified by imposing a symmetry condition of the data used to train the two stack filers. Under this condition, the stack filters obtained are duals of each other. Only one filter must therefore be trained;the other is simply its dual. They also produce statistially unbiased estimates. This new technique is called the symmetric Difference of Estimates (SDoE) approach.

• Water Engineering Research
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• v.2 no.1
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• pp.1-10
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• 2001

The frequency analyses for the precipitation data in Korea were performed. We used daily maximum series, monthly maximum series, and annual series. For nonparametric frequency analyses, variable kernel estimators were used. Nonparametric methods do not require assumptions about the underlying populations from which the data are obtained. Therefore, they are better suited for multimodal distributions with the advantage of not requiring a distributional assumption. In order to compare their performance with parametric distributions, we considered several probability density functions. They are Gamma, Gumbel, Log-normal, Log-Pearson type III, Exponential, Generalized logistic, Generalized Pareto, and Wakeby distributions. The variable kernel estimates are comparable and are in the middle of the range of the parametric estimates. The variable kernel estimates show a very small probability in extrapolation beyond the largest observed data in the sample. However, the log-variable kernel estimates remedied these defects with the log-transformed data.