• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.243-250
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• 2020

Hardy and Littlewood found a relation between the smoothness of the radial limit of an analytic function on the unit disk D ⊂ ℂ and the growth of its derivative. It is reasonable to expect an analytic function to be smooth on the boundary if its derivative grows slowly, and conversely. Gehring and Martio showed this principle for uniform domains in ℝ². Astala and Gehring proved quasiconformal analogue of this principle for uniform domains in ℝⁿ. We consider α-quasihyperbolic metric, k^α_D and we extend it to proper domains in ℝⁿ.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1169-1182
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• 2011

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.487-493
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• 2001

$Let \Omega$ be a bounded convex domain in C^n$ with smooth boundary. Let M be a subvariety of $\Omega$ which intersects $\partial$$\Omega$ transversally. Suppose that $\Omega$ is totally convex at any point of $\partial$M in the complex tangential directions.For f $\epsilon$O(M)$\bigcap$/TEX>$C^{\infty}$($\overline{M}$/TEX>), there exists F $\epsilon$ o ($\Omega$))$\bigcap$/TEX>$C^{\infty}$($\overline{\Omega}$/TEX>) such that F(z) = f(z) for z $\epsilon$ M.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.904-907
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• 2002

In this paper, we describe an algorithm to automatically generate an intermediate scene using the bidirectional disparity morphing from the parallel stereopair. To compute the disparity between two reference images, we use the 2-step fast block matching algorithm that restricts the searching range and accelerates the speed of the computation of the disparity. We also define three occluding patterns so as to smooth the computed disparities, especially for occluded regions. They are derived from the peculiar properties of the disparity map. The smoothed disparity maps present that the false disparities are well corrected and the boundary between foreground and background becomes sharper. We discuss the advantages of this algorithm compared to the commonly used schemes and we show some experimental results with real data.

• ETRI Journal
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• v.23 no.2
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• pp.85-95
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• 2001

The surface modeling capability of CAD systems is widely used to design products bounded by free form surfaces and curves. However, the surfaces or curves generated by popular data fitting methods usually have shape imperfections such as wiggles. Thus, fairing operations are required to remove the wiggles, which makes the surfaces or curves smooth. This paper proposes a new method based on the wavelet transform for fairing the surfaces or curves while preserving the continuity with adjacent surfaces or curves. The wavelet transform gives a hierarchical perspective of the surfaces and the curves, which can be decomposed into the overall sweep and details, i.e., local deviations from sweep like the wiggles. The proposed fairing method provides a similar effect on the mathematical surface as that of the grinding operation using sandpaper on the physical surface.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.190-199
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• 2006

A new approach which combines implicit surface scheme and recursive subdivision method is suggested in order to fill the holes with complex shapes in the polygon model. In the method, a base surface is constructed by creating smooth implicit surface from the points selected in the neighborhood of holes. In order to assure C$^1$ continuity between the newly generated surface and the original polygon model, offset points of same number as the selected points are used as the augmented constraint conditions in the calculation of implicit surface. In this paper the well-known recursive subdivision method is used in order to generate the triangular net with good quality using the hole boundary curve and generated base implicit surface. An efficient anisotropic smoothing algorithm is introduced to eliminate the unwanted noise data and improve the quality of polygon model. The effectiveness and validity of the proposed method are demonstrated by performing numerical experiments for the various types of holes and polygon model.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.108-114
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• 1999

In this paper. a new automatic multi=block grid generation technique for general 2D regions is introduced. According to this simple and robust method, the domain of interest is first triangulated by using Delaunay triangulation of boundary points, and then geometric information of those triangles is used to obtain block topology. Once block boundaries are obtained. structured grid for each block is generated such that grid lines have $C^0-continuity$ across inter-block boundaries. In the final step of the present method, an elliptic grid generation method is applied to smoothen grid distribution for each block and also to re-locale the inter-block boundaries, and eventually to achieve a globally smooth multi-block structured grid system with $C^1-continuity$.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.143-146
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• 2003

A finite element based on the efficient higher order zig-zag theory with multiple delaminations Is developed to refine the predictions of frequency and mode shapes. Displacement field through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions including delaminated interfaces as well as free hounding surface conditions of transverse shear stresses. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Throught the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with multiple delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.993-1002
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• 2017

Let ${\Omega}$ be a bounded, uniformly totally pseudoconvex domain in ${\mathbb{C}}^2$ with the smooth boundary b${\Omega}$. Assuming that ${\Omega}$ satisfies the negative ${\bar{\partial}}$ property. Let M be a positive, finite area divisor of ${\Omega}$. In this paper, we will prove that: if ${\Omega}$ admits a maximal type F and the ${\check{C}}eck$ cohomology class of the second order vanishes in ${\Omega}$, there is a bounded holomorphic function in ${\Omega}$ such that its zero set is M. The proof is based on the method given by Shaw [27].