• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.423-432
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• 2010

We describe the asymptotic behavior of functions of the Royden p-algebra in terms of p-extremal length. We also prove that each bounded $\cal{A}$-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along p-almost every curve.

• Korean Journal of Computational Design and Engineering
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• v.17 no.4
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• pp.262-273
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• 2012

We present a novel GPU algorithm to compute outer cell boundaries of 3D arrangement subdivided by a given set of triangles. An outer cell boundary is defined as a 2-manifold surface consisting of subdivided polygons facing outward. Many geometric problems, such as Minkowski sum, sweep volume, lower/upper envelop, Bool operations, can be reduced to finding outer cell boundaries with specific properties. Computing outer cell boundaries, however, is a very time-consuming job and also is susceptible to numerical errors. To address these problems, we develop an algorithm based on GPU with a robust scheme combining interval arithmetic and multi-level precisions. The proposed algorithm is tested on Minkowski sum of several polygonal models, and shows 5-20 times speedup over an existing algorithm running on CPU.

• Journal of Fisheries and Marine Sciences Education
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• v.25 no.5
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• pp.1102-1109
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• 2013

An numerical analysis was performed to obtain the design parameters for parallel micro-channels. The parallel micro-channels consist of 10 square channels with a hydraulic diameter of 300 ${\mu}m$ and inlet/outlet manifolds. The channel length is 5mm, 10mm and 40mm respectively. Mass flux was set between 200~600kg/m2s as inlet boundary condition and atmospheric pressure was set as outlet boundary condition. The pressure drop in channels and manifolds were estimated by using the Shah and London correlation and the flow uniformity was represented by the velocity distributions with dimensionless velocity. The results show that the flow uniformity in channels depends on shapes of manifolds, length and mass flux.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.337-352
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• 1999

In this paper we find a geometric condition for the weaker principle of spatial averaging (PSA) for a class of polyhedral domains. Let \ulcorner be a polyhedron in R\ulcorner, n$\leq$3. If all dihedral angles of \ulcorner are submultiples of $\pi$, then there exists a parallelopiped \ulcorner generated by n linearily independent vectors {\ulcorner}\ulcorner in R\ulcorner containing \ulcorner so that solutions of $\Delta$u+λu=0 in \ulcorner with either the boundary condition u=0 or ∂u/∂n=0 are expressed by linear combinations of those of $\Delta$u+λn=0 in \ulcorner with periodic boundary condition. Moreover, if {\ulcorner}\ulcorner satisfies rational condition, we guarantee the weaker PSA for the domain \ulcorner.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.6
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• pp.903-909
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• 2012

This study analyzed the temperature distribution in DPF with five partitioned electric heaters. The temperature distribution in DPF is an important design factor for regeneration and durability of filter. The design Factors that influence the temperature distribution in DPF there are several. In this study, the characteristics of temperature distribution in DPF were analyzed according to the following changes. First, the thermal conductivity of the filter was analyzed about effect on the durability of the filter. Second, the length from exhaust manifold to inlet of DPF was analyzed about effect on the temperature distribution in DPF. The boundary conditions of analysis has been verified with comparison to the results of existing experimental study and the numerical analysis. Based on the identified boundary condition, on assuming the condition of the actual driving, the temperature distribution in DPF was analyzed according to material properties of filter and the position of DPF.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.675-689
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• 2010

For a closed symplectic 4-manifold X, let $Diff_0$(X) be the group of diffeomorphisms of X smoothly isotopic to the identity, and let Symp(X) be the subgroup of $Diff_0$(X) consisting of symplectic automorphisms. In this paper we show that for any finitely given collection of positive integers {$n_1$, $n_2$, $\ldots$, $n_k$} and any non-negative integer m, there exists a closed symplectic (or K$\ddot{a}$hler) 4-manifold X with $b_2^+$ (X) > m such that the homologies $H_i$ of the quotient space $Diff_0$(X)/Symp(X) over the rational coefficients are non-trivial for all odd degrees i = $2n_1$ - 1, $\ldots$, $2n_k$ - 1. The basic idea of this paper is to use the local invariants for symplectic 4-manifolds with contact boundary, which are extended from the invariants of Kronheimer for closed symplectic 4-manifolds, as well as the symplectic compactifications of Stein surfaces of Lisca and Mati$\acute{c}$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.311-319
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• 2009

Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.239-247
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.509-536
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• 2010

In this paper, we investigate curvature-adapted and proper complex equifocal submanifolds in a symmetric space of non-compact type. The class of these submanifolds contains principal orbits of Hermann type actions as homogeneous examples and is included by that of curvature-adapted and isoparametric submanifolds with flat section. First we introduce the notion of a focal point of non-Euclidean type on the ideal boundary for a submanifold in a Hadamard manifold and give the equivalent condition for a curvature-adapted and complex equifocal submanifold to be proper complex equifocal in terms of this notion. Next we show that the complex Coxeter group associated with a curvature-adapted and proper complex equifocal submanifold is the same type group as one associated with a principal orbit of a Hermann type action and evaluate from above the number of distinct principal curvatures of the submanifold.