• Journal of the Korean Mathematical Society
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• v.30 no.2
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• pp.275-284
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• 1993

• Honam Mathematical Journal
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• v.27 no.2
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• pp.287-300
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• 2005

In this paper, we classify all taut structures for ideal triangulations with two and three tetrahedra.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.851-860
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• 2008

A countable locally finite triangulation is a strong triangulation if a representation of the graph contains no vertex- or edge-accumulation points. In this paper we exhibit the structure of an infinite strong triangulation and prove the existence of connected spanning subgraph with maximum degree 4 in such a graph

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.577-587
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• 2006

We present several properties concerning infinite maximal planar graphs. Results related to the infinite VAP-free planar graphs are also included. Finally, we extend the result of W. Goddard, who showed that every finite 4-connected maximal planar graph is 4-ordered, to infinite strong triangulations.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.183-196
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• 2005

In this paper we study the chromatic sum functions for rooted nonseparable near-triangular maps on the projective plane. A chromatic sum equation for such maps is obtained.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.839-845
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• 1998

For an oriented compact, connected Seifert fibred 3-manifold M with nonempty boundary, we construct a simplicial complex using the equivalence classes of marked annulus systems and show that it is contractible.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.79-87
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• 2014

Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the two-dimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

• Journal of computational fluids engineering
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• v.20 no.4
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• pp.21-27
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• 2015

Flow field around the KRISO 3600TEU container ship is computed using a surface generated based on interpolations of station lines, which are given in a body plan of the ship, without using any CAD program. An interpolation method is suggested based on inscribed circles to generate curves between two neighboring station lines. The interpolated surface is saved in a STL format to use the snappyHexMesh utility of the openfoam. Computed resistance of the ship is compared with experimental and other computational results and the effects of the interpolation of neighboring station lines on the computed resistance are investigated. The suggested method is applied to calculate the flow field around a submarine with appendages. The surface triangulations for the hull and the appendages are generated without consideration of each other, then those surface triangulations are simply combined to provide a grid generator with the body boundary. The junctures of the hull and the appendages are identified automatically during the grid generation procedure. Tip vortex is captured, which travels downstream from the tip of the appendages.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.293-304
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• 2013

In this paper we analyze an error estimator for the lowest-order triangular Raviart-Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385{395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.587-601
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• 2020

In this paper we propose a way of enhancing eigenvalue approximations with the Bank-Weiser error estimators for the P1 and P2 conforming finite element methods of the Laplace eigenvalue problem. It is shown that we can achieve two extra orders of convergence than those of the original eigenvalue approximations when the corresponding eigenfunctions are smooth and the underlying triangulations are strongly regular. Some numerical results are presented to demonstrate the accuracy of the enhanced eigenvalue approximations.