• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.389-402
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• 2015

A symmetric union is a diagram of a knot, obtained from diagrams of a knot in the 3-space and its mirror image, which are symmetric with respect to an axis in the 2-plane, by connecting them with 2-tangles with twists along the axis and 2-tangles with no twists. This paper presents an invariant of knots with symmetric union presentations, which is called the minimal twisting number, and the minimal twisting number of $10_{42}$ is shown to be two. This paper also presents a sufficient condition for non-amphicheirality of a knot with a certain symmetric union presentation.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2008.11a
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• pp.3-4
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• 2008

• Journal of the Society of Naval Architects of Korea
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• v.45 no.3
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• pp.303-308
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• 2008

The induction heating is more efficient for a plate bending because of its easy operation and control of working parameters, compared with the heating by a gas torch. The existing axis symmetric analysis method could neither handle initial curved plates nor be used in the optimization of coil shapes because of its limit of an axis symmetric coil shape. But the proposed method using some discrete part models and analysis processes could overcome these difficulties and show more accurate results in temperatures and deflections of flat or curved plates with initial curvature than those in the existing axis symmetric analysis method. This method is composed of the multi-disciplinary analyses such as an electro magnetic analysis, a heat transfer analysis and a deformation analysis based on inherent strain approach per each step. Traditionally, the coil shape in the induction heating is circular shape and it needs the moving process along heating lines. To overcome this, the 'Long Type Coil' with some linear parallel coils was proposed. It did not need the moving process along heating lines and reduced the heating process time. The results of experiments were compared with those of the simulation.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.748-754
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• 2010

To reduce the computational cost required for assembling vessel fragments using surface geometry, this paper proposes a fast axis estimation method. Using circular constraint of pottery and local planar patch assumption, it finds the axis of the symmetry. First, the circular constraint on each cylinder is used. A circular symmetric pot can be thought of unions of many cylinders with different radii. It selects one arbitrary point on the pot fragment surface and searches a path where a circumference exists on that point. The variance of curvature will be calculated along the path and the path with the minimum variance will be selected. The symmetric axis will pass through the center of that circle. Second, the planar patch assumption and profile curve is used. The surface of fragment is divided into small patches and each patch is assumed as plane. The surface normal of each patch will intersects the axis in 3D space since each planar patch faces the center of the pot. A histogram method and minimization of the profile curve error are utilized to find the probability distribution of the axis location. Experimental results demonstrate the improvement in speed and robustness of the algorithms.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.21-30
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• 2021

In this paper, we prove some rigidity results about embedded minimal hypersurface M ⊂ ℝn+1 with compact ∂M that has one end which is regular at infinity. We first show that if M ⊂ ℝn+1 meets a hyperplane in a constant angle ≥ ��/2, then M is part of an n-dimensional catenoid. We show that if M meets a sphere in a constant angle and ∂M lies in a hemisphere determined by the hyperplane through the center of the sphere and perpendicular to the limit normal vector nM of the end, then M is part of either a hyperplane or an n-dimensional catenoid. We also show that if M is tangent to a C2 convex hypersurface S, which is symmetric about a hyperplane P and nM is parallel to P, then M is also symmetric about P. In special, if S is rotationally symmetric about the xn+1-axis and nM = en+1, then M is also rotationally symmetric about the xn+1-axis.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.1113-1116
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• 2001

Recently, the needs of non-symmetric spherical lens are increasing. Machining non-symmetric spherical lens by general method is limited. This paper researches grinding machine method for non-symmetric spherical lens and accruable problems at processing lens using CAD/CAM. In addition, this paper researches the relation of curvatures to grinding wheel sizes.

• Composites Research
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• v.24 no.2
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• pp.9-13
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• 2011

,In this paper, the symmetric axis parameter method, which was proposed to identify defects, dislocations and stacking fault, with perfect structures in the zinc-blende materials, was introduced as a way to distinguish between elastic and plastic deformation. LAMMPS, a molecular dynamics programme of Sandia National Laboratories, was used to perform nanoindentation simulation on silicon, a zinc-blende material. Defects in silicon (111) under spherical indentation showed the threefold pattern and the slip system in the form of ring crack. Also simulation results show good agreement with experimental results and existing theoretical analyses.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.48 no.9
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• pp.725-730
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• 2020

This study was conducted to reduce the computation time required for the computational acoustic analysis of the supersonic rocket jet plume. In order to reduce the computation time, computational acoustic analysis was performed assuming that the supersonic jet plume is a two-dimensional axis-symmetric problem. The results of computational acoustic analysis showed similar results to the acoustic load measurement results. Through this study, it was confirmed that the acoustic load prediction of the supersonic rocket jet plume can be predicted using a two-dimensional axis-symmetric computational analysis.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.4B
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• pp.413-419
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• 2008

In this study, we develop analytical solutions for long waves propagating over several types of axis-symmetric topographies where the water depth varies in an arbitrary power of radial distance. The first type is a cylindrical island mounted on a shoal. The second type is a circular island. To get the solution, the methods of separation of variables, Taylor series expansion and Frobenius series are used. Developed analytical solutions are validated by comparing with previously developed analytical solutions. We also investigate various cases with different incident wave periods, radii of the shoal, and the powers of radial distance.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.52 no.2
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• pp.53-60
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• 2003

This paper deals with steady-state analysis of a single-phase line-start permanent magnet synchronous motor. In order to analyze the steady-state characteristics, the asymmetric single-phase line-start synchronous motor is converted to the symmetric two-phase synchronous motor, that is, the asymmetric magnetic field is separated from the positive and the negative symmetric components using symmetrical-component theory. The analysis method of the synchronous motor on the d-q axis coordinates is used for the positive component and the equivalent circuit of the induction motor is applied for the negative component analysis. Moreover, d-q axis inductance considering current phase angle is applied to positive component analysis for precise characteristic analysis. In order to validate the proposed analysis method, the analysis results are compared with the experimental results.