• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1329-1343
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• 2013

In this paper, we define translation surfaces in the 3-dimensional Heisenberg group $\mathcal{H}_3$ obtained as a product of two planar curves lying in planes, which are not orthogonal, and study minimal translation surfaces in $\mathcal{H}_3$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.959-972
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• 2021

In this paper, we define and classify minimal translation surfaces with respect to a kind of semi-symmetric metric connections and a kind of semi-symmetric non-metric connections in ℝ³ and ℝ³₁.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.43-53
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• 2021

We study translation surfaces in the Euclidean 3-space ��3 and the Gauss map N with respect to the so-called Cheng-Yau operator ☐. As a result, we prove that the only translation surfaces with Gauss map N satisfying ☐N = AN for some 3 × 3 matrix A are the flat ones. We also show that the only translation surfaces with Gauss map N satisfying ☐N = AN for some nonzero 3 × 3 matrix A are the cylindrical surfaces.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.337-343
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• 2010

We study affine translation surfaces in $\mathbb{R}^3$ and get a complete classification of such surfaces with constant Gauss-Kronecker curvature.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.36-51
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• 2022

We study the translation surfaces in the pseudo-Galilean space with the condition that one of generating curves is planar. We classify these surfaces whose mean and Gaussian curvatures are functions of one variable.

• Wind and Structures
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• v.33 no.6
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• pp.447-462
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• 2021

High spatial and temporal surface pressure measurements were carried out in the state-of-the-art tornado simulator, the Wind Engineering, Energy and Environment (WindEEE) Dome, to explore the characteristics of stationary and translating tornado-like vortices (TLV) for a wide range of swirl ratios (S=0.21 to 1.03). The translational speed of the TLV and the surface roughness were varied to examine their effects on tornado ground pressures, wandering, and vortex structure. It was found that wandering is more pronounced at low swirl ratios and has a substantial effect on the peak pressure magnitude for stationary TLV (error percentage ≤ 35%). A new method for removing wandering was proposed which is applicable for a wide range of swirl ratios. For translating TLV, the near-surface part lagged behind the top of the vortex, resulting in a tilt of the tornado vertical axis at higher translating speeds. Also, a veering motion of the tornado base towards the left of the direction of the translation was observed. Wandering was less pronounced for higher translation speeds. Increasing the surface roughness caused an analogous effect as lowering the swirl ratio.

• Journal of the Institute of Convergence Signal Processing
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• v.4 no.3
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• pp.21-26
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• 2003

A new method to realize 3-dimensional object pattern recognition system using Fourier-based feature extractor has been proposed. The procedure to obtain the invariant feature vector is as follows ; A closed surface is generated by tracing the surface of object using the 3-dimensional polar coordinate. The centroidal distances between object's geometrical center and each closed surface points are calculated. The distance vector is translation invariant. The distance vector is normalized, so the result is scale invariant. The Fourier spectrum of each normalized distance vector is calculated, and the spectrum is rotation invariant. The Fourier-based feature generating from above procedure completely eliminates the effect of variations in translation, scale, and rotation of 3-dimensional object with closed-surface. The experimental results show that the proposed method has a high accuracy.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.523-535
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• 2015

We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.585-595
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• 2024

We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichmüller space, (c) giving a partial answer of how much power is needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.975-976
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• 2009