• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1345-1356
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• 2013

In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy $L_1G=f(G+C)$ for some constant vector $C{\in}\mathbb{E}^3$ and smooth function $f$, where $L_1$ denotes the Cheng-Yau operator.

• Journal of the Korean Society of Clothing and Textiles
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• v.47 no.2
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• pp.337-352
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• 2023

This study develops a t-shirt design that align bones and balance muscles in order to maintain proper posture using the basic concepts of symmetry. First, theoretical and 3D design studies, existing literature on proper and improper posture, and the basic concepts of symmetry are studied to create the design. Next, the 3D design process applies bilateral, rotational, and scaling symmetries to design the inner lines from the basic application of symmetry. A two-stage design process is used, whereby the strain map and pressure points are analyzed using the CLO virtual clothing software, and the most effective design is determined through virtual testing. The results show that the Y+)( and X+― design, which combines the position and type of inner lines, is the most effective for posture correction and maintenance. Overall, this study helps create a theoretical and practical basis for exploring and understanding basic lines appropriate for the human body, and subsequently, for developing various products that maintain posture more accurately and precisely.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.190-197
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• 2002

A new design methodology is presented for the multi-degree-of-freedom vibration absorber for an elastically suspended rigid body with planes of symmetry in general motion. Unlike the common single degree-of-freedom vibration absorber, the presented methodology makes use of both linear and rotational properties of the absorber. It is suggested that an absorber is designed separately for the in-plane and out-of-plane vibration modes and thereby combined the two cases for a six-degree-of-freedom absorber. The nine possible design methods are suggested for the six-degree-of-freedom absorber when an elastically suspended rigid body has one, two, or three planes of symmetry.

• East Asian mathematical journal
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• v.37 no.4
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• pp.355-379
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• 2021

In this article, we investigated plane figures introduced in elementary school mathematics in the perspective of traditional classification, and also analyzed plane figures focused on the invariance of plane figures out of traditional classification. In the view of traditional classification, how to treat trapezoids was a key argument. In the current mathematics curriculum of the elementary school mathematics, the concept of sliding, flipping, and turning are introduced as part of development activities of spatial sense, but it is rare to apply them directly to figures. For example, how are squares and rectangles different in terms of symmetry? One of the main purposes of geometry learning is the classification of figures. Thus, the activity of classifying plane figures from a symmetrical point of view has sufficiently educational significance from Klein's point of view.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.133-138
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• 2014

We show that a compact immersed annular Bryant surface in $\mathbb{H}^3$ meeting two parallel horospheres in constant contact an gles is rotational.

• Proceedings of the KSMRM Conference
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• 2002.11a
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• pp.133-133
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• 2002

Purpose： The purpose of paper is to implement software to visualize brain fiber tract using a 24-bit color coding scheme and to test its feasibility. Materials and Methods： MR imaging was performed on GE 1.5 T Signa scanner. For diffusion tensor image, we used a single shot spin-echo EPI sequence with 7 non-colinear pulsed-field gradient directions： (x, y, z)：(1,1,0),(-1,1,0),(1,0,1),(-1,0,1),(0,1,1),(0,1,-1) and without diffusion gradient. B-factor was 500 sec/$\textrm{mm}^2$. Acquisition parameters are as follows： TUTE=10000ms/99ms, FOV=240mm, matrix=128${\times}$128, slice thickness/gap=6mm/0mm, total slice number=30. Subjects consisted of 10 normal young volunteers (age：21∼26 yrs, 5 men, 5 women). All DTI images were smoothed with Gaussian kernel with the FWHM of 2 pixels. Color coding schemes for visualization of directional information was as follows. HSV(Hue, Saturation, Value) color system is appropriate for assigning RGB(Red, Green, and Blue) value for every different directions because of its volumetric directional expression. Each of HSV are assigned due to (r,$\theta$,${\Phi}$) in spherical coordinate. HSV calculated by this way can be transformed into RGB color system by general HSV to RGB conversion formula. Symmetry schemes： It is natural to code the antipodal direction to be same color(antipodal symmetry). So even with no symmetry scheme, the antipodal symmetry must be included. With no symmetry scheme, we can assign every different colors for every different orientation.(H =${\Phi}$, S=2$\theta$/$\pi$, V=λw, where λw is anisotropy). But that may assign very discontinuous color even between adjacent yokels. On the other hand, Full symmetry or absolute value scheme includes symmetry for 180$^{\circ}$ rotation about xy-plane of color coordinate (rotational symmetry) and for both hemisphere (mirror symmetry). In absolute value scheme, each of RGB value can be expressed as follows. R=λw｜Vx｜, G=λw｜Vy｜, B=λw｜Vz｜, where (Vx, Vy, Vz) is eigenvector corresponding to the largest eigenvalue of diffusion tensor. With applying full symmetry or absolute value scheme, we can get more continuous color coding at the expense of coding same color for symmetric direction. For better visualization of fiber tract directions, Gamma and brightness correction had done. All of these implementations were done on the IDL 5.4 platform.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.325.2-325
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• 2002

A new methodology is presented for the multi-degree-of-freedom vibration absorber for an elastically suspended rigid body with the planes of symmetry in general motion. Unlike the common single degree-of-freedom vibration absorber, the presented methodology makes use of both linear and rotational properties of the absorber. It is suggested that an absorber is designed separately for the in-plane and out-of-plane axes of vibration and combined the two cases for a six-degree-of-freedom absorber. (omitted)

• Proceedings of the Korean Vacuum Society Conference
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• 2010.08a
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• pp.57-57
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• 2010

Sb(111) is a spin textured surface due to the strong spin-orbit coupling, often viewed as a proto-type topological insulator. We used scanning tunneling microscopy (STM) to characterize various Mn-induced subsurface defects existing at the surface of Mn-doped Sb at 50 K. Our STM images show that every defect exhibits 3-fold symmetry with a single rotational orientation and can be categorized by their shapes and sizes. We found more than 10 types of subsurface defects with distinctive orders, which allows the resolution of the vertical positions of the magnetic dopants lying more than 10 layers down from the surface. We will discuss about our findings in comparison with theoretical results.

• Progress in Superconductivity and Cryogenics
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• v.21 no.4
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• pp.6-8
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• 2019

Iron-based superconductors (IBSs) possess nematic phases in which rotational symmetry of the electronic structure is spontaneously broken. This novel phase has attracted much attention as it is believed to be closely linked to the superconductivity. However, observation of the symmetry broken phase by using a macroscopic experimental tool is a hard task because of naturally formed twin domains. Here, we report on a novel detwinning method by using a magnetic field on FeTe single crystal. Detwinning effect was measured by resistivity anisotropy using the Montgomery method. Our results show that FeTe was detwinned at 2T, which is a relatively weak field compared to the previously reported result. Furthermore, detwinning effect is retained even when the field is turned off after field cooling, making it an external stimulation-free detwinning method.

• Bulletin of the Korean Chemical Society
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• v.21 no.1
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• pp.9-22
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• 2000

Optical-optical double resonance experiments have been used to identify and characterize five ion-pair states and several of the bound and repulsive valence states of ClF. This report provides a description of these experiments for $^{35}CIF$ and $^{37}CIF$, and a summary of the current knowledge of the valence and ion-pair states. The important role of perturbations among the rovibronic levels of the bound valence states and their utilization in the double resonance technique is discussed. The ion-pair states of the same symmetry, ${\Omega}$=$0^+$ (E and f) and 1( $\beta$ and G) interact very strongly and the spectroscopy of these states is anomalous and, hence, interesting. Comparison is made to some recent ab initio calculations for ClF. One possible explanation of the irregular vibrational energy levels and rotational constants of the ion-pair states of $O^+$ and 1 symmetry is a crossing of the diabatic potentials of these states. Some currently unresolved questions about ClF spectroscopy are posed for future work. Where appropriate, analogy is made between the electronic states of ClF and the corresponding valence and ion-pair states of $Cl_2.$.