• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.83-86
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• 2002

Numerical simulations are conducted for laminar flow past a sphere rotating In the transverse direction, in order to investigate the effect of the rotation on the characteristics of flow over a sphere. The Reynolds numbers considered are Re=100, 250 and 300 based on the free-stream velocity and the sphere diameter, and the rotational speeds are in the range of $0{\leq}{\omega}{\leq}1$, where ${\omega}^{\ast}$ is the maximum velocity on the sphere surface normalized by the free-stream velocity. At ${\omega}^{\ast}=0$ (without rotation), the flow past the sphere experiences steady axisymmeoy, steady planar-symmetry and unsteady planar-symmetry, respectively, at Re=100, 250 and 300. However, with rotation, the flow becomes planar-symmetric for all the cases investigated and the symmetry plane is orthogonal to the axis of the rotation. The flow is also steady or unsteady depending on both the Reynolds number and the rotational speed, and the vortical structures behind the sphere are significantly modified by the rotation. For example, at Re=300, hairpin vortices completely disappear in the wake at ${\omega}^{\ast}=0.4\;and\;0.6$, and at ${\omega}^{\ast}=1$ vortical structures of a high frequency are newly generated due to the shear layer instability. It is also shown that with increasing rotational speed, the time-averaged drag and lift coefficients increase monotonically.

• 한국전기전자재료학회논문지
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• 제21권9호
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• pp.829-834
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• 2008

Two-dimensional photonic quasicrystal (PQCs) template patterns have been fabricated on a 1.1 ${\mu}m$-thick DMI-150 photoresist using a multiple-exposure holographic method. A 442-nm HeCd laser was utilized as a light source and the holographic exposure was carried out at a fixed angle of ${\theta}$ = 6$^{\circ}$. After the first holographic exposure, the sample was rotated to a proper angle and the second exposure was performed to the same manner. This exposure process was repeated n/2 times to obtain n-fold symmetric PQC patterns and then the sample was developed. The diffraction patterns of the fabricated PQC template were observed using a 632.8-nm HeNe laser. The fabricated PQCs exhibited 8, 10 and 12-fold rotational symmetry, which was in a good agreement with the interference simulation results. In addition, the diffraction patterns with n-rotation symmetry were observed for the corresponding n-fold PQCs. We believe that the multiple-exposure holography is a good method to fabricate the mesoscale PQCs with a high rotational symmetry.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제5권1호
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• pp.1-11
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• 2001

The purpose of the study is to introduce how tessellation can be used and integrated to connect geometry to pattern in elementary mathematics educations. Tessellation examples include transformations such as translational symmetry, rotational symmetry, reflection symmetry, and glide reflection symmetry. In addition, many examples of tessellation using softwares such as Escher, TesselMania!, and LOGO programs. Further, future study will continue to foster students and teachers to try to construct their alive mathematics knowledge. The study of geometry and patterns require a rich teaching and learning environment provided by in-depth understanding of thinking connections to objects in real world.

• 한국게임학회 논문지
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• 제14권6호
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• pp.109-118
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• 2014

이미지 디자인 등에 사용하기에 용이한 정다각형의 회전대칭성을 갖는 프랙탈 생성에 대해 연구하였다. Loocke의 논문[13]에서 사용한 방법과 같이 회전, 축소 아핀함수를 기반으로 하되 제곱근(square root)함수 대신 줄리아 셋(Julia set)을 생성하는 함수들로 확장하여 IFS(iterated function systems)를 구성하였다. 그 결과 줄리아 셋의 모양에 바탕을 둔 회전 대칭적 프랙탈을 생성할 수 있었으며, 줄리아 셋의 모양이 잘 나타나지 않는 경우에는 IFS 생성 알고리즘의 확률적 함수선택 부분을 변경하여 줄리아 셋의 모양이 뚜렸해지도록 할 수 있음을 보였다. 또한 줄리아 셋의 모양을 지수의 변화를 통해 변형하는 방법을 제안하였다.

• 패션비즈니스
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• 제20권6호
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• pp.79-93
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• 2016

Since the development of patterns using tessellation is applied to a wide range of fields such as clothing, architecture, environment, and products, etc. and its expression principle is also found in various fields such as mathematics and science, etc. However, this pattern is mostly used as a math material with little studies on fashion and culture. In addition, it is thought that Korean traditional culture products need more various and modern design development methods and pattern through preliminary investigation which is simple copy of traditional items, simple copy of Korean Alphabet, Chinese character, and folk paintings. Therefore, it will present the method to make more design cases using Tessellation. Tessellation that combines mathematics and art will be the infinite form of designing of designers as well as creative training way to understand the composition principles of old culture and to raise sense of modern design. Tessellation of regular triangle, regular square, and regular hexagon was performed on the patterns which have meaning of wealth and prosperity of Korean traditional patterns. As the concrete method, first, each side of the regular triangle is developed symmetrically with patterns of fish, turtle, and cicadas. Second, rotational movement after symmetry movement about middle point of one side ${\times}$ 1 symmetry movement about middle point ${\times}$ 1 using crane and cloud, of the regular triangle was performed. Third, the regular square was tessellated parallel movement ${\times}$ 2 with "Da(multi)" and dragon pattern as the source image. Fourth, the sitting tiger was tessellated with symmetry movement about middle point ${\times}$ 2 and parallel movement ${\times}$ 1. Fifth, three bat patterns are tessellated by again rotational movement of two sides after rotational movement of one side and rotational movement of the other side. In addition, It developed traditional culture product design of the scarf, umbrella, aprons, neckties.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.458-461
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• 1995

A new type of rotational motor which is developed has a resolution smaller than 10 $^{-4}$ radian and can be accessed for full rotational angles. The operation principle of the motor is based on inchworm motion of two belt driving mechanism. Flexure hinge mechanism, which is pertinent to symmetry construction of the motor, is designed to minimze the effort to frame and is analyzed by using finite element method. Depending on input signal amplitude, rotational angle by one cycle is varied form 0.2*10 $^{-4}$ rad to 9.76* $^{-4}$ rad. This shows that it has the capability of getting very small rotational angle by considering radius of rotor and amplitude of input signal.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2008년도 하계학술대회 논문집 Vol.9
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• pp.8-8
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• 2008

Two-dimensional photonic quasicrystal (PQCs) template patterns have been fabricated on a $1.1{\mu}m$-thick DMI-150 photoresist using a multiple-exposure holographic method. A 442-nm HeCd laser was utilized as a light source and the holographic exposure was carried out at a fixed angle of $\theta=6^{\circ}$. After the first holographic exposure, the sample was rotated to a proper angle and the second exposure was performed to the same manner. This exposure process was repeated n/2 times to obtain n-fold symmetric PQC patterns and then the sample was developed. The fabricated PQCs exhibited 8, 10 and 12-fold rotational symmetry and the diffraction patterns using a 632.8-nm HeNe laser were observed for n-rotation symmetry corresponding n-fold PQCs. The fabricated PQC template patterns were examined using scanning electron microscopy(SEM). Transmission spectra were measured fourier transform infrared(FTIR) spectrometer.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.115-120
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• 2001

A gyroscope is a rotating body possessing one axis of symmetry and whose rotation about the symmetry axis is relatively large compared with the rotation about any other axis. Tuning fork is this type of structure that various modem gyro-sensors are based on. In this paper, dynamic behavior of a cantilevered beam subjected ta a base rotation with respect to the eccentric axis that is parallel to the beam axis is analyzed. The final equations of motion in terms of generalized coordinates can be solved with numerical scheme with various values of angular velocities and angular accelerations of the rotating axis. In contrast to the case of rotating cantilever beam like helicopter blade, the rotational motion with respect to the beam axis has effect to decrease the stiffness of the beam and has unstable region depending on the magnitude of the rotational angular velocity and angular acceleration.

• 한국수학교육학회지시리즈A:수학교육
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• 제56권3호
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• pp.235-255
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• 2017

This study compared and contrasted the topics related to congruence and symmetry in the elementary mathematics textbooks series of Korea, Japan, Hong Kong, Finland, and Singapore in three aspects: (a) when to teach, (b) what to teach, and (c) how to teach. Firstly, the results of when to teach showed differences across the countries with a variation of teaching the topics among grades from 3 to 6. Secondly, the results of what to teach revealed subtle but significant differences. Regarding congruence, Korea and Japan deal with congruence in a systematic manner, while Finland tends to address the brief definition of congruence, and Hong Kong and Singapore focus on teaching tessellation which implies congruence. Regarding symmetry, Korea and Japan deal only with a symmetric figure for a line and that for a point, while Hong Kong includes a rotational symmetry and Finland extends further to cover the figures positioned in a symmetry both for a line and for a point. Lastly, the results of how to teach demonstrated that Korea tends to focus on the procedure of drawing both triangles to be congruent and symmetric figures. This implies that we need to consider alternative methods such as using various instructional materials and making an explicit connection among mathematical concepts in teaching congruence and symmetry.

• Applied Microscopy
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• 제40권1호
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• pp.21-28
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• 2010

단층 및 복층의 그래핀에 대한 원자분해 투과전자현미경 영상 시뮬레이션 연구에서, 통상의 Boch-wave 방법에 의한 영상이론식들이 고 준위 Laue 영역의 역 격자 회절을 적절히 포함 했을 때 시뮬레이션에 잘 적용될 수 있음을 보여 주었다. 적절한 조건에서 복층 그래핀의 시뮬레이션 영상들은 육방정계의 대칭성 보다는 삼방정계의 대칭성을 보여 주었다. 이 결과는 복층 그래핀이 3차원 공간에서 [0001] 축 방향 회전에 대해 갖는 삼방정계의 격자 대칭성이 영상에 구현되는 것으로 이해될 수 있다. 단층 그래핀에 대해서는, 관측 위상영상이 삼방정계의 대칭성을 보여주는 현상들이 특히 주목되었다. 이 현상은 그래핀 표면에 전자 밀도의 재 배치에 의한 것으로 설명되었다. 그리고 그래핀의 전자 재 배치를 반영하는, 다만 2번째 Laue 준위 영역의 회절 빔까지만 포함하면 관측 영상과 일치하는 시뮬레이션 위상 영상이 얻어졌다.