• The Journal of the Acoustical Society of Korea
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• 제17권2E호
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• pp.47-52
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• 1998

An analysis of dynamic responses is carried out on monoclinic anisotropic system due to a buried harmonic line source. The load is in the form of a normal stress acting along an arbitrary axis on the plane of symmetry within the orthotropic materials: In case that the line load is acting along the symmetry axis normal to the plane of symmetry, plane wave equation is coupled with verital shear wave and longitudinal wave. However, if the line load is acting along an arbitrary axis normal to the plane of symmetry, plane wave equation is coupled with vertical shear wave, longitudinal wave and horizontal shear wave. We first considered the equation of motion in a reference coordinate system, where the line load is coincident with a symmetry axis of the orthotropic material. Then the equation of motion is transformed into one with respect to general coordinate system with azimuthal angle by using transformation tensor. Plane wave solutions of monoclinic systems are derived for infinite media. Finally complete solutions for the plane harmonic wave are obtained by calculating the inverse of the integral transforms, in which bulk wave poles are avoided by deforming the contour of the integration to the complex plane. Numerical results for examples of orthotropic material belonging to monoclinic symmetry are demonstrated.

• 대한수학회지
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• 제60권3호
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• pp.479-501
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• 2023

We study the rationality and symmetry of the Gromov-Witten invariants of the projective line twisted by certain line bundles.

• The Journal of the Acoustical Society of Korea
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• 제17권1E호
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• pp.70-75
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• 1998

The analysis of dynamic responses are carried out on several anisotropic systems due to buried pulsating line sources. These include infinite, semi-infinite spaces. The media possess orthotropic or higher symmetry. The load is in the from of a normal stress acting with parallel to symmetry axis on the plane of symmetry within the materials. The results are first derived for infinite media. Subsequently the results for semi-infinite are derived by using superposition of the solution in the infinite medium together with a scattered solution from the boundaries. The sum of both solutions has to satisfy stress free boundary conditions, thereby leading to the complete solutions. The solutions are simplified to the systems possessing of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic symmetry.

• 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.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1997년도 춘계학술대회논문집
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• pp.136-139
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• 1997

Applications of commercial software DEFORM-3DTM for 3-D simulation in extrusion process are developed for the analysis of twisting of extruded products. Because the elliptical shape has at least one line symmetry, the twisting is not occured during the extrusion. But, the results of extrusion simulation of the elliptical shape show that the twisted boundary of the die surface makes the material inside die surface rotate with the constant angular velocity. Otherwise, the simulation results of the S shaped product show that the twisting can be occured by the only 180$^{\circ}$rotation symmetry of S shape without no line symmetry and show that the angular velocity increases by the only 180$^{\circ}$rotation symmetry without no twisted die surface between on the die entrance section and on the die exit section. The results of the analysis show that the angular velocity of the extruded product changes with die length and friction condition.

• The Journal of the Acoustical Society of Korea
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• 제17권2E호
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• pp.53-58
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• 1998

In this paper, we study the response of several anisotropic systems to buried transient line loads. The problem is mathematically formulated based on the equations of motion in the constitutive relations. The load is in form of a normal stress acting with arbitrary axis on the plane of monoclinic symmetry. Plane wave equation is coupled with vertical shear wave, longitudinal wave and horizontal shear wave. We first considered the equation of motion in reference coordinate system, where the line load is coincident with symmetry axis of the orthotrioic material. Then the equation of motion is transformed with respect to general coordiante system with azimuthal angle by using transformation tensor. The load is first described as a body force in the equations of the motion for the infinite media and then it is mathematically characterized. Subsequently the results for semi-infinite spaces is also obtained by using superposition of the infinite medium solution together with a scattered solution from the free surface. Consequently explicit solutions for the displacements are obtained by using Cargniard-DeHoop contour. Numerical results which are drawn from concrete examples of orthotropic material belonging to monoclinic symmetry are demonstrated.

• 소음진동
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• 제8권5호
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• pp.974-980
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• 1998

본 논문은 직교이방성 탄성계에서 내부 선형하중에 의한 탄성파의 거동을 고찰하였다. 첫째로, 내부 발진원에 대한 탄성과 거동식을 무한계와 반구계에서의 직교이방성 매체에서 유도하였고, 둘째로 Cargniard-DeHoop을 이용하여 순간선형하중에 대한 무한계와 반구계에서의 탄성과 거동식을 유도하였다. 반구계에서 탄성파에 대한 거동식은 무한계에서 유도한 결과와 반구의 표면에서 분산되는 반사파의 합으로 표현되고, 경계영역에서 경계조건을 만족하였다. 여러 가지 이방성 매체에 대한 수치해석 결과를 제시하였고, 이방성 매체의 특성인 bulk wave의 Lacunae 및 표면파의 영향을 고찰할 수 있었다. 본 논문의 결과는 지진연구, 복합소재 특성 연구, 지능형소재 특성연구 등에 응용될 것이다.

• 대한전자공학회논문지SP
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• 제38권4호
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• pp.411-421
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• 2001

일반화 대칭 변환 (generalized symmetry transform, GST)은 주어진 영상에서 사전 분할이 없이 국부성과 반사 대칭성을 결합하여 대칭을 측정하고 관심 영역을 추출한다. GST의 거리 가중치 함수에서 국부적인 대칭성이 반영되며 이 함수의 표준 편차 u에 의해 GST의 수행 범위가 조절된다. 넓은 관심영역을 추출하기 위해 반지름 r이 큰 검색영역 내에서의 대칭성이 추출될 필요가 있다. 이에 따라서 GST의 수행시간은 r에 따라 2차적으로 증가하게 된 본 논문에서는 이를 개선하기 위해 선택적 방향 주의를 가지는 수정된 스캔라인 GST를 제안한다. 제안된 GST는 기존의 GST와 유사한 대칭 특성을 추출하지만 선택적 방향의 기울기만을 고려한 스캔라인 위의 에지 화소쌍에서 GST를 수행함으로써 r에 따라서 이의 수행시간이 선형적으로 증가된다 특히 r이 큰 경우에 선택적 방향에 대해서만 적용하면 기존의 GST의 계산량이 비대해지는 단점을 보완해 줄 수 있다. 제안된 GST가 기존의 GST보다 시간적으로 효과적이며 유용하다는 것이 여러 종류의 영상에 대한 실험으로 확인되었다.

• 한국컴퓨터정보학회논문지
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• 제21권4호
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• pp.9-15
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• 2016

Symmetry is everywhere in the world around us from galaxy to microbes. From ancient times symmetry is considered to be a reflection of the harmony of universe. Symmetry is not only a significant clue for human cognitive process, but also useful information for computer vision such as image understanding system. Application areas include face detection and recognition, indexing of image database, image segmentation and detection, analysis of medical images, and so on. The technique used in this paper extracts edges, and the perpendicular bisector of any two edge points is considered to be a candidate axis of symmetry. The coefficients of candidate axis are accumulated in the coefficient space. Then the axis of symmetry is determined to be the line for which the coefficient histogram has maximum value. In this paper, an improved method is proposed that utilizes the directional information of edges, which is a byproduct of the edge detection process. Experiment on 20 test images shows that the proposed method performs 22.7 times faster than the original method. In another test on 5 images with 4% salt-and-pepper noise, the proposed method detects the symmetry successfully, while the original method fails. This result reveals that the proposed method enhances the speed and accuracy of detection process at the same time.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(II)
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• pp.1090-1093
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• 1987

In this paper, we describe the principle, the procedure and calculation of the measurement. Finally the experimental results are shown and discussions are given. Interpreting of a skewed symmetry in the image as a real symmetry in the 3-D space provides strong constraints on 3-D sharp analysis. In order to apply the idea to the real scene, a method is presented which can find the skewed symmetry in the image of the skewed symmetrical object, even if it is occluded partly. there parameters of the skewed symmetry are estimated by examining peaks in two 2-D hough spaces, onto which the parameters of all candidates of boundary line segments for skewed symmetries are voted. The method is characterized with a small amount of computation, finding of multiple symmetry axes and inference of the occluded parts of the symmetrical object.