• The Journal of the Acoustical Society of Korea
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• v.17 no.2E
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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.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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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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• v.17 no.1E
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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.

• The Mathematical Education
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• v.56 no.3
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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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.03a
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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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• v.17 no.2E
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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.

• Journal of KSNVE
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• v.8 no.5
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• pp.974-980
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• 1998

The analysis of dynamic responses are carried out on several orthotropic systems due to transient line source. These include infinite and semi-infinite spaces. The media possess orthotropic or higher symmetry. The lode is in the form of a normal stress acting with parallel to symmetry axis on the plane of symmetry within the materials. The results are first derived for responses of infinite media due to a harmonic line source. 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. Explicit splutions for the displacements due to transient line loads are then obtaind by using Cargniard-DeHoop contour.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.4
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• pp.411-421
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• 2001

The generalized symmetry transform evaluates symmetry without segmentation and extracts regions of interest in an image by combining locality and reflectional symmetry The demand that the symmetry transform be local is reflected by the distance weight function. When calculating large regions-of-interest, we should select a large standard deviation of distance weight function. But such a large standard deviation makes the execution time increase in the second power of r, which is a radius of search area. In this paper we propose modified scan line based GST with selectively directional attention to improve time complexity The symmetry map of our proposed GST is found to be very similar to that of the existing GST. However the computation time of the proposed GST increases linearly with respect to r because our proposed GST evaluates symmetry between a pair of edge pixels along the scan lines. The GST computation decreases considerably when the proposed GST is peformed with selectively directional attention in case of large r. Several experiments in this paper demonstrate the time efficiency and the usefulness of our proposed GST.

• Journal of the Korea Society of Computer and Information
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• v.21 no.4
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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.

• Proceedings of the KIEE Conference
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• 1987.07b
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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.