• Korean Journal of Remote Sensing
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• v.34 no.6_1
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• pp.969-979
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• 2018

This paper presents reflection symmetry of polarimetric SAR over the Amazon rainforest in terms of correlation coefficients between the pairs of HH- and HV-pol and VV- and VH-pol data by ALOS PALSAR. The reflection symmetry is defined as a non-zero correlation between HH- and HV-pol and VV- and VH-pol over natural distributed targets, and is a fundamental assumption for cross-talk calibration coefficient computation and for three-component decomposition for polarimetric SAR data. The Amazon rainforest is especially one of the common global reference sites for the reflection symmetry. The correlation coefficients for the pairs of reflection symmetry obtained in this study range from 0.018 to 0.097. The results imply that there exists a non-negligible dependency between co-pol and cross-pol in the distributed natural targets, and consequently the non-zero correlation must be considered as a potential contribution to errors of spaceborne SAR polarimetry to some extent.

• Education of Primary School Mathematics
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• v.5 no.1
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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.

• 한국초전도학회:학술대회논문집
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• v.10
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• pp.141-144
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• 2000

We report on the influence of d-wave pairing symmetry in high-T$_c$ superconductor by tunneling spectroscopy. The zerobias conductance peak(ZBCP) which is produced by tunneling through the ab-plane is observed on both of metal Au/YBa$_2$Cu$_3$O$_y$(N/S) tunnel junctions and ferromagnet Co/Au/ YBa$_2$Cu$_3$O$_y$(F/N/S) tunnel junctions. The effects of Andreev reflection on the differential conductance of each junctions are dependent on the tunnel direction. For the S/N/F junction, it appears the suppression of the ZBCP due to the suppression of Andreev reflection at the interface between a ferromagnetic material and a d-wave superconductor. By comparing these experimental results with recent theoretical works on Andreev reflection, the existence of Andreev bound state is verified in high-T$_c$ superconductor, due to the d-wave symmetry of the pair potential.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.951-965
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• 2006

In this paper, we study a topological mirror symmetry on noncommutative complex tori. We show that deformation quantization of an elliptic curve is mirror symmetric to an irrational rotation algebra. From this, we conclude that a mirror reflection of a noncommutative complex torus is an elliptic curve equipped with a Kronecker foliation.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.251-256
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• 2010

In this article, we consider a minimal graph in $R^3$ which is bounded by a Jordan curve and a straight line. Suppose that the boundary is symmetric with the reflection under a plane, then we will prove that the minimal graph is itself symmetric under the reflection through the same plane.

• 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.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.73-88
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• 2007

In this paper, we study the symmetry of figures in elementary geometry. First, we investigate the historical and mathematical background of symmetry of figures and we explore the suitable teaching and learning methods for symmetry in elementary geometry. Also we study the major problem of geometry education that occurring in elementary school.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.434-437
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• 1996

Symmetry is one of the important structural properties of shapes both in perceptual psychology and in computer vision. Recently, a number of automatic symmetry finding algorithms have been reported. Among them, the algorithm based on the use of principal axes of objects is the most general and practical. It is, however, of no use when shapes concerned have some asymmetry. Asymmetric shapes which make us associate with certain kinds of symmetry are practically important and they are called shapes with potential symmetry in this paper. The algorithm we have already proposed can cope with those shapes having potential axial symmetry. The algorithm employs a reflected image of the original and a certain evaluation function. In the former paper, areal minimization was employed for the evaluation function and it yielded satisfactory experimental results. However, it could not cope with those shapes which have larger asymmetry. In this paper, we propose the employment of variance as an alternative evaluation index with respect to the difference image between the reflected and the original shape. The technique is examined its performance by real video images as well as synthetic data. Experimental results are shown and discussion is given.

• Bulletin of the Korean Chemical Society
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• v.13 no.2
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• pp.122-127
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• 1992

Some perovskites $A($Cu_{1}3}Nb_{2}3}$)O_3(A=$Sr^{2+}$$, $Ba^{2+}$ and $Pb^{2+}$) and their series of mixed perovskites have been prepared by solid state reaction. Single perovskite phase was obtained in Sr or Ba rich samples, but pyrochlore phase was found in Pb rich samples. The stability of perovskite phase is dependent on the ionicity of bonding as well as the tolerance factor. All the obtained perovskites have tetragonal symmetry distorted by Jahn-Teller effect of $Cu^{2+}$. In the case of $Sr(Cu_{1}3}Nb_{2}3})O_3$, some superlattice lines caused by threefold enlarging of fundamental unit cell were observed. And, the symmetry of B site octahedron and the bonding character of B-O bond have been studied by IR, ESR and diffuse reflection spectroscopy. It appeared that the symmetry and the bonding character are influenced by such factors as the size and the basicity of A cation.

• Progress in Superconductivity
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• v.2 no.1
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• pp.43-46
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• 2000

We report on the tunneling spectroscopy of tunnel junctions using d-wave superconductor in relation to Andreev reflection. The zero bias conductance peak (ZBCP) which has maximum on [110] direction of ab-plane is observed on metal $Au/YBa_2Cu_3O_y$ tunnel junctions while it is suppressed on the ferromagnetic $Co/Au/YBa_2Cu_3O_y$ tunnel junctions. The effects of Andreev reflection on the differential conductance of each junction are dependent on the tunnel direction. For the $Co/Au/YBa_2Cu_3O_y$ junction, the suppression of Andreev reflection takes place by spin-polarized quasiparticles tunneling from a ferromagnetic material to a d-wave superconductor. By comparing these experimental results with recent theoretical works on Andreev reflection, the existence of Andreev bound state due to the d-wave symmetry of the pair potential is verified in high-$T_c$ superconductor.