• The Mathematical Education
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• v.46 no.3
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• pp.273-292
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• 2007

The purpose of this study was to find out how second, fourth and sixth graders understood the main contents related to spatial sense in the Seventh National Mathematics Curriculum. For this purpose, this study examined students' understanding of the main contents of congruence transformation (slide, flip, turn), mirror symmetry, cubes, congruence and symmetry. An investigation was conducted and the subjects included 483 students. The main results are as follows. First, with regards to congruence transformation, whereas students had high percentages of correct answers on questions concerning slide, they had lower percentages on questions concerning turn. Percentages of correct answers on flip questions had significant differences among the three grades. In addition, most students experienced difficulties in describing the changes of shapes. Second, students understood the fact that the right and the left of an image in a mirror are exchanged, but they had poor overall understanding of mirror symmetry. The more complicated the cubes, the lower percentages of correct answers. Third, students had a good understanding of congruences, but they had difficulties in finding out congruent figures. Lastly, they had a poor understanding of symmetry and, in particular, didn't distinguish a symmetric figure of a line from a symmetric figure of a point.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.290-297
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• 2004

The control laws for cart-pole system are studied to see the schemes on which the control laws are made. Also, the odd symmetry of the relation between the output of the control laws and the system state vector is observed. Utilizing the symmetry in quantizing the system state variables and implementing the control laws into look-up table is discussed. Then, a CMAC is trained for a nonlinear control law for a cart-pole system such that the symmetry is conserved and its learning performance is evaluated. It is found that utilizing the symmetry is to reduce the memory requirement as well as the training period while improving the learning quality in terms of preserving the symmetry.

• 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.

• The Journal of Korean Physical Therapy
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• v.27 no.4
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• pp.228-233
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• 2015

Purpose: Gait is the most basic element when evaluating the quality of life with activities of daily living under ordinary life circumstances. Symmetrical use of the lower extremities requires complicated coordination of all limbs. Thus, this study examined asymmetry of muscle activity quadriceps femoris and tibialis anterior as a baseline for training during over-ground walking and stair walking of stroke patients. Methods: Subjects were 14 stroke patients included as one experimental group. Gait speed used in this study was determined by the subject. Low extremity paretic and non-paretic EMG was compared using the surface EMG system. Results: The low extremity EMG difference was statistically significant during over-ground walking and stair walking (p<0.05). The result of low extremity EMG substituted symmetry ratio formula was compared to EMG symmetry ratio in both legs during over-ground walking and stair walking. The average symmetry ratio of quadriceps femoris during over-ground walking was 0.65, and average symmetry ratio of quadriceps femoris during stair walking was 0.47, with significant difference (p<0.05). Conclusion: EMG data was higher in stair walking than over-ground walking. However, in the comparison of symmetry ratio, asymmetric EMG of quadriceps femoris was significantly increased during stair walking. These findings suggested that application of stair walking for strengthening of both legs can be positive, but the key factor is maintaining asymmetrical posture of both legs. Therefore, physical therapists should make an effort to reduce asymmetry of quadriceps femoris power during stair walking by stroke patients.

• 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.

• Journal of the Korean Society of Propulsion Engineers
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• v.25 no.2
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• pp.66-78
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• 2021

In this study, the effect of Symmetry Breaking was compared according to the equivalent ratio condition and the number of nozzles where combustion instability occurs in an annular combustor. Generally, due to the relatively short combustor length, a longitudinal instability was less likely to occur in the annular combustor, but the combustion instability sometimes happens when ducts such as transition piece in gas turbine power station are present. In this case, due to the duct, only the longitudinal instability mode is observed. The characteristics of Symmetry Breaking were investigated according to the number of five lean nozzles and the equivalent ratio combination, and as the equivalent ratio decreased, the effect of Symmetry Breaking rapidly occurred, and the instability was dramatically disappeared and the amplitude was greatly reduced. In addition, it was confirmed that as the number of lean nozzles increased, a phenomenon such as a reduction in the equivalent ratio appeared.

• Maxillofacial Plastic and Reconstructive Surgery
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• v.40
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• pp.18.1-18.6
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• 2018

Background: Clefts in newborns are associated with severe morphological and functional impairment. Especially the lip is of importance as if the treatment result is unsatisfactory, it can lead to psychological changes in the patient. Different operative procedures have been developed over the last decades. The aim of the presented study was the comparison of the surgical techniques according to Millard and Pfeifer regarding the temporal development of the postoperative symmetry of the lip height and mouth width. Methods: Digitized photographs of patients from the department of oral and maxillofacial surgery at the University of Göttingen were evaluated from 1979 to 1996. With a video analysis program, the lip height and mouth width were analyzed regarding the symmetry. We demonstrated the symmetry values over a period of 8 years in order to show the influence of growth on postoperative results. Results: The development of the vertical symmetry of the Philtrum and the lip vermillion on the cleft side in comparison to the healthy side behaves differently depending on Pfeifer and Millard. The lip height of the cleft lip was shorter in both techniques than on the healthy side, but Pfeifer's difference was significantly more pronounced. The lip vermillion height on the cleft side was slightly shorter in the Millard group and markedly larger in the Pfeifer group. Both techniques can achieve good symmetry results for the vertical dimension of the lip. According to Pfeifer, the development of the horizontal dimension on the cleft side is bigger within the first 4 years than on the healthy side; according to the Millard technique, the horizontal development is smaller. These differences are greater within the first 6 years and approach between the 6th and 8th year. Conclusions: The Millard technique demonstrates better results concerning the philtrum and vermillion symmetry during growth within the first 6 years. Over the whole study period, growth corrects the philtrum and vermillion symmetry within the Pfeifer group.

• Structural Engineering and Mechanics
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• v.11 no.2
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• pp.199-210
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• 2001

Axially compressed circular cylinders repeat symmetry-breaking bifurcation in the postbuckling region. There exist stable equilibria with all symmetry broken in the buckled configuration, and the minimum postbuckling strength is attained at the deep bottom of closely spaced equilibrium branches. The load level corresponding to such postbuckling stable solutions is usually much lower than the initial buckling load and may serve as a strength limit in shell stability design. The primary concern in the present paper is to compute these possible postbuckling stable solutions at the deep bottom of the postbuckling region. Two computational approaches are used for this purpose. One is the application of individual procedures in computational bifurcation theory. Path-tracing, pinpointing bifurcation points and (local) branch-switching are all applied to follow carefully the postbuckling branches with the decreasing load in order to attain the target at the bottom of the postbuckling region. The buckled shell configuration loses its symmetry stepwise after each (local) branch-switching procedure. The other is to introduce the idea of path jumping (namely, generalized global branch-switching) with static imperfection. The static response of the cylinder under two-parameter loading is computed to enable a direct access to postbuckling equilibria from the prebuckling state. In the numerical example of an elastic perfect circular cylinder, stable postbuckling solutions are computed in these two approaches. It is demonstrated that a direct path jump from the undeformed state to postbuckling stable equilibria is possible for an appropriate choice of static perturbations.

• Journal of KSNVE
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• v.7 no.4
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• pp.637-644
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• 1997

In this paper, a method of finite element analysis is presented for efficient calculation of vibration characteristics of not only simply interconnected structure with cyclic symmetry but also multiply interconnected structure with cyclic symmetry by using discrete Fourier trandform by means of a computer with small memory in a short time. Simply interconnected structure means it is composed of substructures which are adjacent themselves in circumferential direction. First, a mathematical model of multiply interconnected structure with cyclic symmetry is defined. The multiply interconnected structure is partitioned into substructures with the same goemetric configuration and constraint eqauations to be satisfied on connecting boundaries are defined. Nodal displacements and forces are transformed into complex forms through discrete Fourier transform and then finite element analysis is performed for just only a representative substructure. In free vibration analysis, natural frequencies of a whole structure can be obtained through a series of calculation for a substructure along the number of nodal diameter. And in forced vibration analysis, forced response of whole structure can be achieved by using inverse discrete Fourier transform of results which come from analysis for a substructure.

• The KIPS Transactions:PartB
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• v.15B no.2
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• pp.81-86
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• 2008

This paper discusses the problem of partial object recognition in image databases. We propose the method to reconstruct and estimate partially occluded shapes and regions of objects in images from overlapping and cutting. We present the robust method for recognizing partially occluded objects based on symmetry properties, which is based on an ellipse of objects. Our method provides simple techniques to reconstruct occluded regions via a region copy using the symmetry axis within an object. Since our method relies on reconstruction of the object based on the symmetry rather than statistical estimates, it has proven to be remarkably robust in recognizing partially occluded objects in the presence of scale changes, rotation, and viewpoint changes.