• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.367-376
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• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권3호
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• pp.205-216
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• 2012

When it comes to Lorentz symmetry violation, there are generally two approaches to studying noncommutative field theory: 1) conventional fields are equivalent to noncommutative fields; however, symmetry groups are larger. 2) The symmetry group is the same as conventional standard model's symmetry group; but fields here are written based on the Seiberg-Witten map. Here by adopting the first approach, we aim to connect Lorentz violation coefficients with noncommutative parameters and compare the results with the second approach's results. Through the experimental values obtained for the Lorentz-violating parameters, we obtain a limit of noncommutative symmetry.

• 한국의류산업학회지
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• 제10권3호
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• pp.364-370
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• 2008

This research aims to recognize necessity of modern expression of traditional pattern, understand the matter which is expressed when developing design using traditional pattern, and find the solutions. As the solutions, this research presents design of traditional pattern using symmetry concept and works on the possibility of symmetry as the pattern design. So this research carried out in-depth interview to textile designer working at Gyeongsangnam-do, analyzed the substances. The main results are as follows. First, the presented problems of developing common pattern design and designing using traditional pattern show the necessities for adequate harmony among conception of creative idea, traditional pattern and present pattern. As the solution, the efficient design principles are required. Second, the seven traditional figures can present design applying symmetry, also draw the 8 mapping models for the visuality and utilization. Third, the symmetry-applied traditional pattern design makes it possible for the traditional figure to be represented with the creative and modern sense and provides easier way to the design development by complementing the pattern design formation. As the result, symmetry-utilized traditional pattern design improvement shows the expectation that it will increase the design development ability and ease the figure drawing. In addition, the pattern development which can be applied to any figure presents the time efficiency as well as possibility of the high added value textile industry.

• The Journal of Korean Physical Therapy
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• 제26권1호
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• pp.1-8
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• 2014

Purpose: The aim of the present study was to understand the relationship between gait symmetry and functional balance, walking performance in stroke patients and to makes recommendation regarding the most suitable measure for standardization of expression of spatiotemporal gait symmetry. Methods: 45 subjects with stroke (31 men, 14 women, $57.3{\pm}10.3$ years old) participated in this study. Gait symmetry was calculated by equations of symmetry ratio (SR) and symmetry criterion (SC) for stance time, swing time, single leg support time (SLST), step length, and stride length. Spatiotemporal parameters were measured respectively by walkway system ($GAITRite^{TM}$ system). Limit of stability (LOS) by using forceplate (Balance Performance Monitor) during voluntary weight displacement and Berg Balance Scale (BBS) were measured as functional balance and Timed Up and Go test (TUG) and Functional Ambulation Category (FAC) were assessed as functional walking. Results: SR in stance time and swing time was correlation with BBS, TUG and FAC (p<0.05). SR in SLST only with BBS (p<0.01), SR in step length only with FAC (p<0.05). SC in stance time was correlation with BBS and TUG (p<0.05). SC in swing time and SLST with BBS, TUG and FAC (p<0.01), SC in step length with TUG and FAC (p<0.01), SC in stride length with BBS and FAC (p<0.01). Conclusion: Gait symmetry in spatiotemporal gait parameters provides meaningful information about functional balance and walking performance in stroke subjects. Our analysis may support the recommendations of the symmetry criterion as equation for standardization of gait symmetry.

• PNF and Movement
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• 제16권3호
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• pp.405-414
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• 2018

Purpose: The purpose of this study was to examine test-retest reliability and criterion-related validity of a trunk stability robot when measuring the weight-bearing symmetry static sitting and standing in stroke patients. Methods: For 27 stroke patients, weight-bearing symmetry was assessed twice, 7 days apart. The intraclass correlation coefficient (ICC2,1) and minimal detectable change (MDC) were used to examine the level of agreement between test and retest. The criterion-related validity of weight -bearing symmetry was demonstrated by Spearman correlation of modified Barthel index (MBI), the sit to stand test (STS), the timed up & go Test (TUG), and the function in sitting test (FIST). Results: the test-retest agreements were excellent for the weight-bearing symmetry of static sitting (ICC2,1: 0.90) and standing (ICC2,1: 0.89). It all showed that the acceptable MDC for the weight-bearing symmetry of static sitting and standing was 0.11 and 0.16, respectively (highest possible score<20 %), indicating that the measures had a small and acceptable degree of measurement error. The weight-bearing symmetry of static sitting was significantly correlated with the TUG(r=-0.45) and FIST(r=0.46)(p<0.05); the weight-bearing symmetry of static standing was also significantly correlated with MBI (r=0.65), TUG (r=-0.67), FIST (r=0.61)(p<0.01), and STS (r=-0.47)(p<0.05). Conclusion: The weight-bearing symmetry of static sitting and standing assessed by the trunk stability robot showed highly sufficient test-retest agreement and mild-to-moderate validity. It could also be useful for clinicians and researchers to evaluate balance performance and monitor functional change in stroke patients.

• Applied Microscopy
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• 제51권
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• pp.10.1-10.9
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• 2021

We investigate the sensitivity of symmetry quantification algorithms based on the profile R-factor (R_p) and the normalized cross-correlation (NCC) coefficient (γ). A DM (Digital Micrograph^©) script embedded in the Gatan digital microscopy software is used to develop the symmetry quantification program. Using the Bloch method, a variety of CBED patterns are simulated and used to investigate the sensitivity of symmetry quantification algorithms. The quantification results show that two symmetry quantification coefficients are significantly sensitive to structural changes even for small strain values of < 1%.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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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.

• 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.

• 대한지구과학교육학회지
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• 제16권1호
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• pp.13-29
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• 2023

본 연구는 대칭성에 대해 이론적으로 고찰하고 이의 과학교육적 함의를 도출하는 것을 목표로 한다. 이를 위해 첫째, 고대 그리스 학자들을 통해 일반적인 서양 과학의 사유방식을 살펴보았다. 둘째, 대칭성에 대한 인식을 고대와 근현대로 나누어 살펴보았다. 셋째, 이에 대한 과학교육적 함의를 도출하였다. 본 연구의 결과는 첫째, 서양 과학의 사유방식은 파르메니데스에서 시작되어 플라톤이 정립한 '추상화'이다. 둘째, 고대의 대칭성 인식은 추상화를 기반으로 한 아름다운 비율과 조화로서의 대칭성, 근현대의 대칭성 인식은 변화에서 불변을 찾고자 했던 추상화를 기반으로 한 불변의 관점으로서의 대칭성이다. 그리고 고대의 대칭성의 예시로서 에라토스테네스의 지구 둘레 측정 실험에 대해 고찰하였으며, 근현대의 대칭성의 예시로서 갈릴레이 상대성 및 변환을 고찰하였다. 셋째, 이에 따른 과학교육적 함의는 다음과 같다. 대칭성에 대한 인식은 고대부터 근현대 과학을 관통하는 핵심주제라는 관점에서 과학의 본성 교육에 도움이 될 수 있다. 둘째, 에라토스테네스 지구 둘레 측정 실험과 갈릴레이 상대성 및 변환의 경우 2022 개정 교육과정에는 제시되어 있지 않지만 과학과 핵심역량 및 개념 이해에 도움이 될 수 있다. 마지막으로, 대칭성을 중심으로한 통합적 접근으로의 과학교육은 과학적 태도와 흥미에 긍정적인 영향을 줄 수 있다.

• 대한수학회지
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• 제37권5호
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• pp.751-761
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• 2000

Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.