• Kyungpook Mathematical Journal
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• v.46 no.3
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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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• v.16 no.3
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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.

• Fashion & Textile Research Journal
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• v.10 no.3
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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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• v.26 no.1
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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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• v.16 no.3
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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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• v.51
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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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• 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.

• 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.

• Journal of the Korean Society of Earth Science Education
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• v.16 no.1
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• pp.13-29
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• 2023

This study aims to provide a theoretical examination of symmetry and its implications for science education. For this purpose, first, we examined the way of thinking of Western science in general through ancient Greek scholars. Second, we divided the perception of symmetry into ancient and modern times. Third, we draw out the implications for science education. The results of this study show that, first, the way of thinking in Western science is 'abstraction', which began with Parmenides and was established by Plato. Second, the ancient perception of symmetry is symmetry as beautiful proportions and harmony based on abstraction, and the modern perception of symmetry is symmetry as an invariant perspective based on abstraction that seeks to find constancy in change. We examined Eratosthenes' experiment to measure the circumference of the earth as an example of ancient symmetry, and Galilean relativity or transformation as examples of modern symmetry. Third, the implications for science education are as follows. Awareness of symmetry can help educate students about the nature of science, as it is a central theme that runs through ancient and modern science. Second, the Eratosthenes' experiment and Galilean relativity or transformations are not represented in the 2022 revised curriculum, but could support understanding of science and key competencies and concepts. Finally, an integrated approach to science education centered on symmetry can have a positive impact on scientific attitudes and interest.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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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.