• 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.

• 한국데이터정보과학회:학술대회논문집
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• 2002.06a
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• pp.51-73
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• 2002

Empirical likelihood ratio method is a new technique in nonparametric inference developed by A. Owen (1988, 2001). Sometimes empirical likelihood has difficulties to define itself. As such a case in point, we discuss the way to define a modified empirical likelihood for the location of symmetry using well-known points of symmetry as a side conditions. The side condition of symmetry is defined through a finite subset of the infinite set of constraints. The modified empirical likelihood under symmetry studied in this paper is to construct a constrained parameter space $\theta+$ of distributions imposing known symmetry as side information. We show that the usual asymptotic theory (Wilks theorem) still hold for the empirical likelihood ratio on the constrained parameter space and the asymptotic distribution of the empirical NPMLE of difference of two symmetric points is obtained.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.182-184
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• 2005

In this study, we propose a chi-squared test of spherical symmetry. The advantage of this test is that the test statistic and its asymptotic p-value are easy to compute. A simulation study is conducted to study the accuracy, in finite samples, of the limiting distribution of the test statistic under spherical symmetry. The power of our test is compared with those of other tests for spherical symmetry in various alternative distributions via simulation.

• 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.

• 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.

• 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.

• 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%.

• 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.

• Proceedings of the IEEK Conference
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• 2000.11d
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• pp.223-226
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• 2000

In this paper, we report detects system algorithm, adapted a perimetric mask and a generalized symmetry system, to detect a transformable material and find out a minute error cannot be noticed by a naked eye. In this thesis, supposed a stable detecting system applied a general image processing theory and perimetric mash algorithm to detect badness. And finally, detected some vague errors with the application of symmetry transform algorithm that accumulate a symmetry of minute error and put stress on it.

• 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.