• Title/Summary/Keyword: Symmetry

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A vision algorithm for finding the centers of steam generator tubes using the generalized symmetry transform (일반화 대칭변환을 이용한 원전 증기발생기 전열관 중심인식 비젼 알고리즘)

  • 장태인;곽귀일
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.1367-1370
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    • 1997
  • This paper presents a vision algorithm for finding the centers of steam generator tubes using the generalized symmetry transform, which is used for ECT(Eddy Current Test) of steam generator tubes in nuclear power plants. The geometrical properties of the image representing steam generator tubes shows that they have amost circular or somewhat elliptic appearances and each tube has strong symmetry about its center. So we apply the generalized symmetry transform to finding centers of steam geneator tubes. But applying the generalized symmetry transform itself without any modification gives difficulties in obtaining the exact centers of steam generator tubes. But applying the generalized symmetry transform itself without any modification gives difficulties in obtaining the exact centers of tubes due to the shadow effect generated by the local light installed inside steam generator. Therefore we make the generalized symmetry transform modified, which uses a modified phase weight function in getting the symmetry magnitude in order to overcome the misleading effect by the local light. The experimental results indicate that the proposed vision algorithm efficiently recongnizes centers of steam generator tubes.

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Problem solving and teaching 'group concept' from the point of symmetry (대칭성' 관점에서 본 '문제해결' 및 '군' 개념지도)

  • 남진영;박선용
    • Journal of Educational Research in Mathematics
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    • v.12 no.4
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    • pp.509-521
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    • 2002
  • The purpose of this paper is as follows: $^{\circleda}$ to disclose the essence of symmetry $^{\circledb}$ to propose the desirable strategy of problem-solving as to symmetry $^{\circledc}$ to clarify the relationship between symmetry and group $^{\circledd}$ to propose a way of introduction of 'group' in school mathematics according to its fundamental characteristic, symmetry. This study shows that the nature of symmetry is 'invariance under a transformation' and symmetry is the main idea of 'group'. In mathematics textbooks and mathematics education literature, we find out that the logic of symmetry is widespread. We illustrate two paradigmatic problem related to symmetrical logic and exemplify a desirable instruction of Pascal's triangle. This study also suggests a possibility of developing students' unformal and unconscious conception of group with sym metry idea from elementary to secondary school mathematics.

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The Relation between asymmetric weight-supporting and gait symmetry in patients with stroke (뇌졸중 환자의 체중지지 비대칭과 보행 대칭성의 관련성)

  • Lee, Yong-Woo;Shin, Doo-Chul;Lee, Kyoung-Jin;Lee, Seung-Won
    • Journal of the Korean Society of Physical Medicine
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    • v.7 no.2
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    • pp.205-212
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    • 2012
  • Purpose : The aim of this study was to investigate the relationship between weight-supporting asymmetry and gait symmetry in patients with stroke. Methods : Sixty two stroke patients with hemiplegia stood quietly with eye opens on a force platform to calculate weight-supporting asymmetry from vertical reaction force. The GAITRite was used to evaluate their gait parameters. The data were analyzed using Pearson correlation. Results : The results of this study was showed that the medio-lateral index (ML) was correlated with symmetry rate (SR), symmetry index (SI), and Gait asymmetry (GA) of step time and length but stronger correlation with spatial gait symmetry than temporal symmetry. In gait symmetry, step length has stronger correlation with weight-supporting asymmetry than step time. Conclusions : The results of this study shows weight-supporting asymmetry was correlated with more spatial gait symmetry than temporal symmetry.

IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS

  • Son, Jin-Woo
    • Journal of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1045-1073
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    • 2014
  • The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss's multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are special cases of the results presented in this paper, including Tuenter's classical results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261] and D. S. Kim's eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math. Appl. 60 (2010), no. 8, 2350-2359].

Symmetry Detection Through Hybrid Use Of Location And Direction Of Edges

  • Koo, Ja Young
    • 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.

Lateral Symmetry of Center of Pressure During Walking in Patients With Unilateral Knee Osteoarthritis

  • Kim, Si-hyun;Park, Kyue-nam
    • Physical Therapy Korea
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    • v.28 no.1
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    • pp.77-83
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    • 2021
  • Background: Although symmetry of spatio-temporal parameter and center of pressure (COP) shift during walking is associated with knee adduction moment, research on clinical association with knee osteoarthritis (OA)-related knee pain and functional scores is lacking. Objects: The aims were 1) to compare symmetry of gait parameters and COP-shift in patients with unilateral knee OA and pain and matched controls, and 2) to investigate the relationship between symmetry of gait parameters and COP-shift, and clinical measures. Methods: Female subjects (n = 16) had with unilateral radiological knee OA and pain. Healthy controls (n = 15) were age-matched to OA group. Symmetry of foot rotation, step length, stance and swing phase, lateral symmetry of COP and anterior/posterior symmetry of COP during walking was assessed. To assess the clinical variables, pain intensity, pain duration and function using Knee Osteoarthritis Outcome Survey (KOOS) subscales were collected. We compared symmetry between groups using Mann-Whitney U-test or independent t-test. Relationships between clinical measures and symmetry index measured using Spearman's correlation test. Statistical significance was set at α = 0.05. Results: Knee OA group showed significantly greater values of only lateral symmetry of COP (p < 0.01) than healthy group. Values of lateral symmetry of COP had moderate or strong correlation significantly with the intensity of knee pain, pain duration, and scores of all KOOS subscales (p < 0.01). Conclusion: Patients with unilateral knee OA and pain showed more asymmetry of lateral COP-shift during walking compared with matched healthy controls. In addition, larger asymmetry of lateral COP-shift has the moderate or strong association with worse of knee pain, worse in KOOS scores and longer duration of knee pain. Asymmetry of lateral COP-shift during walking may be one of the characteristics of unilateral knee OA as the compensatory strategy response to unilateral OA of the knee.

Envelope empirical likelihood ratio for the difference of two location parameters with constraints of symmetry

  • Kim, Kyoung-Mi;Zhou, Mai
    • 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.

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A Test for Spherical Symmetry

  • Park, Cheol-Yong
    • 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.

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