• Communications of Mathematical Education
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• v.28 no.1
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• pp.97-130
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• 2014

The purpose of the study was to investigate the aspects of analogy of high school student's thinking process revealed in the inquiry activity with synthetic division. The case study method of qualitative research was conducted with two high school 10th grade students. Structure-mapping model(SMM) of Gentner and similarity frames which were proposed by other researchers were utilized to analyze the data. Two students used analogy as a tool and they could discover synthetic division of more than 2 degrees, but they revealed different levels of mathematics discovery depending on the different degree of analogical thinking. Surface similarity in the process of inquiry activity played a vital role in analogical thinking. We asked students to explore and discover analogy based on structure similarity. Analogy based on the systematic approach made it possible to predict upper domain. Analogy based on the procedure similarity induced internalization. We could conclude that analogy has instrumental, heuristic and reflective characteristics.

• The Mathematical Education
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• v.10 no.2
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• pp.1-3
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• 1972

• Journal for History of Mathematics
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• v.18 no.3
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• pp.39-54
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• 2005

In Chinese Mathematics, Jia Xian(要憲) introduced Zeng cheng kai fang fa(增乘開方法) to get approximations of solutions of Polynomial equations which is a generalization of square roots and cube roots in Jiu zhang suan shu. The synthetic divisions in Zeng cheng kai fang fa give ise to two concepts of Fan il(飜積) and Yi il(益積) which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) obtained the sufficient conditions for Fan il and Yi il for quadratic equations and proved them in the middle of 19th century.

• Journal of the KSME
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• v.30 no.2
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• pp.146-154
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• 1990

수냉형의 Bo kg/$\textrm{mm}^2$1급 TMCP 고장력 강재를 중심으로, 이 강재 모재의 기계적 특성 및 용접부의 각종 사용특성에 관해 종래의 압연제법에 의한 동일강도레벨의 고장력강판과 비교하여 고찰하고 이 강재의 유효이용에 대하여 설명하였다. TMCP 고장력 강판은 탄소당량이 낮고 결 정립 미세화가 달성되기 때문에 파괴인성이나, 용접부의 내외화, 내용접균열성 면에서 탁월한 특 징을 가지나 용접조립시 용접열사이클로 인한 연화현상 때문에 용접부의 사용특성이 문제로 될 수 있다. 그러나 용접조건이나, 강판의 강도, 화학성분의 배려, 선택에 따라 실용상 별로 문제가 되지 않음이 확인하고 있다. 이와 같은 특징으로 인해 TMCP강은 조선용 소재뿐만 아니고, 북해, 북극해와 같은 한냉빙해역의 가혹한 환경에서 작동되는 해양구조물용이나 라인 파이프용 소재 로서도 그 활용이 확대되어 갈 것으로 생각된다.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.1-13
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• 2011

In Tian mu bi lei cheng chu jie fa(田畝比類乘除捷法) of Yang Hui suan fa(楊輝算法)), Yang Hui annotated detailed comments on the method to find roots of quadratic equations given by Liu Yi in his Yi gu gen yuan(議古根源) which gave a great influence on Chosun Mathematics. In this paper, we show that 'Zeng cheng kai fang fa'(增乘開方法) evolved from a process of binomial expansions of $(y+{\alpha})^n$ which is independent from the synthetic divisions. We also show that extending the results given by Liu Yi-Yang Hui and those in Suan xue qi meng(算學啓蒙), Chosun mathematican Hong Jung Ha(洪正夏) elucidated perfectly the 'Zeng cheng kai fang fa' as the present synthetic divisions in his Gu il jib(九一集).

• Membrane Journal
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• v.22 no.6
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• pp.395-403
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• 2012

R&D of Nanofiber membrane has been carried out in the various fields, gas, water treatment, energy, and etc, with the continuous growth of membrane technology. There are several preparation methods for nanofiber, i.e. drawing, template synthesis, phase separation, self-assembly, and electrospinning. However, an electrospinning has many advantages such as high productivity, low production cost, easy to select law material, high relative surface area, and easy to functionalize. Nanofiber has been used in the field of membrane technologies such as secondary battery and water treatment fields. For the secondary battery separator, the separators having a high power and high thermal stability can be developed with spread of nanofiber on the commercial PP or PE/PP separators. High functional membranes can be also developed by adding the functional additives like antibacterial materials in the nanofiber membrane. It can be expected the high value added with nanofiber membrane because of its diverse applications from the water treatment to the energy field and because of its various functional advantages.