• Journal for History of Mathematics
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• v.19 no.1
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• pp.65-78
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• 2006

The law of refraction, which is called Snell's law in physics, has a significant meaning in mathematics history. After Snell empirically discovered the refraction law $\frac{v_1}{sin{\theta}_1}=\frac{v_2}{sin{\theta}_2$ through countless observations, many mathematicians endeavored to deduce it from the least time principle, and the need to surmount these difficulties was one of the driving forces behind the early development of calculus by Leibniz. Fermat solved it far advance of others by inventing a method that eventually led to the differential calculus. Historically, mathematics has developed in close connection with physics. Physics needs mathematics as an auxiliary discipline, but physics can also belong to the lived-through reality from which mathematics is provided with subject matters and suggestions. The refraction law is a suggestive example of interrelations between mathematical and physical theories. Freudenthal said that a purpose of mathematics education is to learn how to apply mathematics as well as to learn ready-made mathematics. I think that the refraction law could be a relevant content for this purpose. It is pedagogically sound to start in high school with a quasi-empirical approach to refraction. In college, mathematics and physics majors can study diverse mathematical proof including Fermat's original method in the context of discussing the phenomenon of refraction of light. This would be a ideal environment for such pursuit.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.39-57
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• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.

• Journal of the Korean School Mathematics Society
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• v.24 no.2
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• pp.173-190
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• 2021

This study analyzed the proof of the inverse square law, which is said to be the core of Newton's , in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximation, and the limit of the ratio of the line segments. Based on this analysis, we proposed to use Newton's geometric limit as a tool to show the usefulness of mathematics, and to use it as a means to break the conventional notion that the area of the curve can only be obtained using the definite integral. In addition, to help the desirable use of geometric limits in school mathematics, we suggested the following efforts are required. It is necessary to emphasize the expansion of equivalence in the micro-world, use some questions that lead to use as heuristics, and help to recognize that the approach of ratio is useful for grasping the equivalence of line segments in the micro-world.

• Clinical and Experimental Pediatrics
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• v.49 no.11
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• pp.1180-1185
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• 2006

Purpose : The aims of this study were to verify the incidence of hypohidrosis and to determine the predictive value of noninvasive indicator test ($Neurocheck^{TM}$) for sweating after administration of topiramate in newly diagnosed pediatric epileptic patients. Methods : A total of 46 epileptic patients (22 boys; 24 girls) on topiramate treatment were evaluated in this study at the Department of Pediatrics, Chonbuk National University Hospital, from October 2004 to July 2005. We measured sweating functions using a noninvasive sweating test ($Neurocheck^{TM}$) before topiramate medication, and after 3 months when topiramate reached its target dosage. We performed a direct questionnaire survey for the hypohidrosis related symptoms during topiramate treatment. Results : The mean age was $7.8{\pm}3.2year$. The mean dosage of topiramate was $4.5{\pm}0.8mg/kg/day$. Among the patients, there were 40 complex partial seizures, one simple partial seizure, two partial seizures with secondarily generalization, two generalized seizures, and one Lennox-Gastaut syndrome case. Of the 46 epileptic patients, 17 patients (37.0 percent) experienced hypohidrosis and hypohidrosis related symptoms, 12 (26.1 percent) had facial flushing, four (8.7 percent) had heat intolerance, one (2.2 percent) had lethargy, but no one had anhidrosis. Among the 17 patients, the mild group numbered 12 and the severe group totalled five. Hypohidrosis by $Neurocheck^{TM}$ was diagnosed in 16 patients. The overall measures of agreement between $Neurocheck^{TM}$ and the survey was 76.5 percent. The specificity of this test was 89.7 percent. Patients who showed a time delay after medication, especially over 3 minutes, were seen only in the severe group. Conclusion : $Neurocheck^{TM}$ could be clinically useful to detect and predict topiramate induced hypohidrosis in pediatric epileptic patients. We recommend that patients who show a delay over 3 minutes in $Neurocheck^{TM}$ test after topiramate initiation should be monitored for hypohydrosis.

• Korean Journal of Food Science and Technology
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• v.40 no.4
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• pp.365-374
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• 2008

Plastics are comparatively new polymeric materials that are manufactured by chemical synthesis, making them different from natural materials such as wood, paper, stone, metal, and glass. Due to a wide range of properties, including processing capabilities and duration, plastics have become rapidly ubiquitous, being used in all industries, and have improved our quality of life. However, it is true that plastics cause environmental contamination problems that have become important social issues, such as environmental hormone leakage due to incineration or reclamation, difficulty in securing reclamation sites, and deadly poisonous dioxin generated by the incomplete incineration of waste plastic materials. To solve these problems, it is urgent to develop and commercialize degradable plastics that can be stably and conveniently used just as general plastics, and that are easily decomposed by sunlight, soil microbes, and heat generated from reclaimed land after use. This review presents recent worldwide trends in the development and marketing of environmentally degradable plastics.

• 한국신재생에너지학회:학술대회논문집
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• 2010.11a
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• pp.40.1-40.1
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• 2010

인간의 삶과 밀접한 관련이 있는 태양 에너지는 전세계적으로 에너지 부족 문제 해결방안을 위한 대체 에너지 자원으로 각광 받고 있다. 즉 태양으로부터 방출되어 지표면에 도달하는 태양광은 연간 약 23,000 TW(Perez et al., 2009)로써 다른 어떤 종류의 에너지원보다 풍부하기 때문에 태양광 발전은 양적인 측면에서의 무한한 잠재력뿐만 아니라 환경적인 측면에서 무공해라는 장점을 가진다. 특히 국내에서는 2030년까지 태양광 에너지와 풍력 및 수소에너지들은 3대 국가 에너지 전략 분야로 집중 육성되고 있다(한국과학기술정보연구원, 2007). 지표면에 도달하는 태양 에너지 평가 및 분석을 위하여 일사계에 의한 관측 자료가 이용될 수 있으나 관측 영역 및 관측 정밀도 문제 때문에 태양 복사 모델(Solar Radiative Transfer Model)에 의한 계산 자료가 중요하게 활용된다. 이 연구에서 한반도의 지표면 태양광 계산을 위하여 사용된 모델은 Iqbal(1983)에 근거한 것으로써 단일 기층의 모형대기를 가정한 모델이며 상세 모델(Line-by-Line Model)에 의하여 보정하여 2009년 1월부터 2009년 12월까지 한반도의 지표면 태양광 시공간 분포를 계산하였다. 이 계산을 위하여 대기 중의 가스와 에어로졸 및 구름 성분들에 대한 모델 입력자료 등이 요구되며 이 자료들은 기상청의 수치 모델(Regional Date Assimilation and Prediction System; RDAPS)과 기상 관련 인공위성(OMI와 MODIS 및 MTSAT-1R 등)으로부터 발췌하여 사용하였다. 그 결과 이 연구 기간(2009년 1월 ~ 2009년 12월)동안 1 km 간격의 수평면에 대하여 계산된 한반도의 지표면 태양광은 안동과 대구 및 진주를 연결하는 지역에서 최대값($5400MJ/m^2$ 이상)이 나타났다. 그러나 지표면 일사 관측 자료의 공간 분포는 이 연구 결과와 차이가 있었으며 그 원인은 관측소 일사계의 보정 및 관리운영에 따른 자료 정확성 결여 때문으로 평가된다.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.37-62
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• 2014

In this thesis, we inquire into teaching method of decimal fraction concept in elementary mathematics education based on measurement activity. For this purpose, our research tasks are as follows: First, we design a experimental learning-teaching plan of 'decimal fraction' unit in 4th grade textbook and verify its effect. Second, after teaching experiment using experimental learning-teaching plan, we analyze the student's status of understanding about decimal fraction concept. As stated above, we have performed teaching experiment which is ruled by new lesson design and analysed the effects of teaching experiment. Through this study, we obtained the following results. First, introduction of decimal fraction based on measurement activity promotes student's understanding of measuring number and decimal notation. Second, operator concept of decimal fraction is widely used in daily life. Its usage is suitable for elementary mathematics education within the decimal notation system. Third, a teaching method of times concepts using place value expansion of decimal fraction is more meaningful and has less possibility of misunderstanding than mechanical shift of decimal point. Fourth, teaching decimal fraction through the decimal expansion helps students with understanding of digit 0 contained in decimal fraction, comparing of size and place value. Fifth, students have difficulties in understanding conversion process of decimal fraction into decimal notation system using measurement activity. It can be done easily when fraction is used. However, that is breach to curriculum. It is necessary to succeed research for this.

• Journal of Aquaculture
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• v.3 no.1
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• pp.89-125
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• 1990

In order to improve top shell seed production techniques spawning and larvae rearing were done in rearing tanks. Growth of young top shell in the nursing ground were also investigated. For induced spawning, top shells were maintained in still water during night time. Then they were treated with ultra violet iradiated sea water after dried up in air for 60 minutes. Spawning rate were 10 to $39.77\%$. It was found that young top shells moved in the growing grounds from nursing grounds when they reached approximately 30-40mm in shell heignt. Among main food algae for top shell in the natural growing grounds, sea mustard were melted away during June. Therefore, presence of another food algae such as Ecklonia cava or Sargassum spp. seems to be the main limiting factor for survival of top shell during summer. The tolerance of top shells ranging from 30mm to 60mm to low density of seawater for were tested at the temperature between 29.5 and $31.4^{\circ}C$. Hundred percent mortality occoured in 20, 55 and 90 hours after first stocking at the specific gravity of 1.010, 1.015, and 1.020, respectively.

• KDI Journal of Economic Policy
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• v.19 no.2
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• pp.73-157
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• 1997

19세기(世紀) 중반(中盤)에 시작된 선진국(先進國)들의 공업화(工業化)는 약 100년이 소요(所要)되었는데 동(東)아시아 신흥공업국(新興工業國)(NICs)들의 경우에는 20~30년이 소요(所要)된 것으로 추정된다. 후자(後者)의 공업화(工業化) 경험은 흔히 '동(東)아시아의 기적(奇蹟)'이라 불린다. 그러나 이 고속성장(高速成長) 혹은 압축성장(壓縮成長)이 가능했던 이유가 무엇이냐에 관해 경제학계(經濟學界) 내외(內外)에서 그리고 국내외(國內外)에서 일치된 의견이 없고, 특히 이 과정에서의 정부(政府)의 역할(役割)을 어떻게 평가하느냐에 관하여는 더욱 그러하다. 신고전(新古典) 경제학(經濟學)은 이 나라들의 가격왜곡(價格歪曲)의 최소화(最小化), 시장기구(市場機構)의 활용(活用), 국제분업(國際分業)에의 참여(參與)에서 주된 이유를 찾고 있는데 비해, 소위 수정주의(修正主義)는 이같은 견해가 사실과 크게 괴리가 있으며 '기적(奇蹟)'은 시장(市場)의 자원배분(資源配分)에 대한 정부개입(政府介入)이 주효(奏效)하였기 때문이라 주장한다. '동(東)아시아의 기적(奇蹟)'은 동(東)아시아란 지역(地域)에서 일어난 현상일 뿐 아니라 20세기(世紀) 후반(後半)에 일어난 동시대적(同時代的) 현상이기도 하다. 공업화(工業化)를 이룬 나라들은 모두 세계시장(世界市場)과 활발히 교역(交易)하였다는 공통점이 있는데, 세계시장(世界市場)의 규모(規模)를 대표하는 세계총수출(世界總輸出)이 19세기(世紀) 중반(中盤)과 20세기(世紀) 후반(後半) 사이에 실질기준(實質基準)으로 100배 이상 커졌다. 이 글은 세계시장(世界市場)의 규모증대(規模增大)가 동(東)아시아 NICs들의 고속성장(高速成長)의 이유(理由)였을 가능성(可能性)을 이론적(理論的)으로, 실증적(實證的)으로 검토해본 것이다. 이론적(理論的)으로는, A Lewis의 무한노동공급(無限勞動供給)(unlimited supply of labor)이 존재하는 경제(經濟)에서는 세계시장((世界市場) 상대가격(相對價格)이 불변(不變)인 한 제조업내(製造業內) 노동집약도(勞動集約度)가 높은 산업(産業)에 대한 투자유인(投資誘因)이 지속된다는 점에 고속성장(高速成長)의 근거가 있다고 보았다. 이러한 투자(投資)의 지속은 제조업부문(製造業部門)의 산출(産出)과 고용(雇傭)이 경제(經濟)에서 점하는 비중(比重)을 낮은 자원비용(資源費用)으로 증대(增大)시킬 것이기 때문이다. 실증분석(實證分析)에서는, 필요한 통계자료(統計資料)가 있는 19개국의 공업화(工業化) 경험(經驗)을 검토하였는데, 한 나라가 공업화(工業化)를 시작하는 시점(時點)의 세계총수출(世界總輸出)이 클수록 그 나라의 공업화(工業化) 소요기간(所要期間)이 단축(短縮)된다는 매우 확실한 증거가 있었다. 또한 동(東)아시아 NICs의 공업화(工業化) 소요기간(所要期間)이 선진국(先進國) 경험에 비해 약 1/4의 길이로, 혹은 그보다 더 짧게 단축(短縮)된 것은 거의 모두 세계총수출(世界總輸出) 규모(規模)의 증가(增加)로 설명될 수 있었다. 이같은 이론적(理論的) 근거(根據)와 실증적(實證的) 증거(證據)를 감안할 때, 우리 경제(經濟)는 정부주도형(政府主導型)이었으나 고속성장(高速成長)을 가능하게 한 것은 정부주도(政府主導)보다는 그 규모(規模)가 대폭 증대한 세계시장(世界市場)에서의 국제분업(國際分業)이었다.

• Archives of design research
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• v.17 no.1
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• pp.211-220
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• 2004

The Chaos theory of complexity and Fractal theory which became a prominent figure as a new paradigm of natural science should be understood not as whole, and not into separate elements of nature. Fractal Dimensions are used to measure the complexity of objects. We now have ways of measuring things that were traditionally meaningless or impossible to measure. They are capable of describing many irregularly shaped objects including man and nature. It is compatible method of application to express complexity of nature in the dimension of non-fixed number by placing our point of view to lean toward non-linear, diverse, endless time, and complexity when we look at our world. Fractal Dimension allows us to measure the complexity of an object. Having a wide application of fractal geometry and Chaos theory to the art field is the territory of imagination where art and science encounter each other and yet there has not been much research in this area. The formative word has been extracted in this study by analyzing objective data to grasp formative principle and geometric characteristic of (this)distinct figures of Fractals. With this form of research, it is not so much about fractal in mathematics, but the concept of self-similarity and recursiveness, randomness, devices expressed from unspeakable space, and the formative similarity to graphic design are focused in this study. The fractal figures have characteristics in which the structure doesn't change the nature of things of the figure even in the process if repeated infinitely many times, the limit of the process produces is fractal. Almost all fractals are at least partially self-similar. This means that a part of the fractal is identical to the entire fractal itself even if there is an enlargement to infinitesimal. This means any part has all the information to recompose as whole. Based on this scene, the research is intended to examine possibility of analysis of fractals in geometric characteristics in plasticity toward forms in graphic design. As a result, a beautiful proportion appears in graphic design with calculation of mathematic. It should be an appropriate equation to express nature since the fractal dimension allows us to measure the complexity of an object and the Fractla geometry should pick out high addition in value of peculiarity and characteristics in the complex of art and science. At the stage where the necessity of accepting this demand and adapting ourselves to the change is gathering strength is very significant in this research.