실수계의 공리를 이용한 지수 a^r의 학습과 지도

이병수,Lee, Byung-Soo 영남수학회 2012 East Asian mathematical journal Vol.28 No.2

In all Mathematics I Textbooks(Kim, S. H., 2010; Kim, H. K., 2010; Yang, S. K., 2010; Woo, M. H., 2010; Woo, J. H., 2010; You, H. C., 2010; Youn, J. H., 2010; Lee, K. S., 2010; Lee, D. W., 2010; Lee, M. K., 2010; Lee, J. Y., 2010; Jung, S. K., 2010; Choi, Y. J., 2010; Huang, S. K., 2010; Huang, S. W., 2010) in high schools in Korea these days, it is written and taught that for a positive real number $a$, $a^{\frac{m}{n}}$ is defined as $a^{\frac{m}{n}}={^n}\sqrt{a^m}$, where $m{\in}\mathbb{Z}$ and $n{\in}\mathbb{N}$ have common prime factors. For that situation, the author shows his opinion that the definition is not well-defined and $a^{\frac{m}{n}}$ must be defined as $a^{\frac{m}{n}}=({^n}\sqrt{a})^m$, whenever $^n\sqrt{a}$ is defined, based on the field axiom of the real number system including rational number system and natural number system. And he shows that the following laws of exponents for reals: $$\{a^{r+s}=a^r{\cdot}a^s\\(a^r)^s=a^{rs}\\(ab)^r=a^rb^r$$ for $a$, $b$>0 and $s{\in}\mathbb{R}$ hold by the completeness axiom of the real number system and the laws of exponents for natural numbers, integers, rational numbers and real numbers are logically equivalent.

유연한 수학적 사고에 의한 개념의 동치성 비교 - 사례 연구 -

이병수,Lee, Byung-Soo 영남수학회 2011 East Asian mathematical journal Vol.27 No.4

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

반도성 산화물에 의한 $ RuO_2$ 후막저항체의 TCR조정

이병수,이준,Lee, Byung-Soo,Lee, Joon 한국재료학회 1992 한국재료학회지 Vol.2 No.1

$\textrm{RuO}_2$와 glass의 비가 20/80과 12/88인 두종류의 후막저항계에 NTCR 특성을 나타내는 여러종류의 산화물을 첨가하였을때 저항체의 TCR과 전기비저항이 어떻게 변화하는가에 대한 실험을 실시하였다. 첨가된 TCR modifier들이 NTCR특성을 갖는다고해서 저항체의 TCR이 창상 감소되지는 않으며 또한 어떠한 modifier가 모든 저항계에 항상 일정 방향으로만 TCR을 변화시키지는 않았다. 그러나 이들 TCR modifier들을 적당량 첨가함으로써 후막저항체의 TCR과 저항값을 원하는 바대로 얻을 수 있다는 가능성을 확인하였다. 두 종류의 이상의 TCR modifier를 동시에 첨가하였을때에 첨가된 TCR modifier들 각각의 TCR변화가 합해져서 결과로 나타남으로써 이들 사용된 TCR modifier들 간에는 상호작용이 없음을 알 수 있었다. TCR modifier의 첨가량은 2~3%내로 억제하는 것이 바람직함을 알 수 있었다. TCR modifying oxides which have negative TCR were added to the $\textrm{RuO}_2$ thick film resistors and how they affect the TCR and resistivity of the systems were investigated. Two types of resistor systems whose ratio of $\textrm{RuO}_2$ to glass were 20/80 and 12/88 were used as standard resistors. It was observed that the modifiers did not always lower the TCR of the resistors and the direction of the TCR change were different from system to system. It was confirmed, however, that the feasibility of optimization of TCR of the resistors. When more than two TCR modifiers were added simultaneously there was no interaction between them. The resultant TCR of the resistor wart just sum of the effects from individual modifier. It was found to be desirable that the amount of addition of the TCR modifiers should be less than 2 to 3 percent.

대구경(57 mm) 및 고강도(550 MPa) 확대머리 철근의 콘크리트 격납구조물 적용을 위한 코드개정에 관한 연구

이병수,임상준,윤현도,Lee, Byung-Soo,Lim, Sang-Jun,Yun, Hyun-Do 한국구조물진단유지관리공학회 2017 한국구조물진단유지관리공학회 논문집 Vol.21 No.6

일반적으로, 원전구조물은 다량의 철근이 사용되어 시공과정에서 여러 잠재적 문제점이 발생한다. 특히, 구조부재의 연결부위는 수많은 갈고리철근, 매입철물과 주변 철근 등에 의해 심각한 과밀현상이 발생하므로 여타 다른 부위보다 콘크리트 타설에 더 큰 어려움이 야기된다. 원전구조물에 사용되는 일반강도(ASTM A615 Gr.60)의 대구경(43 mm & 57 mm) 표준갈고리 철근을 대신하여 고강도(ASTM A615 Gr.80)의 대구경(43 mm & 57 mm) 확대머리 철근을 사용할 수 있도록 관련 기술기준을 개정하여 철근 과밀배근 문제를 해결하는 데 본 연구의 목적이 있다. 확대머리 철근을 원전구조물에 효과적으로 사용하기 위해서는 기존의 정착성능을 그대로 유지하거나 그 이상으로 증가시키면서 사용 제한요건을 완화는 방안을 찾아야 하므로 철근직경, 철근 항복강도, 측면피복 두께와 같이 확대머리 철근의 사용을 제한하는 변수 영향을 검토할 수 있는 실험결과를 분석하여 정착성능을 평가하였다. Generally, significant amount of reinforcements are used in nuclear power plant structures and it may cause several potential problems during the construction. In particular, it is more difficult to pour concrete into structural member joint area than other areas because of the significant congestion of the joint area due to a lot of hooked bars, embedded materials, and other reinforcements. The purpose of this study is to solve these problems due to the reinforcement congestion by using the high-strength(ASTM A615 Gr.80) headed deformed bars of large-sized diameter(43 mm & 57 mm) in nuclear power plant structures as a alternative of standard hooked bars. In order to use headed deformed bars effectively, It is necessary to find the method how to relax limits on their use while maintaining or improving the anchorage capacity. Therefore, this study will analyze the results of tests planned to evaluate the influence of the restricted variables, such as bar size, yield strength, clear cover thickness.

(예비)교사를 위한 완비성의 학습과 지도에 관한 소고

이병수,Lee, Byung-Soo 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

In this paper, the author focuses on the teaching-level and learning-level of the completeness axiom and its applications on [0,1] and $\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}{\times}\mathbb{R}$ by (expected) teachers in the school mathematics, which is usually introduced in the class of real analysis of university mathematics. Firstly the author considers the properties of the completeness axiom and its 19 equivalent theorems, next he deals with its importances in the school mathematics and finally he suggests the teaching and learning of the concepts on the completeness axiom and its applications on [0,1] and $\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}{\times}\mathbb{R}$ by (expected) teachers in the school mathematics.

이상의 시에 나타나는 프랑스어 차용과 국어의 해체

이병수(Lee, Byung Soo) 한국동서비교문학학회 2013 동서 비교문학저널 Vol.0 No.28

The following research is about the French vocabularies that appear in Lee Sang’s poems. Lee Sang (1910-1937) was Korea’s first surrealist and considered a modernist. During his short 27 years of life, his poems and novels demonstrated an avant-garde type of writing. He utilized Korean, Chinese, Japanese, French, English, Geometry, and Mathematics in his literature. Our research attempts to translate and analyze the function and meaning of the French vocabularies shown in Lee Sang’s poems. As a result, the French expressions in Lee Sang’s poems were proven to appear as Korean vocabularies’ refusal and dissolution. The method of French expressions used by Lee Sang was an experimental method and was difficult to comprehend during that time of Korean literature. Lee Sang used the French vocabularies as a single symbol, such as a mathematical composition of numbers or geometrical graphic markings. The French vocabularies that he makes use of are meaningless and supra-literary, like the poems of the French surrealists. To illustrate, the poet attempts the automatic writing, which was also used by the French surrealist poets. As an outcome, it created Lee Sang’s style of writing that can be seen nowadays. The French vocabularies from Lee Sang’s poems are characterized by the surrealistic features, such as resistance, negation, and dismantlement. Moreover, the poet opened the door for the new poetic languages and literary forms to Korean literature. To conclude, the French vocabularies in his poems are significant vocabularies that show avant-gardist and experimental characteristics. Additionally, the French expressions utilized by the poet are the principal evidence that display the universalism of Korean literature.

고강도철근(550MPa)의 원전구조물 적용을 위한 표준갈고리 정착설계

이병수 ( Lee Byung Soo ) 한국건축시공학회 2018 한국건축시공학회 학술발표대회 논문집 Vol.18 No.1

Because of the congestion problems, the high-strength reinforcements are expected to be used in nuclear power plant structures in the near future. According to ACI 349-13, it is permitted to use the high-strength(550MPa) hooked bars in design of development length, but there is no special equation for high-strength bars. In order to reflect the anchorage capacity and behavior properties of high-strength bars with large-diameter(43 & 57mm), it is necessary to develope the new development length equation for large-size and high-strength bars.

초현실주의 시 비교연구

이병수(Byung Soo Lee) 한국동서비교문학학회 2014 동서 비교문학저널 Vol.0 No.30

The thesis is a comparative study of the poetry of the surrealistic poets, Lee Sang (Korea, 1910-1937) and Paul Eluard (France, 1895-1952). We observed the most central poetic word for love, “amoureuse” image in the poems of the Korean and French poets that are representatives in surrealism. The study demonstrates the attempt to comparatively analyze how detailed “amoureuse”’s image is expressed and how it shows the characteristics of the significance as a poetic language. The image of “amoureuse” shown in Lee Sang’s poem can be seen as a symbolic figure that expresses the love spirit that lies in the poet’s unconsciousness instead of being presented as a French word derived from the foreign language preference. The “amoureuse” expressed along with the geometric figures displays the poet’s autistic and broken love experiences in abstract forms, and can be seen as form of yearning for idealistic love that lies dormant within Lee Sang. The “amoureuse” for Paul Eluard presented a cosmical drama based on the commune with woman, light, dream and assimilating and corresponding with nature, thus making the poetic word as the foundation of metaphysical love. Moreover, the unconscious love makes the poet idealize and is pictured through pure and mysterious poetic expressions. In conclusion, despite the poets’ experimental and extreme poetic language and its artistic values, the expressions of love in the image of “amoureuse” for Lee Sang and Paul Eluard is the origin of the core poetic subject and language that dominates over their life and poetry. Moreover, the “amoureuse”, that can be classified into geometric and metaphysical figure, embodies the inner unconsciousness of automatism that the surrealist poets emphasize. Particularly, the image of the French word “amoureuse” for Lee Sang is longing language about genuine love, and can be seen as the symbolic poetic language that supports the universalism and surrealism that goes beyond the Korean poetic literature.

고강도철근(550MPa)의 원전구조물 적용을 위한 직선철근의 정착설계

이병수 ( Lee Byung Soo ) 한국건축시공학회 2018 한국건축시공학회 학술발표대회 논문집 Vol.18 No.2

Because of the congestion problems, the high-strength reinforcements are expected to be used in nuclear power plant structures in the near future. According to ACI 349-13, it is permitted to use the high-strength(550MPa) straight bars in design of development length, but there is no special equation for high-strength bars. In order to reflect the anchorage capacity and behavior properties of high-strength straight bars with large-diameter(43 & 57mm), it is necessary to find the modified factor or develop the new development length equation for large-size and high-strength bars.

원전구조물 적용을 위한 고강도철근(550MPa)의 정착 및 이음길이

이병수(Lee, Byung Soo) 한국콘크리트학회 2018 한국콘크리트학회 학술대회 논문집 Vol.30 No.1