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.

태백시 북부지역의 화절층 ( 상부 캠브리아기 - 최하부 오도비스기 ) 의 코노돈트화석

이병수,이하영,이종덕 ( Byung Su Lee,Ha Young Lee,Jong Deock Lee ) 한국고생물학회 1989 제5차 정기총회 학술발표 요약론 Vol.- No.-

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.

(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.

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.

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.

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.

<문화, 문학> : 이상(李箱)시의 외래어와 한글 혼용이 보여주는 자동기술법 비교 연구

이병수 ( Byung Soo Lee ) 경희대학교 비교문화연구소 2015 비교문화연구 Vol.39 No.-

The following summarized argument is the comparative research of the characteristics of automatic techniques demonstrated in the mixed expression of foreign language and Korean language in Lee Sang``s poetry. Our research examines the use of foreign languages such as French and English shown in Lee Sang``s poems, and then, recognized the characteristics of the automatic techniques demonstrated by the parallel marks and signs of Korean language. The automatical technique``s element that Lee Sang made use of is a language of loanblend, consisting of free use of French, English, Japanese and Korean. The mathematical and geometric figures such as numbers and shapes can be seen as an important poetic language. In Lee Sang``s poetry, the French words “AMOUREUSES” and “ESQUISSE” and English words “I WED A TOY BRIDE” are considered as parts of Korean language. The use of foreign language is seen by the readers as encodes of a unacquainted language and it provides rhetorical characteritstics that gives off profanatory feeling about the poetry. The poet is seen to have created a new poetic language that excess the standards of the limitations that Korean and Chinese marks have through the application of polysems and poliphonyic effects that foreign languages have. The mathematical and geometric signs are Lee Sang’s special experimental elements that can’t be seen in other literary poetries. They are conversational and the requirements for the expression of abstract artistry and esthetics. The language used in his poetry are external to those traditional poetic languages and they mix freely with other poetic elements to become an automatic technique used in the writing. Lee Sang’s techniques can be considered as the pursuit of defiance and departure, freedom about literature and artistry. Moreover, the avant-garde expressionism is the literary form that demonstrated the sense of inferiority, nervousness and loneliness risen from physical pain and the abnormal relationship with women in the poet’s personal life. The technique shows the longingness of the the Western culture and literature that lay dormant in the poet’s consciousness and it is also the expression of ingenious that created the new guide in the Korean poetic literature, exceeding the European surrealism. Lastly, the automatic technique images that are demonstrated by the mixture of the foreign languages and Korean language are the creations of an innate poetic language and poetic literature that can’t be imitated by anyone in Korean literature.

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.

이상(李箱)의 시 작품에 구사되는 프랑스어와 탈 지방성

이병수 ( Lee Byung-soo ) 경희대학교 비교문화연구소 2018 비교문화연구 Vol.53 No.-

본 논고는 근대한국 문학의 전위인 이상(李箱)의 시작품에 구사되는 프랑스어와 탈 지방성에 대한 연구이다. 이상의 시편들 속에 쓰인 기호와 외래어는 한글로는 표현이 어려운 물리학, 건축학, 수학, 기하학, 이국의 문명과 같은 초감각적인 이미지들을 그려내고, 의미생성과 확장을 불러오는 파생의 시어로 작용한다. 이상의 시작품에서 프랑스어는 알파벳 철자와 한글식의 표기로 나누어지고, 문장들은 고딕 적이며, 병렬적인 이미지를 보여준다. 프랑스어 단어들은 “□, △, ∇” 등의 기호들과 조화를 이루어 상형적인 이미지로 기술된다. 문법의 규범을 이탈한 문장들은 해체와 재조합을 불러오고, 이때 프랑스어는 한글을 대체하고, 모국어가 갖는 한계를 초극하여 이국의 과학문명과 사상, 예술을 차용하는 포스트모던의 시어로 활용된다. 나아가 “ESQUISSE” 등의 프랑스어는 시인 자신의 열등의식을 초월하고, 자유와 상상력, 현대의 예술정신을 구현하기 위한 전위적인 시어로써, “향토”(鄕土)의 조선 문단에 세계의 신경향을 이식하여 성숙시켜 놓은 탈 지방의 시어로 나타난다. This following research is a study on the use of French and de-locality in the modern Korean poet Lee Sang’s poetry (1910-1937). His hometown was Kyung Sung, Seoul. He mainly wrote his works in Korean, Chinese character, and Japanese, using the language of education and his native language at that time. So then, what was the spirit that he wanted to embody through use of French words? By using words like “ESQUISSE”, “AMOUREUSE”, Sang’s French was not a one-time use of foreign words intended to amuse, but to him the words were as meticulously woven as his intentions. French words were harmonized with other non-poetic symbols such as “□, △, ∇”, and described as a type of typographical hieroglyphics. Instead of his mother-tongue language, French was applied as a surrealistic vocabulary that implemented the moral of infinite freedom and imagination, and expressed something new or extrasensory. Subsequently, the de-localized French (words) in his poetry can be seen as poetic words to implement a “new spirit”, proposed by western avant-garde artists. Analysis of French in his poetry, showed a sense of yearning for the scientific civilization, calling for his sense of defeat and escape from the colonized inferior native land. Most of all, comparing his pursuit of western civilization and avant-garde art to French used in his poetry, is regarded as world-oriented poetry intended to implement the new tendency of the “the locomotive of modernity,” transcending the territory of the native country.