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.

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.

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.

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.

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.

이상(Lee Sang)의 시작품에 구사되는 프랑스어와 반문체

이병수 ( Lee Byung Soo ) 경희대학교 비교문화연구소 2017 비교문화연구 Vol.49 No.-

본 논고는 한국 시문학사에서 형이상학적 스캔들로 불리는 이상의 시편들에 구사 되는 프랑스어 연구이다. 이상의 시에서 프랑스어가 차지하는 비중은 식민지 시대에 일본어를 제외하면 가장 중요한 시어로 활용되고 있음을 알 수 있다. 우리의 연구는 기호적인 프랑스어, 기하학적이고 회화적인 프랑스어 활용에 대해 분석하고, 아울러 반복적이고 나열적인 단어와 문장의 구성에 응용되는 프랑스어에 대해 분석했다. 이상의 시편들에서 프랑스어의 활용은 비시어적인 기호의 혼용으로 볼 수 있으며, 전통적인 모국어와 시창작의 문법을 거부한 반문체적인 특성으로 나타남을 확인 할 수 있다. 그의 시에서 프랑스어는 아방가르드 적인 시적 재료와 실험적인 창작기법의 중요한 요소 중에 하나로 나타난다. 시인에게 프랑스어는 언어의 범주를 벗어난 건축학적이고 회화적인 재료들과 함께 한글의 틀을 거부한 전혀 낯선 표현기법의 중요한 요소로 적용되고, 시인의 예술정신을 구현하기 위한 전위적인 언어로 응용되고 있다. 이상에게 프랑스어는 분열적이고 열패적인 자신의 내면적 갈등을 표현하기 위한 도구로 활용되고 있으며, 시인은 프랑스어가 갖는 기표와 기의적인 특성을 이용하여 근대한국문학에 유래를 찾아 볼 수 없는 실험적인 문체를 보여주었다. 이상의 시에서 프랑스어는 식민지하의 억눌린 자의식을 해방시킨 자유의 언어이며, 한국문학뿐만 아니라 세계문학 속에서도 유례를 찾아볼 수 없는 반문체적이고, 형이상학적인 시편들을 구성하는 중요한 요소로 볼 수 있다. This paper is a study on French of Lee Sang's poems called metaphysical scandals in Korean poetry. Is poetic language he used a common poetic word or a non-poetic word in French? What kind of harmony do words and sentences composed of French have with Korean, Chinese character, and non-poetic word? Based on these questions, we analyzed a command of French, that is symbolic, geometrical, and pictorial French as well as repetitive and parallel constitution used in form of words and sentences. In Lee Sang's poems, as a result, the use of French is seen as a mixture of non-poetic word. It shows characteristics that reject traditional native language and the creation of poetry. In his poems, French is also an important factor of avant-garde poetic material and experimental creation technique. In his poems, French is used as a special tool to express internal conflicts of the poet. Lee Sang showed experimental style that could not be found in modern Korean literature by using signifier and signifed that french language has.

<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.

아폴리네르, 폴 엘뤼아르, 이상(LEE Sang) 시의 상형적 시어 비교분석

이병수 ( Lee Byung-soo ) 경희대학교 비교문화연구소 2016 비교문화연구 Vol.45 No.-

본 연구는 프랑스의 시인 기욤 아폴리네르, 폴 엘뤼아르와 한국의 이상의 시에 나타나는 상형적인 시어들에 대한 비교 분석이다. 그들은 글꼴이나 문장의 모양과 행간을 회화적으로 배열하는 타이포그라피 기법을 응용하고, 알파벳의 철자, 수학적 기호, 원이나 점, 선 등의 도형적 요소들을 혼용하여 특징적인 시화를 펼쳐 보인다. 시각적인 서정으로 평가되는 그들의 작품은 반시어들이 조화를 이루고 있으며, 기존의 시어나문법의 규범을 벗어난 글자와 기호들의 자유로운 구사는 병렬적이고 대립적인 특성을 보여준다. 그들의 상형적 시어들은 공간의 확장과 같은 역동적인 이미지를 불러오고, 이상의 기하학적인 기호들을 응용한 상형적 시어들은 형이상학적이고 추상적인 그림시로 형상화된다. 결과적으로, 우리가 분석한 세 시인들의 상형적인 시어들은 조형의 미학으로 귀결된다. 변형된 글자와 암호와 같은 기호의 회화적 구성은 시적공간의 확장이 불러오는 입체적 미학을 구현하고 있다. 나아가 세 시인의 상형적인 시어들은 프랑스와 한국의 현대시문학에 파격적인 표현기법으로 당대의 새로운 예술정신과 해방정신을 실현한 전위적인 시적 언어들로 평가할 수 있다. This study presents a comparative analysis of the calligrammic poetic dictions shown in the poems of the French poets Guillaume Apollinaire and Paul Eluard and in those of the Korean poet Lee Sang. They were adventurers in the avant-garde movement who used experimental techniques that led to futurism, expressionism, cubism, dadaism, and surrealism. They applied a typographic technique that combined pictorial arrangements of fonts, shapes of compositions and between lines, letters of the alphabet, mathematical symbols, and graphical elements, such as circles or lines, to make up a poem that also looked like a painting. Their works, valued as visual lyric poems, break up language and combine anti-poems. They rejected traditional poetic dictions or grammar, but developed a paratactic poem that freely uses letters and symbols. Their calligrammic poetic dictions arouse dynamic images like space extension. Lee Sang`s calligrams seem like abstract paintings that apply geometric symbols like those used in technical drawings. As a result, crossing the boundaries between language and pictorial art by using experimental materials and techniques, their poems deconstruct the creative standards of rational and traditional poetic dictions, creating an adventurous, expressive technique. Their calligrammic, avant-garde poems introduced a new spirit of art into both French and Korean modern poetic literature.