• Title/Summary/Keyword: 지수함수

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Wave Propagatin Characteristics of Optical Fibers with an Exponentially Graded Index (지수함수 굴절율을 갖는 광섬유의 파동전파 특성)

  • 김진사;김상용
    • Textile Science and Engineering
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    • v.19 no.5
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    • pp.37-43
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    • 1982
  • The optical fiber for transmission is now being realized after the many theoretical researches. The dispersive properties have been coped with by the varying index profile. The specific shape of the profile has an effect on the velocities of the various propagation modes. The most important and frequently used one is the parabolic profile. But, the investigation has been carried out on a new fiber with an exponential index profile and the computation has been made for the propagation constant and the group delay of this fiber, assuming the structure is uniform along its length, yielding no mode conversion and assuming negligible losses or equivalently the same loss for all modes. It was found that in a short transmission there is no significant difference between the exponential and the parabolic profiles but in a long transmission the small difference must be considered because of the accumulation.

Pre-Service Teachers' Understanding of Contexts for Constructing Exponential Graph (지수함수 그래프의 구성 맥락에 대한 예비교사들의 이해)

  • Heo, Nam Gu;Kang, Hyangim;Choi, Eunah
    • Journal of Educational Research in Mathematics
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    • v.27 no.3
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    • pp.411-430
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    • 2017
  • This study examined the understanding of 24 pre-service teachers about the three contexts for constructing the exponential graphs. The three contexts consisted of the infinite points context (2009 revision curriculum textbook method), the infinite straight lines context (French textbook method), and the continuous compounding context (2015 revision curriculum textbook method). As the result of the examination, most of the pre-service teachers selected the infinite points context as easier context for introducing the exponential graph. They noted that it was the appropriate method because they thought their students would easily understand, but they showed the most errors in the graph presentation of this method. These errors are interpreted as a lack of content knowledge. In addition, a number of pre-service teachers noted that the infinite straight lines context and continuous compounding context were not appropriate because these contexts can aggravate students' difficulty in understanding. What they pointed out was interpreted in terms of knowledge of content and students, but at the same time those things revealed a lack of content knowledge for understanding the continuous compounding context. In fact, considering the curriculum they have experienced, they were not familiar with this context, continuous compounding. These results suggest that pre-service teacher education should be improved. Finally, some of the pre-service teachers mentioned that using technology can help the students' difficulties because they considered the design of visual model.

A Study on the Process of Constructing the Instantaneous Rate of Change of Exponential Function y=2x at x=0 Based on Understanding of the Natural Constant e (자연상수 e에 대한 이해를 기반으로 지수함수 y=2x의 x=0에서의 순간변화율 구성에 관한 연구)

  • Lee, Dong Gun;Yang, Seong Hyun;Shin, Jaehong
    • School Mathematics
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    • v.19 no.1
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    • pp.95-116
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    • 2017
  • Through the teaching experiments, we investigated a series of processes for obtaining the differential coefficient at x=0 of the exponential function $y=2^x$ based on the process of constructing the natural constant e and the understanding of it. and all of the students who participated in this study were students who had no experience of calculating the derivative of the exponential function. The purpose of this study was not to generalize the responses of students but to suggest implications for mathematical concept mapping related to calculus by analyzing various responses of students participating in experiments. It is expected that the accumulation of research data derived in this kind of research on the way of understanding and composition of learners will be an important basic data for presenting the learning model related to calculus.

Classification of Exponent Permutations over finite fields GF($2^n$) and its applications (유한체 상의 지수 함수의 분류와 암호학에의 응용)

  • Park, Sang-Woo;Kim, Kwang-Jo
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.6 no.4
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    • pp.97-106
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    • 1996
  • In this paper, we define an equivalence relation on the group of all permutations over the finite field GF($2^n$) and show each equivalence class has common cryptographic properties. And, we classify all exponent permutations over GF($2^7$) and GF($2^8$). Then, three applications of our results are described. We suggest a method for designing $n\;{\times}\;2n$ S(ubstitution)-boxes by the concatenation of two exponent permutations over GF($2^n$) and study the differential and linear resistance of them. And we can easily indicate that the conjecture of Beth in Eurocrypt '93 is wrong, and discuss the security of S-box in LOKI encryption algorithm.

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나선 은하의 화학적 진화 : 우리 은하의 초기 질량함수와 별탄생율

  • An, Hong-Bae;Im, Jeong-Ae;Gang, Yong-Hui
    • Publications of The Korean Astronomical Society
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    • v.6 no.1
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    • pp.1-15
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    • 1991
  • 원반 및 해일로의 이중역 (two-zone) 모형을 바탕으로하여 나선은하의 화학적 진화 모형을 만들었다. 모형의 검증을 위하여 구체적인 수치계산을 수행하고 그 결과를 태양 부근에서 관측된 중원소 분포 등, 화학적 진화와 관련된 제반 관측 사실과 비교함으로써 은하계의 진화를 추론하였다. 모형의 수치계산 결과에 의하면 나선은하의 화학적 진화는 헤일로외 붕괴 과정과 별탄생율에 크게 의존하며, 원반의 초기질량함수와 별탄생율에 따라 서로 다른 양상을 보인다. 태양 부근 원반의 중원소 분포 등을 성공적으로 설명할 수 있는 진화 모형에서, 별탄생율은 가스의 질량 또는 표면밀도의 멱승에 비례하거나 시간에 따라 단조 감소하는 지수함수로써 표현되며, 초기질량함수는 헤일로에서는 다양한 형태의 함수 모두로써 가능하지만, 원반의 경우에는 시간에 따라 변화하는 질량함수를 채택하여야 한다. 우리 은하의 헤일로의 고속붕괴 모형에서는 시간에 따라 지수함수로 변화하는 별탄생율이 관측과 부하되지만, 반면 저속붕괴의 경우에는 가스 질량의 멱함수로 표현되는 별탄생율이 관측과 부합된다.

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High-resolution cavity ringdown spectroscopy realized with the combination of an etalon and the cavity (에탈론과 공진기 결합을 이용한 고분해능 공동광자감쇠 분광법)

  • 유용심;김재완;이재용;한재원
    • Proceedings of the Optical Society of Korea Conference
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    • pp.218-219
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    • 2000
  • 공동광자감쇠 분광학(Cavity Ringdown Spectroscopy, CRDS)은 고감도의 흡수분광법으로 미량기체의 농도나 흡수분광선의 연구에 사용되어 왔으며 화염이나 플라스마에도 응용되고 있다. 이 분광법은 시간에 따라 지수함수로 감쇠하는 공동광자감쇠신호의 감쇠상수를 측정하는 기술인데, 레이저의 밴드폭이 흡수선폭보다 넓으면 감쇠신호가 지수함수에서 벗어나 오차를 발생하게 된다. 그러므로 오차를 줄이려면 좁은선폭의 레이저를 사용하거나 공동광자감쇠신호의 주파수를 분리하여야 한다. 분광선폭보다 매우 넓은 선폭의 레이저를 사용하고 분광기를 이용하여 공동광자감쇠신호를 분리하는 방법들이 제안되었다. (중략)

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A Case Study on the Change of Procedural Knowledge Composition and Expression of Derivative Coefficient in Exponential Function Type Distance (지수함수 형태의 거리함수에서 미분계수의 절차적 지식 구성과 표현의 변화에 대한 사례연구)

  • Lee, Dong Gun;Kim, Suk Hui
    • School Mathematics
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    • v.19 no.4
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    • pp.639-661
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    • 2017
  • The purpose of this study is to investigate the relationship between the distance function average speed and the speed function. Particularly, in this study, we investigate the process of constructing the speed function in the distance function (irrational function, exponential function) which is difficult to weaken the argument in the denominator. In this process, students showed various anxieties and expressions about the procedural knowledge that they constructed first. In particular, if student B can not explain all the knowledge he already knows in this process, he showed his reflection on the process of calculating the differential coefficient. This study adds an understanding of the calculation method of students in differential coefficient learning. In addition, it is meaningful that the students who construct procedural knowledge at the time of calculating the differential coefficient have thought about how to provide opportunities to reflect on the procedure they constructed.