• 한국수학교육학회지시리즈A:수학교육
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• 제47권1호
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• pp.1-10
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• 2008

Some of school mathematics contents that have deep mathematical meanings are regarded as obvious and their importance is frequently overlooked. We first reexamined the mathematical meaning of pi as a constant. Then we indicated the educational implications of Archimedes' calculation method of pi and finally underlined the availability of pi as a valuable research topic in school mathematics.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권1호
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• pp.1-29
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• 2014

When taught the precise definition of ${\pi}$, students may be simply asked to memorize its approximate value without developing a rigorous understanding of the underlying reason of why it is a constant. Measuring the circumferences and diameters of various circles and calculating their ratios might just represent an attempt to verify that ${\pi}$ has an approximate value of 3.14, and will not necessarily result in an adequate understanding about the constant nor formally proves that it is a constant. In this study, we aim to investigate prospective teachers' conceptual understanding of ${\pi}$, and as a constant and whether they can provide a proof of its constant property. The findings show that prospective teachers lack a holistic understanding of the constant nature of ${\pi}$, and reveal how they teach students about this property in an inappropriate approach through a proving activity. We conclude our findings with a suggestion on how to improve the situation.

• 대한수학회지
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• 제49권3호
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• pp.659-670
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• 2012

For any $K$ > $2/{\pi}$ we determine the optimal constant $L(K)$ for which the following holds. If $u$, $tilde{u}$ are conjugate harmonic functions on the unit disc with $\tilde{u}(0)=0$, then $$ {\int}_{-\pi}^{\pi}{\mid}\tilde{u}(e^{i\phi}){\mid}\frac{d{\phi}}{2{\pi}}{\leq}K{\int}_{-\pi}^{\pi}{\mid}u(e^{i{\phi}}){\mid}{\log}^+{\mid}u(e^{i{\phi}}){\mid}\frac{d{\phi}}{2{\pi}}+L(K).$$ We also establish a related estimate for orthogonal harmonic functions given on Euclidean domains as well as an extension concerning orthogonal martingales under differential subordination.

• 한국정밀공학회지
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• 제21권4호
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• pp.79-87
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• 2004

The light pattern reflected from a machined surface contains some information like roughness and profile on the projected surface as expected in the Beckmann-Spizzichino model. In applying the theory into a real reliable measuring device, many parameters such as incident light power, wave length, spot size should be kept a constant optical value. However, the reflected light power is likely to change with the environmental noise, the variations of the light source, the reflectivity of the surface, etc. even though the incident light power is constant. In this study, a method for adjusting the incident light power to keep the reflected light power projected on a CMOS image sensor constant was proposed and a simple adjustment algorithm based on PI digital control was examined. Experiments verified that the proposed method made the surface roughness measurement better and more reliable even under variations of the height of light source.

• 한국마이크로전자및패키징학회:학술대회논문집
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• 한국마이크로전자및패키징학회 2001년도 추계 기술심포지움
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• pp.171-177
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• 2001

The adhesion enhancement from inserting a RF bias-sputtered Cr layer between Cu and polyimide (PI) has been studied. The RF bias power applied in this study was ranged from 0 to 400 W. Without the RF bias, the peel strength, which measures the adhesion strength, was nearly o g/mm. As the RF power was increased, the peel strength rose up to ~130 g/mm at 200 W, which remained constant with further increase of the RF bias power. Cross-sectional transmission electron microscopy(TEM) was used to investigate the interfacial reaction between the Cr film and PI substrate during the bias sputtering. The Cr/PI interface without the application of RF dais showed a clean, sharp interface while the RF raised Cr/PI interface had about 10~30 nm thick atomistically mixed interlayer between the metal film and PI substrate. This interlayer appeared to have resulted from the implantation of high energy adatoms during the RF bias sputtering of Cr film. This mixed layer serves as an interlocking layer, which enhances adhesion between the metal and PI layers.

• Bulletin of the Korean Chemical Society
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• 제1권4호
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• pp.123-126
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• 1980

Benzene solution of trans-1,2-bispyrazylethylene and electron deficient olefin, tetracyanoethylene, as a ${\pi}$-acceptor gave 1,2-bispyrazyl-3,3,4,4-tetracyanocyclobutane, a 2${\pi}$ + 2${\pi}$ cycloaddition product, on irradiation with 350 nm UV light. Fluorescence studies revealed the reaction to proceed through a singlet exciplex. The fluorescence of trans-1,2-bispyrazylethylene was quenched very efficiently by tetracyanoethylene with the quenching constant of 1.6 ${\times}$ 10$^{10}$M$^{-1}$s$^{-1}$ while electron rich olefin, tetramethylethylene, did not quench the fluorescence of bispyrazylethylene.

• 대한전기학회논문지
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• 제40권7호
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• pp.696-705
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• 1991

This paper describes the procedures for pre-tuning and re-tuning the gains of PI controller based on output patterns -output error integral- of the unknown process which may not have any information, for example, system order, deadtime, time constant, etc. The key ideas of the proposed adaptive scheme are as follows. The scheme determines the initial gains by using ZNM (Ziegler-Nichols Method) with relay feedback, and then the adaptive algorithms by pattern recognition are introduced for re-runing the PI gains with on-line scheme whenever control conditions are changed. Because, among the various auto-tuning procedures, ANM with relay feedback has the difficulty in re-tuning with on-line and Bristol method has no comment on initial settings and has variables to pre-determine, which makes the algorithm comples, the proposed methods have the combined scheme with above two procedures to recover those problems. And this paper proposes a simple way to determine adaptive constant in Bristol method. To show the validity of the proposed method, an example is illustrated by computer simulation and a laboratory process, heat exchanger, is experimented.

• 마이크로전자및패키징학회지
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• 제29권2호
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• pp.99-105
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• 2022

칩사이즈가 작아짐에 따라 선폭 또한 미세화되면서 인터커넥션의 밀집정도가 증가하고 있다. 그로 인해 캐패시터 층과 전기전도층의 저항 차이로 인해 RC delay가 문제되고 있다. 이를 해결하기 위해서는 높은 전기전도도의 전극과 낮은 유전율의 유전체 개발이 요구된다. 본 연구에서는 PCB (Print Circuit Board)의 회로를 외부요인으로부터 보호하는 상용 PSR (photo solder resist)과 우수한 내열 및 저유전 특성을 보유한 PI (polyimide)를 혼합하여 저유전체 잉크 개발을 진행하였다. 그 결과 PSR과 PI를 10:3으로 혼합한 잉크가 가장 우수한 결과를 보였으며 20 GHz와 28 GHz에서 각각 유전 상수 약 2.6, 2.37을 보였고, 유전손실은 약 0.022, 0.016으로 측정되었다. 차후 어플리케이션 적용 가능성 검증을 위해 테프론에 제작된 다양한 선폭의 전송선로에 평가하였으며 그 결과, PSR만 사용했을 때보다 PI와 혼합한 저유전체 잉크를 사용한 전송선로의 손실이 S21에서 평균 0.12 dB 덜 감소한 결과를 보였다.

• 한국재료학회지
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• 제5권8호
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• pp.1040-1044
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• 1995

Sm의 농도가 각각 0.3, 0.4, 0.6인 세종류인(YSmLuCa)$_3$(FeGe)$_{5}$ $O_{12}$ 가넷트 박막을 LPE법으로 비자성재료인 Gd$_3$Ga$_{5}$ $O_{12}$(GGG)기판상에 성장시켜, 버블 자성재료의 자기적 성질을 조사하였다. 공명폭 ΔH는 4$\pi$Ms의 증가에 따라 증가하였고 Sm 농도의 감소에 따라 감소한다. 수직 자기 이방성에너지 Ku는 Sm증가에 따라 증가하며 같은 Sm농도에서는 4$\pi$Ms의 증가에 따라 증가한다. 자벽 이동도는 4$\pi$Ms의 증가에 따라 증가하며 Sm의 증가에 따라 감소한다. Ms.ΔH의 곱이 일정한 사실로 부터 새로운 자기손실인자 Eι을 구할 수 있으며 이는 Sm의 농도에 의존한다.ι을 구할 수 있으며 이는 Sm의 농도에 의존한다.

• 대한기계학회논문집
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• 제18권4호
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• pp.1031-1038
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• 1994

Characteristics of pulsatile flow and heat transfer have been studied numerically in the constant heat flux curved tube with periodic pressure gradient. As the Womersley number increases, the phase difference between the pressure gradient and the cross section averaged axial velocity becomes larger. In case of the Womersley number $\beta = 2$, when cross section averaged axial velocity reaches periodic state with time, the reverse and the natural flow coexist at phase angle, $\lambda = 1.44\pi$ and $\lambda =1.96\pi$. For all the Womersley numbers of present investigation, the time variation of wall temperature near inner wall is higher than that of near outer wall, independent of phase angle.