• Journal of Advanced Marine Engineering and Technology
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• 제26권2호
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• pp.219-225
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• 2002

Parameter tuning methods by Ziegler-Nichols for PID controllers are generally classified into Z-N(1) and Z-N(2). The purpose of this paper is to describe what relations exist between the methods of Z-N(1) and Z-N(2), or how Z-N(1) can be originated from Z-N(2) by analyzing one loop control system composing of P or PI controller and time delay process. In this paper, for the first step to seek mutual relations, the simple formulas of Z-N(2) are transformed into those composing of the same parameters as Z-N(1) which is derived from the analysis of frequency characteristics. Then, the approximation of the actual ultimate frequency is proposed as important premise in the translation between Z-N(1) and (2). Such equalization and approximation brings a simple approximated formula which can explain how Z-N(1) is originated from the Z-N(2) in the form of formula.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.363-375
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• 2004

In this paper, We show that the bandpass random signals of the form ∑$_{\alpha}$$\alpha$$_{\alpha}$ a Sin(2$\pi$f$_{\alpha}$t + b$_{\alpha}$) where a$_{\alpha}$ being a random number in [0,1], f$_{\alpha}$ a random integer in a given frequency band, and b$_{\alpha}$ a random number in [0, 2$\pi$], generate Gaussian white noise signals and hence they are adequate for simulating Continuous Markov processes. We apply the result to the fluctuation-dissipation formula for the Johnson noise and show that the probability distribution for the long term average of the power of the Johnson noise is a X$^2$ distribution and that the relative error of the long term average is (equation omitted) where N is the number of blocks used in the average.error of the long term average is (equation omitted) where N is the number of blocks used in the average.

• 한국조경학회지
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• 제21권2호
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• pp.1-7
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• 1993

This study suggests one hypothesis: The strength between the catchment foreces of urban community parks can be represented to a gravity model. The gravity model is derived from the related of two subjects, witch is related with their distance. A grvity model for the catchments between parks is represented as followed formula: Iij=${\alpha}$${\times}$ $\frac{Pi$.$Pj}{${\beta}$r}$(formula) Here, Iij is a total number of the vistors of park i and j in a year. Pi is population of the catchment area of park i. Pj is population of the catchment area of park j. ${\alpha}$and, ${\beta}$ are parameters. This formula is testified in the case of Chong-ju community parks.

• 한국의류학회지
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• 제20권6호
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• pp.1116-1124
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• 1996

The factors to presume the shapes of bending and draping were examined in this study, by applying the similar phenomenon and theory of analysis. The findings were as followings: 1. The value of deflection angle (f) of deflection curve were almost consistent with those of K number and the shapes of deflection curve were congruent, under the condition of that the values of EI/w are almost similar and the lengths of samples are consistent. 2. The values of drape area, drape coefficient, mean of deflection angle, and $\pi$ number were consistently estimated and the shapes of drape were almost the same, under the condition of that the values of EI/w are similar and the diameter of samples are consistent. 3. In using the samples with different values of EI/w, scale factor, kl, was obtained from the formula, the shapes of bending of the referent samples and compsactive smaples was geometrically similar, which the lengths of samples were 1,1'and were satisfied with the formula, hi: L'11, and their $\pi$ number were also consistent. 4. In applying the samples with different values of Rllw, scale factor (kl) was obtained and then, when semidiameter of samples was adjusted to be satisfied with the formula, k1=L/L, the shapes of draping of referent samples and comparative samples were geometrically similar. Furthermore, their $\pi$ number was also consistent. 5. The shares of bending and draping could be changed in terms of three factors such as the lengths of samples, bending ridigity, and weigths per unit area. $\pi$ number was obtained from theory of similar phenomenon, which was index to presume shapes of bending and the shapes of draping getting from the three factors.

• 한국수학교육학회지시리즈A:수학교육
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• 제17권2호
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• pp.33-35
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• 1979

• 대한수학회논문집
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• 제30권3호
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• pp.227-237
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• 2015

By employing certain extended classical summation theorems, several surprising ${\pi}$ and other formulae are displayed.

• 대한수학회보
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• 제51권4호
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• pp.1155-1161
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• 2014

In this paper, we rederive the identity ${\Gamma}_q(x){\Gamma}_q(1-x)={\frac{{\pi}_q}{sin_q({\pi}_qx)}$. Then, we give q-analogue of Gauss' multiplication formula and study representation of q-oscillator algebra in terms of the q-factorial polynomials.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권1호
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• pp.91-110
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• 2015

본 연구는 초등수학 영재교육 대상자들이 원주율 개념에 대해서 어떻게 이해하고 있는지를 살펴보고자 하였다. 이를 위해 원주율 계산 방법의 역사 발달 단계를 토대로 세 가지 과제를 개발한 후 6학년 영재교육 대상자 12명을 대상으로 적용하여 그 반응을 분석하였다. 연구결과, 학생들은 '원주율 = 3.14'라는 사고의 고착화로 인하여 원주율의 개념, 근사성, 무한성을 제대로 이해하지 못하였으며, 원주율과 원주율의 근삿값을 혼동하는 오류를 보였다. 또한 학생들은 원주율을 '(원주) ${\div}$ (지름)'의 대수적인 식으로 이해하려는 성향이 강하였으며, 원주율의 상수성과 무한성을 깊이 있게 이해하고 있는 학생은 극히 적었다. 반면에 과제에 대한 토론 활동은 학생들이 원주율의 근사성에 대한 아이디어를 발견할 수 있는 기회를 제공하였다. 이상의 결과를 종합하여, 초등학교에서의 원주율 지도와 관련하여 원주율을 원의 지름을 단위길이로 원의 둘레를 측정하여 얻을 수 있는 값으로 도입할 것과 공학적 도구 등을 이용하여 직관적인 방법을 통해 이해하도록 할 것, 원주율 개념이 가지는 본질적인 의미를 이해할 수 있도록 다양한 상황을 통해 도입할 것을 제안하였다.

• 조명전기설비학회논문지
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• 제23권5호
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• pp.110-119
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• 2009

본 연구에서는 임의의 각도로 분기되어 있는 전력선로 근방의 자계를 유도하여 정식화 하였으며 이 공식을 이용함으로써 그 자계 계산을 쉽게 할 수 있다. 이 공식들은 분기선로가 있는 배전선로의 설계 시 검토자료로서 활용할 수 있을 것으로 생각된다. 예로서 자계요소에 관한 공식들을 분기선로가 있는 3상 배전선로 모델에 적용하여 메틀랩 프로그램에 의해 계산하였으며 그 결과를 제시하였다. 그 분석결과를 요약하면 다음과 같다. 합성자계는 분기각이 작고 관측점의 높이 z가 낮으면 전 y-축상에 걸쳐 By 요소가 지배적이다. 이 합성자계는 분기각 ${\alpha}=\frac{\pi}{2}$[rad]의 경우 Bx의 영향을 크게 받는다. 또한 이 합성자계는 전력선 높이와 같은 전선로 근방에서 Bz요소가 지배적이며 분기각이 ${\alpha}>\frac{\pi}{2}$[rad]의 경우에는 y축의 분기전선 위치에서 매우 큰 값을 나타낸다.

• 대한한의학방제학회지
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• 제9권1호
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• pp.105-136
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• 2001

Objectives : 'Pi Wei Lun' is the principal medical work of Li Dongyuan's writings, which contains most of his medical theories. There are sixty-three prescriptions in 'Pi Wei Lun', and fifty-two of them were originated from him. This study was planned to present assistance to those who apply Dongyuan's theory clinically. Methods : We investigated those fifty-two prescriptions literary, and studied them from a viewpoint of the principle and method of treatment. Results : Dongyuan's fifty-two prescriptions can be classified into eight groups from the viewpoint of the principles and methods of treatment which are composed of 'tonify the spleen and stomach & elevate the spleen Yang', 'elevate the spleen Yang & expel fire', 'elevate the spleen Yang & relieve dampness', 'promote blood flow to eliminate blood stasis', 'invigorate the spleen', 'replenish Ki & and dispel phlegm', 'purgation with drugs warm in nature', and 'the other' eight methods. Conclusions : From above, we concluded that Dongyuan considered 'the primordial energy of the spleen and stomach' as the most important when making up prescriptions, but, at the same time, he used diverse methods of treatment on the ground of differentiation of syndromes.