• Journal of Advanced Marine Engineering and Technology
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• v.26 no.2
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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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• v.15 no.1_2
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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.

• Journal of the Korean Institute of Landscape Architecture
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• v.21 no.2
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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.

• Journal of the Korean Society of Clothing and Textiles
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• v.20 no.6
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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.

• The Mathematical Education
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• v.17 no.2
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• pp.33-35
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• 1979

• Communications of the Korean Mathematical Society
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• v.30 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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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.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.91-110
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• 2015

The purpose of this study is to investigate the understanding of pi of elementary gifted students and explore improvement direction of teaching pi. The results of this study are as follows. First, students understood insufficiently the property of approximation, constancy and infinity of pi from the fixation on 'pi = 3.14'. They mixed pi up with the approximation of pi as well. Second, they had a inclination to understand pi as algebraic formula, circumference by diameter. Third, few students understood the property of constancy and infinity of pi deeply. Lastly, the discussion activity provided the chance of finding the idea of the property of approximation of pi. In conclusion, we proposed several methods which improve the teaching of pi at elementary school.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.23 no.5
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• pp.110-119
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• 2009

In this study magnetic fields near electric power lines with branch lines which have a arbitrary angle were derived and formulated by dipole antenna theory and could be calculated easily using the formula. It seems that those formula could be applicable to the consideration of magnetic fields during the design of distribution lines with branch lines. As an example those formulated equations on elements of magnetic fields were applied to a model of 3 phase distribution lines with branch lines and calculated by Matlab programs and the results were presented The analyzed results are follows. The resultant magnetic field is dominated by the componant By all over y-axis in the case of the smaller branched angle $\alpha$ and the lower observed point z. In case of ${\alpha}=\frac{\pi}{2}$[rad], the resultant field is affected by the componant Bx. The resultant field is dominated by the componant Bz at the vicinity of the power lines and it shows very large value at the branch line position of y-axis in case of ${\alpha}>\frac{\pi}{2}$.

• Herbal Formula Science
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• v.9 no.1
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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.