• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.229-241
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• 2004

Process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. The index $C_{pmk}$ is the third generation process capability index. This index is more powerful than two useful indices $C_p$ and $C_{pk}$. Whether a process distribution is clearly normal or nonnormal, there may be some questions as to which any process index is valid or should even be calculated. As far as we know, yet there is no result for statistical inference with process capability index $C_{pmk}$. However, asymptotic method and bootstrap could be studied for good statistical inference. In this paper, we propose various bootstrap confidence limits for our process capability Index $C_{pmk}$. First, we derive bootstrap asymptotic distribution of plug-in estimator $C_{pmk}$ of our capability index $C_{pmk}$. And then we construct various bootstrap confidence limits of our capability index $C_{pmk}$ for more useful process capability analysis.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.6
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• pp.72-82
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• 2000

Many lot of books introduce the methods to calculate the time of concentration, and these are described as various forms of formulas. There are few formulas appropriate for our basin characteristics Therefone, there are problems to make excessive or less estimation when these formulas are used. To solve these problems, comparison of formulas and sensitivity analysis for them were made with converting parameters. Finally, Time of concentration was estimated to derive Application limits for 3 watersheds by standardized formulas. In the case of input parameters analysis, SCS formula has the highest value by the length, Kerby by the height and SCS by the slope, respectively, while Kraven formula has the lowest value among them. Concerning the relative sensitivity by Taylor series, the time of concentration showed the constant effect while increasing of the length and slope, and the length was more sensitive than the slope in parameters. Finally the standardization formula developed in this study was applied to derive application limits for 3 watersheds(total 17 subbasins). In this case, Rziha(8 subbasins) and SCS(9 subbasins) formulas were the most similar to observed data of total 17 subbasins respectively. Application limits were about 300~500$\textrm{km}^2$ area, 30~60km length and under 0.01 slope for Rziha formula and about 100~200$\textrm{km}^2$ area, 10~30km length, and over 0.01 slope for SCS formula, respectively.

• Journal of the Korean Society of Combustion
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• v.1 no.1
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• pp.51-55
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• 1996

An experimental investigation has been made with the objective of studying the limits of equivalence ratio on mixing enhancement in a tone excited jet flame. The jet is pulsed by means of a loudspeaker-driven cavity and rich flames(${\phi}>1.5$) are used. The excitation frequency is chosen for the resonant frequency identified as a pipe resonance due to acoustic excitation. Methane, propane and butane are used to examine the effect of mixture property on the limit of equivalence ratio. Mixing is always enhanced in a methane/air flame as the excitation intensity increases. Constant lower limits of equivalence ratio for mixing enhancement are present in cases of propane/air and butane/air flames irrespective of mean mixture velocities. The equivalence ratio limits are also found to be related to the flame instability ; the lower Le, the higher the limit of equivalence ratio. Under the equivalence ratio limits, cellular flames are generated as the excitation intensity increases. The amplitude of oscillating velocity for generating a cellular flame in the equivalence ratio limit is proportional to a mean mixture velocity irrespective of fuels.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.609-615
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• 1987

The optimal operation of power system is developed by alternately using real power dispatch and reactive power dispatch problem. The real power system scheduling process is formulated as an optimization problem with linear inequality constraints. A.C. loadflow method is used for the problem solution and line losses are considered. The constraints under consideration are generator power limits, load scehdling limits and line capacity limits. In solving the objective function the Dual Relaxation method is adopted. Tests indicate that the method is practical for real time application. The reactive power control problem uses the Dual Simplex Relaxation method as in the real scheduling case. Insted of minimizing the cost of power system, the objective is selected as to determine the highest possible voltage schedule. The constraints under consideration are the voltage limits at each node and the possibilities of supply or absobtion of reactive energy by generator units and the compensation facilities. Tests indicate that the method is practical for real time applications. The overall optimization methods developed in this paper proved to obtained fine results in minimizing object function compared with the method without using voltage control. And the overall voltage profiles were also improved.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.1-8
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• 1980

논문(論文)[3] (본(本) 논문(論文) 제1부(第1部))에서 미분가능다양체(微分可能多樣體) M 위의 (n-1)차(次) 미분형식(微分型式) ${\beta}^{(n-1)}$이 Compact인 Carrier를 가지면 ${\int}d{\beta}^{(n-1)}=0$이며, (p-1)차(次) 미분형식(微分型式) ${\beta}^{(p-1)}$과 p차(次) 미분가능쇄(微分可能쇄鎖) $C^{(p)}=\Sigma\limits_ik_iS_i{^{(p)}}$에 대(對)하여 ${\int\limits_{c^{(p)}}}d{\beta}^{(p-1)}={\int\limits_{{\partial}{c}^{(p)}}}{\beta}^{(p-1)}$이 성립(成立) (Stokes 정리(定理)의 일반화(一般化))⋯등(等) M위의 적분(積分)에 관한 여러 가지 성질(性質)들을 구명(究明)하였다. 이 성질(性質)들을 토태(土台)로 하여 본(本) 논문(論文)에서는; 제2절(第2節)에서 미분가능다양체(微分可能多樣體) M위의 Lie 도함수(導函數)의 정의(定義)와 Lie적분(微分)에 관(關)한 여러가지 성질(性質)들을 고찰(考察)하고, 제3절(第3節)에서 div X와 Laplace 작용소(作用素) ${\Delta}f$의 정의(定義) 및 실(實) n차원(次元) 가부호미분가능(可符號微分可能) 다양체(多樣體) M 위에서의 divX와 ${\Delta}f$의 적분(積分)에 관(關)한 성질(性質), 즉(卽) $V=\sqrt{{\mid}g{\mid}}dx^1{\Lambda}{\cdots}{\Lambda}dx^n{\in}A^n(M)$에 대(對)하여 $$\int_MdivXV\limits=\int_M{\Delta}fv=0$$인 관계(關係)가 성립(成立)함을 구명(究明)한다. (정리(定理) 3.3)

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.391-398
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• 2000

The index properties of cohesive soils play an important role to examine entire tendency of soil properties. Especially, the Atterberg limits have a good correlation with compression and shear strength of cohesive soils. However, these values strongly depend on their testing methods. In this study, for Pusan clays the Atterberg limits were peformed under different conditions; for example, four kinds of specimen preparation, two kinds of testing equipment, and four kinds of estimating method. And a laboratory vane test was peformed to compare the undrained shear strength with that of the fall cone test. As experimental results, the value of liquid limit performed for oven-dried sample, followed in ASTM D4318, underestimated by about 10% compared to those of another three methods, irrespective to the used equipments. But the value of plastic limit was not influenced by sample preparation methods and equipments. The liquid limits by one-point methods(Leroueil et al., 1996; Nagaraj et al., 1981) were agreed well with those of different methods. Finally, the undrained shear strength by laboratory vane test was relatively larger than that of fall cone test, and the relationship between both showed a bad trend.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.297-303
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• 2007

In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is $Fr\acute{e}chet$-Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits ${\equiv}KC{\equiv}C-closed{\equiv}SC-closed$, and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.177-193
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• 2010

Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type $F_n(x)=\sum\limits_{k=0}^{n}A^n_kG_k(x)$ and $ G_n(x)=\sum\limits_{k=0}^{n}B_k^nF_k(x)$, where 0, 1, 2,$\cdots$. Here $F_n(x)$, $G_n(x)$ denote special polynomial functions, and $A_k^n$, $B_k^n$ denote coefficients found by use of the orthogonal properties of $F_n(x)$ and $G_n(x)$, or by skillful series manipulations. Typically $G_n(x)=x^n$ and $F_n(x)=P_n(x)$, the n-th Legendre polynomial. We give a collection of inverse series pairs of the type $f(n)=\sum\limits_{k=0}^{n}A_k^ng(k)$ if and only if $g(n)=\sum\limits_{k=0}^{n}B_k^nf(k)$, each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.

• Journal of Korean Society for Quality Management
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• v.40 no.2
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• pp.186-198
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• 2012

Since Duncan(1956) first proposed an economic design of $\bar{X}$-control charts, most of the succeeding works on economic design of control charts assumed the exponential failure model like Duncan. Hu(1984), however, assumed a more versatile Weibull failure model to develop an economic design of $\bar{X}$-control charts and Banerjee and Rahim(1988) further improved Hu's design by changing the assumption of fixed-length sampling intervals to variable-length ones. In this article we follow the approach of Banerjee and Rahim(1988) but include a pair of warning limits inside the control limits in order to search for a failure without stopping the process when the sample mean falls between warning and control limits. The computational results indicate that the proposed model gives a lower cost than Banerjee and Rahim's model unless the early failure probability of a Weibull distribution is relatively large. The reduction in cost is shown to become larger as the cost of production loss outweighs the cost of searches for a failure.