• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.253-260
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• 2002

For an outer action $\alpha$ of a finite group G on a factor M, it was proved that H is a, normal subgroup of G if and only if there exists a finite group F and an outer action $\beta$ of F on the crossed product algebra M $\times$$_{\alpha}$ G = (M $\times$$_{\alpha}$ F. We generalize this to infinite group actions. For an outer action $\alpha$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\alpha$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\alpha$ of a compact group G and a closed normal subgroup H, we prove $M^{G}$ = ( $M^{H}$)$^{{beta}(G/H)}$for a minimal action $\beta$ of G/H on $M^{H}$.f G/H on $M^{H}$.TEX> H/.

• Journal of the military operations research society of Korea
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• v.15 no.1
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• pp.54-62
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• 1989

This paper presents a corrective maintenance model to determine either type of maintenance actions upon failure of the system. Types of maintenance actions considered are minimal repair and replacement. Minimal repair cost is assumed to be random, whereas replacement cost is fixed. A policy, B(t), which determines the type of maintenance action based on the estimated minimal repair cost when the system fails at time t is adopted. To obtain an optimal policy, an expected maintenance cost per unit time is derived and is minimized with respect to B(t).

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.261-268
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• 2011

For a compact Hausdorff space X with its p-fold covering map ${\sigma}$, we construct its corresponding topological groupoid ${\Gamma}$, and show that there is a strong relation between the dynamical structures of (X, ${\sigma}$) and the groupoid structures of ${\Gamma}$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1539-1550
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• 2019

We classify minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in ${\mathbb{S}}^3$. First we show that minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric ${\mathbb{S}}^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in ${\mathbb{S}}^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in ${\mathbb{S}}^3$(cf. Theorem 3).

• Journal for History of Mathematics
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• v.17 no.1
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• pp.43-52
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• 2004

In this paper we investigate the origin of the variational calculus with respect to the extremal principle. We also study the role the extremal principle has played in the development of the calculus of variations. We deal with Dido's isoperimetric problem, Maupertius's least action principle, brachistochrone problem, geodesics, Johann Bernoulli's principle of virtual work, Plateau's minimal surface and Dirichlet principle.

• Journal of Applied Reliability
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• v.18 no.2
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• pp.104-113
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• 2018

Purpose: This paper proposes the non-periodic preventive maintenance policy based on the level of cumulative hazard intensity. We aim to construct a cost-effectiveness on the proposed model with relaxing the constraint on reliability. Methods: We use the level of cumulative hazard intensity as a condition variable, instead of reliability. Such a level of cumulative hazard intensity can derive the reliability which decreases as the frequency of preventive maintenance action increases. We also model the imperfect preventive maintenance action using the proportional age setback model. Conclusion: We provide a numerical example to illustrate the proposed model. We also analyze how the parameters of our model affect the optimal preventive maintenance policy. The results show that as long as high reliability is guaranteed, the inefficient preventive maintenance action is performed reducing the system operation time. Moreover, the optimal value of the proposed model is sensitive to changes in preventive maintenance cost and replacement cost.

• The Korean Journal of Pharmacology
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• v.10 no.1 s.15
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• pp.21-39
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• 1974

Certain metabolic aspects of halothane's cardiac depressant action on the contractility of the myocardium were elucidated from a sudy of the effect of pyruvate on halothane-depressed rat atria. Approximately 6 mg% halothane was required to maintain a 50% depression of the contractility of rat atria suspended in a modified Krebs-Ringer bicarbonate glucose medium, pH 7.4, $30^{\circ}C$ for a 2 hr. period. Pyruvate was found to restore partially the contractility of halothane-depressed atria. The maximally effective concentration of pyruvate was 2.5 mM. There was minimal pyruvate effect on the force of contraction of control atria. The effect of pyruvate on halothane-depressed atria was shown to be due to the pyruvate and not the sodium ion of the sodium pyruvate. Pyruvate was found to produce no increase in the contractility of atria depressed by hypertonic medium, but caused a further depression. Selected aspects regarding the action of halothane on glucose metabolism in myocardial cells are discussed. The results are consistent with the hypothesis that at least a part of the negative inotropic action of halothane is due to an inhibition of glucose uptake or utilization in the glycolytic pathway.

• Fire Science and Engineering
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• v.31 no.6
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• pp.67-73
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• 2017

An aircraft maintenance hangar is a building that stores, maintains, and inspects expensive aircraft. The frequency of fire occurrence is low, but the resulting human and material damage can be very serious. Therefore, in this study, we conducted a qualitative analysis of the fire safety of the currently operating fire suppression systems for aircraft maintenance hangars using the Fault Tree method, and then performed a quantitative analysis using the failure rate data for the derived basic events and analyzed the importance of the minimal cut sets. As a result of the qualitative analysis by the minimal cut set, it was found that there were 14 accident paths that could be expanded to a large fire, due to the fire control failure of the aircraft hangar fire suppression system. The quantitative analysis revealed that, the probability of the fire expanding into a large one is $2.08{\times}E-05/day$. The analysis of the importance of the minimal cut set shows that four minimal cut sets, namely the fire detector and foam head action according to the zone and blocking of the foam by the aircraft wing and the fire plume, had the same likelihood of causing the fire to develop into a large one, viz. 24.95% each, which together forms the majority of the likelihood. It was confirmed for the first time by fault tree method that the fire suppression system of aircraft maintenance hangars is not suitable for fires under the aircraft wings and needs to be improved.

• Proceedings of the KSR Conference
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• 2011.05a
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• pp.1358-1363
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• 2011

In this study, GEC, VVVF train is mounted in the cab on the Improvement of Brake Controller checks were carried out. Brake Controller in a single-acting snap action switches, double acting snap action switches, and terminals associated with all the parts individually checked, rather than the current trains, and the same conditions, the overall depth review and analysis through the improvements in the meantime, failure to advance found by processing station Minimal and directly related to the safety of disabled passengers, the train station to contribute to safety in this study began.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1299-1307
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• 2020

We show that the Liechti-Strenner's example for the closed nonorientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial of the action induced on the first cohomology nonpositive. We also show that the Liechti-Strenner's example of orientation-reversing homeomorphism for the closed orientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial p(x) of the action induced on the first cohomology nonpositive or all but the first coefficient of p(x)(x ± 1)², p(x)(x² ± 1), or p(x)(x² ± x + 1) nonpositive.