• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.89-98
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• 2001

Brown and Proschan(1983) introduced a model for imperfect repair. At each failure of a device, with probability p, it is repaired completely or replaced with a new device(perfect repair), and with probability 1-p, it is returned to the functioning state, but it is only recovered to its condition just prior to failure(imperfect repair or minimal repair). In this paper, we limit the number of consecutive minimal repairs by n. We find some useful properties about $\mu$$_{k}$, the expected time between the k-th and the (k+1)-st repair under he assumption that only minimal repairs are performed. Then, we assign cost to each repair and find the value of n which minimized the long-run average cost for a fixed p under the condition that the life distribution F os the device is DMRL.L.

• Proceedings of the Korean Reliability Society Conference
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• 2000.04a
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• pp.63-70
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• 2000

Brown and Proschan(1983) introduced a model for imperfect repair. At each feilure of a device, with probability p, it is repaired completely or replaced with a new device(perfect repair), and with probability 1 - p, it is returned to the functioning state, but it is only recovered to its condition just prior to failure(imperfect repair or minimal repair). In this paper, we limit the number of consecutive minimal repairs by n. We find some useful properties about ${\mu}$$\_$k/, the expected time between the k-th and the (k + 1)-st repair under the assumption that only minimal repairs are performed. Then, we assign cost to each repair and find the value of n which minimizes the long-run average cost for a fixed p under the condition that distribution F of the device is DMRL.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.347-353
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• 2006

In this paper, we show that if the minimal basically disconnected cover ${\wedge}X_\imath\;of\;X_\imath$ is given by the space of fixed a $Z(X)^#$-ultrafilters on $X_\imath\;(\imath=1,2)\;and\;{\wedge}X_1\;{\times}\;{\wedge}X_2$ is a basically disconnected space, then ${\wedge}X_1\;{\times}\;{\wedge}X_2$ is the minimal basically disconnected cover of $X_1\;{\times}\;X_2$. Moreover, observing that the product space of a P-space and a countably locally weakly Lindelof basically disconnected space is basically disconnected, we show that if X is a weakly Lindelof almost P-space and Y is a countably locally weakly Lindelof space, then (${\wedge}X\;{\times}\;{\wedge}Y,\;{\wedge}_X\;{\times}\;{\wedge}_Y$) is the minimal basically disconnected cover of $X\;{\times}\;Y$.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.279-286
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• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.

• Korean Journal of Microbiology
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• v.18 no.3
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• pp.133-147
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• 1980

Washed mycelia of Aspergillus nidulans FGSC159 were incubated in CMC minimal liquid medium and the culture filtrate which contained induced extracellular cellulase was fractionated by a three-step procedure including chromatography on Bio-Gel P-150, chromatography on DEAE-Sephadex A-50 and chromatography on Sephadex G-100. Three CMCase components ; F-I-Ia, F-I-Ib and F-II-Ia were prepared. No enzyme activity toward avicel could be detected in these components. Similarly, there was no ${\beta}-glucosidase$ activity. pH-optima of the three components were all 5.0 in acetate buffer. Temperature-optima for the activities of F-I-Ia, F-Ib and F-II-Ia were $45^{\circ}C,\;40^{\circ}C\;and\;50^{\circ}C$, respectively. F-II-Ia was shown to be more thermostable than the other two components. F-II-Ia was proved to have quite a different substrate specificity and action property and action property from those of F-I-Ia and F-I-Ib by product analysis on liquid chromatography.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.167-173
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• 2010

In this paper, we introduce the concept of a weakly P-space which is a generalization of a P-space and prove that for any covering map f : $X{\rightarrow}Y$, X is a weakly P-space if and only if Y is a weakly P-space. Using these, we investigate the minimal basically disconnected cover of weakly P-spaces and their products.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.73-78
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• 2003

Observing that if f: $Y{\leftrightarro}$Χ is a covering map and Χ is a countably locally weakly Lindelof space, then Y is countably locally weakly Lindelof and that every dense countably weakly Lindelof subspace of a basically disconnected space is basically disconnected, we show that for a countably weakly Lindelof space Χ, its minimal basically disconnected cover ${\bigwedge}$Χ is given by the filter space of fixed ${\sigma}Ζ(Χ)^#$- ultrafilters.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.209-216
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• 2010

A spectrally arbitrary complex sign pattern A is a complex sign pattern of order n such that for every monic nth degree polynomial f(x) with coefficients from $\mathbb{C}$, there is a matrix in the qualitative class of A having the characteristic polynomial f(x). In this paper, we show a necessary condition for a spectrally arbitrary complex sign pattern and introduce a minimal spectrally arbitrary complex sign pattern $A_n$ all of whose superpatterns are also spectrally arbitrary for $n\;{\geq}\;2$. Furthermore, we study the minimum number of nonzero parts in a spectrally arbitrary complex sign pattern.

• International Journal of Oral Biology
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• v.39 no.2
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• pp.115-120
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• 2014

Minimal inhibitory concentration (MIC) is the lowest concentration of antibiotics that inhibits the visible growth of a microorganism. It has been reported that sub-MIC of antibiotics may result in morphological alterations along with biochemical and physiological changes in bacteria. The purpose of this study was to examine morphological changes of periodontal pathogens after treatment with sub-MIC antibiotics. Aggregatibacter actinomycetemcomitans, Fusobacterium nucleatum, and Porphyromonas gingivalis were used in this study. The MIC for amoxicillin, doxycycline, metronidazole, penicillin, and tetracycline were determined by broth dilution method. The bacterial morphology was observed with bright field microscope after incubating with sub-MIC antibiotics. The length of A. actinomycetemcomitans and F. nucleatum were increased after incubation with metronidazole; penicillin and amoxicillin. P. gingivalis were increased after incubating with metronidazole and penicillin. However, F. nucleatum showed decreased length after incubation with doxycycline and tetracycline. In this study, we observed that sub-MIC antibiotics can affect the morphology of periodontal pathogens.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.685-697
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• 2015

For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.