• International Journal of Reliability and Applications
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• v.5 no.4
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• pp.147-154
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• 2004

This work developed and algorithm for a set covering model when the reliability of covers is a concern. This model extended the usage of the set covering model.

• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.1-11
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• 2005

A network consisting of a set of N nodes and a set of links is considered. The nodes are assumed to be perfect and the states of links to be binary and associated to each other. After defining a network structure function, which represents the state of network as a function of the states of links, we obtain some lower and upper bounds on the network reliability by adopting minmax principle and minimal path and cut set arguments. These bounds are given as functions of the reliabilities of links. The bridge network is considered as an example.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• Proceedings of the Korean Society for Applied Microbiology Conference
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• 2001.06a
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• pp.15-19
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• 2001

Creating an artificial strain with a minimal gene set for a specific purpose is every biologist's dream. With the complete genome sequencing of more than 50 microorganisms and extensive functional analyses of their genes, it is possible to design a genetic blueprint for a simple custom-designed microbe with the minimal gene set. Two different approaches are being considered. The first 'top-down' approach is trimming the genome to a minimal gene set by selectively removing genes of an organism thought to be unnecessary based on microbial genomics. The second 'bottom-up' approach is to synthesize the proposed minimal genome from basic chemical building blocks. The 'top-down' approach starting with the genome of a well known microorganism is more technically feasible, whereas the bottom-up approach may not be attainable in the nearest future because of the lack of the complete functional analysis of the genes needed for a life. Here in this study, we used the top-down approach to minimize the E. coli genome to create an artificial organism with 'core' elements for self-sustaining and self-replicating cells by eliminating unnecessary genes. Using several different kinds of sophisticated deletion techniques combined with a p:1age and transposons, we deleted about 19％ of the E. coli genome without causing any damages to cellular growth. This smaller E. coli genome will be further reduced to a genome with a minimal gene l;et essential for cell life. This minimized E. coli genome can lead to the construction of many custom-designed strains with myriad practical and commercial applications.

• Journal of the Korean Society of Safety
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• v.17 no.1
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• pp.87-93
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• 2002

In this thesis using FTA technique, the author proposes a new method of analysis of some accidents in construction work. Some efficient plans of safe facility investment are made out. For this study, I referred to 'The Death Accident in Construction Works', which have been published by Korea Industrial Safety Corporation from 1993 to 1999 for 6 years. I selected some of apartment constructions which have caused many deaths for the purpose of analysis in the study. I found that the concrete work using ferro-deck takes more deaths than the conventional construction. After finding this, I selected GANG FORM works using ferro-concrete which is the most widely used but causes many accidents. On the basis of the classification, I try to do some quantitative analyses by adding the death frequency and material factors. In order to draw up the most efficient investment plan, it is imperative that FT diagram be made out and that factors. In order to draw up the most efficient investment plan, it is imperative that FT diagram be made out and that minimal Cut Set be needed. It requires a great deal to labor and time to get Minimal Cut Set. The Minimal Cut Set which is formed of these process is the main factor to analyze disaster in the work. It is desirable that we add calculated percentage of accidents to these factors to these factors in value order, that is to say, from the high cost to low cost.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.607-617
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• 2014

Let S = C(r,m), the finite cyclic semigroup with index r and period m. Each subsemigroup of S is cyclic if and only if either r = 1; r = 2; or r = 3 with m odd. For $r{\neq}1$, the maximum value of the minimum number of elements in a (minimal) generating set of a subsemigroup of S is 1 if r = 3 and m is odd; 2 if r = 3 and m is even; (r-1)/2 if r is odd and unequal to 3; and r/2 if r is even. The number of cyclic subsemigroups of S is $r-1+{\tau}(m)$. Formulas are also given for the number of 2-generated subsemigroups of S and the total number of subsemigroups of S. The minimal generating sets of subsemigroups of S are characterized, and the problem of counting them is analyzed.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.195-200
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• 2010

Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.24 no.63
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• pp.33-43
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• 2001

To estimate the reliability of a large and complex network with a small variance, we propose two dynamic Monte Carlo sampling methods: the sequential minimal cut set (SMCS) and the sequential minimal path set (SMPS) methods. These methods do not require all minimal cut sets or path sets to be given in advance and do not simulate all arcs at each trial, which can decrease the valiance of network reliability. Based on the proposed methods, we develop the importance sampling estimators, the total hazard (or safety) estimator and the hazard (or safety) importance sampling estimator, and compare the performance of these simulation estimators. It is found that these estimators can significantly reduce the variance of the raw simulation estimator and the usual importance sampling estimator. Especially, the SMCS algorithm is very effective in case that the failure probabilities of arcs are low. On the contrary, the SMPS algorithm is effective in case that the success Probabilities of arcs are low.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.545-550
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• 2005

We find a necessary and sufficient condition that the number of some Betti numbers and shifts appear in the last free module Fn of Fx based on type vectors, where X is a finite set of points in $P^n$.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.1-12
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• 2022

We introduce the notion of a minimal synchronizing word; that is a synchronizing word whose proper subwords are not synchronized. This has been used to give a new shorter proof for a theorem in [6]. Also, the common synchronized components of a subshift and its derived set have been characterized.