• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.53-60
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• 2018

In this paper, we consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra on ${\mathbb{F}}$, where ${\mathbb{F}}$ is an algebraic closed field. By using the Lie product of the basis elements of Heisenberg Lie algebras, all Rota-Baxter operators of 3-dimensional Heisenberg Lie algebras are calculated and left symmetric algebras of 3-dimensional Heisenberg Lie algebra are determined by using the Yang-Baxter operators.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.83-93
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• 2017

The Cayley graph ${\Gamma}=Cay(G,S)$ is called normal edge-transitive if $N_A(R(G))$ acts transitively on the set of edges of ${\Gamma}$, where $A=Aut({\Gamma})$ and R(G) is the regular subgroup of A. In this paper, we determine all hexavalent normal edge-transitive Cayley graphs on groups of order pqr, where p > q > r > 2 are prime numbers.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.509-518
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• 1997

In this paper, we study the developing maps of the Lie groups with left-invariant affinely flat structures. We make some bacis observations on the nature of the developing images and show that the developing map for an incomplete affine structure splits as a product of a covering map of codimension 1 and a diffeomorphism of dimension 1.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.25-27
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• 1993

In our paper [4] we showed that over bar $A_{n-1}$ is a split extension of (n-1) copies of Z by the symmetric group S$_{n}$ of degree n. We show in this paper how over bar $A_{n-1}$ appears naturally as a subgroup of the natural wreath product W=ZS$_{n}$.TEX> n/.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.10a
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• pp.195-199
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• 2001

The flow turning process, an incremental forming process, is a cost-effective forming method for axi-symmetric intricate parts to net shape. However, the flow turning process shows a fairly complicated deformation, it is very difficult to obtain satisfactory results. Therefore extensive experimental and analytical research has not been carried out. In this study, an fundamental experiment was conducted to improve productivity with process parameters such as tool path, angle of roller holder($\alpha$), feed rate(v ) and comer radius of forming roller(Rr). These factors were selected as variables in the experiment because they were most likely expected to have an effect on spring back. The clearance was controlled in order to achieve the precision product which is comparable to deep drawing one. And also thickness and diameter distributions of a multistage cup obtained by flow turning process were observed and compared with those of a commercial product produced by conventional deep drawing.

• Journal of Korean Institute of Industrial Engineers
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• v.30 no.4
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• pp.317-327
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• 2004

In mixed-model production systems, various models of products are produced alternately on the same production line. When the total number of models or the total production quantity is large, it takes a long time to determine the production sequence of the products. In this paper, we will show that in case of product rate variation problem (PRV) problem with nonidentical symmetric convex discrepancy function, an optimum sequence can be obtained by repeating an optimum sequence in a reduced subproblem.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.63-77
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• 2006

Maximum product of spacings estimator is proposed in this paper as a competent alternative of maximum likelihood estimator for the parameters of exponentiated-Weibull distribution, which does work even when the maximum likelihood estimator does not exist. In addition, a Bayes type estimator known as generalized maximum likelihood estimator is also obtained for both of the shape parameters of the aforesaid distribution. Though, the closed form solutions for these proposed estimators do not exist yet these can be obtained by simple appropriate numerical techniques. The relative performances of estimators are compared on the basis of their relative risk efficiencies obtained under symmetric and asymmetric losses. An example based on simulated data is considered for illustration.

• Korean Management Science Review
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• v.32 no.1
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• pp.83-100
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• 2015

We analyze a duopoly competition when two firms face input cost increases. The objective of this study is to determine the firms' optimal strategy between a price increase and downsizing under conditions of a spatially differentiated market and consumers' diminishing utility on the product size. We develop a theoretical model of two competing firms offering homogenous products using the standard Hotelling model to determine how firms' optimal strategies change when facing input cost increases. In this paper, there are two types of duopoly competitions: symmetric and asymmetric. In the symmetric case, the two firms have the same marginal cost and are producing and selling identical products. In the asymmetric case, the two firms have different marginal costs. The results show that the optimal strategy decision depends on the size of the input cost increase and the cost differences between the two firms. We find that when two firms are asymmetric (i.e., they have different marginal costs), the two firms might choose asymmetric pairs of strategies in equilibrium under certain conditions. When the cost differences between the two firms are sufficiently large and the cost increase is sufficiently small, the cost leader chooses price increase, and the cost-disadvantaged firm chooses downsizing in equilibrium. This asymmetric strategy reduces price competition between two firms, and consumers are better off. When the cost differences between the two firms are sufficiently large, downsizing is the dominant strategy for the cost-disadvantaged firm. The cost-disadvantaged firm finds it more profitable to reduce the product size than to increase its price to reduce price competition, because consumers prefer downsizing to price increases. This paper might be a good starting point for further analytical research in this area.

• Journal of Korea Multimedia Society
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• v.18 no.11
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• pp.1332-1341
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• 2015

This paper proposes a novel reversible secret sharing scheme using AES algorithm in encrypted images. In the proposed scheme, a role of the dealer is divided into an image provider and a data hider. The image provider encrypts the cover image with a shared secret key and sends it to the dealer. The dealer embeds the secret data into the encrypted image and transmits encrypted shadow images to the corresponding participants. We utilize Galois polynomial arithmetic operation over 2⁸ and the coefficient of the higher-order term is fixed to one in order to prevent the overflow. In experimental results, we demonstrate that the PSNR is sustained close to 44dB and the embedding capacity is 524,288 bits.