• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.527-535
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• 2021

The fundamental group of a high dimensional graph manifold canonically has a graph of groups structure. We analyze the group action on the associated Bass-Serre tree and study the algebraic ranks of the fundamental groups of high dimensional graph manifolds.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1249-1268
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• 2011

For imaginary quadratic number fields F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1{\ldots}p_{t-1}})$, where ${\varepsilon}{\in}${-1,-2} and distinct primes $p_i{\equiv}1$ mod 4, we give condition of 8-ranks of class groups C(F) of F equal to 1 or 2 provided that 4-ranks of C(F) are at most equal to 2. Especially for F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1p_2)$, we compute densities of 8-ranks of C(F) equal to 1 or 2 in all such imaginary quadratic fields F. The results are stated in terms of congruence relation of $p_i$ modulo $2^n$, the quartic residue symbol $(\frac{p_1}{p_2})4$ and binary quadratic forms such as $p_2^{h+(2_{p_1})/4}=x^2-2p_1y^2$, where $h+(2p_1)$ is the narrow class number of $\mathbb{Q}(\sqrt{2p_1})$. The results are also very useful for numerical computations.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1841-1850
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• 2014

It is known that the ranks of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{\ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $\mathcal{SOP}_n$ and $\mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $\mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{\leq}m{\leq}n-1$, the m-potent ranks of the semigroups $\mathcal{SOP}_n$ and $\mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $\mathcal{SSPOP}_n$ is n + 1.

• Journal of the Korean Society of Costume
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• v.53 no.3
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• pp.121-135
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• 2003

This paper is about the dress styles during the 16th century of the Chosun dynasty, just before the Japanese Invasion of Korea in 1592, through painting-Kiyeonghoido. In the Chosun period, dress styles played an important role in representing the differences in social status. The most remarkable signs of social standing are the hair ornaments. Officials in ranks, noksas, and seoris are wearing a same, a yugakpyeongjeongeon and a mugakpyeongjeongeon respectively. The head ornament for musicians in high ranks is a samo, and, for those in low ranks a hood or a heuklip. Accordingly, head ornaments were important articles among apparels, and especially ripja was an article that sensitively reflected the contemporary fashion. Such a trend also influenced the common people's styles of dress. Thus, the style of the heuklip worn by the chamberlain in Kiyeonghoido resembled of yangban's. Actual official uniforms also diverged from the specifications for them. Sangboks were red for both dangsanggwans and danghagwans, but their ranks were marked by the material of their dress rather than by the breast plates. Dress styles change over time as the society members influence and are influenced by each other. Therefore, owing to the social characteristics of a hierarchical society, dress styles are distinctive according to the wearers' social standings and roles, and various dress styles emerge that deviate from regulations. The significance of the present paper is to review the diversity of the dress styles during the 16th century of the Chosun dynasty.

• The Journal of the Korea Contents Association
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• v.17 no.1
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• pp.233-241
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• 2017

Annual reports on the ease of doing business, published from the World Bank, measure the regulations of economies that enhance business activity and those that constrain it by the 10 areas of business life-cycle. It then calculates the scores and ranks in each of the areas and in aggregate. The aggregate scores are the summation of the scores in the areas. This means that all the areas have the same weight. As evaluation results can vary greatly by the areas used and their weights, it is possible that the areas emphasized by small and medium-sized enterprises(SMEs) of Korea are not appropriately reflected in the evaluation results. From the viewpoint of small and medium-sized Korean enterprises, this paper tries to compare the ease of doing business of economies via determining the weights of the 10 areas. Through an AHP-based survey on Korean professors of a business school and SME CEOs, the weights are determined and then applied to the calculation of the aggregate scores and the ranks of the economies. While the changes in the top and bottom ranks are relatively small, some cases of big changes are found in the middle ranks.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.101-114
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• 2007

For an $m$ by $n$ nonnegative real matrix A, the maximal column rank of A is the maximal number of the columns of A which are linearly independent. In this paper, we analyze relationships between ranks and maximal column ranks of matrices over nonnegative reals. We also characterize the linear operators which preserve the maximal column rank of matrices over nonnegative reals.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.969-990
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• 2011

Assume that X, partitioned into $2{\times}2$ block form, is a solution of the system of quaternion matrix equations $A_1XB_1$ = $C_1,A_2XB_2=C_2$. We in this paper give the maximal and minimal ranks of the submatrices in X, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. As applications, we consider the common inner inverse G, partitioned into $2{\times}2$ block form, of two quaternion matrices M and N. We present the formulas of the maximal and minimal ranks of the submatrices of G, and describe the properties of the submatrices of G as well. The findings of this paper generalize some known results in the literature.

• Journal of Applied Reliability
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• v.17 no.1
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• pp.11-21
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• 2017

Purpose: The occurrence ranks of failure modes can come from the real failure but the severity ranks of failure modes require a highly subjective point of view of users. The severity ranks have to find more objective and scientific values. Methods: We found the optimal values by using the correlation analysis between failure mode effects and the criticality number like RPN (Risk Priority Number) in RCM. Result: This paper shows the result that verified whether the weighted values on each failure effect in criticality number calculation is suitable to the actual failures or not. To get the verification, it used the 5 year data and correlation analysis. Based on the analyzed result, We proposed the more suitable values. Conclusion: This correlation analysis approach can provide guidance of RCM analysis across many industries and situations.

• Asia pacific journal of information systems
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• v.8 no.2
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• pp.85-104
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• 1998

It is assumed that employees' ethical judgements and attitudes in handling personal and organizational information differ, depending upon their hierarchical ranks in organizations and types of information. Therefore we investigated how differently employees at different ranks judge hypothetical behaviors(or situations); their manner of handling various types of information in their daily activities in business organizations. Sixteen hypotheses based on combinations of 3 ethical areas and 5 information types were developed and tested. We found that three management ranks have shown significantly different ethical attitude about i)the accessibility to strategic planning and managerial information and ii)the property of managerial, operational and informal information. This research can help organizations to design better education programs and ethical codes to guide employees who process sensitive information.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.507-521
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• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.