• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.251-259
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• 2002

The fuzzification of an ideal in a Lie algebra is considered. Using a level subset of a fuzzy subset of a Lie algebra, we give a characterization of a fuzzy ideal, and using a family of ideals of a Lie algebra, we establish a fuzzy ideal. With relation to the ascending chain of ideals, a characterization for the set of values of any fuzzy ideal to be a well-ordered subset of the closed unit interval [0,1] is stated.

• 대한수학회보
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• 제50권2호
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• pp.627-637
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• 2013

Let [$n$] = {1, 2, ${\ldots}$, $n$} be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [$n$] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.169-179
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• 2009

Let P be a (n, n − 1, j)-poset, which is a partially ordered set of cardinality n with n − 1 maximal elements and $j(1{\leq}j{\leq}n-1)$ minimal elements, and $P^*$ the dual poset of P. In this paper, we obtain two types of incidence codes of nonempty proper subset S of P and $P^*$, respectively, by using Bogart's method [1] (see Theorem 3.3).

• 대한수학회지
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• 제33권4호
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• pp.801-811
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• 1996

Let $Z^d$ denote the set of all d-tuples of integers$(d \geq 1, a positive integer)$. The points in $Z^d$ will be denoted by $\underline{m},\underline{n}$, etc., or sometime, when necessary, more explicitly by $(m_1, m_2, \cdots, m_d)$, $(n_1, n_2, \cdots, n_d)$ etc. $Z^d$ is partially ordered by stipulating $\underline{m} \underline{<}\underline{n} iff m_i \leq n_i$ for each i, $1 \leq i \leq d$.

• 대한수학회논문집
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• 제20권1호
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• pp.15-21
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• 2005

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is ${\prod}^{t}_{i=0}(1+q^{i})$ for the types $B_N,\;D_N$, whereas for the case of type $C_N$, more isotropic subspaces are needed.

• Journal of the Korean Statistical Society
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• 제25권4호
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• pp.489-497
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• 1996

Lower bounds for the full level probabilities are derived under order restrictions in weights. Discussions are made on typical isotonic cones such as linear order, simple tree order, and unimodal order cones. We also discuss applications of these results for constructing conditional likelihood ratio tests for ordered hypotheses in a contingency table. A real data set on torus mandibularis will be analyzed for illustrating the testing procedure.

• Journal of the Korean Data and Information Science Society
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• 제22권5호
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• pp.967-976
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• 2011

The Box-Cox transformation is a well known family of power transformations that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. Normalization (studentization) of the regressors is a common practice in analyzing microarray data. Here, we implement Box-Cox transformation in normalizing regressors in microarray data. Pridictabilty of the model can be improved using data transformation compared to studentization.

• 대한수학회보
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• 제45권3호
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• pp.437-444
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• 2008

As a weak form of a subtraction algebra, the notion of weak subtraction algebras is introduced, and its examples are given. A method to make a weak subtraction algebra from a quasi-ordered set is provided.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.59-68
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• 2009

We introduce the notion of GT-algebras as a generalization of the concept of Tarski algebras. We introduce the notion of GT-filters in GT-algebras, and we prove some properties of GT-filters.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.541-548
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• 2015

In this paper, concepts of quasi-normal and dually quasi-normal relations are introduced. Characterizations of these relations are obtained. In addition, particulary we show that the anti-order relation ${\nleqslant}$ ($={\leqslant}^C$) is a (dually) quasi-normal relation if and only if the partially ordered set (X, ${\leqslant}$) is an anti-chain.