• 대한수학회지
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• 제56권2호
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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.

• 대한전자공학회논문지
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• 제18권1호
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• pp.25-34
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• 1981

부울 미분의 개념을 응용하여, Allen-Givone implementation oriented algebra에 의한 다치 논리 회로내의 결함을 해석했다. 회로내의 모든 라인을 그 성질에 따라 다섯 가지 유형으로 분류하였으며 각 유형별로 완전한 테스트 세트를 표현하는 식을 유도하고 증명했다. 이들 식의 실제 응용예의 결과는 진리표와의 비교에 따라 옳음이 확인되었다.

• 대한수학회지
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• 제36권6호
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• pp.1181-1190
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• 1999

Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterized the linear operators that preserve zero-term rank of the m×n matrices over binary Boolean algebra.

• 호남수학학술지
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• 제37권3호
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• pp.287-297
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• 2015

In this paper, we investigate $T_1$ Boolean subalgebras of the Boolean algebra consisting all regular closed sets in a space and their Wallman covers. In particular, we will give sufficient and necessary conditions of spaces X satisfying ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• 대한수학회논문집
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• 제19권2호
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• pp.197-204
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• 2004

Every orthomodular lattice satisfying the loop lemma is the direct product of a Boolean algebra and an irreducible path-connected orthomodular lattice.

• 한국수학교육학회지시리즈A:수학교육
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• 제17권1호
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• pp.29-34
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• 1978

• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.539-545
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• 2003

We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.

• 한국산업정보학회논문지
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• 제16권5호
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• pp.9-19
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• 2011

In many instances a concise form of logic is often required for building today's complex systems. The method described in this paper can be used for a wide range of industrial applications that requires Boolean type of logic minimization. Unlike some of the previous logic minimization methods, the proposed method can be used to better gain insights into the logic minimization process. Based on the decimal valued matrix, the method described here can be used to find an exact minimized solution for a given Boolean function. It is a visual based method that primarily relies on grouping the cell values within the matrix. At the same time, the method is systematic to the extent that it can also be computerized. Constructing the matrix to visualize a logic minimization problem should be relatively easy for the most part, particularly if the computer-generated graphs are accompanied.

• 컴퓨터교육학회논문지
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• 제15권1호
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• pp.65-72
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• 2012

일반적으로 논리식은 수많은 인수분해식으로 표현이 가능하다. 논리식에 대한 보다 간략화된 인수분해식을 찾는 것이 논리합성의 기본 기능 중의 하나이며 본 논문에서 논리회로 수업의 교육용 도구로 부울 인수분해식을 산출하는 새로운 방법을 제안한다. 제안하는 방법은 서포트와 함께 2개의 항에 대한 나눗셈을 수행하는 것이다. 인수분해식의 리터럴 개수는 논리식의 간략화 정도를 판단하는 기준이 되는데, 제안하는 방법으로 실험한 결과, 기존의 타 방법들 보다 리터럴 개수를 줄이는 효과를 보였다.

• 대한수학회보
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• 제44권4호
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• pp.721-729
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• 2007

In this paper, we have characterizations of idempotent matrices over general Boolean algebras and chain semirings. As a consequence, we obtain that a fuzzy matrix $A=[a_{i,j}]$ is idempotent if and only if all $a_{i,j}$-patterns of A are idempotent matrices over the binary Boolean algebra $\mathbb{B}_1={0,1}$. Furthermore, it turns out that a binary Boolean matrix is idempotent if and only if it can be represented as a sum of line parts and rectangle parts of the matrix.