• 대한수학회지
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• 제33권2호
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• pp.217-225
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• 1996

An orthomodular lattice (abbreviated by OML) is an ortholattice L which satisfies the orthomodular law: if x $\leq$ y, then $y = x \vee (x' \wedge y)$ [5]. A Boolean algebra B is an ortholattice satisfying the distributive law : $x \vee (g \wedge z) = (x \vee y) \wedge (x \vee z) \forall x, y, z \in B$.

• 전자공학회논문지B
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• 제32B권6호
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• pp.862-867
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• 1995

In this paper a method to perform Exclusive-OR operation between two tabular type Boolean expressions is presented. The proposed method allows to solve the switching equations and the simultaneous equations in a rather direct manner, compared with Unger's method.

• 한국가스학회지
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• 제3권3호
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• pp.29-33
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• 1999

본 연구는 정량적 위험 평가의 기반 조성을 위해서 다양한 위험 평가 기법 중에서 이상 트리 분석(Fault Tree Analysis) 방법을 이용하여 빈도 분석 프로그램을 개발하였다. 빈도 분석 프로그램을 구축하기 위하여 계산 과정에서는 gate-by-gate 방법과 부울 대수 (Boolean algebra) 방법을 이용하였고, minimal cut set 방법을 이용하여 사고 발생 경로를 정량적으로 표현하였다 결론적으로 본 연구에서 개발한 빈도 분석 프로그램을 이용하여 사고 발생 빈도를 낮출 수 있다면 공정 전체의 안전성을 높이는데 큰 도움이 될 것이며, 기존에 사용되고 있는 외국의 S/W를 대체할 수 있을 것이라고 사료된다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제11권2호
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• pp.143-151
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• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.

• 대한수학회지
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• 제42권6호
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• pp.1111-1120
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• 2005

Hong and Nel in [8] obtained a number of spectral dualities between a cartesian closed topological category X and a category of algebras of suitable type in X in accordance with the original formalism of Porst and Wischnewsky[12]. In this paper, there arises a dual adjointness S $\vdash$ C between the category X = Lim of limit spaces and that A of MV-algebras in X. We firstly show that the spectral duality: $S(A)^{op}{\simeq}C(X^{op})$ holds for the dualizing object K = I = [0,1] or K = 2 = {0, 1}. Secondly, we study a duality between the category of Tychonoff spaces and the category of semi-simple MV-algebras. Furthermore, it is shown that for any $X\;\in\;Lim\;(X\;{\neq}\;{\emptyset})\;C(X,\;I)$ is densely embedded into a cube $I^/H/$, where H is a set.

• 대한수학회보
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• 제46권5호
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• pp.845-856
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• 2009

A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\cap$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\cap$ B| < $\infty$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\vee$ generated by the commutators of L is finite, then L is pathconnected.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권1호
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• pp.61-69
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• 2000

Let($X^{\ast},\tau^{\ast}$) be the space with one point Lindeloffication topology of space (X,$\tau$). This paper offers the definition of the space with one point Lin-deloffication topology of a topological space and proves that the retraction regu-lar closed function f: $K^{\ast}(X^{\ast}$) defined f($A^{\ast})=A^{\ast}$ if p $\in A^{\ast}$ or ($f(A^{\ast})=A^{\ast}-{p}$ if $p \in A^{\ast}$ is a homomorphism. There are two examples in this paper to show that the retraction regular closed function f is neither a surjection nor an injection.

• Journal of the Optical Society of Korea
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• 제9권3호
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• pp.111-118
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• 2005

In this paper, a new optical parallel binary arithmetic processor (OPBAP) capable of computing arbitrary n-bit look-ahead carry full-addition is proposed and implemented. The conventional Boolean algebra is considered to implement OPBAP by using two schemes of optical logic processor. One is space-variant optical logic gate processor (SVOLGP), the other is shadow-casting optical logic array processor (SCOLAP). SVOLGP can process logical AND and OR operations different in space simultaneously by using free-space interconnection logic filters, while SCOLAP can perform any possible 16 Boolean logic function by using spatial instruction-control filter. A dual-rail encoding method is adopted because the complement of an input is needed in arithmetic process. Experiment on OPBAP for an 8-bit look-ahead carry full addition is performed. The experimental results have shown that the proposed OPBAP has a capability of optical look-ahead carry full-addition with high computing speed regardless of the data length.

• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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• pp.1-8
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• 2023

This study is on a Boolean B or Boolean lattice L in abstract algebra with closed binary operation *, complement and distributive properties. Both Binary operations and logic properties dominate this set. A lattice sheds light on binary operations and other algebraic structures. In particular, the construction of the elements of this L set from idempotent elements, our definition of k-order idempotent has led to the expanded definition of the definition of the lattice theory. In addition, a lattice offers clever solutions to vital problems in life with the concept of logic. The restriction on a lattice is clearly also limit such applications. The flexibility of logical theories adds even more vitality to practices. This is the main theme of the study. Therefore, the properties of the set elements resulting from the binary operation force the logic theory. According to the new definition given, some properties, lemmas and theorems of the lattice theory are examined. Examples of different situations are given.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2008년도 추계학술발표대회
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• pp.722-725
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• 2008

복합질환(complex disease)의 원인과 작용 모델을 찾기 위해 여러 가지 통계적인 방법들과 기계 학습(machine learning)의 방법 등이 사용되고 있다. 소수 SNP의 작용모델을 찾는 방법은 많이 알려져 있지만 다수 SNP의 작용 모델을 효과적으로 찾는 방법은 거의 연구되어 있지 않다. 본 연구에서는 원인 SNP들의 작용을 부울 식(boolean expression)으로 나타내고, 유전 알고리즘(genetic algorithm)을 이용하여 예측 정확도가 높은 부울 식을 구성하였으며 실제 자료와 생성된 자료에 대하여 제안한 모델의 성능을 측정하였다.