• 한국수학사학회지
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• 제23권2호
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• pp.101-121
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• 2010

본 연구는 격자평면에서의 Pick의 정리에 대한 의의와 증명소개, Pick의 정리를 확장한 3차원 격자다면체에서의 Reeve의 정리 및 n차원 격자다면체로 일반화시킨 Ehrhart 다항식에 대한 소개와 역사적 고찰을 바탕으로 이를 고등학교 교육과정에서 다루고 있는 수열단원에 응용하기위해, Reeve의 정리를 이용하여 3차원 격자다면체의 격자점의 개수와 부피와의 관계를 제시하고, 나아가 Pick의 정리와 Ehrhart 다항식을 적용하여 수열의 합을 구하는 공식들을 새로운 증명법으로 도출하고자 한다.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.465-486
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• 2005

We study the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a distributive lattice. And we prove that the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences on a generalized Boolean algebra.

• 대한수학회보
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• 제35권1호
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• pp.13-24
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• 1998

We define an LI-ideal of a lattice implication algebra and show that every LI-ideal is a lattice ideal. We give an exampl that a lattice ideal may not be an LI-ideal, and show that every lattice ideal is an LI-ideal in a lattice H implication algebra. we discuss the relationship between filters and LI-ideals, and study how to generate an LI-ideal by a set. We construct the quotient structure by using an LI-ideal, and study the properties of LI-ideals related to implication homomorphisms.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
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• pp.372-377
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• 2004

We introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a lattice, and discuss the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruence on a distributive lattice. Also we prove that for a generalized Boolean algebra, the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences. Finally, we consider the products of intuitionistic fuzzy ideals and obtain a necessary and sufficient condition for an intuitionistic fuzzy ideals on the direct sum of lattices to be representable on a direct sum of intuitionistic fuzzy ideals on each lattice.

• 한국재료학회지
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• 제25권8호
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• pp.403-409
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• 2015

Metastable phase characteristics of beta Ti alloys were investigated to consider the relationship of the microstructure and diffraction pattern in TEM. TEM analysis showed that the microstructure was mottled as a modulated structure, and the diffraction pattern was composed of spot streaks between the main spots of a stable beta phase with a specific lattice relationship. The modulated structure may be induced by short distance slip or atom movement during a very short interval of solution treated and quenched (STQ) materials. The athermal ${\omega}$ phase, which could be precipitated at low temperature aging, is also analysed by the metastable phase. The metastable phases including athermal ${\omega}$ phase had a common characteristic of hardened and brittle behavior because the dislocation slip was restricted by a super lattice effect due to short distance atom movement at the metastable state.

• 호남수학학술지
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• 제37권2호
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• pp.187-205
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• 2015

We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

• Applied Microscopy
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• 제45권4호
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• pp.230-235
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• 2015

Crystallographic models are effective tools to interpret, calculate and even to predict the preferred crystallographic morphologies of precipitates in various precipitation systems. The present study gives an introduction on the recently developed secondary constrained coincident site lattice (II-CCSL) model. Using the II-CCSL model, the interface matching condition of the ${\beta}-Mg_{17}Al_{12}$ precipitates with ${\alpha}-Mg$ matrix in an aged AZ91 alloy has been analyzed to rationalize the morphologies of the precipitates. The results show that the characteristic crystallographic features of the observed ${\beta}-Mg_{17}Al_{12}$ precipitates, i.e., the habit plane of the ${\beta}-Mg_{17}Al_{12}$ lath with a Burgers orientation relationship (OR) and the growth direction of the ${\beta}-Mg_{17}Al_{12}$ with a Crawley OR exhibit a better lattice matching degree than their vicinal orientations. Moreover, the Crawley OR is preferred to the Burgers OR due to a better lattice match.

• Korean Journal of Mathematics
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• 제28권3호
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• pp.509-524
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• 2020

The notion of fuzzy closure filters is introduced and discussed in an MS-algebra. In particular, we characterize the prime fuzzy closure filters in terms of boosters. Some relationship between the lattice of fuzzy closure filters and the fuzzy ideal lattice of boosters are explored and investigated.

• 융합정보논문지
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• 제9권5호
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• pp.7-13
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• 2019

클라우드 환경이나 빅데이터 환경에서의 역할기반 또는 속성기반의 접근제어에는 계층적 모델을 표현하는 적당한 수학적 구조가 필요하다. 본 논문에서는 역할기반 또는 속성기반의 접근제어의 계층적 모델을 구현할 수 있는 격자함의 대수에서 멀티플라이어와 단순 멀티플라이어의 개념을 정의하고, 모든 멀티플라이어는 단순 멀티플라이어임을 증명한다. 또한 격자함의대수 L의 멀티플라이어와 준동형사상의 관계를 조사하고, 각각의 $u{\in}L$에 대하여 격자 [0, u]와 격자 $[u^{\prime},1]$이 동치임과 $u{\vee}u^{\prime}=1$인 $u{\in}L$에 대하여 L과 $[u,1]{\times}[u^{\prime},1]$이 격자함의대수로써 동치임을 보인다.

• 한국결정성장학회지
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• 제8권1호
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• pp.91-96
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• 1998

Huntite 구조를 갖는 borate결정의 격자상수($a_0$ 및 $c_0$ ) 산출을 위해 특정관계를 갖는 계산식을 도출하였다. 이를 위해 서로 다른 28종류의 조성을 갖고 있는 결정을 사용하였다. 이와 같은 계산식은 huntite 구조내에 위치하는 이온의 평균 반경을 함수로 하여 미지의 조성을 갖고 있는 결정으로부터 격자상수를 예상하는데 사용될 수 있다.