• 한국수학사학회지
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• 제13권2호
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• pp.95-104
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• 2000

This paper is a sequel to [24]. It is well known that the order structure plays the important role in the study of various mathematical structures. In 1972, Scott has introduced a concept of continuous lattices and has shown the equivalence between continuous lattices and injective $T_0-spaces$. There have been many efforts made to generalize continuous lattices and extend corresponding properties to them. We introduce another class of frames, namely countably approximating frames, generalizing continuous frames and study its basic properties.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2013년도 춘계 종합학술대회 논문집
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• pp.369-370
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• 2013

Orthomodular lattice is a mathematical description of quantum theory which is based on the family CS(H) of all closed subspaces of a Hilbert space H. A partial multiplier is a function F from a non-empty subset D of a commutative semigroup A into A such that F(x)y = xF(y) for every elements x, y in A. In this paper, we define the notion of multipliers on orthomodular lattices and give some properties of multipliers. Also, we characterize some properties of orthomodular lattices by multipliers.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권12호
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• pp.3261-3273
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• 2013

In the paper, we propose a novel adaptively secure hierarchical identity-based signature scheme from lattices. The size of signatures in our scheme is shortest among the existing hierarchical identity-based signature schemes from lattices. Our scheme is motivated by Gentry et al.'s signature scheme and Agrawal et al.'s hierarchical identity-based encryption scheme.

• East Asian mathematical journal
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• 제19권1호
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• pp.41-48
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• 2003

There are many conditions or identities for a lattice to be distributive. In this paper, we study some identities on algebras of type (2,2) and find another set of identities defining distributive lattices. We also study certain identities which define algebras of type (2,2) whose subalgebras generated by two elements are all distributive lattices with at most 4 elements.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.19-29
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• 2022

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. Moreover, their properties and examples are investigated.

• Journal of Applied and Pure Mathematics
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• 제5권5_6호
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• pp.347-362
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• 2023

We introduce an algebraic structure induced by a fuzzy bipartial order on a complete residuated lattices with the double negative law. We undertake an investigation into the properties of fuzzy bi-partial orders, including their various characteristics and features. We demonstrate that the two families of l-stable and r-stable fuzzy sets can be regarded as complete lattices, and we establish that these two families are anti-isomorphic. Furthermore, we provide two examples related to them.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.569-585
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• 2021

In this paper, we introduce the concept of relative co-fuzzy annihilator filters in distributive lattices. We give a set of equivalent conditions for a co-fuzzy annihilator to be a fuzzy filter and we characterize distributive lattices with the help of co-fuzzy annihilator filters. Furthermore, using the concept of relative co-fuzzy annihilators, we prove that the class of fuzzy filters of distributive lattices forms a Heyting algebra. We also study co-fuzzy annihilator filters. It is proved that the set of all co-fuzzy annihilator filters forms a complete Boolean algebra.

• 정보보호학회논문지
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• 제15권2호
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• pp.95-103
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• 2005

순환 법 격자는 NTRU 공개키 암호의 분석에서 처음으로 소개되었다. 본 논문에서는 순환 법 격자에 대한 세가지 추정 후 축소 기법을 제안하고, NTRU의 상용 시스템에 적용하여 본다. 현재까지는 이러한 기법들이 NTRU의 안전성에 심각한 영향을 주지 않는 것으로 보인다. 그러나, 본 논문에서 제시한 방법은 개선의 여지가 많이 있고, 순환법 격자와 관련된 암호 시스템들의 안전성을 더욱 엄밀히 분석하는데 활용될 것으로 기대된다.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.445-460
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• 2022

In this paper, we studied on 𝛽-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of 𝛽-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any 𝛽-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime 𝛽-fuzzy filters and some topological concepts on the collection of prime 𝛽-fuzzy filters of a Stone ADL. Further we show that the collection 𝓣 = {X^𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec_𝛽(A) where X^𝛽(λ) = {𝜇 ∈ 𝓕Spec_𝛽(A) : λ ⊈ 𝜇}.

• Nuclear Engineering and Technology
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• 제56권2호
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• pp.410-418
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• 2024

Study of flow behavior within rod bundles has been an active topic. Surface modification technologies are important parts of the design of the fourth generation reactor, which can increase the strength of the secondary flow within the rod bundle lattices. Quasi-periodic large-scale vortex structure (QLVS) is introduced by arranging micro ribs on the surface of rod bundles, which enhanced the scale of the secondary flow between the rod bundle lattices. Using computational fluid dynamics (CFD) and water experiments, the flow field distribution and drag coefficient of the rod-bundle lattices are studied. The secondary flow between the micro-ribbed rod-bundle lattice is significantly enhanced compared to the standard rod-bundle lattice. The numerical simulation results agree well with the experimental results.