• Korean Journal of Mathematics
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• 제24권3호
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• pp.525-535
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• 2016

We define a fuzzy lattice as a fuzzy relation, prove the distributive inequalities and the modular inequality of fuzzy lattices, and show that the fuzzy totally ordered set is a distributive fuzzy lattice and that the distributive fuzzy lattice is modular.

• 호남수학학술지
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• 제28권1호
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• pp.31-44
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• 2006

We discuss various types of sublattice of the lattice of intuitionistic fuzzy subgroups of a given group. We prove that a special class of intuitionitic fuzzy normal subgroups constitutes a modular sublattice of the lattice of intuitionistic fuzzy subgroups.

• 대한수학회논문집
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• 제11권3호
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• pp.613-626
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• 1996

This paper is a contribution to the study of the properties of the lattice of all lattice varieties. Among the properties, that of finite base is investigated here. The question whether the join of two finitely based modular lattice varieties is finitely based is investigated under certain conditions.

• 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.

• 대한수학회지
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• 제33권2호
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• pp.439-453
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• 1996

In R. McKenzie[12], it is shown that the cardinality of the lattice variety is $2^\aleph_0$ and K. Baker[1] contains the stronger result that M, the variety of all modular lattices, has $2^\aleph_0$ subvarieties. It follows that there exists a variety of modular lattices that is not finitely based. In fact, K. Baker[2] gave an example of such a variety. And it was proved by K. Baker [2] and B. Jonsson [8] that join of two finitely based lattice varieties is not always finitely based. K. Baker[2] gave an explicit example of case of nonmodular lattice variety. Then it is proposed whether the join of two finitely based varieties if finitely based under certain conditions. The answer to the question is not affirmative.

• 대한수학회보
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• 제57권2호
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• pp.481-488
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• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• Nuclear Engineering and Technology
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• 제55권1호
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• pp.330-338
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• 2023

In this study, impacts of an enhanced-moderation Fuel Assembly (FA) named Truly Optimized PWR (TOP) lattice, which is modified based on the standard 17 × 17 PWR FA, are investigated in a natural circulation Soluble-Boron-Free (SBF) Small Modular Reactor (SMR). Two different TOP lattice designs are considered for the analysis; one is with 1.26 cm pin pitch and 0.38 cm fuel pellet radius, and the other is with 1.40 cm pin pitch and 0.41 cm fuel pellet radius. The NuScale core design is utilized as the base model and assumed to be successfully converted to an SBF core. The analysis is performed following the primary coolant circulation loop, and the reactor is modelled as a single channel for thermal-hydraulic analyses. It is assumed that the ratio of the core pressure drop to the total system pressure drop is around 0.3. The results showed that the reactor power could be increased by 2.5% and 9.8% utilizing 1.26/0.38 cm and 1.40/0.41 cm TOP designs, respectively, under the identical coolant inlet and outlet temperatures as the constraints.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권2호
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• pp.154-161
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• 2014

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.

• 대한수학회지
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• 제38권5호
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• pp.937-954
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• 2001

This paper is a natural continuation of [2], [3], [4] and [5]. Localization techniques for modular lattices are developed. These techniques are applied to study liftings of linear order types from quotient lattices and to find Г-dense sets in certain lattices without Г-deviation in the sense of [4], where Г is a set of indecomposable linear order types.

• 대한수학회지
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• 제28권1호
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• pp.127-141
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• 1991