• Korean Journal of Mathematics
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• v.24 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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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.

• Honam Mathematical Journal
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• v.28 no.1
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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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.2
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• pp.95-103
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• 2005

Convolution modular lattices appeared in the analysis of NTRU public key cryptosystem. We present three guess-then-reduce methods on convolution modular lattices, and apply them to practical parameters of NTRU. For the present our methods don't affect significantly the security of them. However, Hey have room for improvement and can be used to estimate mole closely the security of systems related to convolution modular lattices.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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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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• v.55 no.1
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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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• v.14 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.28 no.1
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• pp.127-141
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• 1991