• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.633-641
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• 2005

We investigate the relationship between fuzzy $\sigma$-ideals and fuzzy congruence on a distributive $\sigma$-lattice and obtain some useful results.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.61-82
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• 2005

We characterize Gaussian cotype X operators acting between Banach spaces, where X is a Banach sequence space. Further we give an extensive presentation of results on the connections between cotype and summing operators.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.559-568
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• 1994

A lattice is called bounded if it has both the least element and the largest element which are usually denoted by 0 (zero) and 1(unit), respectively.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.27-34
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• 1998

We introduce ${\delta}$-frames, strong ${\delta}$-frames and completely distributive lattices, and investigate some relationships among those frames.

• The Transactions of the Korea Information Processing Society
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• v.2 no.4
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• pp.477-486
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• 1995

This paper describes and constructs object-oriented analysis models using Galois-lattices that we are always studying in discrete mathematics, shows fundamental approaches to maintain the models, analyzes the construction of object-oriented analysis models through good examples. Also, we define several properties of Galois-lattices that have binary relations between class objects, propose the incremental updating algorithms that can update the Galois-lattice whenever new classes are added. This proposal shows that in case of adding new class nodes the results from simulations can implement in constant time and have linearly the incremental structures in worst cases, and in that the growth rate of lattices is proportioned to class nodes in time complexity. This results can achieve the high understandability of object-oriented analysis models and the high traceability of maintenance models. Furthermore it is possible to make more efficient performances of class reusability in advantages of object-oriented systems and support truly the class hierarchical maintenances.

• Journal of the Korean Chemical Society
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• v.56 no.6
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• pp.768-771
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• 2012

• East Asian mathematical journal
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• v.28 no.5
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• pp.605-615
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• 2012

In this paper, we show that any definite lattice over $\mathbb{F}_q[x]$ is universal if and only if it is quaternary and its discriminant is of degree 2, where $ch(\mathbb{F}_q){\neq}2$. The Four Conjecture follows as an immediate consequence.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.8.1-8
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• 2003

We prove that m-step walks and self-avoiding walks on the 2D triangle lattices can be uniquely characterized (canonized) with no more than m Euclidian distances. We also demonstrate that these canonical distances can be obtained with O(n) physical measurements.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.553-565
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• 2014

In this paper, we investigate the properties of Alexandrov fuzzy topologies and join-meet approximation operators. We study fuzzy preorder, Alexandrov topologies join-meet approximation operators induced by Alexandrov fuzzy topologies.We give their examples.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.527-539
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• 1995

We consider the Schur groups of some module categories, which are subcategories of category of divisorial modules over a Krull domain. Then we obtain the exact sequence connecting class group, Schur class group and Schur groups of these categories.