• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.10
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• pp.1454-1460
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• 1993

The scattering pattern, due to an E-Polarized wave incident on M circular parallel dielectric cylinders, is computed. The multiply-scattered fields between the cylinders are considered. Modeling of infinite cylindrical scatterer of arbitrary cross sections by a number of circular cylinders is executed. By enforcing the boundary conditions on the surface of each cylinder, an infinite set of equations is obtained. The first order of scattering results from the excitation of each cylinder by only the incident wave. The second order results from the excitation of each cylinder by the first order of scattering from the remaining cylinders, and so no to an infinite order of scattering. Although the resulting equation is of infinite size, proper truncation yields very accurate numerical results.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.115-128
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• 2009

In this paper, we modify the axiom of infinity of von Neumann's axioms modified by Pinter([5]), and then discuss an existence of an unknowable class in the system and a relationship between the unknowable class and the axiom of choice.

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.263-269
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• 2014

As a further study on reflexive families of subsets, we introduce the reflexive index for a family of subsets of a given set and show that the index of a finite family of subsets of a finite or countably infinite set is always finite. The reflexive indices of some special families are also considered.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.271-279
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• 2009

Using an index theory for countably condensing maps, we show the existence of eigenvalues for countably k-set contractive maps and countably condensing maps in an infinite dimensional Banach space X, under certain condition that depends on the quantitative haracteristic, that is, the infimum of all $k\;{\geq}\;1$ for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.4
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• pp.443-449
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• 2014

Preferences of users on movies are observables of various factors that are related with user attributes and movie features. For movie recommendation, analysis methods for relation among users, movies, and preference patterns are mandatory. As a relational analysis tool, we focus on the Infinite Relational Model (IRM) which was introduced as a tool for multiple concept search. We show that IRM-based co-clustering on preference patterns and movie descriptors can be used as the first tool for movie recommender methods, especially content-based filtering approaches. By introducing a set of well-defined tag sets for movies and doing three-way co-clustering on a movie-rating matrix and a movie-tag matrix, we discovered various explainable relations among users and movies. We suggest various usages of IRM-based co-clustering, espcially, for incremental and dynamic recommender systems.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.135-147
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• 1997

Let k be an infinite field and let $X = {P_1, \cdots, P_s}$ be a set of s-distinct points in $P^n$. We denote by $I(X)$ the defining ideal of $X$ in the polynomial ring $R = k[x_0, \cdots, x_n]$ and by A the homogeneous coordinate ring of $X, A = \sum_{t = 0}^{\infty} A_t$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1669-1675
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• 2017

The group of automorphisms of the first Weyl algebra acts on commuting ordinary differential operators with polynomial coefficient. In this paper we prove that for fixed generic spectral curve of genus two the set of orbits is infinite.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.107-127
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• 2014

The goal of this note is to describe the asymptotic behaviour of problems set in cylinders when the size of them is becoming infinite. This leads to consider problems in unbounded domains as well as new singular perturbations issues.

• East Asian mathematical journal
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• v.15 no.1
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• pp.147-151
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• 1999