• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.449-473
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• 2012

In the present paper, we study the relationship between continuous order-representability and the fulfillment of the usual covering properties on topological spaces. We also consider the case of some algebraic structures providing an application of our results to the social choice theory context.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.381-391
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• 2011

One of the main interesting things of a matroid theory is the representability by a matroid from a matrix over some field F. The representability of uniform matroid $U_{m,n}$ over some field are studied by many authors. In this paper we construct a matrix representing $U_{3,6}$ over the field GF(4). Also we find out matrix of the affine matroid AG(2, 3) over the field GF(4).

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.445-463
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• 2023

The paper introduces the concept of direct product and discusses some basic facts about distant ideals. We also introduce the definition of directly indecomposable in an autometrized algebra. Furthermore, we present the concept of a subdirect product and simple autometrized algebra and its behavior. We also introduce the definition of subdirectly irreducible in an autometrized algebras. In particular, we prove that every subdirectly irreducible monoid autometrized algebra is directly indecomposable. Finally, we discuss different properties of chain autometrized algebras and introduce the representability in the autometrized algebra. We also prove that if a weak chain monoid normal autometrized l-algebra is nilradical, then it is representable.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.809-824
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• 1997

With the primitive orders in quaternion algebra, theta series associated with these orders are constructed. Here, we studied the space of modular forms generated by these theta series.

• Journal of Korean Institute of Industrial Engineers
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• v.9 no.1
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• pp.7-15
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• 1983

This paper analyses and represents the various static and dynamical aspects of the production management problems by graphical methods. For this, eight graphical formal models are investigated and compared in terms of their ability to express twelve typical features for the structure of production planning.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.343-358
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• 2008

The primitive orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study theta series generated by Brandt matrices and its applications to almost Ramanujan graphs.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.701-711
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• 2009

We prove that every non-separable connected metric space can be endowed with a total preorder that is order-isomorphic to a nonrepresentable subset of the lexicographic plane and semicontinuous with respect to the metric topology.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.63-71
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• 2010

In this paper, we analyze a zero-knowledge identification scheme presented in [1], which is based on an average-case hard problem, called distributional matrix representability problem. On the contrary to the soundness property claimed in [1], we show that a simple impersonation attack is feasible.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.159-181
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• 2006

The objective of this paper is to show further results concerning the problem of extending total preorders from a subset of a topological space to the entire space using the approach introduced by Gyoseob Yi.

• Journal of Korean Society on Water Environment
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• v.29 no.4
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• pp.531-539
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• 2013

In order to apply a water quality indicator as a certain target pollutant, the indicator should have the representability of an index for the management of Total Maximum Daily Loads (TMDLs). Scientific groundwork and treatment technologies also should be provided for the application of the indicator. This study analyzed the applicability of major water quality indicators for target pollutants. The results showed that four water quality indicators of TOC, T-N, SS & T-Coli can be considered as target pollutants besides existing BOD and T-P. These indicators can be applied with the preparations such as essential basic data, pollution load estimation framework as well as legal criteria setting when the need is raised. As the importance of TOC, which is considered as a replacement of BOD, is emphasized, technical and institutional terms are being prepared in order to determine TOC as another target pollutant in the near future. It could be considered to combine TOC with BOD for the time being during the $3^{rd}$ stage of TMDLs in view of the present conditions for the management of TOC. TOC can be the most effective index for the organic matter and help to be managed more systematically in the waterbodies where rivers and lakes are mutually connected.