• Journal of the Korean Society of Costume
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• v.52 no.3
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• pp.149-160
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• 2002

Symbolism found in a certain object inherits characteristics from the culture that contains the objects. The purpose of this study was investigate the formative beauty of Korean trousers twisted the pieces together based on the way of Korean thinks and the Topology. The shape is formed by cutting from the fabric. From the perspective of semiology, the fabric and the pattern shape correspond to ground and figure. Ground and figure are identical with the principle of the whole and the part, which is the same in Korea, China, and the West. But In Korea, the 3-dimensional garment is made by adding a twist. This is very important and defines the difference in the way of thinking and topology. Korean trousers consist of three parts : Hury, Marupok, and Sapok. The small Sapok can be made by removing the Marupok and large Sapok (figure) from the fabric (ground) when making Korean trousers. A Mobius strip is made when the large Sapok is adjoined with the small Sapok by reversing the small Sapok, making a 180$^{\circ}$twist and then stitching together. The theory of Mobius strip can be applied in Joining Bajiburi. thus when the trousers are completed the Klein's bottle is seen because of the 2 existing Mobius strop. The theory of Mobius strip can be applied in Joining Bajiburi, thus when the trousers are completed the Klein's bottle is seen because of the 2 existing Mobius strip. Hury is cylinder while the small and large Sapok make up the Mobius strip. As a result, Mobius strip, Kleins'bottle, protective plan can be applied in cutting Hanbok used in the countryside, so I have come to see that the traditional Korean way of thinking is closely related to the theory of topological.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.621-633
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• 2002

This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-13
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• 1999

Let G be the 3-dimensional Heisenberg group. A discrete subgroup of Isom(G), acting freely on G with non-compact quotient, must be isomorphic to either 1, Z, Z2 or the fundamental group of the Klein bottle. We classify all discrete representations of such groups into Isom(G) up to affine conjugacy. This yields an affine calssification of 3-dimensional non-compact infra-nilmanifolds.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.159-172
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• 2004

A map is singular if each edge is on the same face on a surface (i.e., those have only one face on a surface). Because any map with loop is not colorable, all maps here are assumed to be loopless. In this paper po-vides the explicit expression of chromatic sum functions for rooted singular maps on the projective plane, the torus and the Klein bottle. From the explicit expression of chromatic sum functions of such maps, the explicit expression of enumerating functions of such maps are also derived.

• Korean Institute of Interior Design Journal
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• v.13 no.3
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• pp.69-75
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• 2004

Since 1990s, several rising western architects have been moving their theoretical background from the modern paradigm to new science and philosophy. Architectural spaces are based on the philosophy and science of their own age and the architectural theories made by them. And specially, it seems that topological spaces are different to theoretical backgrounds from idealized spaces of modern architecture. From these backgrounds, this study was performed to search for the spacial relationship and characteristics shown in the recently folding architecture and the results of this study that starts this purpose are as follows. First, the architecture that introduced by the theory of topology has appeared as the circulation forms like as Mobius band or Klein bottle, and was made the space fused with structure pursuing liquid properties of matter. As follows, second, the concept of topological space made the division of traditional concept of floor, wall, ceiling disappeared and had built up the space by continual transformation. Third, about the relationship between two spaces in topological space, the two spaces were happened by transformation of these and they have always continuity and the same quality.