• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.749-762
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• 2017

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful. We will also derive new presentations for the surface singular braid monoid, one with reduced the number of defining relations, and the other with reduced the number of its singular generators. We include surface singular braid formulations of all knotted surfaces in Yoshikawa's table.

• Bulletin of the Korean Chemical Society
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• v.30 no.3
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• pp.667-670
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• 2009

The understanding of behaviors of hydroperoxyl/superoxide anion radicals (${H_2O_2}^./{O_2}^{-.}$) generated from a photoirradiated $TiO_2$ surface is essential to improve the efficiency of $TiO_2$ photocatalytic reactions by decreasing the recombination of photoinduced electron-hole ($e^--h^+$) pairs. In contrast with previous studies, we found that ${H_2O_2}^./{O_2}^{-.}$ generated on the surface of illuminated $TiO_2$ particles are mobile. ${H_2O_2}^./{O_2}^{-.}$ formed by the photocatalysis of $TiO_2$ particles immobilized onto the inner surface of a coil-quartz tube were forced under a continuous flow through a knotted tubing reactor (KTR) and into the aqueous phase completely separated from the $TiO_2$ particles, and were measured by a chemiluminescence (CL) technique using 2-methyl-6-(p-methoxyphenyl)-3,7-dihydroimidazo[ 1,2-a]pyrazin-3-one (MCLA) as the reagent. The initial concentration of the ${H_2O_2}^./{O_2}^{-.}$ stream entering the KTR was determined by its half-life (98 s) at pH 5.8. We suggests that the efficiency of $TiO_2$ photocatalytic reactions may be further improved by utilizing the mobility of ${H_2O_2}^./{O_2}^{-.}$.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.403-414
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• 2012

A voltage assignment on a graph was used to enumerate all possible 2-cell embeddings of a graph onto surfaces. The boundary of the surface which is obtained from 0 voltage on every edges of a very special diagram of a complete bipartite graph $K_{m,n}$ is surprisingly the ($m,n$) torus link. In the present article, we prove that every link is the boundary of a complete bipartite multi-graph $K_{m,n}$ for which voltage assignments are either -1 or 1 and that every link is the boundary of a complete bipartite graph $K_{2,n}$ for which voltage assignments are either -1, 0 or 1 where edges in the diagram of graphs may be linked but not knotted.

• Journal of the Korea Fashion and Costume Design Association
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• v.6 no.1
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• pp.34-45
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• 2004

The purpose of the study was to investigate weaving, traditional dyeing, fiber material, pattern how carpet developing according to Turkey area for using the data that can rear to the export strategic industry for carpet production and development that is correct in culture. The result are followed: 1) Life of the age was expressed in color and pattern using according to geographical environment, climate, lifestyle, religion etc. 2) In the case of weaving, there is Kilim, Soumak that appears only weft on the surface as plane weaving without knot and carpet of knotted pile weaving and knot of carpet is duplex knot difference with carpet of the other country. 3) In the case of textile material, there is use most wool fiber that can get easily from breeded sheep by nomads. 4) In the case of dyeing, did the local traditional color to use dye extracting in dyeing material that can get easily in the area. Red that can extract in madder that can get easily in which area of Turkey, dark navy blue of indigo dye that indigo plant fermentation and cream beige that is wool's natural color were exposed representative traditional color of Turkey carpet. 5) Pattern was advanced uniquely as culture of the area; weaving person's sensitivity and desire are reflected through centuries. Amulet, riches ＆ honors, fecundity and happiness appeared most pattern in any area.