• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.993-1015
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• 2012

In this paper, we study the quantum sl($n$) representation category using the web space. Specially, we extend sl($n$) web space for $n{\geq}4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl($n$). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial ($n=0$) and Jones polynomial ($n=2$) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.625-636
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• 2015

The Boolean rank of a nonzero $m{\times}n$ Boolean matrix A is the least integer k such that there are an $m{\times}k$ Boolean matrix B and a $k{\times}n$ Boolean matrix C with A = BC. We investigate the structure of linear transformations T : $\mathbb{M}_{m,n}{\rightarrow}\mathbb{M}_{p,q}$ which preserve Boolean rank. We also show that if a linear transformation preserves the set of Boolean rank 1 matrices and the set of Boolean rank k matrices for any k, $2{\leq}k{\leq}$ min{m, n} (or if T strongly preserves the set of Boolean rank 1 matrices), then T preserves all Boolean ranks.

• Archives of design research
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• v.12 no.3
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• pp.237-246
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• 1999

The study ooramed has the meanngs as a goal, to examine a character and changes of function a "Maru" in the literatures historically. Methodically the literatures in the temporal oonsequences were selected, and the "Maru", whidl oomes into it, was interpreted in its historical oonnections. By the investigation I oould oome to the following results. First of all, those terms "Maru" and "Daechll1Q" were cfifferently used after the sizes and p1ares of the spaces concerned. I.e, the "Maru" in the center of the house is called "Daed1ung", With the Maru does not concern actually its p1are, Secondly, the functions of the spare "Maru" are characterized as follows. ·Space for the important ceremonies ·Spare for the passage and the switching of two or several spaces. ·Determination of the hierardly of spares in the whole house. ·Spare for the receipt. ·Spare for sleeping and for living. ·Spare for work, storage etc. Thirdly, the meanings of the "Maru" were dlanged as follows in the time. ·The term "Man! was used from the past to today without interrujjion. Arot.l1d 1930 the tenns "Yangsil" and "Geosil" for the tenn "Maru" were emerged. ·The different dlaraderistics for the space "Maru" are found in the cortemporary literatures only rare. This thing explains itself by the fad that the "Maru" becomes the inner-spare after 1900 by the restructuring of the dwelling spares.hing explains itself by the fad that the "Maru" becomes the inner-spare after 1900 by the restructuring of the dwelling spares.

• Economic and Environmental Geology
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• v.51 no.2
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• pp.87-97
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• 2018

The cesium (Cs) removal from the contaminated water system has been considered to be difficult because the cesium likes to exist as soluble phases such as ion and complexes than the solid in water system. Many researches have focused on developing the breakthrough adsorbent to increase the cesium removal efficiency in water. In this study, the laboratory scale experiments were performed to investigate the feasibility of the adsorption process using the bamboo charcoal for the Cs contaminated water system. The Cs removal efficiency of the bamboo charcoal were measured and the optimal adsorption conditions were determined by the adsorption batch experiments. Total 5 types of commercialized bamboo charcoals in Korea were used to identify their surface properties from SEM-EDS and XRD analyses and 3 types of bamboo charcoals having large specific surface areas were used for the adsorption batch experiment. The batch experiments to calculate the Cs removal efficiency were performed at conditions of various Cs concentration (0.01 - 10 mg/L), pH (3 - 11), temperature ($5-30^{\circ}C$), and adsorption time (10 - 120 min.). Experimental results were fitted to the Langmuir adsorption isotherm curve and their adsorption constants were determined to understand the adsorption properties of bamboo charcoal for Cs contaminated water system. From results of SEM-EDS analyses, the surfaces of bamboo charcoal particles were composed of typical fiber structures having various pores and dense lamella structures in supporting major adsorption spaces for Cs. From results of adsorption batch experiments, the Cs-133 removal efficiency of C type bamboo charcoal was the highest among those of 3 bamboo charcoal types and it was higher than 75 % (maximum of 82 %) even when the initial Cs concentration in water was lower than 1.0 mg/L, suggesting that the adsorption process using the bamboo charcoal has a great potential to remove Cs from the genuine Cs contaminated water, of which Cs concentration is low (< 1.0 mg/L) in general. The high Cs removal efficiency of bamboo charcoal was maintained in a relatively wide range of temperatures and pHs, supporting that the usage of the bamboo charcoal is feasible for various types of water. Experimental results were similar to the Langmuir adsorption model and the maximum amount of Cs adsorption (qm:mg/g) was 63.4 mg/g, which was higher than those of commercialized adsorbents used in previous studies. The surface coverage (${\theta}$) of bamboo charcoal was also maintained in low when the Cs concentration in water was < 1.0 mg/L, investigating that the Cs contaminated water can be remediated up with a small amount of bamboo charcoal.