• East Asian mathematical journal
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• v.30 no.3
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• pp.303-310
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• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.1069-1105
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• 2001

Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familar examples of regular maps. The gret dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps goes back at least to Klein (1878) who described in [59] a regular map of type (3, 7) on the orientable surface of genus 3. In its early times, the study of regular maps was closely connected with group theory as one can see in Burnside’s famous monograph [19], and more recently in Coxeter’s and Moser’s book [25] (Chapter 8). The present-time interest in regular maps extends to their connection to Dyck\`s triangle groups, Riemann surfaces, algebraic curves, Galois groups and other areas, Many of these links are nicely surveyed in the recent papers of Jones [55] and Jones and Singerman [54]. The presented survey paper is based on the talk given by the author at the conference “Mathematics in the New Millenium”held in Seoul, October 2000. The idea was, on one hand side, to show the relationship of (regular) maps and hypermaps to the above mentioned fields of mathematics. On the other hand, we wanted to stress some ideas and results that are important for understanding of the nature of these interesting mathematical objects.

• Horticultural Science & Technology
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• v.34 no.5
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• pp.677-691
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• 2016

To assess South Korean commercial tomato cultivars, regular and cherry tomato cultivars were grown in the greenhouse and evaluated for color attributes, titratable acidity, pH, total soluble solids, carotenoids (lycopene and ${\beta}$-carotene), total phenols, flavonoids, vitamin C, and antioxidant activity. Significant differences (p < 0.05 using Duncan's multiple range test (DMRT)) were observed in the levels of most phytochemicals, quality parameters, and antioxidant activity among the twenty South Korean tomato cultivars tested. Lycopene and ${\beta}$-carotene contents varied significantly (p < 0.05 using DMRT), from $0.95mg{\cdot}100g^{-1}$ to $5.12mg{\cdot}100g^{-1}$ and $0.65mg{\cdot}100g^{-1}$ to $3.56mg{\cdot}100g^{-1}$ of fresh weight, respectively. ${\beta}$-carotene contents exhibited the highest genetic variation (59.2%), followed by naringenin (52.8%) and other phytochemicals. Most of the cherry tomato cultivars had statistically higher levels (p < 0.05 using DMRT) of carotenoids, phenols, flavonoids, vitamin C, and antioxidant activity compared to the regular tomato varieties, suggesting their higher nutritional value. Lycopene content was highest in the cultivars YoYo, Jicored, Titi-Chal, TY-Endorphin, and Rubyking. Cultivars Rubyking, TY-Endorphin, and Titi-Chal also showed relatively higher antioxidant activities in three assays: 2,2-diphenyl-1-picrylhydrazyl (DPPH), 2,2'-azino-bis (3-ethylbenzothiazoline-6-sulfonic acid) (ABTS), and ferric ion reducing antioxidant power (FRAP) assays. All the antioxidants, except luteolin, were positively correlated with antioxidant activities; the highest correlation was observed between total phenol and antioxidant activities, followed by the correlation between rutin and vitamin C. Cultivars identified to have superior nutritional status would be useful in tomato breeding programs to further improve quality and health benefits of tomatoes for the fresh and processed markets.

• Computers and Concrete
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• v.16 no.1
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• pp.125-140
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• 2015

This paper describes the numerical calculation of elastic properties of a simulated microstructure of cement paste from very early age, when most previous models fail to give accurate results. The development of elastic properties of tricalcium silicate pastes was calculated by discretising a numerical resolution-free 3D vector microstructure to a regular cubic mesh. Due to the connections formed in the microstructure as an artefact of the meshing procedure, the simulated elastic moduli were found to be higher than expected. Furthermore, the percolation of the solids was found to occur even before hydration started. A procedure to remove these artefacts, on the basis of the information available in the vector microstructures was developed. After this correction, a better agreement of the experimental results with calculations was obtained between 20% and 40% hydration. However, percolation threshold was found to be delayed significantly. More realistic estimates of percolation threshold were obtained if either flocculation or a densification of calcium silicate hydrate with hydration was assumed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.11
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• pp.2967-2972
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• 1994

The multiple character of the contact interaction and the collective behavior of elementary microcontacts play a significant role in all the processes occurring in the surface layers, including the failure due to friction and wear. The array of metal spheres compressed between flat plates has been used for simulation of the contact behavior of multiple contact of solids under normal loading. An experimental design has been made providing regular array of the spheres at the same size with different spatial order. Measurement of electrial contact resistance has been made using the equipment providing the adequate accuracy in the range of micro Ohms. The data on electrical contact resistance have been compared with theoretical predictions using the multiple contact model of constriction resistance. The effect of single spots number and array on conductivity of contact has been evaluated.

• Applied Chemistry for Engineering
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• v.33 no.5
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• pp.532-537
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• 2022

The need for obtaining treated wastewater that meets high quality standards for discharge or reuse necessitates the use of highly efficient wastewater treatment techniques. In the present study, experiments have been carried out to reduce the concentration level of biological oxygen demand (BOD), chemical oxygen demand (COD), and total dissolved solids (TDS) from the wastewater sample. Treatment of sample of a real municipal wastewater collected from a sewage treatment plant (STP) was carried out in an electrochemical membrane bioreactor (EMBR). The EMBR was operated continuously for five days, and readings were taken at regular intervals. This paper has experimental results conducted in EMBR that indicate reduction of BOD, COD, and TDS levels of up to 32.25%, 29.25%, and 31.93%, respectively. Further, it was observed that a current of magnitude of 0.00752 mA was generated due to the metabolic activities of bacteria present in municipal wastewater, which gradually decreased day by day due to the decay of bacteria.

• Proceedings of the Korean Society for Food Science of Animal Resources Conference
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• 2005.05a
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• pp.290-296
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• 2005

This study was carried out to develop the efficient freeze concentration process of milk through controlling the recrystallisation phenomena of ice. Freeze-concentration was progressed with multi-stage freeze concentrator and there was artificial temperature control to induce recrystallisation phenomena. In each stage of freeze concentration process, the regular recrystallisation time was fixed as 1, 2, 4 and 8 hr to compare the solute increment, yield, brix and ice-crystal size among experimental conditions. Higher concentration as total solids was observed due to the elapse of recrystallisation time, and the maximum total solids in final products: 32.67% was obtained at the ripening time of 8 hr in two-stage process. This result was excessively high concentration comparing to the existing researches and presented the possibilities of milk freeze concentration in the dairy industry, The results of brix and ice-crystal size showed the direct correlation with the recrystallisation time that meant the increased processing time showed the increment of brix and ice-crystal size. Obtained results were numerically modelled to predict the progress of concentration in the industrial process and all of them had fairly high R2 of determination. Therefore, we regarded that these numerical models could be utilized for the development of efficient technology in industrial freeze concentration process.

• The Korean Journal of Community Living Science
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• v.14 no.3
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• pp.53-58
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• 2003

This study on the processing of noodles was carried out to increase utilization of Allium fistulosum L., In the areas of total solids in residual liquid, swelling volume, and water absorption, a mixture of 10.0% dried Allium fistulosum L. flour and wheat flour, and a mixture of 25.0% raw Allium fistulosum L. flour and wheat flour both perform similarly to noodles made with just wheat flour. In the area of texture- the gumminess, cutting factor, and chewiness increase as the percentage of dried Allium fistulosum L. flour increases. There is no great difference in these factors between the 10.0% dried and the 25.0% raw mixtures. The color of the noodles with a mixed Allium fistulosum L. flour is green-yellow. As the quantity of Allium fistulosum L. flour increases the color gets darker The over all perception of the noodles made with a mixed Allium fistulosum L. flour was rated higher in color, taste, and smell than regular noodles. This study shows that mixing wheat flour with 10.0% dried Allium fistulosum L. flour or 25.0% raw Allium fistulosum L. flour produces a better noodle product.

• Journal of Korean Society of Water and Wastewater
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• v.33 no.5
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• pp.353-366
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• 2019

This research proposes an optimal flushing operation technique in an effort to prevent secondary water pollutions and accidents in aged pipes, and to improve the cleaning effect of unidirectional flushing. Water flow directions were analyzed using EPANET 2.0, while flushing and air scouring experiments in forward and reverse directions were performed in the field. In 42 experiments, average residual chlorine concentration and turbidity were improved after cleaning compared to before cleaning. It was found that even when the same cleaning method was used, further improvement of cleaning effect was possible by applying air injection and reverse direction cleaning techniques. By means of one-way ANOVA(Analysis of variance), it was also possible to statistically verify the need of actively utilizing air injection and reverse direction cleaning. Based on correlation between turbidity and TSS, the total amount of suspended solids removal was estimated for 874 flushing operations and 194 air scouring operations. The result showed that air scouring used more discharge water than flushing by an average of $4.9m^3$ yet with larger amounts of suspended solids removal by an average of 145.9 g. The result of analysis on turbidity values from 887 flushing operations showed low cleaning effect of unidirectional flushing for the pipes with diameters over 300 mm. In addition, the turbidity values measured during cleaning showed an increasing tendency as pipe age increased. The methodology and results of this research are expected to contribute to the efficient maintenance and improvement of water quality in water distribution networks. Follow-up research involving the measurement of water quality at regular time intervals during cleaning would allow a more accurate comparison of discharge water quality characteristics and cleaning effects between different cleaning methods. To this end, it is considered necessary to develop a standardized manual that can be used in the field and to provide relevant trainings.

• Journal of Korean Society on Water Environment
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• v.24 no.6
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• pp.801-805
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• 2008

A fibrous material (p-phenylene-2,5-benzobisoxazole, PBO) was used as an adsorbent for solid phase extraction in order to simplify the extraction procedure. The extraction performance for di-(2-ethylhexyl) phthalate (DEHP) was examined with two types of PBO fibers (HM (High modulus) and AS (Regular type) types) by batch type sorption/desorption experiments. When 100 mg of the HM fibers were applied to 20 mL of the aqueous DEHP solution (less than $50{\mu}g/L$), more than 95% of DEHP was adsorbed on the fibers, however, the AS type fibers adsorbed alkyl phthalate up to 80%. In the case of $50{\mu}g/L$ of the initial concentration of DEHP, the adsorbed DEHP was extracted effectively with methanol and the maximum overall recovery ratio was 92.3%. The results indicated that the PBO fibers could be used as an adsorbent for alkyl phthalate analysis, and that the extraction procedure was not affected by suspended solids in a water sample.