• Journal of Korean Society of Water and Wastewater
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• v.22 no.1
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• pp.31-38
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• 2008

The primary objective of this study was to evaluate the variation of the molecular size distribution by granular activated carbon (GAC) adsorption. GAC adsorption was assessed by using the rapid small-scale column test (RSSCT) and high-performance size-exclusion chromatography (HPSEC) was used to analyze the molecular size distribution (MSD) in the effluent of GAC column. RSSCT study suggested that GAC adsorption exhibited excellent interrelationship between dissolved organic carbon (DOC) breakthrough and MSD as function of bed volumes passed. After GAC treatment, the nonadsorbable fraction which was about 25percents of influent DOC corresponded to the hydrophilic (HPI) natural organic carbon (NOM) of NOM fractions and was composed entirely of <300 molecular weight (MW) in the HPSEC at the initial stage of the RSSCT operation. The dominant MW fraction in the source water was 1,000~5,000daltons. At the bed volumes 2,500, MW <500 of GAC treated water was risen rather than it of source water. After the bed volumes 7,300 of operation, the MW 1,000~3,000 fraction was closed to about 80percents of DOC found in the GAC influent. The Number-average molecular weight (Mn) value determined using HPSEC for the effluent of GAC column was gently increased as DOC breakthrough progress. The quotient p(Mw/Mn) can be used to estimate the degree of polydispersity was shown greatest value for the GAC effluent at the initial stage of the RSSCT operation.

• School Mathematics
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• v.11 no.4
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• pp.685-706
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• 2009

This dissertation is aimed to investigate the reason why a contextualization is needed to help the meaningful teaching-learning concerning multiplications and divisions of fractions, the way to make the contextualization possible, and the methods which enable us to use it effectively. For this reason, this study intends to examine the differences of situations multiplying or dividing of fractions comparing to that of natural numbers, to recognize the changes in units by contextualization of multiplication of fractions, the context is set which helps to understand the role of operator that is a multiplier. As for the contextualization of division of fractions, the measurement division would have the left quantity if the quotient is discrete quantity, while the quotient of the measurement division should be presented as fractions if it is continuous quantity. The context of partitive division is connected with partitive division of natural number and 3 effective learning steps of formalization from division of natural number to division of fraction are presented. This research is expected to help teachers and students to acquire meaningful algorithm in the process of teaching and learning.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.17-35
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• 2013

The purpose of this study was to analyze the extendibility of division algorithm and Euclid algorithm for integers to algorithms for rational numbers based on word problems of fraction division. This study serviced to upgrade professional development of elementary and secondary mathematics teachers. In this paper, fractions were used as expressions of rational numbers, and they also represent rational numbers. According to discrete context and continuous context, and measurement division and partition division etc, divisibility was classified into two types; one is an abstract algebraic point of view and the other is a generalizing view which preserves division algorithms for integers. In the second view, we raised some contextual problems that can be used in school mathematics and then we discussed division algorithm, the greatest common divisor and the least common multiple, and Euclid algorithm for fractions.

• Journal of Korean Society on Water Environment
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• v.23 no.1
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• pp.97-102
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• 2007

The present investigation deals to achieve an accurate determination of the phosphorous present in the wastewater samples using the membrane reactor. The study may enable to quantify the dissolved (DP) and adsorbed phosphorous (AP), also the adsorbed phosphorous categorically identified as inorganic coupled phosphorous (DRP) and organic coupled phosphorous (NRP). Moreover, the study has been conducted separately in anaerobic and aerobic chamber. The results obtained showed that dissolved phosphorous only can occur in anaerobic chamber with ca. 25%. The study conducted for adsorbed phosphorous showed that the DRP has the percent composition in anaerobic and aerobic chamber respectively 33% and 40% i.e., 7% more in aerobic chamber. The similar values obtained for NRP was found to be 42% and 60% i.e., 18% more in aerobic chamber. On the other hand while comparing the results for NRP and DRP, it has to be noted that NRP has 9% and 20% more percent composition than DRP respectively in anaerobic and aerobic chamber. Further, the adsorbed phase showed the species Al-P, Fe-P in the aerobic chamber with the quotient of 7.73 mg/g TS (total solid) whereas in the anaerobic chamber it showed the species Fe-P and $Fe(OH)_3$-P with the 7.16 mg/g TS.

• School Mathematics
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• v.14 no.1
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• pp.29-43
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• 2012

This paper investigated the conceptual schemes in which four children constructed a strategy representing the situation as a figure and partitioning it related to the work which they quantify the result of partitioning to various types of fractions when an equal sharing situation was given to them in contextual or an abstract symbolic form of division. Also, the paper researched how the relationship of factors and multiples between the numerator and denominator, or between the divisor and dividend affected the construction. The children's partitioning strategies were developed such as: repeated halving stage ${\rightarrow}$ consuming all quantity stage ${\rightarrow}$ whole number objects leftover stage ${\rightarrow}$ singleton object analysis/multiple objects analysis ${\rightarrow}$ direct mapping stage. When children connected the singleton object analysis with multiple object analysis, they finally became able to conceptualize division as fractions and fractions as division.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.1-18
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• 2011

The purpose of this study was to investigate the effects of estimation strategy on placing decimal point in multiplication and division of decimals. To examine the effects of improving calculation ability and reducing decimal point errors with this estimation strategy, the experimental research on operation with decimal was conducted. The operation group conducted the decimal point estimation strategy for operating decimal fractions, whereas the control group used the traditional method with the same test paper. The results obtained in this research are as follows; First, the estimation strategy with understanding a basic meaning of decimals was much more effective in calculation improvement than the algorithm study with repeated calculations. Second, the mathematical problem solving ability - including the whole procedure for solving the mathematical question - had no effects since the decimal point estimation strategy is normally performed after finishing problem solving strategy. Third, the estimation strategy showed positive effects on the calculation ability. Th Memorizing algorithm doesn't last long to the students, but the estimation strategy based on the concept and the position of decimal fraction affects continually to the students. Finally, the estimation strategy assisted the students in understanding the connection of the position of decimal points in the product with that in the multiplicand or the multiplier. Moreover, this strategy suggested to the students that there was relation between the placing decimal point of the quotient and that of the dividend.