• Journal for History of Mathematics
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• v.28 no.5
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• pp.207-231
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• 2015

We discuss several issues relating to the meaning of the terms and phrases in the first half of Chapter One fang tian 方田章 of ${\ll}$Jiuzhang suanshu九章算術${\gg}$. I understood those issues more clearly in the course of the translation of ${\ll}$Kujang sulhae 九章術解${\gg}$. Those are '今有' in the beginning of each problem, '積' and '冪' in the method of square field 方田術, '齊' in the method of reduction to a common denominator 齊同術, '經' and '有分者通之重有分者同而通之' in the method of dividing fraction 經分術, '實如法而一' in the calculation using the rods, '兩邪' in the method of trapezium field with a perpendicular side 邪田術. We may find out the value of ${\ll}$Kujang sulhae 九章術解${\gg}$ through our discussion.

• The Mathematical Education
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• v.52 no.2
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• pp.217-230
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• 2013

This study attempts to propose the construction of textbook contents of fraction division and to suggest a method to strengthen the connection among problem context, manipulation activities and symbols by proposing an algorithm of dividing fractions based on problem contexts. As showing the suitable algorithm to problem context, it is able to understand meaningfully that the algorithm of fractions division is that of multiplication of a reciprocal. It also shows how to deal with remainder in the division of fractions. The results of this study are expected to make a meaningful contribution to textbook development for primary students.

• Journal of the Korean Society of Tobacco Science
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• v.27 no.2
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• pp.219-225
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• 2005

Characterizing nicotine delivery from tobacco products is important in the understanding of their addictive potential. Most previous studies report total nicotine and have not differentiated between nicotine in its protonated or free-base form. The amount of free nicotine calculated by determining pH and nicotine contents. The pH and nicotine contents in smokeless tobacco product, tobacco products and tobacco leaves were analyzed by Health Canada-Official Method T-310 and CORESTA Recommended Method $N^{\circ}62$. The content of free nicotine was calculated according to the Henderson-Hasselbalch equation and the value of $\alpha_{fb}$(the fraction of nicotine that is in the free base form) by using a pKa value of 8.02 for nicotine. The percentage of free nicotine then was calculated by dividing the free nicotine content by total nicotine content. The pH value and percentage of free nicotine ranged from 5.01 to 5.45 and $0.10\%\;to\;0.27\%$ in cut tobacco and 5.10 to 7.10 and $0.12\%\;to\;10.73\%$ in tobacco leaves, respectively.

• Journal of Korea Water Resources Association
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• v.47 no.5
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• pp.483-490
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• 2014

The design procedures for a biological reactor and a secondary settling tank (SST) of an activated sludge system are based on the steady state design method (Ekama et al., 1986; WRC, 1984) and the 1-D flux theory design method (Ekama et al., 1997), respectively. This study combined both of the design procedures, to determine the optimum sludge concentration in the reactor and the best design with the lowest cost. The best design of the reactor volume and the SST diameter at the optimum sludge concentration were specified with varying wastewater and sludge characteristics, temperature, sludge retention time (SRT) and peak flow rate. The effects of the influent wastewater characteristics, such as substrate concentration and unbiodegradable particulate fraction, were found to be considerable, but the effect of unbiodegradable soluble fraction was to be negligible. The effects of sludge settling characteristics, were also significant. SRT, as an operating parameter, was found to be an important factor for determining the optimum sludge concentration. However, the effect of temperature was found to be small. Furthermore, for designing a large scale wastewater treatment plant, the number of reactors or SSTs could be estimated, by dividing the total reactor volume or SST area. The new combined design procedure, proposed in this research, will be able to allow engineers to provide the best design of an activated sludge system with the lowest cost.

• Earthquakes and Structures
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• v.13 no.3
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Korean Journal of Heritage: History & Science
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• v.53 no.3
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• pp.80-109
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• 2020

The Sacheonwangsa Temple in Silla is an esoteric temple that was founded provisionally in 670, and was completed in 679. This study attempted to elucidate the planning method of the Sacheonwangsa Temple based on the results of research on excavations and investigations into its construction processes and construction measures thereof. The research results are as follows. (1) In the site construction, assuming the size of one Bang (坊) on the south of Nangsan Mountain, after dividing the north-south width into three equal parts, there is a possibility that two of these parts were set to the flat portion. (2) In the 'Jochang (祖創, 670)', it is estimated that an area of 300 cheoks by 300 cheoks was postulated on the flat surface, and, as an initial conception, the mandala's plane design of the outer square 2 hasta (3 cheoks) and inner square 1 hasta (1.5 cheoks) was originally devised for the setting of 'Mudra (神印)', and an area 100 times greater has been set as the basis in the scale and layout planning of the central block. (3) During 'Gaechang (攺刱, ~679)', it is judged that because of the narrowness of the distance between the Pagoda and Geumdang Hall, which occurs when the center of the Geumdang Hall coincides with the center of 'the first stage of the foundation (先築基壇)', the scale and layout planning were adjusted from the initial conception. (4) The arrangement of the building was determined by dividing the fixed size of the central block (280 cheoks by 320 cheoks). Specifically, the east-west direction is set on the quartile's line of the east-west width of the central block, and in contrast, the north-south direction is based on the structural characteristics of the central block. It is presumed that the position of the transept was determined through the division and adjustment of the column spacing of the east-west corridor, then the Geumdang Hall and Altar were based on this. (5) The scale of the Geumdang Hall and Pagoda is determined by the petition of the division by the unit fraction starting from the quartile's line of the central block's east-west width. This planning is understood to be based on the self-similarity, which is rooted in the mandala's plane design as the model.

• 한국신재생에너지학회:학술대회논문집
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• 2007.11a
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• pp.417-423
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• 2007

Oxy-gasification or oxygen-blown gasification, enables a clean and efficient use of coal and opens a promising way to CO2 capture. The coal gasification process of a slurry feed type, entrained-flow coal gasifier was numerically predicted in this paper. The purposes of this study are to develop an evaluation technique for design and performance optimization of coal gasifiers using a numerical simulation technique, and to confirm the validity of the model. By dividing the complicated coal gasification process into several simplified stages such as slurry evaporation, coal devolatilization, mixture fraction model and two-phase reactions coupled with turbulent flow and two-phase heat transfer, a comprehensive numerical model was constructed to simulate the coal gasification process. The influence of turbulence on the gas properties was taken into account by the PDF (Probability Density Function) model. A numerical simulation with the coal gasification model is performed on the Conoco-Philips type gasifier for IGCC plant. Gas temperature distribution and product gas composition are also presented. Numerical computations were performed to assess the effect of variation in oxygen to coal ratio and steam to coal ratio on reactive flow field. The concentration of major products, CO and H2 were calculated with varying oxygen to coal ratio (0.2-1.5) and steam to coal ratio(0.3-0.7). To verify the validity of predictions, predicted values of CO and H2 concentrations at the exit of the gasifier were compared with previous work of the same geometry and operating points. Predictions showed that the CO and H2 concentration increased gradually to its maximum value with increasing oxygen-coal and hydrogen-coal ratio and decreased. When the oxygen-coal ratio was between 0.8 and 1.2, and the steam-coal ratio was between 0.4 and 0.5, high values of CO and H2 were obtained. This study also deals with the comparison of CFD (Computational Flow Dynamics) and STATNJAN results which consider the objective gasifier as chemical equilibrium to know the effect of flow on objective gasifier compared to equilibrium. This study makes objective gasifier divided into a few ranges to study the evolution of the gasification locally. By this method, we can find that there are characteristics in the each scope divided.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.2
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• pp.85-110
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• 2005

The purpose of this study is to examine the characteristics of visual representation used in problem solving process and examine the representation types the students used to successfully solve the problem and focus on systematizing the visual representation method using the condition students suggest in the problems. To achieve the goal of this study, following questions have been raised. (1) what characteristic does the representation the elementary school students used in the process of solving a math problem possess? (2) what types of representation did students use in order to successfully solve elementary math problem? 240 4th graders attending J Elementary School located in Seoul participated in this study. Qualitative methodology was used for data analysis, and the analysis suggested representation method the students use in problem solving process and then suggested the representation that can successfully solve five different problems. The results of the study as follow. First, the students are not familiar with representing with various methods in the problem solving process. Students tend to solve the problem using equations rather than drawing a diagram when they can not find a word that gives a hint to draw a diagram. The method students used to restate the problem was mostly rewriting the problem, and they could not utilize a table that is essential in solving the problem. Thus, various errors were found. Students did not simplify the complicated problem to find the pattern to solve the problem. Second, the image and strategy created as the problem was read and the affected greatly in solving the problem. The first image created as the problem was read made students to draw different diagram and make them choose different strategies. The study showed the importance of first image by most of the students who do not pass the trial and error step and use the strategy they chose first. Third, the students who successfully solved the problems do not solely depend on the equation but put them in the form which information are decoded. They do not write difficult equation that they can not solve, but put them into a simplified equation that know to solve the problem. On fraction problems, they draw a diagram to solve the problem without calculation, Fourth, the students who. successfully solved the problem drew clear diagram that can be understood with intuition. By representing visually, unnecessary information were omitted and used simple image were drawn using symbol or lines, and to clarify the relationship between the information, numeric explanation was added. In addition, they restricted use of complicated motion line and dividing line, proper noun in the word problems were not changed into abbreviation or symbols to clearly restate the problem. Adding additional information was useful source in solving the problem.