• Education of Primary School Mathematics
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• v.27 no.1
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• pp.91-110
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• 2024

The purpose of this study is to explore visual models for deriving the fractional division algorithm, to see how students understand this integrated model, the rectangular partition model, when taught in elementary school classrooms, and how they structure relationships between fractional division situations. The conclusions obtained through this study are as follows. First, in order to remind the reason for multiplying the reciprocal of the divisor or the meaning of the reciprocal, it is necessary to explain the calculation process by interpreting the fraction division formula as the context of a measurement division or the context of the determination of a unit rate. Second, the rectangular partition model can complement the detour or inappropriate parts that appear in the existing model when interpreting the fraction division formula as the context of a measurement division, and can be said to be an appropriate model for deriving the standard algorithm from the problem of the context of the inverse of a Cartesian product. Third, in the context the inverse of a Cartesian product, the rectangular partition model can naturally reveal the calculation process in the context of a measurement division and the context of the determination of a unit rate, and can show why one division formula can have two interpretations, so it can be used as an integrated model.

• Composites Research
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• v.31 no.5
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• pp.276-281
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• 2018

In this paper, elastic behavior of woven fabric composites with various fiber yarn structure were predicted through a theoretical calculation model. A representative volume elements (RVE) that can represent the mechanical properties of the woven composites were selected and crimp angle of the weave yarn was defined by several sinusoidal functions. The effective material properties of the woven composite such as young's modulus, shear modulus and poisson's ratio was predicted by classical laminate theory (CLT). The fiber volume fractions were calculated according to the shape and pattern (plain, twill weave) of the fiber yarn, and the elastic behavior of each woven composite was obtained through a theoretical calculation model. Also, to verify the theoretical predictions, woven composite specimens of plain and twill weave were fabricated by vacuum assisted resin transfer molding (VARTM) process and then mechanical test was conducted. As a results, a good correlation between theoretical and experimental results for the elastic behavior of woven composites could be achieved.

• Nuclear Engineering and Technology
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• v.31 no.5
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• pp.465-475
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• 1999

The objective of the present work is to assess the analysis capability of two wall film condensation models, the default and the alternative models, of RELAP5/MOD3.2 on condensation experiments in the presence of noncondensable gas in a vertical tube of PCCS of CP-1300. In the calculation of a base case the default model of RELAP5/MOD3.2 under-predicts the heat transfer coefficients, and Its alternative model over-predicts them throughout the condensing tube, Also, both models over-predict the void fractions. The nodalization study shows that the variation of the node number does not change both modeling results of RELAP5/MOD3.2 Sensitivity study for varying input parameters shows that the inlet steam-air mixture flow rate, the inlet air mass fraction, and the inlet saturated steam temperature give significant changes of their heat transfer coefficients Run statistics show that the grind time of the default model is always higher than that of the alternative model by about 23%.

• Journal of Korea Foundry Society
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• v.37 no.6
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• pp.199-206
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• 2017

In this study, the variations of microstructures and tensile properties of Ti-(44-54)at.%Al binary alloys were investigated. The heat-treated microstructure depended greatly on their solidification structure and annealing temperature. We measured the variations of volume fractions of primary and secondary lamellar structure as a function of the heat treatment temperature in a Ti-47at.%Al alloy. The variation of ductility as a function of Al content was in good agreement with the change of fracture mode in the tensile fracture surface. It can be inferred that the variations of yield stress and hardness of ${\gamma}$ phase in a single ${\gamma}$-phase field region are enhanced by anti-site defects created by deviations from the stoichiometric composition. In a Ti-47at.%Al alloy within the (${\alpha}_2+{\gamma}$) two-phase field, the yield stress tended to be the maximum at a near equal volume fraction of lamellar and ${\gamma}$ grains. The ductility depended sensitively on the overall grain size and Al content. The calculation of fracture strain using Chan's model indicated that the change of ductility as a function of annealing temperature was primarily determined by the variations in the overall grain size and lamellar volume fraction.

• Journal of the Korean Society of Safety
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• v.26 no.5
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• pp.1-6
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• 2011

Flame extinction and the chemistry of stoichiometric methane/air mixture were investigated numerically in the PSR(perfectly stirred reactor). For the study, PSR code was modified to be possible to unsteady calculation, and the sinusoidal fluctuation was subjected to the residence time. In the region of residence time far from the extinction limit, combustion mode was strongly dependent on the frequency. The low frequency excitation provided the quasi-steady behavior on the temperature and the concentrations of related species, but small variation of temperature was observed under high frequency. In the region of residence time near the extinction limit, the mixture subjected above 1 KHz was still reacting even though extinction had to be occurred under quasi-steady concept. The attenuation of extinction limit resulted from that chemical time was comparable to the flow time. The mean mole fractions of both NO and CO were almost same regardless of imposed frequency. However, the average mole fraction of $C_2H_2$ was decreased as increasing frequency, which implies that soot yield might be reduced at the higher frequency of flow excitation. The result provides the basic concept for flame stabilization, and it will be used to design a mild combustor.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.2073-2082
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• 1991

The vaporization and combustion of liquid spray in a cylindrical shape combustor was studied numerically. Mixture of liquid drops and air was assumed to be ejected from the center-hole and assisting air from the concentric annulus with swirling. Eulerian-Lagrangian scheme was adopted for the two phase calculation, and the interactions between the phases were considered with the PSIC model. Also adopted were the infinite conductivity model for drop vaporization, the equation of Arrhenius and the eddy break-up model for reaction rate, and the k-epsilon model for turbulence calculations. Gas flow patterns, drop trajectories and contours of temperature and mass fractions of the gas species were predicted with swirl number, drop diameter, and equivalence ratio taken as parameters. Calculations show that the vaporization and the consequent combustion efficiency enhance with the increase of the swirl number and/or with the decrease of drop size, and the higher maximum temperature is attained with the higher equivalence ratio.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.40 no.5
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• pp.241-249
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• 2003

Carry lookahead(CLA) circuitry of decimal adders is proposed aiming at delay reduction. The truncation error in calculation of monetary interests may accumulate yielding a substantial amount of errors. Binary Coded Decimal(BCD) additions. for example, eliminate the truncation error in a fractional representation of decimal numbers. The proposed BCD carry lookahead scheme is aiming at the speed improvements without any truncation errors in the addition of decimal fractions. The delay estimation of the BCD CLA is demonstrated with improved performance in addition. Further reduction in delay can be achieved introducing non-weighted number system such as the excess-3 code.

• Nuclear Engineering and Technology
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• v.54 no.8
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• pp.3027-3033
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• 2022

Background: In this study, various types of deep-learning models for predicting in vitro radiosensitivity from gene-expression profiling were compared. Methods: The clonogenic surviving fractions at 2 Gy from previous publications and microarray gene-expression data from the National Cancer Institute-60 cell lines were used to measure the radiosensitivity. Seven different prediction models including three distinct multi-layered perceptrons (MLP), four different convolutional neural networks (CNN) were compared. Folded cross-validation was applied to train and evaluate model performance. The criteria for correct prediction were absolute error < 0.02 or relative error < 10%. The models were compared in terms of prediction accuracy, training time per epoch, training fluctuations, and required calculation resources. Results: The strength of MLP-based models was their fast initial convergence and short training time per epoch. They represented significantly different prediction accuracy depending on the model configuration. The CNN-based models showed relatively high prediction accuracy, low training fluctuations, and a relatively small increase in the memory requirement as the model deepens. Conclusion: Our findings suggest that a CNN-based model with moderate depth would be appropriate when the prediction accuracy is important, and a shallow MLP-based model can be recommended when either the training resources or time are limited.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.105-122
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• 2014

In this paper, fraction division algorithms in Korean elementary mathematics textbooks are analyzed as a part of the groundwork to improve teaching methods for fraction division algorithms. There are seemingly six fraction division algorithms in ${\ll}Math\;5-2{\gg}$, ${\ll}Math\;6-1{\gg}$ textbooks according to the 2006 curriculum. Four of them are standard algorithms which show the multiplication by the reciprocal of the divisors modally. Two non-standard algorithms are independent algorithms, and they have weakness in that the integration to the algorithms 8 is not easy. There is a need to reconsider the introduction of the algorithm 4 in that it is difficult to think algorithm 4 is more efficient than algorithm 3. Because (natural number)${\div}$(natural number)=(natural number)${\times}$(the reciprocal of a natural number) is dealt with in algorithm 2, it can be considered to change algorithm 7 to algorithm 2 alike. In textbooks, by converting fraction division expressions into fraction multiplication expressions through indirect methods, the principles of calculation which guarantee the algorithms are explained. Method of using the transitivity, method of using the models such as number bars or rectangles, method of using the equivalence are those. Direct conversion from fraction division expression to fraction multiplication expression by handling the expression is possible, too, but this is beyond the scope of the curriculum. In textbook, when dealing with (natural number)${\div}$(proper fraction) and converting natural numbers to improper fractions, converting natural numbers to proper fractions is used, but it has been never treated officially.

• Journal of Soil and Groundwater Environment
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• v.17 no.3
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• pp.21-31
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• 2012

This paper presents the short-term and long-term measures to determine the fugitive dust concentration in a contaminated site, which is a crucial step for the determination of particulate emission factor (PEF) for risk assessment. As a long-term measure, USEPA method employing Q/C value (inverse of the ratio of the geometric mean air concentration to the emission flux at center of a 0.5-acre square source) seems to be suitable as it reflects regional-specific meteorological conditions. However, it requires nation-wide database collection and interpretation. Use of ASTM method is an alternative as a short-term measure. The method is readily field-applicable as PEF calculation equation is simple and input parameters can be easily derived at the site of interest as well without the nation-wide efforts. Using ASTM method, PEF at the Former Janghang Smelter Site was determined. According to various mode of aggregate size distribution and fractions of vegetative cover, which are the most important factors in PEF calculation, PEF values at the Former Janghang Smelter Site varied greatly. When the mode of aggregate size distribution was set at 0.25 mm, PEF values at the Former Janghang Smelter Site was 5~20 times higher than the default PEF value (i.e., 35 ${\mu}g/m^3$) shown in the current Korean Soil Contamination Risk Assessment Guidance. On contrast, when the mode was set at 2 mm, PEF values at the Former Janghang Smelter Site was 160~640 times lower than the default PEF value in the Korean Guidance.