• School Mathematics
• /
• v.7 no.2
• /
• pp.139-168
• /
• 2005

The purpose of this study is to investigate children's informal knowledge of the fractional multiplication and to develop a teaching material connecting the informal and the formal knowledge. Six lessons of the pre-teaching material are developed based on literature reviews and administered to the 7 students of the 4th grade in an elementary school. It is shown in these teaching experiments that children's informal knowledge of the fractional multiplication are the direct modeling of using diagram, mathematical thought by informal language, and the representation with operational expression. Further, teaching and learning methods of formalizing children's informal knowledge are obtained as follows. First, the informal knowledge of the repeated sum of the same numbers might be used in (fractional number)$\times$((natural number) and the repeated sum could be expressed simply as in the multiplication of the natural numbers. Second, the semantic meaning of multiplication operator should be understood in (natural number)$\times$((fractional number). Third, the repartitioned units by multiplier have to be recognized as a new units in (unit fractional number)$\times$((unit fractional number). Fourth, the partitioned units should be reconceptualized and the case of disjoint between the denominator in multiplier and the numerator in multiplicand have to be formalized first in (proper fractional number)$\times$(proper fractional number). The above teaching and learning methods are melted in the teaching meterial which is made with corrections and revisions of the pre-teaching meterial.

• Journal of the Korea Concrete Institute
• /
• v.27 no.6
• /
• pp.687-693
• /
• 2015

The present study proposed a k-value to determine the water-to-binder ratio of concrete using fly ash (FA) or ground granulated blast-furnace slag (GGBS) as a partial replacement of ordinary portland cement (OPC) with regard to an equivalent strength of OPC concrete. From the regression analysis using an extensive database including 7076 concrete mixes, k-values were determined for various water-to-binder ratios when the replacement ratio of OPC by the addition of FA or GGBS were below 50%. For deriving an equation to identify k-value, the relationship of concrete compressive strength and water-to-binder ratio was generalized by an exponential function. In general, k-values decreased with the increases in the addition of FA or GGBS for replacement of OPC and water-to-binder ratio. The rate in decreasing k-value against water-to-binder ratio was marginally affected by the addition of FA or GGBS, although a higher k-value was commonly obtained for GGBS concrete than for FA concrete at the same water-to-binder ratio. Consequently, the determined k-values were simplified as a function of water-to-binder ratio and the addition ratio of FA or GGBS as replacement of OPC.

• Journal of Biomedical Engineering Research
• /
• v.37 no.2
• /
• pp.90-103
• /
• 2016

This research was aimed to analyze load sharing ratios between cortical shell and trabecular bone of a degraded lumbar vertebra with aging, and also evaluate elastic moduli assigned into an FE model, using finite element method. For the better analysis of trabecular bone, effective elastic moduli, that is, nominal elastic moduli divided by the volumetric porosities was used. The elastic moduli of the cortical shell suitable for the trabecular bone were obtained from the equations on the basis of idealized stress-strain relations, including areal porosities. To minimize numerical errors, p-element was used. Using eight parameters that refer to some published papers, the geometry of L3 with a removed posterior part. After the constant compressive displacement was applied, the load sharing ratios were obtained by using both every elastic strain energy and every vertical force between two bones in each 8-volume. As results, 1) according to an increase in age from 20-year to 80-year, load sharing ratios of trabecular bone decreased from 55% to 49%; 2) the maximal ratios of each bone were occurred in the mid-plane of centrums and the endplate of cortical shells, respectively; 3) effective elastic moduli assigned into a porous centrum/cortex were found to be adequate; 4) for load sharing ratios, the difference of two methods showed that the total ratios were almost same within less than 1% but the partial ratios at every depth were more or less different each other.

• Journal of the Korean Society of Propulsion Engineers
• /
• v.21 no.6
• /
• pp.64-72
• /
• 2017

The longitudinal dynamic instability which can occur in the fueling process of a space launch vehicle is called pogo. It is caused by coupling between the fuselage and propulsion system and they would be formed as a closed-loop system. so that the amplitude of the response may increase or decrease. In this paper, a mathematical model which is applicable to the systematic pogo analysis of a general launch vehicle is developed for an example of space shuttle. The formulations are composed of the linearized second-order differential equation for the propulsion system, and of the pressure, weight displacement, and generalized displacement. Those are important parameters for pogo analysis, are derived through eigenvalue analysis. By the formulation suggested in this paper, it is expected that mathematical modeling method of the pogo system can be obtained and systematic pogo stability analysis for any launch vehicle will be enabled.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.31 no.6
• /
• pp.293-299
• /
• 2018

Steel truss outriggers can be replaced by reinforced concrete walls to control the lateral drift of tall buildings. When reinforced concrete outrigger walls are connected to perimeter columns, not only axial forces but also shear forces and moments can be induced on the perimeter columns. In this study, the shear force of the perimeter column due to the rotation of the outer edge of the outrigger wall is derived as analytic equations and the result is compared with the finite element analysis result. In the finite element analysis, the effects of connecting beams at each floor and the effect of modeling shear walls and outriggers with beam element and plane stress element was analyzed. The effect of the connecting beam was almost negligible and the plane stress element was determined to have greater stiffness than the beam element. The inter-story rotation and the shear force of the perimeter column due to the rotation of the outer edge of the outrigger wall was considerably smaller than the allowable value. Therefore, even if the outrigger wall made of reinforced concrete is applied to a tall building, it is considered that there is no need to study the shear force and moment induced in the perimeter columns.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.37 no.4
• /
• pp.267-277
• /
• 2019

Photogrammetry and computer vision are identical in determining the three-dimensional coordinates of images taken with a camera, but the two fields are not directly compatible with each other due to differences in camera lens distortion modeling methods and camera coordinate systems. In general, data processing of drone images is performed by bundle block adjustments using computer vision-based software, and then the plotting of the image is performed by photogrammetry-based software for mapping. In this case, we are faced with the problem of converting the model of camera lens distortions into the formula used in photogrammetry. Therefore, this study described the differences between the coordinate systems and lens distortion models used in photogrammetry and computer vision, and proposed a methodology for converting them. In order to verify the conversion formula of the camera lens distortion models, first, lens distortions were added to the virtual coordinates without lens distortions by using the computer vision-based lens distortion models. Then, the distortion coefficients were determined using photogrammetry-based lens distortion models, and the lens distortions were removed from the photo coordinates and compared with the virtual coordinates without the original distortions. The results showed that the root mean square distance was good within 0.5 pixels. In addition, epipolar images were generated to determine the accuracy by applying lens distortion coefficients for photogrammetry. The calculated root mean square error of y-parallax was found to be within 0.3 pixels.

• Applied Chemistry for Engineering
• /
• v.35 no.1
• /
• pp.16-22
• /
• 2024

Polymer electrolyte membrane fuel cells have the advantage of low operating temperatures and fast startup and response characteristics compared to others. Simulation studies are actively researched because their cost and time benefits. In this study, the resistance of water residual in the gas diffusion layer (GDL) of the unit cell was added to the existing equation to compare the actual data with the model data. The experiments were conducted with a 25 cm² unit cell, and the samples were separated into stopping times of 0, 10, and 60 minutes following primary impedance measurement, activation, and polarization curve data acquisition. This gives 0, 10, and 60 minutes for the residual water in the GDL to evaporate. Without the rest period, the magnitude of the performance improvement was not significantly different at the same potential and flow rate, but the rest period did improve the performance of the membrane electrode assembly when measuring impedance. By changing the magnitude of the resistance reduction to an overvoltage, the voltage difference between the fuel cell model with and without residual water was compared, and the error rate in the high current density region, which is dominated by concentration losses, was reduced.