• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 2014

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

• Journal of Navigation and Port Research
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• v.43 no.5
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• pp.320-327
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• 2019

This study examined the port expansion plan for the fishery port at the east coast of Korea, in accordance with permission conditions for coastal ports such as a limit on the cargo volume and passenger demand for the coastal tourism belt formation. The site was chosen as a municipal coastal port attracting the new ocean industry and building waterfront zone as a hub of new marine tourism. Two different numerical models (Swan and Bouss 2D) were used. Before applying to the target sea area, some numerical tests were conducted for the variation according to Bouss-2D's strong/weak and nonlinear technique compared to the irregular diffraction of semi-infinite breakwater with a theoretical solution. As a result, there was a difference in strong nonlinearity with breaking waves and it was necessary to experiment with a strong nonlinear analysis technique for the actual site. Two numerical models were applied to the fishery port site and the tranquility of some alternatives were analyzed. The numerical results show the most suitable plan was ALT-1, with satisfied harbor tranquility and reasonable economic sense. The extension of the east breakwater and enlarged turning basin of the F-Land plan have brought generally more stable harbor tranquility than the ALT-1. The result can be used as a reference for the port expansion plan in the future.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.63-63
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• 2021

Bed shear stress is important variable in river flow analysis. The bed shear stress has an effects on bed erosion, sediment transport, and mean flow characteristics. Quadratic formula to estimate bed shear stress is widely used, 𝜏=𝜌c_fu|u| in which friction coefficient, c_f, needs to be assigned to numerical models. The aim of this study is to estimate Chezy coefficient using bathymetry data measured by ADCP. Bed form geometry variables will be estimated form bed profile, then Chezy coefficient will be determined using estimated bed form geometry variables in order to set friction coefficient to numerical model. From the probability density function obtained from the bathymetry data, Chezy coefficient will be randomly generated since Chezy coefficient is not uniform over the space and it does not depend on spatial variables such as water depth and distance from river bank. Numerical test will be performed to find to demonstrate randomly extracted Chezy coefficient is appropriate. The result of this study is valuable in that the friction coefficient is estimated in consideration of the bed profile, and as a result, uncertainty of the friction coefficient can be reduced.

• Management & Information Systems Review
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• v.30 no.4
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• pp.475-509
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• 2011

Taking 195 Korean businesses and sorting them out according to the unit types, this study looks into how flexibility strategy in labor market, which consists of numerical flexibility and functional flexibility, takes effect on the organization's outcome variable, which in turn consists of productivity, labor-management cooperation, and job security. In addition, the present study analyzes the role of labor union's moderating effect on the relationship among labor market flexibility, labor-management cooperation, and job security. It is found out as a result that numerical flexibility has no meaningful relation with productivity, labor-management cooperation, and job security, while functional flexibility has a considerably positive relation with them. This result confirms the importance of functional flexibility of business strategy in labor market. The West has continuously insisted the importance of functional flexibility, pointing out problems of numerical flexibility. On the other hand, considering that this study has confirmed functional flexibility's meaningful relation, while it has not found out numerical flexibility's negative relation, it is necessary to study further on the relationship between these two kinds of flexibility. The result of analysis on the role of union power's moderating effect confirms only the union power's interaction effect in the relation between numerical flexibility and labor-management cooperation. The possibility of union's opportunistic behavior can be detected in this result.

• Journal of computational fluids engineering
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• v.10 no.1
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• pp.39-44
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• 2005

The numerical investigation of the interaction between the underexpanded supersonic jet and the perpendicular plate is carried out using the TVD numerical method. The wave structure in the flowfield and the pressure and temperature distributions on the plate surface are obtained by the numerical analysis. Especially, the influence of self-induced flow oscillation caused by the impinging jet and the characteristic of impinging jet are shown. From the result of the numerical analysis, it is concluded that the pressure and the temperature fluctuations on the plate surface strongly depends on the pressure ratio in the flowfield and the position of plate.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.3
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• pp.32-41
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• 1995

In the analysis of metal forming processes by the finite element method, there are many numerical instabilities such as element locking, hourglass mode and shear locking. These instabilities may have a bad effect upon accuracy and convergence. The present work is concerned with improvement of stability and efficiency in two-dimensional rigid-plastic finite element method using various type of elemenmts and numerical intergration schemes. As metal forming examples, upsetting and backward extrusion are taken for comparison among the methods: various element types and numerical integration schemes. Comparison is made in terms of stability and efficiency in element behavior and computational efficiency and a new scheme of adaptive directional reduced integration is introduced. As a result, the finite element computation has been stabilized from the viewpoint of computational time, convergency, and numerical instability.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.492-497
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• 1998

Thermoacoustic oscillation is a significant problem in cylindrical-type combustors such as common internal combustion engines, industrial furnaces, gas turbine, etc. This kind of low frequency oscillation can give rise to serious troubles such as the destruction of system or producing of a strong noise. Accurate numerical simulation of thermoacoustic phenomena is a complex and challenging problem. Especially, considering the reaction of mixture intensifies the difficulty of analysis. Like as other simulations of the aerodynamics and aeroacoustics, direct computation of thermoacoustic phenomena requires that the Navier-Stokes equations be solved using accurate numerical differentiation and time-marching schemes, with non-reflecting boundary conditions. In this study,, numerical approach aims at qualitative analysis and efficient prediction of problem, not at the development of an accurate scheme. Overally speaking, numerical prediction is reasonably matched with experimental result.

• Progress in Superconductivity and Cryogenics
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• v.7 no.4
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• pp.14-19
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• 2005

A transient numerical simulation was conducted to have variation of temperature on an element of resistive Superconducting Fault Current Limiter (SFCL) under quench condition. It is very important engineering information for an optimum design of cryogenic system for cooling of a resistive SFCL element. A bifilar coil for resistive SFCL for 10 MVA system was incorporated as a model in this numerical study. From the numerical simulation result, it was found that the averaged temperature on the shunt and Bi-2212 element at 500 kW, 100 ms was 711.1 K and 198.4 K respectively. The temperature variation with the change of the hot-spot size and time is also obtained. The maximum temperature was continuously increased in all cases until the hot-spot stops at 100ms and it was going down after then. Such as, the details of temperature distribution on the SFCL element obtained from this numerical study and it should be very valuable information on the decision of the cooling capacity of cryogenic system.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.865-875
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• 1988

A two-dimensional stepped wall jet was numerically investigated by applying three different models : One is the standard k-.epsilon. and the other is the modified k-.epsilon. model which takes account of the streamline curvature effect by modifying the Reynolds shear stress and a source term in the dissipation equation, and a third is curvature dependent third-order correlation model. In order to test the influences of the numerical result, both the upwind scheme and the skew-upwind scheme were sued for the computations. By comparing the numerical results with available experiments, it was found that the modified k-.epsilon. model gives best overall prediction accuracy only when the numerical diffusion is eliminated by using the skew-upwind scheme. The numerical scheme was found to have more pronounced effect on the accuracy of the turbulence computation than the turbulence models.

• Journal of Environmental Science International
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• v.11 no.12
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• pp.1321-1326
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• 2002

A numerical model is investigated to predict a behavior of the gaseous volatile organic compounds and a subsurface contamination caused by them in the unsaturated zone. Two dimensional advective-dispersion equation caused by a density difference and two dimensional diffusion equation are computed by a finite difference method in the numerical model. A laboratory experiment is also carried out to compare the results of the numerical model. The dimensions of the experimental plume are 1.2m in length, 0.5m in height, and 0.05m in thickness. In comparing the result of 2 methods used in the numerical model with the one of the experiment respectively, the one of the advective-dispersion equation shows better than the one the diffusion equation.