• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.57-75
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• 2003

The goal of this paper is to offer material which make mathematising Fruedenthal(1991) proposed be experienced through the process of teaching and learning mathematics. In this paper, the number of unit squares a diagonal passes through for an m$\times$n lattice rectangle is studied and its generalization is discussed. Through this discussion, the adaptability of this material Is analysed. Especially, beyond inductional conjecture, the number of unit squares is studied by more complete way, and generalization in 3-dimension and 4-dimension are tried. In school mathematics, it is enough to generalize in 3-dimension. This material is basically appropriate for teaching and learning mathematising in math classroom. In studying the number of unit squares and unit cubes, some kinds of mathematising are accompanied. Enough time are allowed for students to study unit squares and unit cubes to make them experience mathematising really. To do so, it is desirable to give students that problem as a task, and make them challenge that problem for enough long time by their own ways. This material can be connected to advanced mathematics naturally in that it is possible to generalize this problem in n-dimension. So, it is appropriate for making in-service mathematics teachers realize them as a real material connecting school mathematics and advanced mathematics.

• The Journal of Engineering Geology
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• v.20 no.4
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• pp.415-424
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• 2010

A prototype of a Concrete-Faced Rock-fill Dam (CFRD) was constructed to evaluate the behavior of the materials in each zone within the dam. The tested materials, selected based on their grain size distribution, were used in constructing the prototype dam with layers of variable thickness, settlement ratio, and water content. We investigated the suitability of various values of hydraulic conductivity, water content, dry unit weight, and settlement ratio for zones within the dam. The test results revealed the relationships between the number of passes and the dry unit weight, between the dry unit weight and the settlement ratio, and between the settlement ratio and the number of passes. This paper focuses on the relationship between hydraulic conductivity and the number of passes. The results of the present analysis could be used to establish reasonable compaction standards for materials used in dam construction.

• Korean Journal of Metals and Materials
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• v.49 no.6
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• pp.474-487
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• 2011

Bars of OFHC Cu with the diameter of 45 mm were processed by equal channel angular pressing up to 16 passes via route $B_c$, and homogeneity of their microstructures and mechanical properties was examined at every four passes which develop the equiaxed ultrafine grains. In general, overall hardness, yield strength and tensile strength increased by 3, 7, and 2 times respectively compared with those of unECAPed sample. Cross-sectional hardness exhibited a concentric distribution. Hardness was the highest at the center of bar and it decreased gradually from center to surface. After 16 passes, overall hardness decreased due to recovery and partial recrystallization. Regardless of the number of passage, yield strength and tensile strength were quite uniform at all positions, but elongation showed some degree of scattering. At 4 passes, coarse and ultrafine grains coexisted at all positions. After 4 passes, uniform equiaxed ultrafine grains were obtained at the center, while uniform elongated ultrafine grains were manifested at the upper half position. At the lower half position, grains were equiaxed but its size were inhomogeneous. It was found that inhomogeneity of grain morphology and grain size distribution at different positions are to be attributed to scattering in elongation but they did not affect strength. The present results reveal the high potential of practical application of equal channel angular pressing on fabrication of large-sized ultrafine grained bars with quite homogeneous mechanical properties.

• Journal of the Korean Society for Heat Treatment
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• v.31 no.6
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• pp.269-274
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• 2018

Grain-oriented electrical steel sheets are mainly used as core materials for transformers and motors. They should have excellent magnetic properties such as low core loss, high magnetic flux density and high permeability. In order to improve the magnetic properties of the electrical steel sheet, it is important to form Goss oriented grains with a very strong {110}<001> orientation. Recently, efforts have been made to develop Goss grains by controlling processes such as hot rolling, cold rolling, and primary and secondary recrystallization. In this study, the sheets containing 3.2 and 3.4wt.% Si were used, which were rolled with 1 and 10 passes with total thickness reduction of 89%. Heating was carried out for primary recrystallization with different heating rates of $25^{\circ}C/s$ and $24^{\circ}C/min$ until $720^{\circ}C$. The behavior of Goss-, {411}<148>-, and {111}<112>-oriented grains were analyzed using X-ray diffraction(XRD) and electron back-scatter diffraction(EBSD) analysis. The area fraction of Goss-oriented grains increased with the number of rolling passes during cold rolling; however, after the primary recrystallization, the area fraction of the Goss grains was higher and exact Goss grains were found in the specimens subjected to rapid heating after one rolling pass.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.4
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• pp.402-406
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• 1991

In this paper, we find a set of conditions on weights under which a recursive weighted median filter preserves monotone or localy monotone sequence and under which any input sequence converges to a locally monotone sequence after a finite number of passes.

• Transactions of Materials Processing
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• v.28 no.6
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• pp.361-367
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• 2019

Microstructure evolution and tensile properties of Al-8mass%Mg alloy casting billet by biaxial alternative forging were investigated in this study. An alternative forging system tailored in this study was used to allow continuous strain accumulations on the alloy workpiece. A finite element (FE) simulation results revealed that the strain was mainly concentrated in the core and that the shear bands developed into a form with an X shape in the cross-section of workpiece after the alternative forging using octangular rod shaped dies. With increasing the forging passes, it was observed that the Al-8mass%Mg alloy workpieces were significantly deformed, and cracks began to form and propagate on the both ends of the forged workpieces after five passes at room temperature. In as-forged microstructures taken by microscopes, twins, clustering of dislocations, and fine subgrains were found. Tensile strengths of the forged specimens showed significant increases depending on the number of forging passes, and a trade-off relationship was observed between the elongation and strength. At room temperature and 100℃ the workpieces showed similar behaviors in microstructural evolution and tensile properties depending on forging passes, while the increase range in strength was reduced at 200℃.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.46 no.6
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• pp.78-86
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• 2014

Since cellulose nanofibrils (CNF) has large specific surface area and high water holding capacity, it is very difficult task to remove water from the CNF suspension. However, dewatering of CNF suspension is a prerequisite of following processes such as mat forming and drying for the application of CNF. In this study, we evaluated the drainage of cellulose fibers suspension under vacuum and pressure conditions depending on the number of grinding passes. Also, the effect of the addition of cationic polyelectrolyte on dewatering ability of CNF suspension was investigated. Regardless of dewatering condition, the total drained water amount as well as the drainage rate were decreased with an increase in the number of grinding passes. Pressure dewatering equipment enables us to prepare wet CNF mat with relatively higher grammage. The cationic polyelectrolytes improved the dewatering ability of CNF suspension by controlling the zeta potential of CNF. The fast drainage was obtained when CNF suspension had around neutral zeta potential.

• East Asian mathematical journal
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• v.36 no.5
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• pp.561-570
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• 2020

We compute the extended four operations of the 2-dimensional quadratic fuzzy numbers. Then we calculate the intersection between a plane perpendicular to the x-axis, which passes through each vertex, and the resulting 2-dimensional quadratic fuzzy number. We confirm that the equations of the two intersections acquired in this way and the graphs are actually identical, respectively.

• Transactions of Materials Processing
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• v.26 no.1
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• pp.35-40
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• 2017

Laser forming is an advanced process in sheet metal forming in which thermal stress originated from the laser heat source is used to shape the metal sheet. However, substantial waiting time is normally necessary for the workpiece to cool down between consecutive scans so that a steep temperature gradient can be reestablished in the next scan. In order to solve this drawback, laser bending characteristics are experimentally implemented in underwater condition. Laser forming effects under various conditions, including different laser power, scanning velocity, beam diameter, number of passes and material, are investigated. The results show that the underwater laser forming facilitates deliberate forming. The bending angle per respective laser scan is decreased with increasing the number of passes and scanning velocity.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.10a
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• pp.207-210
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• 2004

The deformation behavior of copper during equal channel angular pressing (ECAP) was calculated using a three-dimensional version of a constitutive model based on the dislocation density evolution. Finite element simulations of the variation of the dislocation density and the dislocation cell size with the number of ECAP passes are reported. The calculated stress, strain and cell size are compared with the experimental data for Cu deformed by ECAP in a modified Route C regime. The results of FEM analysis were found to be in good agreement with the experiments. After a rapid initial decrease down to about 200 nm in the first ECAP pass, the average cell size was found to change little with further passes. Similarly, the strength increased steeply after the first pass, but tended to saturate with further pressings. The FEM simulations also showed strain non-uniformities and the dependence of the resulting strength on the location within the workpiece.