• Geomechanics and Engineering
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• v.31 no.3
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• pp.249-263
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• 2022

The specially-shaped Polycrystalline Diamond Compact (PDC) cutter is widely used in drill bit design due to its advantages of high rock cutting efficiency, strong impact resistance and long service life in hard and abrasive formation drilling. A detailed understanding of rock cutting behavior of worn specially-shaped PDC cutter is essential to improve the drilling efficiency and decrease the drilling costs. In this paper, the theoretical models of two new principles (loading performance (LP) and cutting performance (CP)) are derived for evaluating the cutting process of worn specially-shaped cutter, the theoretical models consider the factors, such as cutter geometry, aggressiveness, stress state, working life, and rock cutting efficiency. Besides, the numerical model of heterogeneous granite is developed using finite element method combined with Voronoi tessellation, the LP and CP of 12 kinds of worn specially-shaped PDC (SPDC) cutters are analyzed. The results found that the mechanical specific energy (MSE) of worn cutters first increase and then decrease with increasing the cutting depth, and the MSE increase with the increase of back rake angle except for Conical cutter and Wedge-shaped cutter. From the perspective of CP, the worn PDC cutters are more suitable for the smaller cutting depths, and the back rake angle has little effect on the CP of the specially-shaped worn PDC cutters. Conical cutter, Saddle-shaped cutter and Ellipse-shaped cutter have the highest CP value, while Rhombus-shaped cutter, Convex cutter and Wedge-shaped cutter have the lowest value in selecting cutters. This research leads to an enhanced understanding of rock-breaking mechanisms of worn SPDC cutters, and provides the basis to select of specially-shaped PDC cutters for the specific target formation.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.247-282
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• 2011

In the elementary school mathematics textbooks of the 7th national curriculum, just simple construction education is provided by having students draw a circle and triangle with compasses and drawing vertical and parallel lines with a set square. The purpose of this study was to examine the mathematical thinking of sixth-grade elementary school students in the construction process in a bid to give some suggestions on elementary construction guidance. As a result of teaching the sixth graders in gifted and nongifted classes about the equal division of line segments and evaluating their mathematical thinking, the following conclusion was reached, and there are some suggestions about that education: First, the sixth graders in the gifted classes were excellent enough to do mathematical thinking such as analogical thinking, deductive thinking, developmental thinking, generalizing thinking and symbolizing thinking when they learned to divide line segments equally and were given proper advice from their teacher. Second, the students who solved the problems without any advice or hint from the teacher didn't necessarily do lots of mathematical thinking. Third, tough construction such as the equal division of line segments was elusive for the students in the nongifted class, but it's possible for them to learn how to draw a perpendicular at midpoint, quadrangle or rhombus and extend a line by using compasses, which are more enriched construction that what's required by the current curriculum. Fourth, the students in the gifted and nongifted classes schematized the problems and symbolized the components and problem-solving process of the problems when they received process of the proble. Since they the urally got to use signs to explain their construction process, construction education could provide a good opportunity for sixth-grade students to make use of signs.

• Korean Journal of Ichthyology
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• v.18 no.4
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• pp.339-346
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• 2006

In this study we conducted artificial hybridization between two sibling species, Rhodeus uyekii and R. notatus, and observed the morphological characteristics in early developmental stage. The two species showed difference in egg shape having rhombus and club respectively. The morphology of yolk of larva just hatched also showed well specific characteristics, that is the bean chaff type for R. uyekii (U type) and anchor type for R. notatus (N type). The rate of fertilization between female R. uyekii and male R. notatus (UN type) and between female R. notatus and male R. uyekii (NU type) were complete and its hatching rate were very high, 71.6% for UN type and 97.5% for NU type. The differences occurred in the yolk shape of hatched larvae for each combination of hybrids. In the group of UN, U type of larvae were found very rarely, but almost all the larvae showed intermediate shape polarized to NN type. Similar phenomenon was observed in the NU having intermediate polarized to UU, but without any NN type. These hybrids will be analyzed for their external morphology, sex ratio, the function of sexual organ and karyology after they grown up to adult.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.565-586
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• 1998

Like many other school subjects, terminology is a starting point of mathematical thinking, and plays a key role in mathematics learning. Among several areas in mathematics, geometry is the area in which students usually have the difficulty of learning, and the new terms are frequently appeared. This is why we started to investigate geometric terms first. The purpose of this study is to investigate geometric terminology in school mathematics. To do this, we traced the historical transition of geometric terminology from the first revised mathematics curriculum to the 7th revised one, and compared the geometric terminology of korean, english, Japanese, and North Korean. Based on this investigation, we could find and structuralize the following four issues. The first issue is that there are two different perspectives regarding the definitions of geometric terminology: inclusion perspective and partition perspective. For example, a trapezoid is usually defined in terms of inclusion perspective in asian countries while the definition of trapezoid in western countries are mostly based on partition perspective. This is also the case of the relation of congruent figures and similar figures. The second issue is that sometimes there are discrepancies between the definitions of geometric figures and what the name of geometric figures itself implies. For instance, a isosceles trapezoid itself means the trapezoid with congruent legs, however the definition of isosceles trapezoid is the trapezoid with two congruent angles. Thus the definition of the geometric figure and what the term of the geometric figure itself implies are not consistent. We also found this kind of discrepancy in triangle. The third issue is that geometric terms which borrow the name of things are not desirable. For example, Ma-Rum-Mo(rhombus) in Korean borrows the name from plants, and Sa-Da-Ri-Gol(trapezoid) in Korean implies the figure which resembles ladder. These terms have the chance of causing students' misconception. The fourth issue is that whether we should Koreanize geometric terminology or use Chinese expression. In fact, many geometric terms are made of Chinese characters. It's very hard for students to perceive the ideas existing in terms which are made of chines characters. In this sense, it is necessary to Koreanize geometric terms. However, Koreanized terms always work. Therefore, we should find the optimal point between Chines expression and Korean expression. In conclusion, when we name geometric figures, we should consider the ideas behind geometric figures. The names of geometric figures which can reveal the key ideas related to those geometric figures are the most desirable terms.

• Korean Journal of Materials Research
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• v.21 no.11
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• pp.587-591
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• 2011

The effect of the precipitator (NaOH, $NH_4OH$) and the amount of the precipitator (150, 200, 250, 300 ml) on the formation of $Fe_3(PO_4)_2$, which is the precursor used for cathode material $LiFePO_4$ in Li-ion rechargeable batteries was investigated by the co-precipitation method. A pure precursor of olivine $LiFePO_4$ was successfully prepared with coprecipitation from an aqueous solution containing trivalent iron ions. The acid solution was prepared by mixing 150 ml $FeSO_4$(1M) and 100 ml $H_3PO_4$(1M). The concentration of the NaOH and $NH_4OH$ solution was 1 M. The reaction temperature (25$^{\circ}C$) and reaction time (30 min) were fixed. Nitrogen gas (500 ml/min) was flowed during the reaction to prevent oxidation of $Fe^{2+}$. Single phase $Fe_3(PO_4)_2$ was formed when 150, 200, 250 and 300 ml NaOH solutions were added and 150, 200 ml $NH_4OH$ solutions were added. However, $Fe_3(PO_4)_2$ and $NH_4FePO_4$ were formed when 250 and 300 ml $NH_4OH$ was added. The morphology of the $Fe_3(PO_4)_2$ changed according to the pH. Plate-like lenticular shaped $Fe_3(PO_4)_2$ formed in the acidic solution below pH 5 and plate-like rhombus shaped $Fe_3(PO_4)_2$ formed around pH 9. For the $NH_4OH$, the pH value after 30 min reaction was higher with the same amount of additions of NaOH and $NH_4OH$. It is believed that the formation mechanism of $Fe_3(PO_4)_2$ is quite different between NaOH and $NH_4OH$. Further investigation on this mechanism is needed. The prepared samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and the pH value was measured by pH-Meter.