• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.423-444
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• 2005

Despite the importance of number sense, computational skills have been emphasized in elementary mathematics curriculum. There is lack of research on number sense. Against this background, this study analyzed the way 137 sixth grade students coped with routine computation problems and with problems requiring number sense. Students performed better on the computation tasks than on the number sense tasks. With regard to the number sense tasks, many students had a tendency to implement direct computation rather than to use number sense appropriate to the given contexts. Students also had difficulties in making use of effective benchmarks or applying the knowledge of number and operation to various problem contexts. An implication is that students should explore multiple tasks requiring number sense as an integral part of their mathematics learning in order to develop number sense.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.20 no.12
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• pp.795-801
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• 2008

An experimental study has been performed on the single phase flow and convective heat transfer in trapezoidal microchannels. The microchannel was about $270{\mu}m$ wide, $800{\mu}m$ deep. and 7 mm long, which might ensure hydrodynamically fully-developed laminar flow at a low Reynolds number. The experiments were conducted with R1l3 and water, with the Reynolds number ranging from approximately 30 to 5000 for friction factor and 30 to 700 for the Nusselt number. Friction factors in laminar are found to be in good agreement with the predictions of existing correlation suggesting that a conventional analysis approach can be employed in predicting flow friction behavior in microchannels. However turbulent friction factors are hardly predictable by the existing correlations. The experimental results show that the Nusselt number is not a constant but increases almost linearly with the Reynolds number even the flow is fully developed (Re < 100). The dependence of the Nusslet number on the Reynolds number is contradictory to the conventional theory. At a Reynolds number greater than 100, the Nusselt number increases slowly with the Reynolds number, where thennally developing flow is responsible for the increase of the Nusselt number with the Reynolds number.

• Journal of Korean Society of Water and Wastewater
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• v.23 no.6
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• pp.865-870
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• 2009

In this study, the adequacy of Reynolds numbers and Froude numbers derived from about sixty domestic water treatment plants (WTPs) were analyzed in order to estimate the characteristics of hydraulic behavior within the rectangular shaped sedimentation basins used widely. From the results of analysis, most of domestic WTPs have satisfied the criteria regulated as that Reynolds number should less than 1,000(dimensionless). On the other hand, they have not been able to satisfy the Froude number criteria, which should be higher than $1.0{\times}10^{-6}$. The reasons why most of domestic WTPs could not satisfy the criteria are that its criteria basis has been not only inadequate, but also the concept of external flow occurred around a settling particle has been ignored. Accordingly, this study proved the feasibility of Archimedes number, which indicates the ratio between particle Reynolds number and Froude number, to evaluate the hydraulic efficiency and its function of scale factor.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.353-372
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• 2015

This study investigated how to utilize number line related number concept learning and analyzed problems related utilization of number line focused on natural number and rational number(fraction, decimal), in elementary school mathematics textbook. The purpose of this study is to identify desirable direction about the utilization of number line, based on analysis of the introduction of time, introduction contents and utilization method in elementary school mathematics textbook.

• International Journal of Fluid Machinery and Systems
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• v.1 no.1
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• pp.101-108
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• 2008

The effect of Reynolds number on the performance of a regenerative pump was examined in a low Reynolds number range in experiment. The head of the regenerative pump increased at low flow rates and decreased at high flow rates as the Reynolds number decreased. The computation of the internal flow was made to clarify the cause of the Reynolds number effect. At low flow rates, the head is decreased with increasing the Reynolds number due to the decrease of the shear force exerted by the impeller caused by the increase of leakage and hence local flow rate. At higher flow rates, the head is increased with increasing the Reynolds number with decreased loss at the inlet and outlet as well as the decreased shear stress on the casing wall.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.257-267
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• 2005

When notions of numbers are expanded from natural number to complex number, a similar mathematical phenomenon can be observed in each number. As a case study, to complex number, the phenomenon is investigated carefully and teaching materials are created. Then complex number is expressed with matrices and is geometrically treated, so a new number which is an extension of complex number is discovered. Thus, teaching material regarding to complex number and matrices is made for students of ordinary level. Moreover, for talented students, material about an extension of complex number can be added to the previous one.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1251-1264
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• 2005

Let D be an acyclic digraph. The competition graph of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that (u, x) and (v, x) are arcs of D. The competition number of a graph G, denoted by k(G), is the smallest number k such that G together with k isolated vertices is the competition graph of an acyclic digraph. It is known to be difficult to compute the competition number of a graph in general. Even characterizing the graphs with competition number one looks hard. In this paper, we continue the work done by Cho and Kim[3] to characterize the graphs with one hole and competition number one. We give a sufficient condition for a graph with one hole to have competition number one. This generates a huge class of graphs with one hole and competition number one. Then we completely characterize the graphs with one hole and competition number one that do not have a vertex adjacent to all the vertices of the hole. Also we show that deleting pendant vertices from a connected graph does not change the competition number of the original graph as long as the resulting graph is not trivial, and this allows us to construct infinitely many graph having the same competition number. Finally we pose an interesting open problem.

• School Mathematics
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• v.4 no.4
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• pp.643-655
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• 2002

In this paper we emphasize the introduction of ‘incommensurability’ on the teaching and learning the irrational number because we think of the origin of number as ‘ratio’. According to Greek classification of continuity as a ‘never ending’ divisibility, discrete number and continuous magnitude belong to another classes. That is, those components were dealt with respectively in category of arithmetic and that of geometry. But the comparison between magnitudes in terms of their ratios took the opportunity to relate ratios of magnitudes with numerical ratios. And at last Stevin coped with discrete and continuous quantity at the same time, using his instrumental decimal notation. We pay attention to the fact that Stevin constructed his number conception in reflecting the practice of measurement : He substituted ‘subdivision of units’ for ‘divisibility of quantities’. Number was the result of such a reflective abstraction. In other words, number was invented by regulation of measurement. Therefore, we suggest decimal representation from the point of measurement, considering the foregoing historical development of number. From the perspective that the conception of real number originated from measurement of ‘continuum’ and infinite decimals played a significant role in the ‘representation’ of measurement, decimal expression of real number should be introduced through contexts of measurement instead of being introduced as a result of algorithm.

• Journal of Life Science
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• v.7 no.1
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• pp.59-65
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• 1997

In this experiment, gene actions were analysized for seven barley parents in order to obtain basic information on their genetic improvement by diallel crosses. The results obtained were summarized as follows. In analysis of variance, additive, dominant, maternal and reciprocal effects were observed significantly for culm length, tiller number, number of spiked per plant, culm diameter, awn length, leaf width, number of grains per spike, and 1000 grain weight. Over-dominance was shown by Vr-Wr graphic analysis in five characters such as tiller number, number of spikes per plant, length of flag leaf, number of grains per spike, and 1000 grain weight, and partial dominance in four characters such as culm length, culm diameter, awn length, and leaf width. Component of genetic varience analyzed for four characters such as culm diameter, awn length, length of flag leaf, and leaf width showed that additive effects were higher than dominant effects. Culm length, tiller number, number of spikes per plant, number of grains per spike, and 1000 grain weight showed dominant effects higher than additive effects. The narrow-sense heritability for awn length, leaf width, and number of grains per spike showed high values as more than 0.62, while broad-sense heritability for culm length, number of spikes per plant, culm diameter, awn length, leaf width, number of grains per spike, and 1000 grain weight showed high values as more than 0.65.

• Korean Journal of Plant Resources
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• v.1 no.1
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• pp.1-7
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• 1988

This experiment were carried out to study the heritability, genotypic, pheno-typic and environmental correlation in four edible oil crops. Heritabilities of flowering date, maturing date, plant height and weight of 1, 000 grains in rape were high. A highly significant positive correlation was found between flowering date and maturing date, plant hight and ear length, number of pods per ear and flowering date, maturing date and plant hight, The number of seed per pod showed also significant positive correlation with flowering or maturing date as well as with the relationship between weight of 1, 000 grains and plant height or ear length inrapeseed, respectively. Heritabilities of maturing date, length of stem with eapsule and number of seed per capsule were high, in sesame. Genotypic correlation between plant height and length of stem with capsule, length of stem with capsule and number of capsule per plant, number of capsule per plant and weight of 1, 000 grains, weight of 1, 000 grains and yield were highy positive in sesame. Heritabilities of flowering date, length of main stem, weight of 100 grains and number of shells per square meter in peanut were high, There was positive genotypic correlation between length of main stem and yield, number of shells per quare meter and matured seed ratio, number of shells per square meter and yield, 100 grains weight and yield. On the other hand, a significant negative correlation appeared between flowering date and yield. Heritabilities of days to flowering, stem length, stem diameter and weight of 1, 000 grains in perila were high. There was positive genotypic correlation between stem length and stem diameter, number of pods per plant, stem weight etc, between number of internodes and number of pods per plant, stem weight, number of valid branches and number of pods plant as well, respectively. While, a significant negative correlation was observed between number of valid branches and weight of 1, 000 grains, between number of pods per plant and weight of 1, 000 grains.