• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

• 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.

• Communications of Mathematical Education
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• v.30 no.2
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• pp.121-138
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• 2016

Most of elementary and secondary school mathematical terms in Korean are Sino-Korean words. We check Chinese characters relating to such Sino-Korean words by using Chinese dictionaries, and critically judge how much we can understand Sino-Korean words by Chinese characters. Through this search, we classify Sino-Korean words into three categories; words which can be understood by Chinese characters, words which can not be understood by Chinese characters, words which are misunderstood by Chinese characters.

• Research in Mathematical Education
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• v.26 no.4
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• pp.271-289
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• 2023

This research investigates the development of elementary students' concepts of line segments, straight lines, and rays, employing metaphor analysis as a research methodology. By analyzing metaphorical expressions, the research aims to explore how elementary students form these geometric concepts line segments, straight lines, and lays and evolve their understanding of them across different grades. Surveys were conducted with elementary school students in grades three to six, focusing on metaphorical expressions and corresponding their reasons associated with line segments, straight lines, and rays. The data were analyzed through coding and categorization to identify the types in students' metaphorical expressions. The analysis of metaphorical expressions identified five types: straightness, infinity or direction, connections of another geometric concepts, shape and symbols, and terminology.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.2
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• pp.192-201
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• 2008

The design process becomes more difficult due to the increasing complexity of products. Thus, without any proper design experience, designer cannot handle his design problems systematically. Besides, the conventional optimal design method cannot be used effectively at the early design stage, since most design problems must be formulated in terms of objective and constraint functions based on the mathematical concepts of Operation Research. Thus, in this paper, new design concept based on FBS (Function-Behavior-Structure) design model is introduced to help the novice designer formulate the complex design problems systematically into a mathematical form. In this FBS model, function means the designer's new intents designer wants to create for, structure stand for a final product configuration and behaviour is a product's performance. FBS design model is thus rather totally different concept used for formulating design problem, compared with conventional optimal design method. To validate this new FBS model, 330K VLCC design case is performed, and we found, though it is one design example case, that this new design concept could be effectively used for future ship design problems since, during the formulating design problem, the only engineering terminology such as function, structure, and behaviour of design product is used based on the engineering concepts, instead of mathematical terminology such as objective and constraints.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.549-557
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• 2015

We introduce strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces which are stronger than ${\kappa}$-$Fr{\acute{e}}chet$ and ${\kappa}$-net spaces respectively. For convenience, we use the terminology "${\kappa}$-sequential" instead of "${\kappa}$-net space", introduced by R.E. Hodel in [5]. And we study some properties and topological operations on such spaces. We also define strictly ${\kappa}$-$Fr{\acute{e}}chet$ and strictly ${\kappa}$-sequential spaces which are more stronger than strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces respectively.

• School Mathematics
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• v.1 no.1
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• pp.187-216
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• 1999

The purpose of this study is to develop mathematics performance assessment items for the 8th graders and to analyze their performance ability. First, five-themes were selected : 'Calculator', 'Cut and Paste', 'Rule finding', 'Place Assignment', 'My thinking'. Then, the assistance of Mathematics education specialists and Teachers, 10 P. A. items consisting of two subtasks and their evaluation rubric were developed. Then, items were revised by the results of pilot test. And, final version of items were administrated to the 8th graders of three regions(Seoul, Chongiu, Chungp$\acute{y}$ong). Through analyzing the performance ability of the subjects assessment items, the following conclusion were obtained: They were very insufficient in the ability to find some patterns in the given problem situation and to describe logically the patterns in terms of mathematical terminology. It is believed because they were familiar with the objective test to take one or short answer.

• The Mathematical Education
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• v.51 no.3
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• pp.211-221
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• 2012

We discovered that definition of a Geometrical Progression(Sequence) have some differences in domestic textbooks & some foreign countries' books. This will be able to cause a chaos when students divide whether a sequence is a Geometrical Progression(Sequence) or not, and a question error when teachers compose questions about convergence conditions of Infinite Geometric progressions & series. We took a question investigation for students about definition of a Geometrical Progression(that is called G. P.), we discovered that high level students have an error about definition of a G. P.. So We modified expressions of terminology in domestic textbooks appropriately through a Geometrical Progression(Sequence), infinite series, & infinite geometrical series in some foreign countries' books.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.117-124
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• 1993

In this paper, we introduce a concept of quasi $O_{z}$ -spaces which generalizes that of $O_{z}$ -spaces. Indeed, a completely regular space X is a quasi $O_{z}$ -space if for any regular closed set A in X, there is a zero-set Z in X with A = c $l_{x}$ (in $t_{x}$ (Z)). We then show that X is a quasi $O_{z}$ -space iff every open subset of X is $Z^{#}$-embedded and that X is a quasi $O_{z}$ -spaces are left fitting with respect to covering maps. Observing that a quasi $O_{z}$ -space is an extremally disconnected iff it is a cloz-space, the minimal extremally disconnected cover, basically disconnected cover, quasi F-cover, and cloz-cover of a quasi $O_{z}$ -space X are all equivalent. Finally it is shown that a compactification Y of a quasi $O_{z}$ -space X is again a quasi $O_{z}$ -space iff X is $Z^{#}$-embedded in Y. For the terminology, we refer to [6].[6].

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.713-742
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• 2024

From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a σ-algebra is proposed. Some basic properties of this terminology and further properties of conditionally strictly stationary sequences are derived. By means of these properties, several conditional central limit theorems for a sequence of conditionally strong mixing and conditionally strictly stationary random variables are established, some of which are the conditional versions corresponding to earlier results under non-conditional case.