• East Asian mathematical journal
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• v.32 no.2
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• pp.175-192
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• 2016

This study aimed to understand the needs of changes in the teaching-learning environment in the university and to develop the liberal art subject of mathematics. The changes of mathematical belief in the university students were investigated to understand how the liberal art subject of mathematics affected them related to mathematics. Upon the study results, the significant changes were occurred from the utility factor on the subject of mathematics in mathematical belief, the importance factor of the answers in the teaching-learning belief, teaching activity factor of the teachers, and inborn capability factor in the belief on the self-concept. The meaningful learning environment and teaching method for the liberal art subject of mathematics are suggested further by these results.

• The Mathematical Education
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• v.54 no.2
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• pp.167-194
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• 2015

The purpose of this study is to analyze effects of the mathematics integrated career education on students' affective characteristics. For this purpose, 3 hours of lesson materials of the mathematics integrated career education were developed and applied to 65 students of the 10th ~11th graders selected in two high schools. After 3 hours of lessons, the following research findings are obtained. Fisrt, it is revealed from the pre-post test of 65 subjects that the mathematics integrated career education can help students improve their mathematical attitude and belief. Second, it is shown from the interview with 4 students that they became not only to recognize the usefulness and value of mathematics, but also got changed their self-concept for mathematics.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.603-616
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• 2011

We introduce the concept of an interval-valued fuzzy generalized bi-ideal of a semigroup, which is an extension of the concept of an interval-valued fuzzy bi-ideal (and of a noninterval-valued fuzzy bi-ideal and a noninterval-valued fuzzy ideal of a semi-group), and characterize regular semigroups, and both intraregular and left quasiregular semigroup in terms of interval-valued fuzzy generalized bi-ideals.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1097-1105
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• 2015

The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of $2_{\otimes}$-auto Engel groups is introduced and we prove that if G is a $2_{\otimes}$-auto Engel group, then $G{\otimes}$ Aut(G) is abelian. Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.

• Research in Mathematical Education
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• v.12 no.1
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• pp.49-66
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• 2008

In this paper we present a cognitive developmental analysis of the arithmetic mean concept. This analysis leads us to a hierarchical classification at different levels of understanding of the responses of 227 students to a questionnaire which combines open-ended and multiple-choice questions. The SOLO theoretical framework is used for this analysis and we find five levels of students' responses. These responses confirm different types of difficulties encountered by students regarding their conceptualization of the arithmetic mean. Also we have observed that there are no significant differences between secondary school and university students' responses.

• Research in Mathematical Education
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• v.6 no.1
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• pp.97-106
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• 2002

Educators have found that the concept of randomness is often misunderstood by students. Chance recently pointed out that students should be introduced to the concept of randomness through the use of simulations. In this article, we studied various aspects of the probability distribution off linear random path in a circle and introduce some related simulations to guide student exploration and discovery. Consider a random line segment that crosses a circle with a certain radius. Perhaps it can be considered to be a path that an airplane shows up and flies into a random direction in a monitor. What is the expected amount of flying distance through the monitor, and the expected variation\ulcorner Are we monitoring what we see scientifically\ulcorner This article studies the probability distribution and some related aspects of a linear random path within a circular monitor. Some simulative activity is also introduced which can be used in a statistics or probability classes.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.10
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• pp.1451-1457
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• 2013

Recently, new concept of energy systems such as microgrid, smart grid, supergrid, and energy network has been introducing. In this paper, the concept of the centralized micro-energy network, which is an energy community of a building group without district heating system, is introduced. In addition, a mathematical model for optimal operation of the micro-energy network as a main function of an energy management system (EMS) for the micro-energy network is proposed. In order to show the validation, the proposed model is tested through the simulation and analyzed.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.247-261
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• 2010

An associative ring R with identity is called a clean ring if every element of R is the sum of a unit and an idempotent. In this paper, we introduce the concept of f-clean rings. We study various properties of f-clean rings. Let C = $\(\array{A\;V\\W\;B}\)$ be a Morita Context ring. We determine conditions under which the ring C is f-clean. Moreover, we introduce the concept of rings having many full elements. We investigate characterizations of this kind of rings and show that rings having many full elements are closed under matrix rings and Morita Context rings.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2001-2011
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• 2013

Cho and Kim [4] have introduced the concept of the competition index of a digraph. Similarly, the competition index of an $n{\times}n$ Boolean matrix A is the smallest positive integer q such that $A^{q+i}(A^T)^{q+i}=A^{q+r+i}(A^T)^{q+r+i}$ for some positive integer r and every nonnegative integer i, where $A^T$ denotes the transpose of A. In this paper, we study the upper bound of the competition index of a Boolean matrix. Using the concept of Boolean rank, we determine the upper bound of the competition index of a nearly reducible Boolean matrix.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.245-259
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• 2007

We define and study a concept of $T^f$-space for a map, which is a generalized one of a T-space, in terms of the Gottlieb set for a map. We show that X is a $T_f$-space if and only if $G({\Sigma}B;A,f,X)=[{\Sigma}B,X]$ for any space B. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain a sufficient condition to having a lifting $T^{\bar{f}}$-structure on $E_k$ of a $T^f$-structure on X. Also, we define and study a concept of co-$T^g$-space for a map, which is a dual one of $T^f$-space for a map. We obtain a dual result for a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from ${\iota}:X^{\prime}{\rightarrow}cX^{\prime}$.