• Honam Mathematical Journal
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• v.43 no.4
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• pp.691-700
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• 2021

In this paper, we compute directly the Hankel matrix representation of the Hankel operator on the Hardy space of the unit disc without using any classical kernel functions with respect to special orthonormal bases for the Hardy space and its orthogonal complement. This gives an elementary proof for the formula.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.113-120
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• 2023

In this paper, we investigate the dimension and the structure of the centralizer of a square matrix with entries from an arbitrary field.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.303-310
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• 1996

The Gottlieb group of a compact connected ANR X, G(X), consists of all $\alpha \in \prod_{1}(X)$ such that there is an associated map $A : S^1 \times X \to X$ and a homotopy commutative diagram $$ S^1 \times X \longrightarrow^A X $$ $$incl \uparrow \nearrow \alpha \vee id $$ $$ S^1 \vee X $$.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.13-23
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• 2022

Let G be a semialgebraic group not necessarily compact. Let M be a proper semialgebraic G-set whose orbit space has a semialgebraic structure. In this paper, we prove the embeddability of M into a G-representation space when G is linear.

• Education of Primary School Mathematics
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• v.27 no.2
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• pp.139-153
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• 2024

This analysis was intended to present pedagogical implications related to the guidance of solid figures in elementary mathematics textbooks. The definitions of mathematical concepts and visually represented examples presented in the prism and pyramid units were analyzed. As a result of the analysis, differences were observed in both the method and content of defining mathematical concepts, even though the same curriculum was reflected. Additionally, various forms of visual examples were provided during the learning process of prisms and pyramids. Based on the results of this analysis, it is necessary to understand the definition of mathematical concepts and to teach students in an appropriate manner, considering the goals of each session and the objectives of the activities involved in presenting visual examples.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.535-563
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• 2012

This study was conducted to confirm the necessity of analogical thinking and to empirically verify the effectiveness of analogical reasoning through the visual representation by analyzing the factors of problem solving depending on analogical conditions. Four conditions (a visual representation mapping condition, a conceptual mapping condition, a retrieval hint condition and no hint condition) were set up for the above purpose and 80 twelfth-grade students from C high-School in Cheong-Ju, Chung-Buk participated in the present study as subjects. They solved the same mathematical problem about sequence of complex numbers in their differed process requirements for analogical transfer. The problem solving rates for each condition were analyzed by Chi-square analysis using SPSS 12.0 program. The results of this study indicate that retrieval of base knowledge is restricted when participants do not use analogy intentionally in problem solving and the mapping of the base and target concepts through the visual representation would be closely related to successful analogical transfer. As the results of this study offer, analogical thinking is necessary while solving mathematical problems and it supports empirically the conclusion that recognition of the relational similarity between base and target concepts by the aid of visual representation is closely associated with successful problem solving.

• School Mathematics
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• v.17 no.1
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• pp.19-33
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• 2015

This study examined mathematics class using the CAS(Computer Algebra Systems, CAS) targeted for high school first grade students. We examined what kind of transforming of representations got up according to mathematics subject contents at this classroom. This study analyzed 15 math lessons during one month and the focus of analysis was on the classroom teacher. In particular, for transformations among representations this study mainly investigated from theoretical frameworks such as transparent and opaque representation of Lesh, Behr & Post(1987), descriptive and depictive representation of Kosslyn(1994). According to the results of this study, CAS technology affected the transforming of representations in high school math class and this transforming of representations improved the students' thinking and understanding of mathematical concepts and provided the opportunity to create the representation of individual student. Such results of this study suggest the importance of CAS technology's role in transforming of representations. and they offer the chance to reconsider the fact that CAS technology could be used to improve students' ability of transforming representations at the mathematics class.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.219-236
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• 2023

This study examined the relationship between preservice teachers' mathematical understanding and problem posing in fractions multiplication and division. To this purpose, 41 preservice teachers performed visual representation and problem posing tasks for fraction multiplication and division, measured their mathematical understanding and problem posing ability, and examined the relationship between mathematical understanding and problem posing ability using cross-tabulation analysis. As a result, most of the preservice teachers showed conceptual understanding of fraction multiplication and division, and five types of difficulties appeared. In problem posing, most of the preservice teachers failed to pose a math problem that could be solved, and four types of difficulties appeared. As a result of cross-tabulation analysis, the degree of mathematical understanding was related to the ability to pose problems. Based on these results, implications for preservice teachers' mathematical understanding and problem posing were suggested.

• Korean Journal of Child Studies
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• v.30 no.2
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• pp.195-209
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• 2009

This study analyzed aspects of multiple intelligences related to rhythm, melody, understanding and representation of traditional Korean music. Subjects were 60 4-to 6-years-old children. Instruments were the Children's Korean Traditional Music (KTM) Ability Test (Park 2006)and Korean Multiple Intelligence Development Assessment Scale-My Young Child (MIDAS-MYC, Shearer, 1996). Data were analyzed by correlations and t-test. Findings were that (1) average scores on KTM rhythm and understandings were higher than melody and representation. (2) Traditional rhythm ability correlated most with linguistic intelligence. (3) Multiple intelligences by representation ability for KTM differed significantly in Linguistic intelligence and relationships to Naturalist, Musical, Logical-mathematical, Interpersonal, and Bodily-Kinesthetic intelligences.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.489-495
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• 2000

Stress and strain in continuum mechanics have a mathematical form of the second order tensor. it is well-known that the usefulness of tensor components could be explained in a relation with coordin ates system transformation and Mohr's circle could be easily used to make a coordinate system transformation of tensors. However, Mohr's circle is applied mainly to plane problems and its use to three dimensional cases is limitedly employed. In this paper, we propose a matrix and dyadic representation of stress and strain tensors which could equivalently replace the graphical representation of second order tensors. The use of the proposed representation might provide a valuable means for the educational respects as well as research view point.