• 한국수학교육학회지시리즈A:수학교육
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• 제46권3호
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• pp.273-292
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• 2007

The purpose of this study was to find out how second, fourth and sixth graders understood the main contents related to spatial sense in the Seventh National Mathematics Curriculum. For this purpose, this study examined students' understanding of the main contents of congruence transformation (slide, flip, turn), mirror symmetry, cubes, congruence and symmetry. An investigation was conducted and the subjects included 483 students. The main results are as follows. First, with regards to congruence transformation, whereas students had high percentages of correct answers on questions concerning slide, they had lower percentages on questions concerning turn. Percentages of correct answers on flip questions had significant differences among the three grades. In addition, most students experienced difficulties in describing the changes of shapes. Second, students understood the fact that the right and the left of an image in a mirror are exchanged, but they had poor overall understanding of mirror symmetry. The more complicated the cubes, the lower percentages of correct answers. Third, students had a good understanding of congruences, but they had difficulties in finding out congruent figures. Lastly, they had a poor understanding of symmetry and, in particular, didn't distinguish a symmetric figure of a line from a symmetric figure of a point.

• 대한기계학회논문집A
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• 제24권1호
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• pp.110-117
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• 2000

Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as the twisting motion on a screw in a three dimensional space. This paper, presents the method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation. It also describes that the stiffness matrix diagonalized by a congruence transformation, can have the planes of symmetry depending on the location of the center of elasticity. For a plane of symmetry, any vibration mode can be expressed by the axis of vibration. Analytical solutions for the axis of vibration has been derived.

• The Journal of Asian Finance, Economics and Business
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• 제8권2호
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• pp.353-364
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• 2021

Originating in value congruence theory, this study aims to give a clear understanding of the transformation process of consumers from incumbent technology to disruptive innovation technology. Moreover, the moderating effect of personal innovativeness in the process of consumers' switching to disruptive innovation is investigated. This study combines value congruence with expectation-disconfirmation theory, technology-switching theory, and the personal innovativeness of the disruptive innovation product, explaining why consumers have transformed from an incumbent product into a disruptive innovation. Data was collected through a questionnaire from 280 smartphone users in China. The respondents were mainly potential consumers who had never bought Redmi phones, namely, a smart product owned by the renowned Chinese company Xiaomi. The hypothesis of the research model is based on the example of the Redmi smartphone, which has been confirmed by existing smartphone users in China. Through investigation, the results of multivariable regression analysis show the decisive variables that influence consumer intentions, and we analyze the role of personal innovativeness in moderating between dissatisfaction with the incumbent product and purchase intention of a product based on disruptive innovation. The findings of this study can provide a certain reference for the sustainable growth of Xiaomi and the development of new products.

• 한국수학교육학회지시리즈A:수학교육
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• 제40권1호
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• pp.93-102
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• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• 대한수학회논문집
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• 제21권1호
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• pp.165-175
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• 2006

We associate the surfaces of constant Gaussian curvature K = 1 with no umbilics to a subclass of the solutions of $O(4,\;1)/O(3){\times}O(1,\;1)-system$. From this correspondence, we can construct new K = 1 surfaces from a known K = 1 surface by using a kind of dressing actions on the solutions of this system.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.751-760
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• 2021

We study in this paper the right Rényi mean for a quantum divergence induced from the α - z Rényi relative entropy. Many properties including homogeneity, invariance under permutation, repetition and unitary congruence transformation, and determinantal inequality have been presented. Moreover, we give the identity of two right Rényi means with respect to tensor product.

• 대한기계학회논문집A
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• 제37권8호
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• pp.961-966
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• 2013

열전 복합재의 성능을 파악하기 위해 결합된 형태의 지배방정식은 결합되지 않은 형태로 변환되며, 여기에 수정된 에쉘비 모델을 적용하여 복합재의 등가지벡계수를 유도한다. 모재와 충전재가 직렬 및 병렬로 배치된 복합재와 모재 속에 구형의 충전재가 포함된 복합재에 대한 본 연구결과는 참고 문헌에 알려진 이론적 및 실험적 결과와 비교되며, 이론적 결과와는 완전히 일치하고 실험적 결과와 잘 일치함을 보인다. 지배방정식의 단순화를 통해 열전 복합재의 등가지벡계수는 수정된 에쉘비 모델로 성공적으로 예측될 수 있음을 보였다.

• 대한기계학회논문집A
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• 제24권2호
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• pp.362-369
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• 2000

Via screw theory, a vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as a twisting motion on a screw in a three dimensional space. In thi s paper, applying the conditions that can be used to diagonalize the stiffness matrix by a parallel axis congruence transformation, the vibration modes and frequency response of an elastically suspended optical disc drive have been analyzed. It is first shown that the system has one plane of symmetry, which enables one to decouple the complicated vibration modes into two sets of modes independent of each other. Having obtained the analytical solutions for the axes of vibrations, the frequency response for a given applied input force has been demonstrated. Most importantly, it has been explained that this research result could be used in the synthesis process of a linear vibration system in order to improve the frequency response.

• 대순사상논총
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• 제29집
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• pp.141-170
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• 2017

이 글에서는 한국불교의 진묵설화와 대순사상의 진묵설화를 비교하고자 한다. 자세히 말하자면, 『진묵조사유적고』와 『전경』의 진묵설화를 비교하고 그 차이점에 대해 검토하고자 한다. 2장에서는 『진묵조사유적고』에 나타난 진묵의 사상을 다음의 4가지로 나누어서 접근한다. 첫째, 진묵은 석가모니의 화신불이라는 것이다. 『진묵조사유적고』의 서문에서 초의(艸衣)는 진묵이 석가모니의 화신이라고 밝히고 있다. 둘째 무애행의 정신이고, 셋째 선교일치의 정신이며, 넷째 유불일치의 정신이다. 3장에서는 대순사상에 나타난 진묵설화에 관한 관점을 살펴보고, 『진묵조사유적고』의 진묵설화와 비교한다. 우선 『전경』에서 진묵의 설화는 천지공사와 해원상생의 관점에서 활용된다. 이것이 불교의 진묵설화와 가장 다른 점이다. 그 다음 진묵설화 가운데 『진묵조사유적고』와 『전경』에 공통된 주제를 말하는 것이 있는데, 그 설화들을 비교해보면 역시 차이점이 존재한다. 그러면 이러한 차이점이 생기는 이유는 무엇일까? 여기서는 엘리아데의 신화이론에 근거해서 설명하고자 한다. 엘리아데는 신화는 그것을 전달하는 사람의 희망사항이 투영된 것이라고 한다. 이 이론에 근거해서 『진묵조사유적고』와 『전경』에 나타난 진묵설화의 차이점을 설명하면, 불교계의 『진묵조사유적고』에는 불교의 가치관이 투영된 진묵설화가 전승되었고, 대순사상의 『전경』에는 대순사상의 가치관이 반영된 진묵설화가 전승되었다고 말할 수 있다. 이처럼 한국불교와 대순사상은 서로의 가치관이 다르기 때문에 같은 주제의 진묵설화라고 해도 전승된 내용에 차이점이 생겼다.

• 대한수학회논문집
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• 제31권2호
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• pp.217-227
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• 2016

Let X be a nonempty set, and let $\mathfrak{F}=\{Y_i:i{\in}I\}$ be a family of nonempty subsets of X with the properties that $X={\bigcup}_{i{\in}I}Y_i$, and $Y_i{\cap}Y_j={\emptyset}$ for all $i,j{\in}I$ with $i{\neq}j$. Let ${\emptyset}{\neq}J{\subseteq}I$, and let $T^{(J)}_{\mathfrak{F}}(X)=\{{\alpha}{\in}T(X):{\forall}i{\in}I{\exists}_j{\in}J,Y_i{\alpha}{\subseteq}Y_j\}$. Then $T^{(J)}_{\mathfrak{F}}(X)$ is a subsemigroup of the semigroup $T(X,Y^{(J)})$ of functions on X having ranges contained in $Y^{(J)}$, where $Y^{(J)}:={\bigcup}_{i{\in}J}Y_i$. For each ${\alpha}{\in}T^{(J)}_{\mathfrak{F}}(X)$, let ${\chi}^{({\alpha})}:I{\rightarrow}J$ be defined by $i{\chi}^{({\alpha})}=j{\Leftrightarrow}Y_i{\alpha}{\subseteq}Y_j$. Next, we define two congruence relations ${\chi}$ and $\widetilde{\chi}$ on $T^{(J)}_{\mathfrak{F}}(X)$ as follows: $({\alpha},{\beta}){\in}{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}={\chi}^{({\beta})}$ and $({\alpha},{\beta}){\in}\widetilde{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}{\mid}_J={\chi}^{({\alpha})}{\mid}_J$. We begin this paper by studying the regularity of the quotient semigroups $T^{(J)}_{\mathfrak{F}}(X)/{\chi}$ and $T^{(J)}_{\mathfrak{F}}(X)/{\widetilde{\chi}}$, and the semigroup $T^{(J)}_{\mathfrak{F}}(X)$. For each ${\alpha}{\in}T_{\mathfrak{F}}(X):=T^{(I)}_{\mathfrak{F}}(X)$, we see that the equivalence class [${\alpha}$] of ${\alpha}$ under ${\chi}$ is a subsemigroup of $T_{\mathfrak{F}}(X)$ if and only if ${\chi}^{({\alpha})}$ is an idempotent element in the full transformation semigroup T(I). Let $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ be the sets of functions in $T_{\mathfrak{F}}(X)$ such that ${\chi}^{({\alpha})}$ is injective, surjective and bijective respectively. We end this paper by investigating the regularity of the subsemigroups [${\alpha}$], $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ of $T_{\mathfrak{F}}(X)$.