• The Mathematical Education
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• v.46 no.3
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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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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• v.8 no.2
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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.

• The Mathematical Education
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• v.40 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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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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• v.39 no.5_6
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.8
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• pp.961-966
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• 2013

A coupled governing equation of thermoelectric materials can be converted into an uncoupled form to predict the effective Seebeck coefficient of thermoelectric composites, where modified Eshelby model is adopted. The predicted results by the present approach for serial- and parallel-connected composites and composite with spherical inclusions are compared with theoretical and experimental results from literatures to be justified. It is shown that the predictions by the theoretical approaches coincide exactly and show in good agreement with the experiments.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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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.

• Journal of the Daesoon Academy of Sciences
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• v.29
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• pp.141-170
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• 2017

In this paper, I will compare the Jinmuk tales from Korean Buddhism and those which appear in Daesoon Thought. Specifically, I will compare the Jinmuk tales from the Jinmukjosayujeokko (震黙祖師遺蹟攷, A Study on the Remains of Patriarch Jinmuk) and those from the Jeongyeong (典經), and then study the differences between the two sources. In chapter two, I approach Jinmuk's thought as conveyed in the Jinmukjosayujeokko by examining four points. The first point is that Jinmuk is a transformation-body (an incarnation) of Sakyamuni (釋迦牟尼) Buddha. In the preface of the Jinmukjosayujeokko, Choui (艸衣) says that Jinmuk is a transformation-body of Sakyamuni Buddha. The second point is the spirit of unobstructed action (無礙行), the third point is the spirit of the fundamental congruence between meditative and doctrinal approaches (禪敎一致), and the fourth is the spirit of the fundamental congruence between Confucianism and Buddhism (儒佛一致). In chapter three, I study on the viewpoints which can be derived from Jinmuk tales in Daesoon Thought, and compare the Jinmuk tales from the Jinmukjosayujeokko and the Jeongyeong. The Jinmuk tales from the Jeongyeong can be characterized by the Daesoon concepts 'Cheonji Gongsa (天地公事, The Reordering Works of Heaven and Earth)' and 'Haewon Sangsang (解冤相生, The Resolution of Grievances for Mutual Beneficience)'. This is the key difference between the Jinmuk tales from Korean Buddhism and those from Daesoon Thought. If I compare the common subject matter of the Jinmuk tales in the Jinmukjosa yujeokko and the Jeongyeong, the Jinmuk tales from these two sources likewise contain differences. Why do these differences occur? I will explain these differences based on Mircea Eliade's approach to mythology. Eliadian theory posits that myths contain the desires of those who deliver the myths. If I explain the difference between the Jinmuk tales in the Jinmukjosayujeokko and the Jeongyeong based on Eliade's theory, Buddhism has Jinmuk tales composed to reflect Buddhist values, whereas Daesoon Thought has Jinmuk tales composed to reflect the values of Daesoon Thought. As Korean Buddhism and Daesoon Thought promote different values, they thereby have different Jinmuk tales.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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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 $T_{\mathfrak{F}}(X)$.