• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.471-479
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• 1995

A random shock model for a linearly deteriorating system is introduced. The system deteriorating linearly with time is subject to random shocks which arrive according to a Poisson process and decrease the state of the system by a random amount. The system is repaired by a repairmen arriving according to another Poisson process if the state when he arrives is below a threshold. Explicit expressions are deduced for the characteristic function of the distribution function of X(t), the state of the system at time t, and for the distribution function of X(t) if X(t) is over the threshold. The stationary case is briefly discussed.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.637-644
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• 1997

Sometimes, the first principal component may come logically from the established knowledge and premises. For example, for the high school students' test scores of Korean, English, Mathematics, Social Study, and Science, it is natural to define the first principal component as the average of all subject scores. In such cases, we need to respect both the background knowledge and the data exploration. The aim of this study is to find the remaining components in principal component analysis of multivariate data when the first principal component is defined a priori by the researcher. Moreover, we study related matrix decomposition and their application to the graphical display.

• The Mathematical Education
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• v.55 no.1
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• pp.91-106
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• 2016

The aim of this study was to analyze characteristics of teachers' knowledge about reductio ad absurdum. In order to achieve the aim, this study conducted didactical analysis about reductio ad absurdum through examining previous researches and developed a questionnaire with reference to the results of the analysis. The questionnaire was given to 34 high school teachers and qualitative methods were used to analyze the data obtained from the written responses by the participants. This study also elaborated the framework descriptors for interpreting the teachers' responses in the light of the didactical analysis and the data was elucidated in terms of this framework. The specific features of teachers' knowledge about reductio ad absurdum were categorized into five types as a result. This study raised several implications for teachers' professional development for effective mathematics instruction related to reductio ad absurdum.

• Proceedings of The KACE
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• 2018.08a
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• pp.25-27
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• 2018

교구에 대한 적절한 조작 및 탐구 활동은 수학의 개념과 원리를 이해하는 데 도움을 준다. 본 연구에서는 중학교 수학 교과 과정에 부합하는 함수의 개념과 성질에 대한 이해를 도울 수 있는 안드로이드 기반의 앱을 개발하였다. 개발한 앱은 앱인벤터(App Inventor) 2를 기반으로 사용자가 구체적인 함수 그래프를 그리도록 요구하는 것이 아니라 대략적인 개형을 이해하도록 하여 학습 부담 경감을 도모한다. 즉, 계산 능력 배양을 목표로 하지 않는 교수학습 상황에서 스팀 기반으로 공학적 도구를 이용하여 2015 개정 수학과 교수학습방법에서 요구되는 정보처리 능력 및 문제해결 능력을 함양시킬 수 있도록 학습 도구를 개발하였다.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.445-457
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• 2008

Although both theory and experiment are very important parts in sciences, especially in mathematics, theory only seems to be very important. But the subject of numerical analysis needs both theory and practice in computer. In this paper, I provide some Matlab program codes and matrices which are used in good understanding OR methods in class.

• The Mathematical Education
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• v.49 no.2
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• pp.267-279
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• 2010

Mathematics is the subject which is distinctive in logical hierarchy, so the dificiency of prior learning or lack of understanding can result in learning disabilities of follow-up study. To minimize the learning disabilities, we should percieve student's problems and correct them through "Error Analysis" so that they can make up meaningful learning. Especially, in the case of division, its meaning is various, and the interpretation of the quotient and the remainder is the difference according to the caculation results, so students are likely to make errors often. Therefore, in this study, I presented the measures of how to instruct them under the circumstances in which division is applied by analyzing examples of incorrect answers.

• International Journal of Reliability and Applications
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• v.2 no.2
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• pp.81-97
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• 2001

Lifetesting problems have been the subject of investigations for over three decades. Most suggested approaches are markedly different from those used in the related but wider goodness of fit problems. In the current investigation, it is demonstrated that a goodness of fit approach is possible in many lifetesting problems and that It results in simpler procedures that are asymptotically equivalent or better than standard ones. They may also have superior finite sample behavior. Several perennial classes are addressed here. The class of increasing failure rate (IFR) and the class of new better than used (NBU) are addressed first. In addition, we provide testing for a newer and practical class of new better than used in convex ordering (NBUC) due to Cao and Wang (1991). Other classes can be developed similarly and this point is illustrated with the classes of new better than used in expectation (NBUE) and harmonic new better than used in expectation (HNBUE).

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.9
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• pp.7-12
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• 2018

In the society where the paradigm of knowledge is rapidly changing and developing, convergence emphasizing the connection between knowledge and technology in various fields is significant. In order to cultivate these creative-convergent talents, STEAM(Science, Technology, Engineering, Arts, and Mathematics) is being considered important to make them equipped with creative thinking ability and core competence required in the future society and help them devise new ideas escaping from the branches of study. This study is about convergence instructional design of computer with marketing subject, which aims to foster talent. The results of this study are as follows. First, the structured process of convergence lessons. Second, the convergence lesson was based on a cyclic process with steps : selection of the subject concerned, selection of a topic, designing the lesson, mapping out the lesson plan and developing problems, having a final discussion on the whole lesson, performing the lesson and evaluating the lesson. Third, the development of the problems about the introduction of computer engineering and Internet marketing subject for convergence lessons. To make an effect of this model, studies applying this instructional design to many lectures should be implemented.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.4
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• pp.518-524
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• 2020

This study conducted basic research on an LED lighting design to improve the learning effect from brain wave analysis. The ideal environments of mathematics, language, and creative region can be different. Inside the space where the lighting environment can be experienced directly, the test subject consisted of common elements. Other lighting was blocked completely in controlled lighting conditions. The brain waves were analyzed according to the change in color temperature and illumination. The analyzer used was fabricated by EMOTIV Company. In the variable RGB LED light, the color of the light was measured, and the brain wave of each subject was determined. LED lights have variable color temperature (3000 [K], 4500 [K]. 250 [lux], 70% -350 [lux], 100% -500 [lux]). As research results, the highest concentration in a mathematics study was in the general condition of a high color temperature, in which the optimal condition was a 6000[K] color temperature and 350[lux] illumination. The optimal condition for a language study was a 4500[K] color temperature and 500[lux] illumination, and that of the creative study was 3000[K] color temperature and 500[lux] illumination. Overall, the possibility of emotional ability and concentrated learning efficiency can be improved by the LED lighting design with the color temperature and illumination.