• School Mathematics
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• v.17 no.3
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• pp.407-421
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• 2015

Linear system is a basic subject matter of school mathematics courses. Even though elimination is a useful method to solve linear systems, its fundamental principles were not discussed pedagogically. The purpose of this study is to help the development of mathematical content knowledge on linear systems conceptions. To do this, various representations and translations among them were considered, and in particular, the basic principles for elimination method are analyzed geometrically. Rectangular representation is used to solve word problem treated in numbers of things in elementary mathematics and it is useful as a pre-stage to introduce elimination. Slopes and intercepts of lines associated linear equations are used to obtain the Cramer's formula and this solving method was showing the connection between algebraic and geometric procedures. Strategy deleting variables of linear systems by elementary operations is explored and associated with the movements of lines in the family of lines passing through a fixed point. The development of mathematical content knowledge is expected to enhance pedagogical content knowledges.

• Communications of Mathematical Education
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• v.22 no.3
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• pp.337-347
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• 2008

'Slope' is an invariant of a straight line and 'Linear Equation' is an algebraic representation of a straight line in the cartesian plane. The concept 'slope' is necessary for algebraically representing a geometrical figure, line. In this article, we investigate how those concepts are dealt with in school mathematics and suggest some improvement methods.

• Journal of Internet Computing and Services
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• v.11 no.5
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• pp.27-35
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• 2010

In this paper, we propose a method that can compensate the geometric distortions of image caused from an arbitrary nonflat display surface(or wall) under the environment of portable overhead projector without a flat screen. In the proposed method, we first project a grid pattern to an arbitrary nonflat display surface and then derive an equation of straight line that represents the geometry relationship between the distorted grid pattern and the original grid pattern. Next, after determining the proper size of the original grid pattern according to the form of the display surface, we generate a compensation pattern from the derived equation of straight line, which can symmetrically compensate for the distorted image. Finally, we compensate for the geometric distortions of the projected image by segmenting the real image to be projected from portable overhead projector and prewarping it according to the compensation pattern. To evaluate the proposed method, we performed experiments of image compensation on inclined surface, bent surface and curved surface that are frequently occurred in the environment of portable overhead projector without a flat screen. From the experimental results, we found that the proposed method could be very effective in compensating for the general types of the geometric distortions of the projected images.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.18 no.2
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• pp.110-114
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• 2004

This paper deals with the dynamic characteristic analysis of linear actuator(LA) considered with coupling of mechanical spring system This application of linear actuator is increasing due to simple mechanical structure, a high efficiency, and a stable motional action. This paper proposed and analyzed the Serial Piston Actuator(SPA) by using mechanical spring system coupled with linear actuator through the simplified structure which was verified practical experiments.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.10a
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• pp.383-386
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• 2007

허프 변환(Hough transform)은 영상에서 몇 개의 파라미터로 표현되는 기하학적 요소 추출을 위해 널리 사용되고 있는 방법 중 하나이다. 하지만 허프 변환은 영상의 한 픽셀이 허프 공간(Hough space)의 한 방정식에 대응되는 일대다 특성으로 인해 잡음에 민감한 특성을 갖는다. 이러한 잡음 민감성은 검출되는 직선의 개수뿐만이 아니라 검출된 직선의 품질에도 영향을 미칠 수 있다. 즉, 실제 직선에서 벗어난 직선이 검출되거나 하나의 실제 직선에 대해 여러 개의 직선이 검출되는 등의 직선 왜곡이 발생할 수 있다. 이러한 직선 왜곡은 잡음 이외에도 허프 공간의 설정, 특히 각 해상도의 설정에 영향을 받는다. 이 논문에서는 기존의 허프 변환에서 발생하는 이러한 직선 왜곡을 분석하고, 잡음 민감성을 줄이기 위해 제안된 경계선 강도 허프 변환(Edge Strength Hough Transform, ESHT)에서 이러한 왜곡이 적게 발생함을 보인다. 또한 ESHT에서만 발생할 수 있는 왜곡을 분석하고 해결방안을 제시한다. 제시한 방법에 의해 직선의 왜곡이 감소하는 것은 실험 결과를 통해 확인할 수 있다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.10B
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• pp.1436-1443
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• 2001

본 연구는 고속도로에 설치된 CCTV 카메라에서 교통량, 속도, 점유율 등의 교통정보를 수집하기 위하여 검지영역을 자동으로 설치하는 알고리즘을 제안한다. 이를 위하여 교통정보센터에 설치된 콘트롤러에서 CCTV 카메라의 Pan, Tilt, Zoom 요소값을 보내면 이 값만큼 CCTV 카메라가 panning, tilting이 되고, 이에 따른 변화된 영상이 교통정보센터로 전송이 된다. 기존의 연구로는 영상 내에서 도로를 추출하기 위하여 차 영상(difference image)에 의한 도로추출방법과 윤곽선 추출방법에 의한 도로추출 방법이 있으나, 전자는 도로를 추출하는데 있어서 시간이 많이 소요된다는 문제점이 있으며, 후자는 정확한 도로를 추출하지 못한다는 문제점이 있다. 이러한 문제를 해결하기 위하여 본 연구에서는 우선 각 차로 상의 직선의 방정식을 구하고, 이 직선의 방정식에서 CCTV 카메라가 Panning, Tilting하는 중심점을 찾은 다음 CCTV 카메라의 Pan, Tilt 값에 의하여 3차원상의 원근비율에 따라 각 차로 별 좌표변환방법을 이용한다. 본 연구를 위한 실험은 고속도로 기흥IC에 15m 높이로 설치된 CCTV 카메라에서 영상을 캡쳐하였으며, 차후 교통량, 속도, 점유율 등 교통정보를 산출하는데 처리 속도를 고려하여 영상의 해상도는 640480픽셀과 256명암값에서 계산되었다.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.4
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• pp.455-461
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• 2002

This paper presents a new parametric log line equation of polar form for Hough transform in log-polar plane, in which it can remove the well-known unboundedness problem of Hough parameters. Bolduc's method is used to generate a log-polar image dividing the fovea and periphery from a Cartesian image. Edges of the fovea and periphery are detected by using the Sobel mask and the proposed space-variant gradient mask, and are combined in the log-polar plane. The sampled points that might constitute a log line are quite sparse in a deep peripheral region due to severe under-sampling, which is an inherent property of LPM. To cope with such under-sampling, we determine the values of cumulative cells in Hough space by using the space-variant weighting. In our experiments, the proposed method demonstrates its validity of detecting not only the lines passing through both the fovea and periphery but also the lines in a deep periphery.

• Communications of Mathematical Education
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• v.10
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• pp.125-141
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• 2000

현행 교육과정에서는 서로 만나는 두 직선의 둘레로 회전하여 얻는 곡면 즉 직원뿔을 꼭지점을 지나지 않는 평면으로 잘라 만들어지는 원추곡선 중에서 원을 제외한 포물선, 타원, 쌍곡선에 대한 시각적 직관적 개념 형성 지도가 미흡한 실정이다. 이에 시각적, 직관적 개념 형성에 적합한 상황과 대상을 제공할 수 있는 컴퓨터 응용소프트웨어를 이용하여 이차곡선을 도입하고 Computer Algebra System을 적용한 MathView를 이용하여 포물선, 타원, 쌍곡선 방정식의 개념 지도 방안을 구안하였다.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.179-203
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• 2013

The purpose of this study was to discuss the example that developed geometry model textbook based on storytelling using real-life context. To achieve this purpose, we first elaborated the meaning of the textbook based on storytelling with real-life context, and then we discussed the outline of the story and the summary of each lesson. This study defined the storytelling textbook with real-life context as the textbook consisting of activities that explored and organized mathematical concepts by using real-life situations as materials of stories. The geometry textbook we developed employed two real-life materials, a map and a set square: we used a map for the coordinate geometry and a set square for the equation of a line. To attract students' interest, we introduced confrontation between a teacher and two students and a villain. We implemented experimentation with the textbook based on storytelling in order to verify its validity. The participants were 25 students that were enrolled in a high school in Seoul. Among them, 17 participants were surveyed. Students' answers from the survey questionnaire suggested that the geometry textbook we developed based on storytelling helped them learn mathematics and that the instruments such as a map and a set square helped them understand mathematical concepts. However, their opinion implied that the story of the textbook needed to be improved so that the story reflected more realistic contexts that were familiar with students.

• Fire Science and Engineering
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• v.30 no.1
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• pp.49-56
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• 2016

This paper numerically examines, straight and twisted electrical heat trace installations for their anti-freezing effects on water inside a pipe. The unsteady incompressible Navier-Stokes equations coupled with an energy equation were solved to compare the two installation methods. The heat conduction of the pipe with a heat source interacts with the natural convection of the water, and the conjugate heat transfer was considered using a commercial code (ANSYS-FLUENT) based on a SIMPLE-type algorithm. Numerical experiments, were done to investigate the isotherms and the vector fields in the water region to extract the evolutions of the minimum and maximum temperatures of the water inside the pipe. There was no substantial difference in the anti-freezing effects between the straight and twisted. Therefore, the straight installation is recommended after considering the damage and short circuit behavior of the electrical heat trace.