• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 2014

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.407-407
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• 2010

본 논문에서는 확장된 히든마코브모델을 이용하여 플라즈마 식각공정에서 식각종료검출을 위한 방법을 연구하였다. 플라즈마 식각장비는 유도성 결합플라즈마 시스템을 사용하였으며, 종료점 검출을 위해 식각공정이 진행됨에 따른 플라즈마의 상태를 확인할 수 있는 광학 방사 분광기(Optical Emission Spectroscopy: OES)를 사용하였다. 식각이 진행되는 동안 여기되는 입자들은 특정한 재료에 해당하는 파장에서 빛을 방출한다. 플라즈마상태에서 여기되는 원자와 분자들에 의해서 방출되는 빛은 OES를 통해 식각되는 물질을 확인하기 위해서 특별한 파장의 빛을 선택하여 분석한다. 본 논문에서는 확장된 히든마코브모델을 이용해 산화물이 식각될 때 방출하는 고유한 파장의 빛을 분석하여 식각이 종료되는 시점을 찾는 연구를 하였다. 제안된 확장형 히든마코브 모델은 세미-마코브모델과 분절특징 히든마코브모델을 결합한 것으로, 확률적 통계기법을 통해 종료시점을 찾아내는 방법이다. OES를 통해 얻은 데이터는 식각 종료가 일어나기 전의 파장의 상태와 식각이 종료된 후의 파장의 상태로 구분되어지는데, 식각종료시점에서 파장의 상태가 변화하며 이를 감지하여 식각종료점을 검출한다. 분절특징 히든마코브모델을 이용하여 식각종료시점 전후의 파장의 상태를 모델링 하였으며, 일반적인 마코브 모델의 특정상태가 유지될 시간의 확률을 변형된 세미-마코브 모델을 이용하여 OES를 통해 얻은 데이터 내에서 식각 종료가 일어나기 전의 상태가 유지될 수 있는 확률을 모델링 하였다. 실험을 통해 얻어진 6개의 데이터중 4개를 학습을 위해 사용하여 모델링을 하였고 나머지 2개의 데이터를 검증을 위해 사용한 결과, 확장형 히든마코브모델의 식각종료시점검출에 있어 뛰어난 정확성과 우수성을 증명하였다.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.5 no.1
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• pp.29-37
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• 2007

A conventional single compartment model cannot simulate reasonably the migration phenomenon of contaminants through unsaturated zone, due to the intrinsic unrealistic assumption of the compartment model that contaminants entering a compartment are immediately and uniformly mixed. Although, a multi-compartments model, in which even physically identical layer is divided into multiple compartments, may be used for explaining the retardation of contaminant mass flux along with increasing number of compartments, its numerical modeling is usually time-consuming and appropriate analytical solutions have not been reported yet. In order to improve the conventional compartment models on contaminant migration through unsaturated zone, a series of analytical solutions for multi-compartments model were derived and a generalized constraint under which the results from multi-compartments model can be simply approximated by single compartment model was proposed. The simplified approximation method was verified by a simple numerical analysis on the constraint under hypothetical conditions. It was also proved that the influent contaminant transfer rate from the bulk unsaturated zone can be generally represented into a time-dependent nominal transfer rate rather than a constant. In addition, the nominal transfer rate turned out to be very sensitive to the contaminant transfer rate between compartments in unsaturated zone, but to be almost insensitive to the transfer rate from contaminated zone. It is expected that the simplified approximation method developed in this study can be used for rapid and reasonable estimation of the migration phenomenon of contaminant through unsaturated zone, instead of time-consuming multi-compartments modeling.

• Journal of the Korea Society of Computer and Information
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• v.15 no.11
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• pp.31-39
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• 2010

In some image processing system or the users who want to see a specific region of image simply, if a part of the image has higher quality than other regions, it would be a nice service. Specifically in mobile environments, preferential service was needed, as the screen size is small. So, JPEG2000 supplies this function. But this doesn't support the process to extract specific regions or service and does the functions to add some techniques. It is called by ROI(Region-of-Interest). In this paper, we use images including human faces, which are processed most preferentially and compressed with high quality. Before an image is served to the users, it is compressed and saved. Here, the face parts are compressed with higher quality than the background which are relatively with lower quality. This technique can offer better service with preferential transferring of the faces, too. Besides, whole regions of the image are compressed with same quality and after searching the faces, they can be preferentially transferred. In this paper, we use a face extraction approach based on neural network and the preferential processing with EBCOT of JPEG2000. For experimentation, we use images having several human faces and evaluate objectively and subjectively, and proved that this approach is a nice one.