• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.669-674
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• 2000

다면체에 대한 오일러 수의 개념은 잘 알려져 있다. 이 수는 위상 불변량이기 때문에 중요하다. 본 논문에서는 다면체의 꼭지점, 모서리, 면의 개수로 정의된 함수 중에서 본질적으로 올리러 수만이 위상 불변량임을 증명한다.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.389-425
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• 2004

심프렉틱 다양체는 미분다양체와 케러다양체 사이에 있는 다양체로서 심프렉틱 구조를 갖는 다양체이다. 케러다양체의 성질들을 얼마나 확장할수 있는지, 미분다양체와 다른 성질은 무엇이 있는지 연구함은 흥미있는 일이다. 심프렉틱 구조로부터 준복소구조가 정의되어 2차원 부분다양체를 나타내는 슈도-호로모르픽 사상이 정의되고, 이들은 모듀라이 공간이 된다. 또한 심프렉틱 구조는 메트릭과 에너지를 정의하여 노비코프환을 정의한다. 여기서 모듀라이 공간의 위상구조가 그로모브-위튼 불변량을 정의한다. 이 불변량은 심프렉틱 다양체 연구에 핵심적인 역할을 한다. 이 논문은 그로모브-위튼 불변량의 여러 가지 성질과 그 응용에 대한 여러 학자들의 결과를 소개하는 해설 논문이다.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.85-92
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• 2007

In this paper We study Some history and development of Geometry from the early 19th century to the late 20th century.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.23-35
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• 2011

The sphere theorem is one of the main streams in modern Riemannian geometry. In this article, we survey developments of pinching theorems from the classical one to the recent differentiable pinching theorem. Also we include sphere theorems of metric invariants such as diameter and radius with historical view point.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.6
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• pp.81-87
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• 1998

This paper proposes an efficient face recognition system using phase difference between the face images. We use a Karhunen-Loeve transform for image compression and reconstruction, and obtain the phase difference by using normalized inner product of the two compressed images. The proposed system is rotation and light-invariant due to using the normalized phase difference, and somewhat shift-invariant due to applying the cosine function. The faster recognition than the conventional system and incremental training is possible in the proposed system. Simulations are conducted on the ORL images of 40 persons, in which each person has 10 facial images, and the result shows that the faster recognition than conventional recognizer using convolution network under the same recognition error rate of 8% does.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.4
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• pp.905-912
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• 2011

Interaocular pressure (IOP) sensor and external coil to detect the resonance frequency of the IOP sensor are designed and implemented using MEMS technology. The IOP sensor is designed using 3-D electromagnetic (EM) simulation. The resonance frequency of IOP sensor needs to be lower than that of the external coil. Additionally, the resonance frequency of the IOP sensor needs to be located near the resonance frequency of the coil to get the sufficient amplitude of phase variation. The frequency where the phase peak appears must be constant according to the distance between the IOP sensor and the external coil. From the measurement results, we demonstrated that the designed IOP sensor has the same resonance frequency with various distances between the IOP sensor and the coil.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.131-148
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• 2013

Euler's formula provides the topological characteristics of geometrical objects including polyhedra, and so an important mathematical concept. Descriptions on Euler's formula had been in the textbooks according to the 3rd through 7th National Mathematics Curriculum. However, they are gone after that. In this study, we focus on Euler characteristic and Euler's formula as an educational material for educations for the gifted or after-school educations. We first look at the mathematical history and the applications of Euler's formula and national curriculums to search for its mathematical and educational meaning. We further make a suggestion for a learning environment which provides a better education relying on search activities, not just depending on memorization, illuminated from the education of Euler's formula.

• The Journal of Korean Institute of Information Technology
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• v.16 no.11
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• pp.97-103
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• 2018

In this paper, the estimation method for the power signal harmonics is proposed by using the time-varying optimal finite impulse response (FIR) filter. To estimate the magnitude and phase-angle of the harmonic components, the time-varying optimal FIR filter is designed for the state space representation of the noisy power signal which the magnitude and phase is considered as a stochastic process. Since the time-varying optimal FIR filter used in the proposed method does not use any priori information of the initial condition and has FIR structure, the proposed method could overcome the demerits of Kalman filter based method such as poor estimation and divergence problem. Due to the FIR structure, the proposed method is more robust against to the model uncertainty than the Kalman filter. Moreover, the proposed method gives more general solution than the time-invariant optimal FIR filter based harmonic estimation method. To verify the performance and robustness of the proposed method, the proposed method is compared with time-varying Kalman filter based method through simulation.