• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.51-62
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• 2008

In the 7th-curriculum, only basic arithmetics of complex numbers have been taught. They are taught formally like literal manipulations. This paper analyzes mathematically essential relations between algebra of complex numbers and plane geometry. Historical analysis is also performed to find effective methods of teaching complex numbers in school mathematics. As a result, we can integrates this analysis with school mathematics by help of Viete's operations on right triangles. We conclude that teaching geometric interpretation of complex numbers is possible in school mathematics.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.141-152
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• 2008

In this article, the didactical analysis of complex numbers was explored in the context of mathematical connection. The result of the analysis can provide the useful tools for problem solving. The article shows that the complex numbers system plays the key roles in the school mathematics.

• Journal for History of Mathematics
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• v.25 no.3
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• pp.53-75
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• 2012

When imaginary numbers were first encountered in the 16th century, mathematicians were able to calculate the imaginary numbers the same as they are today. However, it required 200 years to mathematically acknowledge the existence of imaginary numbers. The new mathematical situation that arose with a development in mathematics required a harmony of real numbers and imaginary numbers. As a result, the concept of complex number became clear. A history behind the development of complex numbers involved a process of determining a comprehensive perspective that ties real numbers and imaginary numbers in a single category, complex numbers. This came after a resolution of conflict between real numbers and imaginary numbers. This study identified the new perspective and way of mathematical thinking emerging from resolving the conflicts. Also educational implications of the analysis were discussed.

• 한국신재생에너지학회:학술대회논문집
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• 2007.11a
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• pp.213-216
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• 2007

PEMFC의 전기화학적 반응은 촉매, 이오노머, 기공이 만나는 삼상계면에서만 일어나므로, 전극 구조의 최적화가 성능 향상 및 장기안정성 확보에 있어 매우 중요하다. 본 연구에서는 전극 미세구조를 실시간으로 분석하기 위해 임피던스 복소캐패시턴스법을 도입하고자 하였다. 즉, PEMFC의 양극에 질소를 공급하면 0.4 V 부근에서 전기이중층 형성 반응만이 일어나는 것을 확인하였으며, 이때 음극에는 수소를 공급하여 기준전극 및 반대전극으로 사용하였다. 측정된 임피던스를 복소캐패시턴스로 변환하고 허수부를 주파수에 대해 도시하면 피크 형태의 곡선이 얻어지는데, (1) 피크 면적은 전극/전해질의 계면면적, (2) 피크 위치는 이오노머 네트워크에 의한 수소이온 전도 특성, (3) 피크 폭은 다공성 구조의 균일도를 각각 나타내므로, 피팅 없이 직접적인 해석이 가능하다는 장점을 가진다. 반면, 기존의 Nyquist 도시법은 피팅에 의한 분석이 필요하며, 전극층의 불균일한 구조로 인해 단순한 등가회로 구성이 어려운 문제점을 가진다. 최종적으로, MEA 제작 조건 및 운전 조건을 변수로 하여 임피던스를 측정하고 복소캐패시턴스 분석을 수행하여, 퇴화 경로를 규명하고 운전 조건을 최적화하고자 하였다.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• fall
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• pp.308-309
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• 2021

본 논문에서는 복소 홀로그램 압축을 위해 타일링을 사용한 결과를 비교하고 이를 분석한다. 복소 홀로그램의 실수부와 허수부를 1024×1024의 크기로 타일링하여 코덱의 입력으로 사용한다. area-based tiling과 pixel-based tiling을 사용하여, JPEG2000 코덱 내부에서 적용할 수 있는 타일링 방법과 비교하고, 디코딩된 홀로그램의 SNR(Signal-to-Noise Ratio)과 수치적 복원 결과를 분석한다.

• School Mathematics
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• v.10 no.3
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• pp.357-374
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• 2008

The complex number system is supposed to introduce first chapter in the first grade of high school. When number system is expanded to complex numbers, the main aim is to understand preservation of algebraic structure with regard to the flow of curriculum and textbook. This research reviewed overall alternative articulation and treatment of textbooks from a logical viewpoint. Two research questions are developed below. First, in the structure of the current curriculum, when we consider student's 'level', how are the alternative articulation and treatment of textbooks in complex unit on a logical point of view? Second, What are more logical alternative articulation and treatment? What alternative articulation and treatment are suitable for a running goal? and what are the improvement which is definitive?

• Proceedings of the KSEEG Conference
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• 2001.04a
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• pp.147-147
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• 2001

• Proceedings of the KIPE Conference
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• 2011.07a
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• pp.192-193
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• 2011

자기유도방식 무선전력전달용 DQ 인버터의 정적 동작 특성 및 동적 응답 특성을 해석하는데 복소 라플라스 변환을 페이저 변환된 회로에 적용하는 방법을 사용하였다. 최근에 발표된 복소 라플라스-페이저 변환이론이 교류 컨버터의 동적특성을 해석하는데 있어 실용적으로 아주 유용하다는 것이 연구를 통해서 확인되었다. 기존의 라플라스 변환을 복소수 영역으로 확대한 복소 라플라스 변환을 페이저 변환된 회로에 적용하면 전달함수를 구할 수 있어, 시스템의 안정도 분석과 제어기 설계가 가능해진다. 본 논문에서는 이론식을 유도하고 시뮬레이션을 통해 검증하였다.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.69-82
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• 2012

The objective of this paper is to study De Morgan's perspective on teaching and learning complex numbers. De Morgan's didactical approaches reflect the process of development of his thoughts about algebra from universal arithmetic, symbolic algebra to meaning algebra. De Morgan develop his perspective on algebra by justifying and explaining complex numbers. This implies that teaching and learning complex numbers is a catalyst for mathematical development of De Morgan.

• Composites Research
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• v.22 no.3
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• pp.44-54
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• 2009

In this paper, we proposed a numerical model the complex permittivity for the E-glass fabric/epoxy composite laminate containing electrical conductive carbon black. The model is based on the percolation theory and for the composites over than the percolation threshold and in higher frequency band in that the AC conductivity is fully proportional to the frequency. The measurement for the complex permittivity wasperformed at the frequency band of 0.5 GHz $\sim$ 18.0 GHz using a vector network analyzer with a 7 mm coaxial air line. The proposed model is composed of the numerical equations of the scaling law used in percolation theory and constants obtained from experiments to quantify the model itself. The model describes the complex permittivity as the function of frequency and filler concentration. The model was verified by being compared with the measurements.