• 충청수학회지
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• 제25권2호
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• pp.299-312
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• 2012

In 1970s, B. C. Berndt proved a transformation formula for a large class of functions that includes the classical Dedekind eta function. From this formula, he evaluated several classes of infinite series and found a lot of interesting infinite series identities. In this paper, using his formula, we find new infinite series identities.

• 대한수학회논문집
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• 제33권1호
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• pp.207-236
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• 2018

We obtain recursion formulas for q-hypergeometric and q-Appell series. We also find recursion formulas for the general double q-hypergeometric series. It is shown that these recursion relations can be expressed in terms of q-derivatives of the respective q-hypergeometric series.

• 전기학회논문지
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• 제57권3호
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• pp.494-500
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• 2008

This paper presents the analyzed result of the series arc fault current by using the discrete wavelet transform. The series arcing is caused by a loose connection in series with the load circuit. The series arc current is limited to a moderate value by the resistance of the device connected to the circuit, such as an appliance or a lighting system. The amount of energy in the sparks from the series arcing is less than in the case of parallel arcing but only a few amps are enough to be a fire hazard. Therefore, it is hard to detect the distinctive difference between a normal current and a intermittent arc current. This paper, presents the variation of the ratio of peak values and RMS values of the series arc fault current, and proposes the novel series arc fault detecting method by using the discrete wavelet transform. Loads such as a CFL lamp, a vacuum cleaner, a personal computer, and a television, which has the very similar normal current with the arc current, were selected to confirm the novel method.

• 한국수학사학회지
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• 제28권4호
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• pp.167-179
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• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권7호
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• pp.3112-3127
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• 2018

Since time series clustering is performed without prior information, it is used for exploratory data analysis. In particular, clusters of time series with similar shapes can be used in various fields, such as business, medicine, finance, and communications. However, existing time series clustering algorithms have a problem in that time series with different shapes are included in the clusters. The reason for such a problem is that the existing algorithms do not consider the limitations on the size of the generated clusters, and use a dimension reduction method in which the information loss is large. In this paper, we propose a method to alleviate the disadvantages of existing methods and to find a better quality of cluster containing similarly shaped time series. In the data preprocessing step, we normalize the time series using z-transformation. Then, we use piecewise aggregate approximation (PAA) to reduce the dimension of the time series. In the clustering step, we use density-based spatial clustering of applications with noise (DBSCAN) to create a precluster. We then use a modified K-means algorithm to refine the preclusters containing differently shaped time series into subclusters containing only similarly shaped time series. In our experiments, our method showed better results than the existing method.

• 응용통계연구
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• 제36권5호
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• pp.457-471
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• 2023

월별 시계열은 일별 시계열의 월별 합이지만, 일별 시계열을 대체로 관측할 수 없어서 요일구성변동, 명절·공휴일변동 등 달력변동을 가상적으로 가정한 가변수를 포함한 RegARIMIA 모형을 이용하여 추정하고 있다. 일별 시계열을 관측할 수 있다면 요일구성변동, 명절·공휴일변동 등 달력변동을 일별 시계열을 바탕으로 추정할 수 있고 이를 이용하여 월별 시계열의 계절조정을 개선할 수 있다. 이 논문에서는 일별 시계열의 달력변동 추정을 이용하여 월별 시계열의 계절조정을 개선하는 방법을 제안하고, 이 방법을 적용하여 3개의 월별 시계열을 계절조정하고 기존의 X-13ARIMA-SEATS를 이용한 계절조정과 비교하였다.

• 한국콘텐츠학회논문지
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• 제10권9호
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• pp.97-106
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• 2010

시계열 데이터를 효율적이고 효과적으로 처리하기 위해 다양한 시계열 표현 방법들이 제안되었다. SAX(Symbolic Aggregate approXimation)는 단편화와 이산화 기법들을 결합한 시계열 표현 방법으로, 시계열 분류 문제에 성공적으로 적용되었다. 그러나 SAX는 시계열의 움직임을 평활하여 시계열의 중요한 동적 패턴들을 정확히 표현하기 위해 세그먼트 수를 크게 해야 한다. 본 논문은 PIPs (Perceptually Important Points)탐지 기법과 Persist 이산화 방법을 결합한 시계열 표현 방법을 제안한다. 제안된 방법은 시계열의 중요한 변곡점들을 나타내는 PIP 들을 탐지하여 고차원 시계열의 동적 움직임을 저차원 공간에서 표현한다. 그리고 시계열의 자기 전이와 주변 확률 분포를 KL 다이버전스에 적용하여 최적의 이산화 영역들을 결정한다. 제안된 방법은 시계열의 차원 축소과정에서 정보 손실을 최소화하여 시계열 분류의 성능을 향상시킨다.

• 대한수학회보
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• 제57권2호
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• pp.481-488
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• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• International Journal of Reliability and Applications
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• 제12권2호
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• pp.103-116
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• 2011

A series-parallel system with independent but non-identical components is considered. The expressions have been derived for the joint reliability importance (JRI) of m (${\geq}2$) components, chosen from a series-parallel system. JRIs of components of two different series-parallel systems are studied analytically and graphically.

• Korean Journal of Mathematics
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• 제19권4호
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• pp.465-480
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• 2011

B. C. Berndt established many identities about infinite series. In this paper, continuing his work, we find new identities about infinite series containing hyperbolic functions and trigonometric functions.