• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.3
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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.

• Journal for History of Mathematics
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• v.28 no.4
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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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• v.12 no.7
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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.

• The Korean Journal of Applied Statistics
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• v.36 no.5
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• pp.457-471
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• 2023

The monthly series is an aggregation of daily values. In the absence of observable daily data, calendar effects such as trading day and holidays are estimated using a RegARIMA model. However, if the daily series were observable, these calendar effects could be estimated directly from the daily series, potentially improving the seasonal adjustment of the monthly time series. In this paper, we propose a method to improve the seasonal adjustment of monthly time series by using calendar variation estimation based on daily time series. We apply this seasonal adjustment method to three monthly time series and compare our results with those obtained using X-13ARIMA-SEATS.

• The Journal of the Korea Contents Association
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• v.10 no.9
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• pp.97-106
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• 2010

Various time series representation methods have been suggested in order to process time series data efficiently and effectively. SAX is the representative time series representation method combining segmentation and discretization techniques, which has been successfully applied to the time series classification task. But SAX requires a large number of segments in order to represent the meaningful dynamic patterns of time series accurately, since it loss the dynamic property of time series in the course of smoothing the movement of time series. Therefore, this paper suggests a new time series representation method that combines PIPs detection and Persist discretization techniques. The suggested method represents the dynamic movement of high-diemensional time series in a lower dimensional space by detecting PIPs indicating the important inflection points of time series. And it determines the optimal discretizaton ranges by applying self-transition and marginal probabilities distributions to KL divergence measure. It minimizes the information loss in process of the dimensionality reduction. The suggested method enhances the performance of time series classification task by minimizing the information loss in the course of dimensionality reduction.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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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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• v.12 no.2
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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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• v.19 no.4
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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.