• Journal for History of Mathematics
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• v.30 no.6
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• pp.353-365
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• 2017

In general, there is summability among the mathematical tools that are the criterion for the convergence of infinite series. Many authors have studied on the summability of infinite series, the summability of Fourier series and the summability factors. Especially, $H{\ddot{u}}seyin$ Bor had published his important results on these topics from the beginning of 1980 to the end of 1990. In this paper, we investigate the minor academic genealogy of teachers and pupils from Fourier to $H{\ddot{u}}seyin$ Bor in section 2. We introduce the $H{\ddot{u}}seyin$ Bor's major results of the summability for infinite series from 1983 to 1997 in section 3. In conclusion, we summarize his research characteristics and significance on the summability of infinite series. Also, we present the diagrams of $H{\ddot{u}}seyin$ Bor's minor academic genealogy from Fourier to $H{\ddot{u}}seyin$ Bor and minor research lineage on the summability of infinite series.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.21 no.2
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• pp.182-187
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• 2008

This paper dealt with the detection algorithm of series arcing, which is a cause of electric fires in low-voltage wiring systems. To find the distinguished electrical features of series arc, we simulated series arcing by the arc generator specified in UL1699. An electric heater, an inverter-controlled vacuum cleaner, and a phase-controlled incandescent lamp were used as loads to generate series arcing. A high-pass filter (HPF) with the low cut-off frequency of 3 kHz at -3 dB was fabricated and applied to separate the series arc signal from the AC voltage source. The experiment showed that the high frequency signal generates randomly during series arcing, and the phase-controlled incandescent lamp produces high frequency pulses even in normal state. In this case, the magnitude, the width, and the randomness of high frequency signal should be analyzed to estimate series arcing precisely.

• Journal for History of Mathematics
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• v.30 no.1
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• pp.17-29
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• 2017

This paper is concerned with the $Ces{\grave{a}}ro$ summability of Fourier series. Many authors have studied on the summability of Fourier series up to now. Also, G. H. Hardy and J. E. Littlewood [5], Gaylord M. Merriman [18], L. S. Bosanquet [1], Fu Traing Wang [24] and others had studied the $Ces{\grave{a}}ro$ summability of Fourier series until the first half of the 20th century. In the section 2, we reintroduce Ernesto $Ces{\grave{a}}ro^{\prime}s$ life and the meaning of mathematical history for $Ces{\grave{a}}ro^{\prime}s$ work. In the section 3, we investigate the classical results of summability for Fourier series from 1897 to the mid-twentieth century. In conclusion, we restate the important classical results of several theorems of $Ces{\grave{a}}ro$ summability for Fourier series. Also, we present the research minor lineage of $Ces{\grave{a}}ro$ summability for Fourier series.

• Smart Structures and Systems
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• v.24 no.5
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• pp.587-595
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• 2019

Deformation measurement of large scale structures, such as the ground beds of high-rise buildings, tunnels, bridge, and railways, are important for insuring service quality and safety. The pose-relay videometrics method and displacement-relay videometrics method have already presented to measure the pose of non-intervisible objects and vertical subsidence of unstable areas, respectively. Both methods combine the cameras and cooperative markers to form the camera series networks. Based on these two networks, we propose two novel videometrics methods with closed-loop camera series network for deformation measurement of large scale structures. The closed-loop camera series network offers "closed-loop constraints" for the camera series network: the deformation of the reference points observed by different measurement stations is identical. The closed-loop constraints improve the measurement accuracy using camera series network. Furthermore, multiple closed-loops and the flexible combination of camera series network are introduced to facilitate more complex deformation measurement tasks. Simulated results show that the closed-loop constraints can enhance the measurement accuracy of camera series network effectively.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.707-719
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• 2018

Various time series representation methods have been proposed for efficient time series clustering and classification. Lin et al. (DMKD, 15, 107-144, 2007) proposed a symbolic aggregate approximation (SAX) method based on symbolic representations after approximating the original time series using piecewise local mean. The performance of SAX therefore depends heavily on how well the piecewise local averages approximate original time series features. SAX equally divides the entire series into an arbitrary number of segments; however, it is not sufficient to capture key features from complex, large-scale time series data. Therefore, this paper considers data-adaptive local constant approximation of the time series using the unbalanced Haar wavelet transformation. The proposed method is shown to outperforms SAX in many real-world data applications.

• KDI Journal of Economic Policy
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• v.34 no.3
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• pp.187-214
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• 2012

Korea's national income statistics have been compiled by the Bank of Korea since 1953. However, there is a break in the time series. The current time series (1970 onward) is based on the '1993 SNA (System of National Accounts)' suggested by the UN, and the previous time series (1953~1970) was based on the '1953 SNA'. The difference between the previous and current time series is 4.8% in 1970 when the two series overlap. The difference is even greater in terms of comparisons across industries. In addition, it has now become even more difficult to connect the current and the previous time series because, in 2009, the Bank of Korea introduced a chain weighted method for calculating the current time series (1970 onward). Under the chain weighted method, the time series underwent substantial modification; for instance, the economic growth rate during 1970~2005 is 0.9%p higher than the rate under the general method. This paper applies chain weighted values and the '1993 SNA' to the previous time series (1953~1970) by utilizing various national account manuals published by the UN and previous Korean input-output tables in order to calculate a long term time series from 1953 to 2010 based on the same criteria as the current time series (1970 onward). In the revised time series, it appears that 1953 GDP at current basic prices is 3.5% higher and the growth rate for the period of 1953~1970 is 1.5%p higher each year than under the previous time series. Under the revised time series the size of the Korean economy as of 2010 is 50-fold bigger than that of 1953. In terms of industries, manufacturing and SOC show significant expansion whereas the extent of that of the service industry is relatively small.

• Wind and Structures
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• v.6 no.2
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• pp.107-126
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• 2003

This paper describes a simple and practical approach through the application of Linear Stochastic Estimation (LSE) to reconstruct wind-induced pressure time series from the covariance matrix for structural load analyses on a low building roof. The main application of this work would be the reduction of the data storage requirements for the NIST aerodynamic database. The approach is based on the assumption that a random pressure field can be estimated as a linear combination of some other known pressure time series by truncating nonlinear terms of a Taylor series expansion. Covariances between pressure time series to be simulated and reference time series are used to calculate the estimation coefficients. The performance using different LSE schemes with selected reference time series is demonstrated by the reconstruction of structural load time series in a corner bay for three typical wind directions. It is shown that LSE can simulate structural load time series accurately, given a handful of reference pressure taps (or even a single tap). The performance of LSE depends on the choice of the reference time series, which should be determined by considering the balance between the accuracy, data-storage requirements and the complexity of the approach. The approach should only be used for the determination of structural loads, since individual reconstructed pressure time series (for local load analyses) will have larger errors associated with them.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.792-796
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• 2005

The methods of times series analysis have been recognized as important tools for assisting in solving problems related to the management of water resources. Especially, After more than 40 years the so-called Hurst effect remains an open problem in stochastic hydrology. Until now, its existence has been explained fly R/S analysis that roots in early work of the British hydrologist H.E. Hurst(1951). Today, the Hurst analysis is mostly used for the hydrological studies for memory and characteristics of time series and many methodologies have been developed for the analysis. So, there are many different techniques for the estimation of the Hurst exponent(H). However, the techniques can produce different characteristics for the persistence of a time series each other. We found that DFA is the most appropriate technique for the Hurst exponent estimation for both the shot term memory and long term memory. We analyze the SOI(Southern Oscillations Index) and 6 tree-ring series for USA sites by means of DFA and the BDS statistic is used for nonlinearity test of the series. From the results, we found that SOI series is nonlinear time series which has a long term memory of H=0.92. Contrary to earlier work of Rao(1999), all the tree- ring series are not random from our analysis. A certain tree ring series show a long term memory of H=0.97 and nonlinear property. Therefore, we can say that the SOI and tree-ring series may show long memory and nonlinearity.

• Journal of Korea Water Resources Association
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• v.42 no.4
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• pp.355-363
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• 2009

The purpose of this paper is to investigate the influence of noise on chaotic time series. We used two time series of Lorenz system and of Great Salt Lake's volume data which are well known as chaotic systems. This study investigated the attractors, correlation dimensions, and Close Returns Plots and Close Returns Histograms of two time series to investigate the influence of noise as increasing noise level. We performed Chi-square test to the relative frequency of Close Returns Histogram from Close Returns Plot for the investigation of stochastic process of chaotic time series as increasing noise level of time series. As the results, two time series were changed from chaotic to stochastic series as noise level is increased. Finally, we analyzed the effect of noise cancellation by using Simple Moving Average method. The results of applications of Simple Moving Average method to Lorenz and GSL time series showed that we could effectively cancel the noise. Then we could confirm the applicability of Simple Moving Average method to cancel the noise for the hydrologic time series having chaotic characteristics.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.338-341
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• 2003

Recently, the chaotic method is employed to forecast a near future of uncertain phenomena. This method makes it possible by restructuring an attractor of given time-series data in multi-dimensional space through Takens' embedding theory. However, many economical time-series data are not sufficiently chaotic. In other words, it is hard to forecast the future trend of such economical data on the basis of chaotic theory. In this paper, time-series data are divided into wave components using wavelet transform. It is shown that some divided components of time-series data show much more chaotic in the sense of correlation dimension than the original time-series data. The highly chaotic nature of the divided component enables us to precisely forecast the value or the movement of the time-series data in near future. The up and down movement of TOPICS value is shown so highly predicted by this method as 70％.