• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.95-108
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• 2020

The aim of this paper is to show that for the one-sided symbolic system, there exist an uncountable distributively chaotic set contained in the set of irregularly recurrent points and an uncountable distributively chaotic set in a sequence contained in the set of proper positive upper Banach density recurrent points.

• Korean Journal of Agricultural Science
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• v.46 no.1
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• pp.67-78
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• 2019

The purpose of this study was to predict the water quality using the RNN (recurrent neutral network) and LSTM (long short-term memory). These are advanced forms of machine learning algorithms that are better suited for time series learning compared to artificial neural networks; however, they have not been investigated before for water quality prediction. Three water quality indexes, the BOD (biochemical oxygen demand), COD (chemical oxygen demand), and SS (suspended solids) are predicted by the RNN and LSTM. TensorFlow, an open source library developed by Google, was used to implement the machine learning algorithm. The Okcheon observation point in the Geum River basin in the Republic of Korea was selected as the target point for the prediction of the water quality. Ten years of daily observed meteorological (daily temperature and daily wind speed) and hydrological (water level and flow discharge) data were used as the inputs, and irregularly observed water quality (BOD, COD, and SS) data were used as the learning materials. The irregularly observed water quality data were converted into daily data with the linear interpolation method. The water quality after one day was predicted by the machine learning algorithm, and it was found that a water quality prediction is possible with high accuracy compared to existing physical modeling results in the prediction of the BOD, COD, and SS, which are very non-linear. The sequence length and iteration were changed to compare the performances of the algorithms.