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ITERATED EULER'S INTEGRALS AND NORMALIZED MULTIPLE SINE FUNCTIONS
International Journal of Mathematics, 2009We introduce iterated Euler's integrals, and we give expressions using zeta functions. Moreover, we prove that normalized multiple sine functions are expressed via iterated Euler's integrals. Then, we show basic properties of multiple sine functions from these results containing Kummer type formula.
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Central values of generalized multiple sine functions
Forum Mathematicum, 2009For \(\text{Re}\,z>0\) and \(\text{Re}\,s>r\in \mathbb{N}\), the multiple Hurwitz zeta function \(\zeta_r(s, z, \underline{\omega})\), \(\underline{\omega}=(\omega_1, \dots , \omega_r)\), is defined by \[ \zeta_r(s, z, \underline{\omega})=\sum_{n_1, \dots , n_r}^\infty (n_1\omega_1+\cdots +n_r\omega_r+z)^{-s}, \] and by analytic continuation elsewhere.
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The 2014 2nd International Conference on Systems and Informatics (ICSAI 2014), 2014
The restoration of missing data is an important concern for data analysis. In this paper, an algorithmically innovative model termed multiple sine function decomposition (MSFD) model is proposed and developed for restoring the missing data about monthly average temperature (MAT) of Guangzhou, which is a representative major city of China.
Yunong Zhang +4 more
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The restoration of missing data is an important concern for data analysis. In this paper, an algorithmically innovative model termed multiple sine function decomposition (MSFD) model is proposed and developed for restoring the missing data about monthly average temperature (MAT) of Guangzhou, which is a representative major city of China.
Yunong Zhang +4 more
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2018 International Conference on Machine Learning and Cybernetics (ICMLC), 2018
With the development of economy, the stock market of China is booming rapidly. In recent years, a method called multiple sine functions extraction (MSFE) has been proposed, e.g., to predict the potential stock market. In this paper, we use the MSFE to roughly forecast the peak-point of Chinese stock market, in which the inputs are stock data of ...
Yunong Zhang +4 more
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With the development of economy, the stock market of China is booming rapidly. In recent years, a method called multiple sine functions extraction (MSFE) has been proposed, e.g., to predict the potential stock market. In this paper, we use the MSFE to roughly forecast the peak-point of Chinese stock market, in which the inputs are stock data of ...
Yunong Zhang +4 more
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2017 36th Chinese Control Conference (CCC), 2017
Over the past 100 years, especially in the recent 20 years, the global average surface temperature has increased significantly, and global warming has become an important issue of global concern. In this paper, multiple sine functions decomposition (MSFD) method is presented to forecast the colder-winter years of Guangzhou.
Yunong Zhang +4 more
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Over the past 100 years, especially in the recent 20 years, the global average surface temperature has increased significantly, and global warming has become an important issue of global concern. In this paper, multiple sine functions decomposition (MSFD) method is presented to forecast the colder-winter years of Guangzhou.
Yunong Zhang +4 more
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2014 International Joint Conference on Neural Networks (IJCNN), 2014
In this paper, a novel weighted-combination-of-components (WCC) method Is proposed for modeling and forecasting trend and seasonal time series, and such a method is based on decomposition model which regards the time series as the weighted combination of trend, seasonality and other components.
Wenchao Lao +4 more
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In this paper, a novel weighted-combination-of-components (WCC) method Is proposed for modeling and forecasting trend and seasonal time series, and such a method is based on decomposition model which regards the time series as the weighted combination of trend, seasonality and other components.
Wenchao Lao +4 more
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Moscow University Mathematics Bulletin, 2007
Functions being sums of sine series with multiple-monotone coefficients are considered. Upper and lower estimates for norms of such functions via their coefficients are presented in the spaces Lp (0 < p < ∞).
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Functions being sums of sine series with multiple-monotone coefficients are considered. Upper and lower estimates for norms of such functions via their coefficients are presented in the spaces Lp (0 < p < ∞).
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Moscow University Mathematics Bulletin, 2013
In this paper we prove lower and upper bounds for mixed norms of functions, i.e., sums of double sine series with multiple-monotone coefficients.
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In this paper we prove lower and upper bounds for mixed norms of functions, i.e., sums of double sine series with multiple-monotone coefficients.
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Moscow University Mathematics Bulletin, 2014
Lower and upper bounds for norms of mixed functions being sums of series in products of cosine and sine functions are proved in the paper.
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Lower and upper bounds for norms of mixed functions being sums of series in products of cosine and sine functions are proved in the paper.
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