• Industrial Engineering and Management Systems
• /
• 제14권3호
• /
• pp.312-317
• /
• 2015

The dynamic system approach in time series has been used in many real problems. Based on Taken's embedding theorem, we can build the predictive function where input is the time delay coordinates vector which consists of the lagged values of the observed series and output is the future values of the observed series. Although the time delay coordinates vector from multivariate time series brings more information than the one from univariate time series, it can exhibit statistical redundancy which disturbs the performance of the prediction function. We apply dimension reduction techniques to solve this problem and analyze the effect of this approach for prediction. Our experiment uses delayed Lorenz series; least squares support vector regression approximates the predictive function. The result shows that linearly preserving projection improves the prediction performance.

• 호남수학학술지
• /
• 제38권3호
• /
• pp.479-494
• /
• 2016

In this paper, using a transformation formula for a certain series which comes from the generalized non-analytic Eisenstein series, we obtained some infinite series identities which contain Ramanujan's formula and author's previous results.

• 호남수학학술지
• /
• 제34권3호
• /
• pp.391-401
• /
• 2012

B. C. Berndt has found a transformation formula for a large class of functions, which comes from a transformation formula for a more general class of Eisenstein series. In this paper, using his formula which is 'twisted' by change of variables, we find a class of infinite series identities.

• Korean Journal of Mathematics
• /
• 제21권3호
• /
• pp.285-292
• /
• 2013

B. C. Berndt computed the Fourier series of a class of generalized Eisenstein series, which gives an analytic continuation to the generalized Eisenstein series. In this paper, continuing his work, we consider generalized non-holomorphic Eisenstein series and give an analytic continuation to the $s$-plane.

• Korean Journal of Mathematics
• /
• 제20권4호
• /
• pp.451-461
• /
• 2012

B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.

• East Asian mathematical journal
• /
• 제39권3호
• /
• pp.299-303
• /
• 2023

The aim of this note is to provide three derivations of the well-known Gregory-Leibniz series for π via a hypergeometric series approach.

• 대한수학회논문집
• /
• 제30권2호
• /
• pp.73-79
• /
• 2015

Todd series are associated to maximal non-degenerate lattice cones. The coefficients of Todd series of a particular class of lattice cones are closely related to generalized Dedekind sums of higher dimension. We generalize this construction and obtain an explicit formula for coefficients of the Todd series. It turns out that every maximal non-degenerate lattice cone, hence the associated Todd series can be obtained in this way.

• 대한수학회지
• /
• 제42권4호
• /
• pp.695-708
• /
• 2005

Certain observations about formal Dirichlet series whose coefficients are arithmetic functions are made. These include for example algebraic independence and representation as infinite series of logarithms.

• Journal of Radiation Protection and Research
• /
• 제30권4호
• /
• pp.161-165
• /
• 2005

The gamma-ray dose rates in air at 233 locations in Korea have been determined. The contribution to the gamma-ray dose rates in air due to the presence of $^{232}Th-series,\;^{238}U-series\;and\;^{40}K$ is as follows: 47.3% $(36\;nGyh^{-1})\;^{232}Th-series$ 14.5% $(11\;nGyh^{-1})\;^{238}U-series$ and 38.2% $(29\;nGyh^{-1})\;^{40}K$. The mean gamma-ray dose rate theoretically derived from $^{232}Th-series,\;^{238}U-series\;and\;^{40}K\;was\;76{\pm}17\;nGyh^{-1}$. This corresponds to an annual effective dose of $410\;{\mu}Sv$ and an annual collective dose of 18900 person-Sv for all provinces under study. The results have been compared with other global radiation dose.

• Journal of applied mathematics & informatics
• /
• 제31권1_2호
• /
• pp.263-276
• /
• 2013

We discuss the effects of the ${\delta}^2$ and Lubkin acceleration methods on the partial sums of Fourier Series. We construct continuous, even H$\ddot{o}$lder continuous functions, for which these acceleration methods fail to give convergence. The constructed functions include some interesting trigonometric series whose properties were investigated by Hardy and Littlewood.