• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1047-1057
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• 2015

In [6], it is proved that the lengths of periods occurring in the ${\beta}$-expansion of a rational series r noted by $Per_{\beta}(r)$ depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic ${\beta}$-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if $r=\frac{P}{Q}$ is written in reduced form with |P| < |Q|, we will generalize the curious property "$Per_{\beta}(\frac{P}{Q})=Per_{\beta}(\frac{1}{Q})$".

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1003-1015
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• 2005

Klein proved that polynomial rings over nil rings of bounded index are also nil of bounded index; while Puczylowski and Smoktunowicz described the nilradical of a power series ring with an indeterminate. We extend these results to those with any set of commuting indeterminates. We also study prime radicals of power series rings over some class of rings containing the case of bounded index, finding some examples which elaborate our arguments; and we prove that R is a PI ring of bounded index then the power series ring R[[X]], with X any set of indeterminates over R, is also a PI ring of bounded index, obtaining the Klein's result for polynomial rings as a corollary.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.5
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• pp.233-240
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• 2001

This paper presents a time series prediction method using a fuzzy rule-based system. Extracting fuzzy rules by performing a simple one-pass operation on the training data is quite attractive because it is easy to understand, verify, and extend. The simplest method is probably to relate an estimate, x(n+k), with past data such as x(n), x(n-1), ..x(n-m), where k and m are prefixed positive integers. The relation is represented by fuzzy if-then rules, where the past data stand for premise part and the predicted value for consequence part. However, a serious problem of the method is that it cannot handle nonstationary data whose long-term mean is varying. To cope with this, a new training method is proposed, which utilizes the difference of consecutive data in a time series. In this paper, typical previous works relating time series prediction are briefly surveyed and a new method is proposed to overcome the difficulty of prediction nonstationary data. Finally, computer simulations are illustrated to show the improved results for various time series.

• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.453-458
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• 2006

It is well known fact for the iid data that the limiting standard errors of sample autocorrelations are all unity for all time lags and they are asymptotically independent for different lags (Brockwell and Davis, 1991). It is also usual practice in time series modeling that this fact continues to be valid for white noise series which is a sequence of uncorrelated random variables. This paper contradicts this usual practice for white noise. We consider a sequence of martingale differences which belongs to white noise time series and derive exact joint asymptotic distributions of sample autocorrelations. Some implications of the result are illustrated for conditionally heteroscedastic time series.

• Journal of Environmental Science International
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• v.8 no.3
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• pp.349-354
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• 1999

The transfer function was introduced to establish the prediction method for the DO concentration at the intaking point of Kongju Water Works System. In the mose cases we analyze a single time series without explicitly using information contained in the related time series. In many forecasting situations, other events will systematically influence the series to be forecasted(the dependent variables), and therefore, there is need to go beyond a univariate forecasting model. Thus, we must bulid a forecasting model that incorporates more than one time series and introduces explicitly the dynamic characteristics of the system. Such a model is called a multiple time series model or transfer function model. The purpose of this study is to develop the stochastic stream water quality model for the intaking station of Kongju city waterworks in Keum river system. The performance of the multiplicative ARIMA model and the transfer function noise model were examined through comparisons between the historical and generated monthly dissolved oxygen series. The result reveal that the transfer function noise model lead to the improved accuracy.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.219-227
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• 2007

The time series models have been used to analyze and predict the network traffic. In this paper, we compare the performance of the time series models for prediction of network traffic. The feasibility study showed that a class of nonlinear time series models can be outperformed than the linear time series models to predict the network traffic.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.91-109
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• 1995

The rate of convergence to a random variable S for an almost certainly convergent series $S_n = \sum^n_{j=1} X_j$ of independent random variables is studied in this paper. More specifically, when $S_n$ converges to S almost certainly, the tail series $T_n = \sum^{\infty}_{j=n} X_j$ is a well-defined sequence of random variable with $T_n \to 0$ a.c. Various sets of conditions are provided so that for a given numerical sequence $0 < b_n = o(1)$, the tail series strong law of large numbers $b^{-1}_n T_n \to 0$ a.c. holds. Moreover, these results are specialized to the case of the weighted i.i.d. random varialbes. Finally, example are provided and an open problem is posed.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.657-666
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• 2002

ThE Gibbs' phenomenon in the classical Fourier series is well-known. It is closely related with the kernel of the partial sum of the series. In fact, the Dirichlet kernel of the courier series is not positive. The poisson kernel of Cesaro summability is positive. As the consequence of the positiveness, the partial sum of Cesaro summability does not exhibit the Gibbs' phenomenon. Most kernels associated with wavelet expansions are not positive. So wavelet series is not free from the Gibbs' phenomenon. Because of the excessive oscillation of wavelets, we can not follow the techniques of the courier series to get rid of the unwanted quirk. Here we make a positive kernel For Meyer wavelets and as the result the associated summability method does not exhibit Gibbs' phenomenon for the corresponding series .

• Journal for History of Mathematics
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• v.23 no.1
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• pp.53-66
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• 2010

This study concerns with partial sum of Fourier series, Fourier coefficients and the $L^1$-convergence of Fourier series. First, we introduce the $L^1$-convergence results. We consider equivalence relations of the partial sum of Fourier series from the early 20th century until the middle of. Second, we investigate the minor lineage of $L^1$-convergence theorem from W. H. Young to G. A. Fomin. Finally, we compare and reinterpret the $L^1$-convergence theorems.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.73-80
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• 2007

Cointegration(together with VARMA(vector ARMA)) has been proven to be useful for analyzing multivariate non-stationary data in the field of financial time series. It provides a linear combination (which turns out to be stationary series) of non-stationary component series. This linear combination equation is referred to as long term equilibrium between the component series. We consider two sets of Korean bivariate financial time series and then illustrate cointegration analysis. Specifically estimated VAR(vector AR) and VECM(vector error correction model) are obtained and CV(cointegrating vector) is found for each data sets.