• Journal of Electrical Engineering and information Science
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• 제2권6호
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• pp.123-130
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• 1997

This paper presents a generalized expansion method for calculating reliability index in power generation systems. This generalized expansion with a gamma distribution is a very useful tool for the approximation of capacity outage probability distribution of generation system. The well-known Gram-Charlier expansion and Legendre series are also studied in this paper to be compared with this generalized expansion using a sample system IEEE-RTS(Reliability Test System). The results show that the generalized expansion with a composite of gamma distributions is more accurate and stable than Gram-Charlier expansion and Legendre series as addition of the terms to be expanded.

• 대한수학회보
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• 제52권4호
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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 "$Per_{\beta}(\frac{P}{Q})=Per_{\beta}(\frac{1}{Q})$".

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.31-35
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• 2022

In the note, by virtue of Abel's theorem and Abel's limit theorem in the theory of power series, the author provides three proofs for a sum of an alternating series involving central binomial numbers.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.285-288
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• 1998

A least-squares identification method is studied that estimates a finite number of coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions, We will expand and generalize the orthogonal functions as basis functions for dynamical system representations. To this end, use is made of balanced realizations as inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. We show that the Laplace transform of the expansion for some sets$\Psi_{\kappa}(Z)$ is equivalent to a series expansion . Techniques based on this result are presented for obtaining the coefficients $c_{n}$ as those of a series. One of their important properties is that, if chosen properly, they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only a few coefficients to be estimated. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained.

• 대한수학회보
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• 제49권1호
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• pp.127-133
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• 2012

It is well known that if the ${\beta}$-expansion of any nonnegative integer is finite, then ${\beta}$ is a Pisot or Salem number. We prove here that $\mathbb{F}_q((x^{-1}))$, the ${\beta}$-expansion of the polynomial part of ${\beta}$ is finite if and only if ${\beta}$ is a Pisot series. Consequently we give an other proof of Scheiche theorem about finiteness property in $\mathbb{F}_q((x^{-1}))$. Finally we show that if the base ${\beta}$ is a Pisot series, then there is a bound of the length of the fractional part of ${\beta}$-expansion of any polynomial P in $\mathbb{F}_q[x]$.

• 대한수학회보
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• 제53권3호
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• pp.699-709
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• 2016

Our paper is devoted to the study of certain diophantine equations on the ring of polynomials over a finite field, which are intimately related to algebraic formal power series which have partial quotients of unbounded degree in their continued fraction expansion. In particular it is shown that there are Pisot formal power series with degree greater than 2, having infinitely many large partial quotients in their simple continued fraction expansions. This generalizes an earlier result of Baum and Sweet for algebraic formal power series.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.26.1-26
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• 2001

In this paper, we will expand and generalize the orthogonal functions as basis functions for dynamical system representations. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown row we can exploit these generalized basis functions to increase the speed of convergence in a series expansion. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained. And so we will present the influence of noises to use Kautz function on the identification accuracy.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.591-600
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• 2020

This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let L_p,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂ_p, |α|_p ≤ 1, we give a power series expansion of L_p,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂ_p with |t|_p < 1. Some further properties for L_p,E(s, t; χ) has also been shown.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 정기총회 및 창립40주년기념 학술대회 학회본부
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• pp.457-462
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• 1987

This paper deals with the PWM controlled active AC power filter. A new PWM control method from the viewpoint of speed and simplicity is proposed. And a microprocessor-based controller is used to realize the active AC power filter. The existing PWM control methods are primarily based on Fourier series expansion and these methods need FFT calculation and solving nonlinear harmonic equations, which are heavy burden to real-time control. The proposed method is based upon generalized pulse series expansion and needs only definite integrals of harmonic signal. So, computational effort can be reduced by a large margin. The digital circuit using 16-bit microprocessor is designed to implement the actual active power filler.

• Kyungpook Mathematical Journal
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• 제52권3호
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• pp.347-357
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• 2012

When Newton's method, or Halley's method is used to approximate the pth root of 1-z, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case, using an interesting link to Chebyshev's polynomials. It allows the determination of the sign of the coefficients of the power series expansion of these rational functions. This answers positively the square root case of a proposed conjecture by Guo(2010).