• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.3
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• pp.394-400
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• 2012

In this paper, charging modes of series resonant converter for a high voltage energy storage capacitor are compared in terms of charging time, peak resonant current, normalized peak resonant current and voltage in each operation mode. Operating principles of the full bridge series resonant converter with capacitor load are explained and analyzed in discontinuous and continuous operation mode. Based on the analysis and simulation result, $0.6{\omega}_r$ < ${\omega}_s$ < $0.75{\omega}_r$ and $1.3{\omega}_r$ < ${\omega}_s$ < $1.4{\omega}_r$ are evaluated to the best range of switching frequency for charging of an high voltage energy storage capacitor. 1.8 kJ/s SRC prototype is assembled with TI 28335 DSP controller and 40 kJ, 7 kV energy storage capacitor. Design rules based on the comparative analysis are verified by experiment.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.107-110
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• 1996

Usng the Pochhammer symbol $(\lambda)_n$ given by $$ (1.1) (\lambda)_n = {1, if n = 0 {\lambda(\lambda + 1) \cdots (\lambda + n - 1), if n \in N = {1, 2, 3, \ldots}, $$ we define a general double hypergeometric series by [3, pp.27] $$ (1.2) F_{q:s;\upsilon}^{p:r;u} [\alpha_1, \ldots, \alpha_p : \gamma_1, \ldots, \gamma_r; \lambda_1, \ldots, \lambda_u;_{x,y}][\beta_1, \ldots, \beta_q : \delta_1, \ldots, \delta_s; \mu_1, \ldots, \mu_v; ] = \sum_{l,m = 0}^{\infty} \frac {\prod_{j=1}^{q} (\beta_j)_{l+m} \prod_{j=1}^{s} (\delta_j)_l \prod_{j=1}^{v} (\mu_j)_m)}{\prod_{j=1}^{p} (\alpha_j)_{l+m} \prod_{j=1}^{r} (\gamma_j)_l \prod_{j=1}^{u} (\lambda_j)_m} \frac{l!}{x^l} \frac{m!}{y^m} $$ provided that the double series converges.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1079-1092
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• 2009

The purpose of this study is to investigate Newton's binomial theorem that was on epistemological basis of the emergent background and developmental course of infinite series and power series. Through this investigation, it will be examined how finding the approximate of square root of given numbers, the method of the inverse method of fluxions by Newton, and Gregory and Mercator series were developed in the course of history of mathematics. As the result of this study pedagogical analysis and discussion of the history of mathematics on Newton's binomial theorem will be presented.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.295-304
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• 2019

This article deals with threshold-asymmetric volatility models for over-dispersed and zero-inflated time series of count data. We introduce various threshold integer-valued autoregressive conditional heteroscedasticity (ARCH) models as incorporating over-dispersion and zero-inflation via conditional Poisson and negative binomial distributions. EM-algorithm is used to estimate parameters. The cholera data from Kolkata in India from 2006 to 2011 is analyzed as a real application. In order to construct the threshold-variable, both local constant mean which is time-varying and grand mean are adopted. It is noted via a data application that threshold model as an asymmetric version is useful in modelling count time series volatility.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.575-583
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• 2022

In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role. The aim of this research paper is to provide generalizations of Bailey's identity involving products of generalized hypergeometric series in the most general form. A few known, as well as new results, have also been obtained as special cases of our main findings.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.53-60
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• 2007

Conditionally heteroscedastic time series models such as GARCH processes have frequently provided useful approximations to the real aspects of financial time series. It is not uncommon that financial time series exhibits near non-stationary, say, integrated phenomenon. For stationary GARCH processes, a shock to the current conditional variance will be exponentially converging to zero and thus asymptotically negligible for the future conditional variance. However, for the case of integrated process, the effect will remain for a long time, i.e., we have a persistent effect of a current shock on the future observations. We are here concerned with providing empirical evidences of persistent GARCH(1,1) for various fifteen domestic financial time series including KOSPI, KOSDAQ and won-dollar exchange rate. To this end, kurtosis and Integrated-GARCH(1,1) fits are reported for each data.

• Journal of the Society of Naval Architects of Korea
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• v.49 no.5
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• pp.416-424
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• 2012

The MAU series has been usually used for the fishing vessel's propeller, which has been improved in consideration of the efficiency as well as the cavitation point of view in Pusan National University. The high efficiency standard series propeller(KF series) has been applied to the design of 52ton class fishing vessel's propeller in the previous study. The experimental study for the performance of the design propellers called KF series for 52 ton class fishing vessel has been conducted with five cases in Korea Ocean Research & Development Institute towing tank. The model tests have been carried out at different pitch ratio and expanded area ratio in comparison with the standard propeller to make the series chart. The KF series chart and the formula for performance expression have been completed on the basis of the experiment result.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.743-751
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• 2007

The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.843-850
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• 1999

The object of this paper is to give certain classes of pre-sumably new product formulas involving the generalized hypergeo-metric series by modifying the elementary method suggested by Bai-ley.