• Korean Journal of Hydrosciences
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• v.4
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• pp.51-63
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• 1993

This study is to verify the applicability of statistical models in predicting flood frequency at the stage gaging stations of which the flow is under natural condition in the Han River basin. The results of the study show that the statistical flood frequency models were proven to be fairly reasonable to apply in practice, and also were compared with sampling variance to calibrate the statistical efficiency of the estimators of the T year floods Q(T) by two different flood frequency models. As a result, it was showed that for return periods greater than about T = 10 years the annual exceedance series estimators of Q(T) has smaller sampling variance than the annual maximum series estimators. It was showed that for the range of return periods the partial duration series estimators of !(T) has smaller sampling variance than the annual maximum series estimate only if the POT model contains at least 2N(N : record length) items or more in order to estimate Q(T) more efficiently than the ANNMAX model.

• 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.

• East Asian mathematical journal
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• v.33 no.5
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• pp.527-531
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• 2017

We aim to prove a known summation formula for the series $_4F_3(1)$ by mainly using a similar method as in [2], which is different from that in [3]. The method of proof here as well as that in [2] is potentially useful in getting some other summation formulas for $_pF_q$.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.55-107
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k,\;q=e^{{\pi}i\tau}$. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, $\frac{q^{1/8}}{1}+\frac{-q}{1+q}+\frac{-q^2}{1+q^2}+\cdots$ ([1]) is transcendental.

• Water for future
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• v.25 no.2
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• pp.89-97
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• 1992

This study is to verify the applicability of statistical models for predicting flood frequency at the stage gaging stations selected by considering whether the flow is natural condition in the Han River basin. From the result of verification, this statistical flood frequency models showed that is fairly reasonable to apply in practice, and also were compared with sampling variance to calibrate the statistical dfficiency of the estimate of the T year flood Q(T) by two different flood frequency models. As a result, it was showed that for return periods greater than about T=10 years the annual exceedence series estimate of Q(T) has smaller sampling variance than the annual maximum series estimate. It was showed that for the range of return periods the partial duration series estimate of Q(T) has smaller sampling varianed than the annual maximum series estimate only if the POT model contains at least 2N(N:record length)items or more in order to estimate Q(T) more efficiently than the ANNMAX model.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.759-771
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• 2020

In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for q-Hermite based Apostol type Frobenius-Genocchi polynomials of order α associated with q-Apostol Bernoulli polynomials, q-Apostol Euler polynomials and q-Apostol Genocchi polynomials.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.395-403
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• 2005

The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series $series\;_2{\phi}_1$ corresponding to Gauss's contiguous relations for the hypergeometric series $series\;_2F_1$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known q-analogue of Kummer's theorem.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.864-865
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• 2008

This paper deals with d-q axis inductance measurements of IPMSM considering core loss at low speed. d-q axis inductance measurements generally are conducted at rated speed and parallel core loss model can be used to exclude core loss effects on inductances. Core loss is generally modeled parallel to input terminal of d-q axis equivalent circuit. Therefore, the effect of core loss on inductance calculation can be varied by core loss modeling. In this paper, d-q axis inductance is calculated parallel and series core loss modeling. Calculated inductances are compared to FEA results and it is concluded that series core loss modeling is more closed to FEA results at low speed.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.569-575
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• 2006

We aim mainly at presenting two generalizations of the well-known Gauss's second summation theorem and Bailey's formula for the series $_2F_1(1/2)$. An interesting transformation formula for $_pF_q$ is obtained by combining our two main results. Relevant connections of some special cases of our main results with those given here or elsewhere are also pointed out.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.51 no.6
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• pp.321-329
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• 2002

A protection scheme for series active compensator is presented and analyzed in this paper. The proposed series active compensator operated as a high impedance K($\Omega$) to the fundamentals when short-circuit faults occur in the power distribution system, and two control strategies are proposed in this paper The first is the method by detecting the fundamental source current through the p-q theory, the second is the method by detecting the fundamental component of load current in Synchronous Reference Frame(SRF). When the short-circuit faults occur in the power distribution system, the proposed scheme can protect the series active compensator without additional protection circuits. The validity of the Proposed Protection scheme was investigated through experimental results.