• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.489-493
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• 1989

In this paper a new approach to adaptive control using a combination of both direct and indirect methods has been proposed. Based on the estimates of the plant parameters and the current values of the control parameters, closed-loop estimation errors .epsilon.$_{\theta}$(t) and .epsilon.$_{k}$(t) are defined. These in turn are used in the adaptive laws for updating both identification as well as control parameters. The global uniform stability of the overall system is shown by constructing a Lyapunov function.n.

• 한국수학교육학회지시리즈A:수학교육
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• 제15권1호
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• pp.18-21
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• 1976

Lagrange proved that any positive integer is the sum of at most four squares. We consider a elliptic function f$_{\alpha}$(v│$\tau$) of periods 1. $\tau$ derived from $\theta$-functions. From the important number-theoretical interpretation (equation omitted) we obtain $A_4$(n) the number of representations entations of n as a sum of 4-squares.m of 4-squares.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 2005년도 추계학술발표회
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• pp.121-122
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• 2005

• 대한수학회보
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• 제46권1호
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• pp.1-10
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• 2009

Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.

• 대한수학회지
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• 제59권5호
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• pp.1015-1045
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• 2022

Zagier introduced the term "strange identity" to describe an asymptotic relation between a certain q-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.

• 대한수학회지
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• 제59권5호
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• pp.945-962
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• 2022

For a positive integer ℓ, $\bar{A}_{\ell}(n)$ denotes the number of over-partitions of n into parts not divisible by ℓ. In this article, we find certain Ramanujan-type congruences for $\bar{A}_{r{\ell}}(n)$, when r ∈ {8, 9} and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for $\bar{A}_{13}(n)$ by using an algorithm developed by Radu and Sellers [15].

• 대한수학회보
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• 제60권1호
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• pp.237-255
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• 2023

In this article, we find bases for the spaces of modular forms $M_2({\Gamma}_0(88),\;({\frac{d}{\cdot}}))$ for d = 1, 8, 44 and 88. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients 1, 2, 11 and 22.

• 한국자기학회지
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• 제6권3호
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• pp.158-164
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• 1996

동시진공증착으로 제조한 Tb/Co 조성변조 다층박막의 자기적 성질 및 광자기적 성질을 Tb의 두께 및 Tb/Co 각 층의 두께 비에 대하여 연구하였으며 열처리시 자기적 거동의 변화를 분석하였다. Tb의 두께가 $12{\AA}$일 때가 가장 큰 범위에서 수직자기이방성을 보였고, 최고 $6.52{\times}10^{6}erg/cc$의 수직자기이방성 에너지 값을 얻었다. Tb의 두께가 $12{\AA}$에서 최대 수직자기이방성을 보이는 것은 Tb/Co 계면에서의 Tb-Co이종 원자쌍뿐만 아니라 Tb-Tb, Co-Co 동종 원자쌍도 수직자기이방성에 기여하기 때문으로 사려된다. Kerr 회전각$({\theta}_k)$은 수직자기이방성 에너지$(K_{u})$와 비례, 평균 스핀분산각$(\alpha)$과는 반비례하는 거동을 보였으며 Tb두께 $12{\AA}$, 두께비 1.55에서 최대 Kerr 회전각 $0.28^{\circ}$를 얻었다. 열처리시 나타나는 비정상적인 이력곡선은 Tb층의 우선적인 산화로 Tb의 유효조성이 감소하여 조성이 보상점 근처로 이동하게 되어 Co층과의 보자력 차이가 커져서 나타난다.

• 한국안광학회지
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• 제11권3호
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• pp.225-229
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• 2006

강자성체인 철과 니켈의 박막에서 전류와 자기장이 이루는 각도의 변화에 따른 자기저항의 변화를 관찰하였다. 경사각에 따른 PMR과 NMR의 크기가 같은 ${\phi}_{mix}$의 변화는 전류에 수직한 자기장의 성분과 평행한 자기장의 성분이 같게 되는 각도에서 자기저항 루프의 역전이 되는 것을 이용하면 ${\phi}_{mix}=tan^{-1}(1+tan{\theta})$와 같이 구해진다. 위 관계식은 실험치와 잘 일치함을 보여준다. 반면에 철박막의 경우에는 니켈박막과 자화축이 다르게 나타나서 ${\phi}_{mix}$가 위 식으로 주어진 관계와 일치하지 않는다.

• 대한기계학회논문집A
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• 제26권2호
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• pp.380-386
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• 2002

Damage behaviors induced in silicon carbide by an impact of particle having different material and size were investigated. Especially, the influence of the impact velocity of particle on the cone crack shape developed was mainly discussed. The damage induced by spherical impact was different depending on the material and size of particles. Ring cracks on the surface of specimen were multiplied by increasing the impact velocity of particle. The steel particle impact produced larger ring cracks than that of SiC particle. In the case of high velocity impact of SiC particle, radial cracks were produced due to the inelastic deformation at the impact site. In the case of the larger particle impact, the damage morphology developed was similar to the case of smaller particle one, but a percussion cone was farmed from the back surface of specimen when the impact velocity exceeded a critical value. The zenithal angle of cone cracks developed into SiC material decreased monotonically with increasing of the particle impact velocity. The size and material of particle influenced more or less on the extent of cone crack shape. An empirical equation, $\theta$= $\theta$$\sub$st/, v$\sub$p/(90-$\theta$$\sub$st/)/500 R$\^$0.3/($\rho$$_1$/$\rho$$_2$)$\^$$\frac{1}{2}$/, was obtained as a function of impact velocity of the particle, based on the quasi-static zenithal angle of cone crack. It is expected that the empirical equation will be helpful to the computational simulation of residual strength in ceramic components damaged by the particle impact.