• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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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.

• The Mathematical Education
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• v.15 no.1
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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.

• Proceedings of the Korean Nuclear Society Conference
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• 2005.10a
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• pp.121-122
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• 2005

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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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].

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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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.

• Journal of the Korean Magnetics Society
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• v.6 no.3
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• pp.158-164
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• 1996

The magnetic and magneto-optical properties of the Tb/Co multilayers as a function of the layer thickness and the ratio of Tb/Co thicknesses were studied. When the thickness of Tb layer was $12{\AA}$, the maximum perpendicular anisotropy energy and the maximum thickness ratio which displays the perpendicular anisotropy were obtained. This result indicated that the Tb-Tb and Co-Co pairs as well as the Tb-Co pairs contribute to the perpendicular anisotropy. The Kerr rotation angle, $({\theta}_k)$ was proportional to the perpendicular anisotropy energy and was inversely proportional to the average spin dispersion angle, $(\alpha)$. The maximum $({\theta}_k)$ of $0.28^{\circ}$ was obtained in the film of $12{\AA}$ Tb and the thickness ratio of 1.55. The abnormal hysteresis loops were appeared during the aging treatment because the coercivity difference between the Co layer and the Tb layer was increased by the preferential oxidation of Tb.

• Journal of Korean Ophthalmic Optics Society
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• v.11 no.3
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• pp.225-229
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• 2006

In our angle configuration, several peculiar characteristic behaviors of MR could be observed, the mixing of positive MR(PMR) and negative MR(NMR) in the inclined sample was observed. The complete mixing angle, ${\phi}_{mix}$ as a function of inclination angle, ${\theta}$ was observed to fit well to the relation of ${\phi}_{mix}=tan^{-1}(1+tan{\theta})$ in nickel films. The above theoretical relation was obtained by decomposing the magnetic field into the components parallel and perpendicular to the current flow and identifying ${\phi}_{mix}$ as the angle satisfying that the above two components of magnetic field were identical. We also observed that the data of ${\phi}_{mix}$ did not satisfy the above theoretical relation in the iron film. This was explained by the fact that the growth direction in the iron film was an intermediate direction of magnetization, while the growth direction in the nickel film was an easy axis of magnetization.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.2
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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.