• Journal of the Korean Society of Manufacturing Process Engineers
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• v.4 no.1
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• pp.43-48
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• 2005

This paper is described about the technique of ultra-precision machining for an aerospace aspheric mirror. The reflection mirror system generates parallel beams inside a thermal vacuum chamber. A 200mm diameter aspheric mirror was fabricated by SPDTM. Aluminum alloy as mirror substrates is known to be easily machined, but not polishable due to its ductility. Aspheric large reflector without a polishing process, the surface roughness of 10nm Ra, and the form error of ${\lambda}/2$ (${\lambda}$=632.8nm) for reference curved surface 200mm has been required. The purpose of this research is to find the optimum machining conditions for cutting reflector using Al6061-T651 and apply the SPDTM technique to the manufacturing of ultra precision optical components of Al-alloy aspheric reflector.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-256
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• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

• Journal of the Korean Statistical Society
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• v.8 no.1
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• pp.65-83
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• 1979

The general description concerning the multi-line systems with the switching rules have been presented by Ahn. In this paper we derive some steady state probabilities for three mainly different kinds of systems. We assume that all of the systems are to have poisson input with the finite mean $1/\lambda$ and two servers with the negative exponentional service distribution where each has its own mean $1/u_i$. The notations follow the paper (Ahn, 1979).

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.749-759
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• 2005

We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1829-1832
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• 2004

Closed loop stability of Extended Dynamic Matrix Control (EDMC) is investigated for limited sampling time. Linear approximation of the sensitivity functions is employed in the derivation of the stability condition. It is shown that the closed loop system will be stable if the control moves suppression coefficient ${\lambda}$ is taken arbitrarily large. Special cases such as M=P=1 and M=1, P>1 are discussed in more details.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.4
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• pp.54-61
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• 1997

In this paper, a new holographic display system that can in real-time reconstruct the complex hologram without the bias and the conjugate image, which is obtained form the modified triangular interferometer, is presented. The proposed system is made of adding liquid crystal displays(LCDs), a $\lambda$/2 wave plate, and a polarizing beam splitter to the conventional mach-zehnder interferontric configuration. We demonstrate through theoretical analysis and experiment that real-time image reconstruction from the complex hologram is possible using the proposed system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.307-312
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• 1996

A torsional vibration analysis of a multi-stage reduction gear box connected to a gas turbine system is presented. For a free vibration analysis the Modified Hibner Branch Method, so called "Blank Matrix Method", and the .lambda.-Matrix Method are used in the modeling and the eigenvalue solution, respectively. Also, a short circuit forced analysis of the system is performed, utilizing the energy method modeling. It is shown that the results of the free vibration analysis have the same tendency as those of the short circuit analysis. analysis.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.173-179
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• 2018

In this paper, we investigate the stability of positive weak solution for the singular p-Laplacian nonlinear system $-div[{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u]+m(x){\mid}u{\mid}^{p-2}u={\lambda}{\mid}x{\mid}^{-(a+1)p+c}b(x)f(u)$ in ${\Omega}$, Bu = 0 on ${\partial}{\Omega}$, where ${\Omega}{\subset}R^n$ is a bounded domain with smooth boundary $Bu={\delta}h(x)u+(1-{\delta})\frac{{\partial}u}{{\partial}n}$ where ${\delta}{\in}[0,1]$, $h:{\partial}{\Omega}{\rightarrow}R^+$ with h = 1 when ${\delta}=1$, $0{\in}{\Omega}$, 1 < p < n, 0 ${\leq}$ a < ${\frac{n-p}{p}}$, m(x) is a weight function, the continuous function $b(x):{\Omega}{\rightarrow}R$ satisfies either b(x) > 0 or b(x) < 0 for all $x{\in}{\Omega}$, ${\lambda}$ is a positive parameter and $f:[0,{\infty}){\rightarrow}R$ is a continuous function. We provide a simple proof to establish that every positive solution is unstable under certain conditions.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.921-936
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• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• Proceedings of the Microbiological Society of Korea Conference
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• 1991.04a
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• pp.82-96
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• 1991

To understand the mechanism of illegitimate recombination in mammalian cells, we have examined the recombination role of DNA topoisomerase II (Topo II ). We found that purified calf thymus Topo II mediates recombination between two phage $\lambda$ DNA molecules in an in vitro system. The enzyme mainly produced a linear monomer recombinant DNA that can be packaged in vitro. Novobiocin and anti-calf thymus Topo II antibody inhibit this ATP-dependent recombination. The recombinant molecules contain duplications or deletion, and most crossovers take place between nonhomologous sequences of $\lambda$ DNA, as judged by the sequences of recombination junctions. In order to study the effects of Topo II on illegitimate recombination in mammalian cells, we have developed a new shuttle vector, pNKl, which contains three bacterial genes, amp(APR), galK and neo($Km^R$). Using this system, we have shown that a Topo II inhibitor, VM26, stimulated deletion formation in pNK1 DNA in monkey COS1 cells. Both in vitro and in vivo results suggest that Topo II participates in illegitimate recombination in mammalian cells.