• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1664-1670
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• 1991

For kinematically redundant manipulators, conventional dynamic control methods of local torque optimization showed the instability which resulted in physically unachievable torque requirements. In order to guarantee stability of the null space vector method which resolves redundancy at the acceleration level, Maciejewski[1] analyzed the kinetic behavior of homogeneous solution component and proposed the condition to identify regions of stability and instability for this method. 'In this paper, a modified null space vector method is first presented based on the Maciejewski's condition which is a function of a manipulator's configuration. Secondly, a new control method which is based on the concept of aspects is proposed. It was shown by computer simulations that the modified null space vector method and the proposed method have a common property that a preferred aspect is preserved during the execution of a task. It was also illustrated that both methods demonstrate a drastic reduction of torque loadings at the joints in the tracking motion of a long trajectory when compared with the null space vector method, and thus guarantee the stability of joint torque.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.1
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• pp.52.2-53
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• 2017

We develop a methodology to use the redshift dependence of the galaxy 2-point correlation function (2pCF) as a probe of cosmological parameters. The positions of galaxies in comoving Cartesian space varies under different cosmological parameter choices, inducing a redshift-dependent scaling in the galaxy distribution. This geometrical distortion can be observed as a redshift-dependent rescaling in the measured 2pCF. The shape of the 2pCF exhibits a significant redshift evolution when the galaxy sample is analyzed under a cosmology differing from the true, simulated one. Other contributions, including the gravitational growth of structure, galaxy bias, and the redshift space distortions, do not produce large redshift evolution in the shape. We show that one can make use of this geometrical distortion to constrain the values of cosmological parameters governing the expansion history of the universe. This method could be applicable to future large scale structure surveys, especially photometric surveys such as DES, LSST, to derive tight cosmological constraints. This work is a continuation of our previous works as a strategy to constrain cosmological parameters using redshift-invariant physical quantities.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.1
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• pp.68.4-69
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• 2018

GMACS is one of the instruments for the Giant Magellan Telescope (GMT) which will provide wide field, multi-object, moderate resolution spectroscopy of faint targets. KHU (Kyung Hee University) is in charge of control software of GMACS. As a first step, the Slit Mask Exchange Mechanism Prototype (SMEM-P) will be used as a preliminary example to make development process between electronics and high level software. Recently, we have developed a sample program to communicate with low level devices via EtherCAT. It is expected to be a mockup design for software and control system of GMACS. In this poster, we show the development process and test operation results of control software for SMEM-P.

• Bulletin of the Korean Space Science Society
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• 2005.10a
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• pp.40-40
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• 2005

• Bulletin of the Korean Space Science Society
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• 2005.10a
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• pp.67-67
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• 2005

• Bulletin of the Korean Space Science Society
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• 2001.11a
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• pp.71-71
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• 2001

• Bulletin of the Korean Space Science Society
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• 2007.04a
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• pp.39-39
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• 2007

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.201-207
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• 1996

If a torus has $L^p$-bounded second fundamental form then it is included in the lower part of the moduli space. That is, its conformal class is bounded.

• Magazine of korean Tunnelling and Underground Space Association
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• v.22 no.4
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• pp.22-34
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• 2020