• Korean Journal of Mathematics
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• v.6 no.2
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• pp.291-298
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• 1998

The $L^p-L^q$ mapping properties of convolution operators with measures supported on curves in $\mathbb{R}^3$ have been studied by many authors. Oberlin provided examples of nondegenerate compact space curves whose arclength measures enjoy $L^p$-improving properties. This was later extended by Pan who showed that such properties hold for all nondegenerate compact space curves. In this paper, we will prove that the operator norm of the convolution operator with the arclength measure supported on a nondegenerate compact space curve depends only on certain quantities of the underlying curve.

• Journal of the Optical Society of Korea
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• v.1 no.2
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• pp.100-103
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• 1997

We perform degenerate and nondegenerate pump-probe experiments on bulk GaAs at 100 K below the band gap. We mostly observe a negative differential transmission signal both in the degenerate and nondegenerate experiments. We interpret our signal as due to two-photon absorption. This negative signal has a different origin from the normally considered band gap renormalization for resonant excitations.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.253-267
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• 2015

Given a complex submanifoldM of the projective space $\mathbb{P}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\mathbb{P}$(T) in the following sense: for any two nondegenerate complex submanifolds $M{\subset}\mathbb{P}$(T) and $M^{\prime}{\subset}\mathbb{P}$(T'), there is a projective linear transformation that sends an open subset of M onto an open subset of M' if and only if (M,R) is locally equivalent to (M', R'). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.21-24
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• 2001

This study is concerned with the development of efficient p-median approach to nondegenerate cell formation(CF) in group technology(GT) manufacturing. Unlike most of existing CF methodologies allowing degenerate cells or families that contains no parts or machines, this study attempts to find cell configuration where each machine cell contains at least two or more machines processing at least two or more parts so as to fully utilize the similarity in designing and processing parts. Nondegenerate CF seeks to minimize both the exceptional elements outside the diagonal block and the voids within the diagonal block. To find nondegenerate cells, a two-phase p-median methodology is proposed. In phase 1, the classical p-median model is implemented to find initial cells. In phase 2, bottleneck machines and parts are reassigned until no further degenerate cells and families are found. Test results on moderately medium-sized CF problems show the substantial efficiency of the proposed approach.

• Proceedings of the Optical Society of Korea Conference
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• 2009.02a
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• pp.199-200
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• 2009

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.237-249
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• 2002

We study nondegenerate immersions of Riemannian manifolds of constant sectional curvatures into Lorentzian manifolds of the same constant sectional curvatures with flat normal bundles. We also give a method to produce such immersions using the so-called Grassmannian system. .

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.57-69
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• 2002

We study a unifying method to obtain nondegenerate isometric immersions of manifolds of constant sectional curvatures c with flat normal bundles into the space forms of curvature c for c= -1,0,1.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.103-109
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• 2000

In this paper, we present the proof of generalized Fenchel's theorem by estimating the Gauss-Kronecker curvature of the tube of a nondegenerate closed curve in R$^{n}$ .

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.729-737
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• 2006

We study Ribaucour transformations on nondegenerate local isometric immersions of Riemannian space forms into Lorentzian space forms with flat normal bundles. They can be explained by dressing actions on the solution space of Lorentzian Grassmannian systems.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1577-1590
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• 2008

We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.