• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.265-277
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• 1997

Let E be a real, non-degenerate, indefinite inner product space with dim $E \geq 3$. It is shown that any bijection of E which preserves the light cones is an affine map.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.487-499
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• 2021

We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1151-1164
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• 2020

The aim of this paper is to establish Liouville type results for the stationary MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero. Moreover, we also obtain Liouville type theorem for the case of axially symmetric MHD equations. Our results generalize previous works by Schulz [14] and Seregin-Wang [18].

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.957-964
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• 2014

In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {($M_{\alpha},d_{\alpha}$)} of compact globally hyperbolic interpolating spacetimes with $C^{\pm}_{\alpha}$-properties and curvature bounded below. Using this, we also obtain that every maximal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {($M_{\alpha},d_{\alpha}$)}. Finally, we show that the limit space (M, d) satisfies a timelike triangle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.231-242
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• 2004

Let $A_b(B_E)$ be the Banach algebra of all complex valued bounded continuous functions on the closed unit ball $B_E$ of a complex Banach space E, and holomorphic in the interior of $B_E$, endowed with the sup norm. We present some sufficient conditions for a set to be a boundary for $A_b(B_E)$ in case E belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in [6]. We also prove the non-existence of the Shilov boundary for $A_b(B_E)$ and give some examples of boundaries.

• Journal of the Korean Society of Marine Environment & Safety
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• v.27 no.5
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• pp.675-682
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• 2021

Fire accidents on land and at sea can cause serious casualties; specifically, owing to the nature of marine plants and ships, the mortality rate at sea from suffocation in confined spaces is significantly higher than that on land. To prevent such cases of asphyxiation, it is essential to install ventilation fans that can outwardly direct these toxic gases from fires; however, considering the scale of marine fires, the installation of large ventilation fans is not easy owing to the nature of marine structures. Therefore, in this study, we developed a new concept for fire safety technology to control toxic gases generated by fires from applied direct current (DC) electric fields. In the event of a fire, most flames contain large numbers of positive and negative charges from chemi-ionization, which generates an "ionic wind" by Lorentz forces through the applied electric fields. Using these ionic winds, an experimental study was performed to artificially control the fire smoke caused by burning paper and styrofoam, which are commonly used as insulation materials in general buildings and ships. The experiments showed that a fire smoke could be artificially controlled by applying a DC voltage in excess of ±5 kV and that relatively effective control was possible by applying a negative voltage rather than a positive voltage.