• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.157-174
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• 2004

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.

• Korean Journal of Optics and Photonics
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• v.20 no.4
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• pp.241-248
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• 2009

We suggest a new method to determine the off-alignment error of the composite film, together with in-plane($R_{in}$) and out-of-plane retardation($R_{th}$) of the compensation film, simultaneously. The composite film consists of a polarizing film and a compensation film for improvement of viewing angle of a liquid crystal display. We regarded the compensation film as o-plate with its optic axis along an arbitrary direction. By using an extended Jones matrix method, the polarization characteristics of the composite film are examined. The calculated Fourier constants, ($\alpha$, $\beta$) curves of the composite film as the azimuth angle is varied at the incident angles of $0^{\circ}$ and $50^{\circ}$, respectively, are used to determine the axis misalignment, the tilt angle and the azimuth angle of the compensation film by adopting the linear regressional analysis technique. Since this method can be applied for the inspection of the composite film even after laminating the polarizing film and the compensation film, it will be useful for simplifying the manufacturing process and reducing the production cost of liquid crystal display panels.

• Journal of the Korean Geotechnical Society
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• v.18 no.6
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• pp.129-139
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• 2002

Dielectric constant measurement has drawn much attention in the investigation of the properties and contaminations of subsurface. In this study, by varying the frequency from 75 kHz to 12 MHz, dielectric constant was measured for the weathered granite soil and Jumunjin sand having different water contents and dry density. The dielectric constant of sand showed the dispersive behavior indicating that dielectric constant decreased with frequency of an electric field. And the dielectric constant of soil increased as water content and/or dry density increased due to the decrease of air portion and/or the increase of amount of water molecules which could contribute to the development of orientation polarization. The dielectric constant of sand showed a linear relationship with the moisture density, considering both water content and dry density. At low frequency, the dielectric constants calculated by Maxwell's, Topp's and CRIM equation deviated from measured values. It could be explained by the fact that those equations did not consider dispersive behavior of dielectric constant with the frequency.