• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.11-18
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• 1999

To estimate the mean and the variance of a lognormal distribution, Finney (1941) derived the uniformly minimun variance unbiased estimators(UMVUE) in the form of infinite series. However, the conditions ${\sigma}^{2}\;>\;n\;and\;{\sigma}^{2}\;<\;\frac{n}{4}$ for computing $E(\hat{\theta}_{AM})\;and\;E(\hat{\eta}^{2}_{AM})$ are necessary. In this paper, we give an alternative derivation of the UMVUE's.

• Journal of the Korean Chemical Society
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• v.6 no.1
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• pp.36-46
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• 1962

The author assumes that pure liquid metal is composed of molecular oscillators whose energy states are classified into two subgroups, i.e., A and B states, each being accesible to either one of the two sorts of lattice sites. The partition function involves constants characteristic of substance, which are obtainable from the Debye characteristic temperature assigned to its solid state. Calculation has been made for the various thermodynamic properties such as the vapor pressure, the entropy, and the heat capacity of liquid metals of GroupⅠelements over the temperature range from the melting points to the boiling points. The theoretical values thus obtained are in good accordances with those observed, within experimental error, although a slight derivation is observed in the atomic heat capacity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.836-839
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• 2005

The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.

• Geophysics and Geophysical Exploration
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• v.11 no.2
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• pp.137-147
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• 2008

Fault rupture directivity of the Odaesan earthquake, which was inferred to be the main cause of the high PGAvalue (> 0.1 g) unusually observed at the near-source region, was analyzed by using the data from the nearby (R < 100 km) dense seismic stations. The Boatwright's method (2007) was adopted for this purpose in which the azimuth and takeoff angle of the unilateral rupture directivity function could be estimated based on the relative peak ground-motions of seismic stations resulting from the nature of the rupture directivity. In this study, the approximate values of the relative peak ground-motions was derived from the difference between the log residuals of the point-source spectral model (Boore, 2003) for the main and secondary events based on the Random Vibration Theory. In this derivation, the spectral difference for a frequency range between the source corner frequencies of main and secondary events was considered to reflect only the effect of the fault directivity. The inversion result of the model parameters for the fault directivity function showed that the fault-plane of NWW-SEE direction dipping steeply to the North with high rupture velocity near upward in SE direction is responsible for the observed high level of ground-motion at the near-source region.