• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.23-30
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• 1997

We show that the Maximum Penalized Likelihood Estimate uniquely exits in a Sobolve spece which consists of bivariate density functions. The Maximum Penalized Likehood Estimate is represented as the square of the sum of the solutions of the Modified Helmholtz's equation on the compact subset of R$^{2}$.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.915-918
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• 2005

Acoustic holography uses Kirchhoff·Helmholtz integral equation and Green's function which satisfies Dirichlet boundary condition Applications of acoustic holography have been taken to the sound field neglecting the effect of flow. The uniform flow, however, changes sound field and the governing equation, Green's function and so on. Thus the conventional method of acoustic holography should be changed. In this research, one possibility to apply acoustic holography to the sound field with uniform flow is introduced through checking for the plane wave in a duct. Change of Green's function due to uniform flow and one method to derive modified form of Kirchhoff·Heimholtz integral is suggested for 1-dimensional sound field. Derivation results show that using Green's function satisfying Dirichlet boundary condition, we can predict sound pressure in a duct using boundary value.

• Journal of the Korean Society for Marine Environment & Energy
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• v.13 no.3
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• pp.174-180
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• 2010

The inhomogeneous Helmholtz equation is introduced for variable water depth and potential function and separation of variables are introduced for the derivation. Only harmonic wave motions are considered. The governing equation composed of the potential function for irrotational flow is directly applied to the still water level, and the inhomogeneous Helmholtz equation for variable water depth is obtained. By introducing the wave amplitude and wave phase gradient the governing equation with complex potential function is transformed into two equations of real variables. The transformed equations are the first and second-order ordinary differential equations, respectively, and can be solved in a forward marching manner when proper boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a side boundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set of equations. The equation set is applied to two test cases, Booij’ inclined plane slope profile, and Bragg’ wavy bed profile. The present equations set is satisfactorily verified against other theories including the full linear equation, Massel's modified mild-slope equation, and Berkhoff's mild-slope equation etc.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.7
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• pp.625-638
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• 2014

In this study, the uncertainties in the critical flow functions (CFFs) calculated by the AGA8-dc equation of state were estimated. To this end, the formulas for enthalpy, entropy, and speed of sound, which are used in calculating the CFF, were expressed in the form of dimensionless Helmholtz free energy and its derivatives, and the uncertainty in Helmholtz free energy was inferred. To consider the variations in the compressibility-dependent variables induced by the variation (i.e., uncertainty) in compressibility, the form of the AGA8-dc equation was modified to have a deviation equal to the uncertainty under each flow condition. For each independent uncertainty component of the CFF, a model for uncertainty contribution was developed. All these changes were applied to GASSOLVER, which is KOGAS's thermodynamic database. As a result, the uncertainties in the CFF were estimated to be 0.025, 0.055, and 0.112 % at 10, 50, and 100 bar, respectively, and are seen to increase with the increase in pressure. Furthermore, these results could explain the deviations in the CFFs across the different labs in which the CFF international comparison test was conducted under the ISO management in 1999.