• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.733-763
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• 2006

We study quasi-stationary Stokes flow in a dihedral domain arising from a study of a free boundary problem of viscous fluid in a container. We construct an exact solution of quasi-stationary Stokes equations and derive its estimates with norm in a weighted Sobolev spaces.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.9
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• pp.1244-1249
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• 1995

Wavelet transform technique is applied to two important electromagnetic problems:1) to analyze the frequency-domain radar echo from finite-size targets and 2) to the integral solution of two- dimensional electromagnetic scattering problems. Since the frequency- domain radar echo consists of both small-scale natural resonances and large-scale scattering center information, the multiresolution property of the wavelet transform is well suited for analyzing such ulti-scale signals. Wavelet analysis examples of backscattered data from an open- ended waveguide cavity are presented. The different scattering mechanisms are clearly resolved in the wavelet-domain representation. In the wavelet transform domain, the moment method impedance matrix becomes sparse and sparse matrix algorithms can be utilized to solve the resulting matrix equationl. Using the fast wavelet transform in conjunction with the conjugate gradient method, we present the time performance for the solution of a dihedral corner reflector. The total computational time is found to be reduced.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.337-352
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• 1999

In this paper we find a geometric condition for the weaker principle of spatial averaging (PSA) for a class of polyhedral domains. Let \ulcorner be a polyhedron in R\ulcorner, n$\leq$3. If all dihedral angles of \ulcorner are submultiples of $\pi$, then there exists a parallelopiped \ulcorner generated by n linearily independent vectors {\ulcorner}\ulcorner in R\ulcorner containing \ulcorner so that solutions of $\Delta$u+λu=0 in \ulcorner with either the boundary condition u=0 or ∂u/∂n=0 are expressed by linear combinations of those of $\Delta$u+λn=0 in \ulcorner with periodic boundary condition. Moreover, if {\ulcorner}\ulcorner satisfies rational condition, we guarantee the weaker PSA for the domain \ulcorner.