• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.807-814
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• 1996

Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x \times Y \to S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X \times RP^{2n-k} \to S^{2n}$ is homotopically trivial.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.949-961
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• 1995

Let f be a smooth G map from a nonsingular real algebraic G variety to an equivariant Grassmann variety. We use some G vector bundle theory to find a necessary and sufficient condition to approximate f by an entire rational G map. As an application we algebraically approximate a smooth G map between G spheres when G is an abelian group.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.35 no.4
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• pp.241-248
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• 2017

GCPs (Ground Control Points) are needed to correct the DEM (Digital Elevation Model) produced from high-resolution satellite images and the RPC (Rational Polynomial Coefficient). It is difficult to acquire the GCPs through field surveys such as GPS surveys and to read the image coordinates corresponding to the GCPs. In addition, GCPs cannot cover the entire image of the test site, and the RPC correction results may be influenced by the arrangement and distribution of the GCPs in the image. Therefore, a new method for the RPC correction is needed. In this study, an LHD (Least-squares Height Difference) DEM matching method was applied using previous DEMs: SRTM DEM, digital map DEM, and corrected IKONOS DEM. This was carried out to correct the DEM produced from KOMPSAT-3 satellite images and the provided RPC without GCPs. The IKONOS DEM had the highest accuracy, and the height accuracy was about ${\pm}3m$ RMSE in a mountainous area and about ${\pm}2m$ RMSE in an area with only low heights.

• Journal of the Korean Geotechnical Society
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• v.15 no.5
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• pp.217-228
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• 1999

The three methods of analysis (i) REV(representative elemental volume), (ii) non-REV and (iii) joint network analysis are introduced in this paper to analyze the groundwater flow in jointed rock mass and the inflow into underground excavations. The results from those methods are compared one another to reveal their characteristics by varying the number of joints and the diameter of the opening. The pre-processor, the so-called sequential analysis, is introduced to predict the equivalent hydraulic conductivity of a jointed rock mass having a number of intersecting joints. Using the finite element mesh, joint map and sequential analysis, the equivalent hydraulic conductivities are calculated for all 445 elements. The hydraulic inhomogeneity and the determination of the representative properties of jointed rock masses are discussed. In the REV analysis where the entire rock mass is homogenized through the representative properties, the inflow is increased regularly and consistently by increasing the joint density, the opening size and the conductivity contrast value. Though the non-REV analysis showed irregular variation of the inflow due to the local inhomogeneity allowed to individual elements, the inflow approached the REV results as the characteristic length increases. The joint network analysis showed the most sensitive reaction to the joint density, the opening size and the presence of the network crossing the opening. The reliability of the network analysis depends on the geometric data of individual joints. In view of the limited field data on joint geometry and possible uncertainty the REV and non-REV methods are considered more practical and rational than the joint network analysis.