• Honam Mathematical Journal
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• v.27 no.3
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• pp.405-419
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• 2005

We present some properties characterizing the Mandelbrot set of quadratic rational maps. Any quadratic rational map is conjugate to either $z^2+c$ or ${\lambda}(z+1/z)+b$. For ${\mid}{\lambda}{\mid}=1$, we find the figure of the Mandelbrot set $M_{\lambda}$, the set of parameters b for which the Julia set of ${\lambda}(z+1/z)+b$ is connected. It is seen to be the whole complex plane if ${\lambda}{\neq}1$, but it is intricate fractal if ${\lambda}=1$. This supplements the work already investigated for the case ${\mid}{\lambda}{\mid}>1$.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.151-159
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• 1997

Observing that for any dense weakly Lindelof subspace of a space Y, X is $Z^{#}$ -embedded in Y, we show that for any weakly Lindelof space X, the minimal Cloz-cover ($E_{cc}$(X), $z_{X}$) of X is given by $E_{cc}$(X) = {(\alpha, \chi$) : $\alpha$ is a G(X)-ultrafilter on X with $\chi\in\cap\alpha$}, $z_{X}$=(($\alpha, \chi$))=$\chi$, $z_{X}$ is $Z^{#}$ -irreducible and $E_{cc}$(X) is a dense subspace of $E_{cc}$($\beta$X).

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.956-959
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• 2005

The overall goal of this thesis is to develop a new algorithm based on the octree model for geometric and mechanistic milling operation at the same time. Most commercial machining simulators are based on the Z map model, which has several limitations in terms of achieving a high level of precision in five-axis machining simulation. Octree representation being a three-dimensional (3D) decomposition method, an octree-based algorithm is expected to be able to overcome such limitations. With the octree model, storage requirement is reduced. Moreover, recursive subdivision is processed in the boundaries, which reduces useless computations. To achieve a high level of accuracy, fast computation time and less memory consumption, the advanced octree model is suggested. By adopting the supersampling technique of computer graphics, the accuracy can be significantly improved at approximately equal computation time. The proposed algorithm can verify the NC machining process and estimate the material removal volume at the same time.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.575-590
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• 2017

A new class of functions called $R_{\theta}$-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of $R_{\theta}$-supercontinuous functions properly contains the class of $R_z$-supercontinuous functions [39] which in turn properly contains the class of $R_{cl}$-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of $R_{\delta}$-supercontinuous functions [24].

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.251-263
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• 2012

A CW complex B is said to be I-trivial if there does not exist a $\mathbb{Z}_2$-map from $S^{i-1}$ to S(${\alpha}$) for any vector bundle ${\alpha}$ over B a any integer i with i > dim ${\alpha}$. In this paper, we consider the question of determining whether $\Sigma^k\mathbb{R}P^n$ is I-trivial or not, and to this question we give complete answers when k $\neq$ 1, 3, 8 and partial answers when k = 1, 3, 8. A CW complex B is I-trivial if it is "W-trivial", that is, if for every vector bundle over B, all the Stiefel-Whitney classes vanish. We find, as a result, that $\Sigma^k\mathbb{R}P^n$ is a counterexample to the converse of th statement when k = 2, 4 or 8 and n $\geq$ 2k.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.361-368
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• 2011

In this paper, we construct a cover ($\mathcal{L}(X)$, $c_X$) of a space X such that for any cloz-cover (Y, f) of X, there is a covering map g : $Y{\longrightarrow}\mathcal{L}(X)$ with $c_X{\circ}g=f$. Using this, we show that every Tychonoff space X has a minimal cloz-cover ($E_{cc}(X)$, $z_X$) and that for a strongly zero-dimensional space X, ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$ if and only if $E_{cc}(X)$ is $z^{\sharp}$-embedded in $E_{cc}({\beta}X)$.

• Journal of Information Technology Services
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• v.7 no.4
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• pp.139-149
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• 2008

We propose expert system for restoration the original character form of ancient relics based on image processing and computer graphics. Letters engraved in relief like relics and intaglio like curved tombstones and letters engraved in plane or curved part of cultural asset may have been broken by a lot of rubbed copy, a long time and tide. In this paper, we suggest a new method for extracting and recovering the broken letters of cultural asset into an original form by using Z-map, morphological filter, and high frequency filter. Based on the suggested method. we develop the character recovering system.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.2
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• pp.112-122
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• 1995

While many surfaces such as automobile outer panels, ship hulls and airfoils are characterized by their smooth, free-form shapes, a far larger class of functional surfaces are characterized by highly irregular, multi-featured shapes consisting of pockets, channels, ribs, etc. In constaract to the design of aesthetic, free-form surfaces, functional surface design can perhaps best be viewed as a process of assembling a collection of known component surfaces to form a single compound surface. In this paper, we presents a feature-based functional surface modeling method. A single feature involves a secondary surface, which we must join to a primary surface with a smooth transition between two boundary courves. Through recursive blending of a secondary surface with the primary surface, the mullti-featured surface is represented. After constructing a compound surface, we generate the Z-map for NC machining of the surface. Offsetting the Z-map using the inverse offsetting technique, we get CL tool paths with out gouging.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.26 no.4
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• pp.365-371
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• 1990

In this paper, the authors calculate GDOP(Geometric Dilution of Precision) with the mast and slave transmitting stations at the past and present and simulation positions in the 9970 chain and 5970 chain of the loran C system, and analyzed variations of the GDOP and effective ranges in accordance with the shifting of transmitting stations. The results obtained are as follows; 1) The line 3.0 of equi-GDOP map that the Z slave station of 9970 chain is Guam island is falled on with line 2.0 of it's map that it is Yap island approximately, and units of GDOP of calculating with Guam island are increased then them with Yap island on the south parts of mast station. 2) If the control right of Z slave station of 9970 chain could be not transfered to japan and be closed on account of the territorial problems, the units of GDOP to calculate without it's station at any positions are very increased and the accuracy is down on the south parts of mast station. The line 5.0 of it's map is falled on with line 2.0 in case of Yap island, its Z station, and line 3.0 in case of Guam island with Z slave station approximately. 3) The X slave station of 9970 chain and 5970 chain are required rearrangement for the purpose of accurating position fix and expending service area in view of propagation route of wave and arrangement of transmitting station.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.33 no.2
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• pp.83-94
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• 2015

Recently, the necessity of spatial data in unaccessible area was challenged to set up various plans and policies for preparing the unification and the cooperative projects between South-North Korea. Therefore, this paper planned to evaluate the possibility of adopting the error tolerance in Geometric correction for 1/5,000 digital topographic mapping, using the PLEIADES images and the TerraSAR GCPs (Ground Control Points). The geometric correction was performed by changing the number and placement of GCPs by GPS (Global Positioning System) surveying, as the optimal placement of 5 GCPs were selected considering the geometric stability and steady rate. The positional accuracy evaluated by the TerraSAR GCPs, which were selected by optimal placement of GCPs. The RMSE in control points were X=±0.64m, Y=±0.46m, Z=±0.28m. While the result of geometric correction for PLEIADES images confirmed that the RMSE in control points were X=±0.34m, Y=±0.27m, Z=±0.11m, the RMSE in check points were X=±0.50m, Y=±0.30m, Z=±0.66m. Through this study, we believe if spatial data can integrate with the PLEIADES images and the optimal TerraSAR GCPs, it will be able to obtain the high-precision spatial data for adopting the regulation of 1/5,000 digital topographic map, which adjusts the computation as well as the error bound.