• Publications of The Korean Astronomical Society
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• v.34 no.1
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• pp.1-16
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• 2019

"Hon-Chon-Jeon-Do" is a woodcut star map with the size of $79.4cm{\times}127.5cm$, and was widely disseminated as it was made into a set with Kim, Jung Ho's "Yeoji-Jeon-Do". This study confirmed that Yixiang kaocheng xubian ("의상고성속편") star catalogue was used as a source to produce the star map, and the stereographic projection was applied with the projection center being the mid-point (Q) between the celestial and ecliptic north poles. The 'mid-circle' around the Q is arisen between the equator and the ecliptic, and on this circle, the hour angle and the ecliptic longitude of a star can be marked using the same scale. This means that the hour of the day and the season of the year can be read on the same dial of the mid-circle, and the application of this character in the practical use was the key point of the star map production. By observing either transits or positions of the 28 xiu (宿), it is easy to find the corresponding season and time by simply reading the dial on the mid-circle. This is just the function of a portable almanac and thus by disseminating it widely, the convenience of the people would have been promoted. For this reason, it can be stated that "Hon-Chon-Jeon-Do" was a practical astronomical tool which was produced by the western astronomical projection method and was used to find time and season. Choi, Han Ki and Kim, Jung Ho are strong candidates for the makers of this star map. The time of production is estimated to be 1848 ~ 1857, and "Hon-Chon-Jeon-Do" could be regarded as a good contributor to popularization of astronomy in the late Joseon Dynasty.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.101-107
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• 2000

For a continuous map f of the circle to itself, we show that if P(f) is closed, then ${\Gamma}(f)$ is closed, and ${\Omega}(f)={\Omega}(f^n)$ for all n > 0.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.549-553
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• 2000

For a continuous map of the circle to itself, we give necessary and sufficient conditions for the $\omega$-limit set of each nonwandering point to be minimal.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.04a
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• pp.97-99
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• 2003

Lineament density maps can be used for the quantitative evaluation of relationship between lineaments and groundwater occurrence. There are several kinds of lineament density maps including lineament length density, lineament cross-points density, and lineament counts density maps. This paper reports the usefulness of the representative elementary area (REA) concept for lineament analysis. This concept refers to the area size of the unit circle to calculate the lineament density factors distributed within the circle: length, counts and cross-points counts. The circle is a unit circle that calculates the sum of the lineament length, lineament counts and the number of cross-points within it. The REA is needed to obtain the best representative lineament density map prior to the analysis of relation between lineaments and groundwater well yield or other groundwater characteristics. A basic lineament map for the Yongsangang-Seomjingang watershed of Korea, drawn from aerial black-and-white photographs of 1/20, 000 scale was used for demonstrating the concept. From this study, the conclusions were as follows: (1) the REA concept can be efficiently applied to the lineament density analysis and mapping, (2) for whole Yongsangang-Seomjingang watershed which has 6, 502 lineaments with an average lineament length of 3.3 km, the lower limits of each REA used for drawing the three density maps were about 1.77 $\textrm{km}^2$ (r=750 m) for lineament length density, 7.07 $\textrm{km}^2$ (r=1, 500 m) for lineament counts density, and 4.91 $\textrm{km}^2$ (r=1, 250 m) for lineament cross-points density, respectively, (3) the lineament densities are inversely proportional to the size of REA, and the REA can be calculated with this inversely linear regression model, (4) if the average lineament density values for the whole study area are known, the most accurate density maps can be drawn using the REAs obtained from each linear regression model, and (5) but critical attention should be paid to draw lineament counts density and lineament cross-points density maps because.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.29 no.2
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• pp.162-167
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• 1993

We have investigated analytically and numerically on both the generalized dimension D sub(n) and the fractal dimensionality f sub($\alpha$) in the dissipative Willbrink map. and discussed both the mode-locking phenomenon and the dissipative trajectory when z=0.03, b=0.9 and K sub(d) =0.272313668. In the mode-locking phenomenon. we find that the generalized dimension D sub(-n) and superconverged $\delta$ sub(n) are very close to D sub(-$\infty$) =0.92403 and $\delta$ sub($\infty$) =2.16442 even for n～20 as listed in Table 1. In dissipative trajectory, the values of D sub(+n) and D sub(-n) for n～20 are estimated to be very close to D sub(+$\infty$) =0.63267 and D sub(-$\infty$) =1.89802 on the circle map. Thus, the values of the generalized dimension as nlongrightarrow$\infty$ on dissipative Willbrink map are expected to be the same results as those for the circle map and to have the universal scaling exponents for a special scaling structure when the values of overbar(w), z, b, and k sub(d) have the different values.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.239-244
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• 1993

The purpose of this paper is to determine conditions under which equicontinuity of the family of iterates {f$^{n}$ } of a continuous function that maps the circle S$^{1}$ into itself does occur. We shall see that equicontinuity of the family of iterates {f$^{n}$ } occurs only under special cases. Actually, we will show that this happens only for rotations when degree of the function is 1, and for involutions when degree of the function is -1.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.707-716
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• 1999

In this pater we study the continuity of rotation numbers of liftings of circle maps with degree one. And apply our result to prove that a positively equicontinuous flow of homeomorphisms on the circle $S^1$ is topologically conjugate to a continuous flow of rotation maps.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.27-32
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• 2000

In this paper, we show that for any continuous map $f$ of the circle $S^1$ to itself, (1) $x{\in}{\Omega}(f){\backslash}\overline{R(f)}$, then $x$ is not a turning point of $f$ and (2) if $P(f)$ is non-empty, then $R(f)$ is closed if and only if $AP(f)$ is closed.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.157-162
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• 1995

Let I be the interval, $S^1$ the circle and let X be a compact metric space. And let $C^{circ}(X,\;X)$ denote the set of continuous maps from X into itself. For any f$f\in\;C\circ(X,\;X),\;let\;P(f),\;R(f),\;\Gamma(f),\;\Lambda(f)\;and\;\Omega(f)$ denote the collection of the periodic points, recurrent points, ${\gamma}-limit{\;}points,{\;}{\omega}-limit$ points and nonwandering points, respectively.(omitted)

• Korean System Dynamics Review
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• v.11 no.2
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• pp.77-102
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• 2010

This paper examines a mechanism of the Electronic Territory Expansion and the Information-oriented Society. Especially, a strategy for the territory development based on intelligence is suggested. The strategy is divided into a strategy for the domestic electronic territory and a plan for the global electronic territory. To examine the strategy and the plan, this paper is using the causal map analysis based on the System Thinking Approach. The causal map of the mechanism is characterized by a positive feedback loop. The paper has concluded that it is important to make the positive loops as a virtuous circle. It means that when a society dominates the advantageous position firstly in the field of intelligent and electronic territory, the competitiveness can grow in arithmetical progression.