• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2004.04a
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• pp.279-284
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• 2004

This paper presents on adjustment methods of the vendor-provided RPC(Rational Polynomial Coefficient) of GEO-level stereo images for the IKONOS satellite. RPC are adjusted with control points by the first-order polynomial and the block adjustment method in this study. As results, the maximum error of 3D ground coordinates by the adjusted RPC model did not exceed 4m. The block adjustment method is more stability than the first-order polynomial method.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.643-649
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• 2013

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a strict mixed g-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.137-145
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• 2017

We consider some simple periodic functions on the field of rational numbers with values in ${\mathbb{Q}}/{\mathbb{Z}}$ which are defined in terms of lowest-term-expression of rational numbers. We prove the density of graphs of these functions by constructing explicitly points on the graphs close to a given point using continued fractions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.25-30
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• 2002

Let $E/{\mathbb{Q}$ be an elliptic curve defined over rationals, P is a non-torsion rational point of E and $$S=\{[n]P{\mid}n{\in}{\mathbb{Z}}\}$$. then S is dense in the component of $E({\mathbb{R}})$ which contains the infinity in the usual Euclidean topology or in the topology defined by the invariant Haar measure and it is uniformly distributed.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.1143-1145
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• 2003

Some of satellites such as IKONOS don't provide the orbital elements so that we can’ utilize the physical sensor model. Therefore, Rational Function Model(RFM) which is one of mathematical models could be a feasible solution. In order to improve 3D geopositioning accuracy of IKONOS stereo imagery, Rational Polynomial Coefficients(RPCs) of the RFM need to be updated with Ground Control Points(GCPs). In this paper, a method to improve RPCs of RFM using GCPs and 3D cube is proposed. Firstly, the image coordinates of GCPs are observed. And then, using offset values and scale values of RPC provided, the image coordinates and ground coordinates of 3D cube are initially determined and updated RPCs are computed by the iterative least square method. The proposed method was implemented and analyzed in several cases: different numbers of 3D cube layers and GCPs. The experimental results showed that the proposed method improved the accuracy of RPCs in great amount.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.123-135
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• 2011

In this paper, we present arc-length estimations for quadratic rational B$\acute{e}$zier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve exactly when the weight ${\omega}$ is 0, 1 and ${\infty}$. We show that for all ${\omega}$ > 0 our estimations are strictly increasing with respect to ${\omega}$. Moreover, we find the parameter ${\mu}^*$ which makes our estimation coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve when it is a circular arc too. We also show that ${\mu}^*$ has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of ${\mu}^*$ is an optimal estimation.

• Journal of the Korean Institute of Landscape Architecture
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• v.15 no.3
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• pp.1-10
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• 1988

The initial selection of plants is the decisive step in the ultimate success of any landscape planting. This study intended to establish a reasonable selecting criteria of tree in the landscape through the holistic consideration of aesthetic, functional, cultural, operational and ecological viewpoints. The matrices of evaluating the fitness of tree were modulated to 10 categories ; availability from the established nursery. aesthetic value, indigenous to the locality, maintenance, soil fertility requirement, environmental tolerances. growth rate. wild-life food production. use of plants in design and user's likes. This 10 categories were weighted to their fitness as high(10 points), medium(8 points) and low(5points). Thus suitable plants were identified which got 70 more points from total 100 points. Such a method was believed as a rational process to get trust from client. to persuade uneducated client and to be free from designer's prejudice through a case study. But it is important to landscape designer to recognize the relationship between the rationality which prevails throughout the modern technical world and the intuitive aspects of design that are essential for developing creative solutions to encourage creativity as well as analytical responsibility.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.163-167
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• 2001

The paper introduce the basic concept for the variable graph description of blending functions in NURBS using some control method; the control points, knot vectors and weight points in 3D space.

• Proceedings of the KSRS Conference
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• 2004.10a
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• pp.344-346
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• 2004

IKONOS 1m satellite imagery is particularly well suited for 3-D feature extraction and 1 :5,000 scale topographic mapping. Because the image line and sample calculated by given RPCs have the error of more than 11m, in order to be able to perform feature extraction and topographic mapping, rational polynomial coefficients(RPCs) camera model that are derived from the very complex IKONOS sensor model to describe the object-image geometry must be refined by several Ground Control Points(GCPs). This paper presents a quantitative evaluation of the geometric accuracy that can be achieved with IKONOS imagery by refining the offset and scaling factors of RPCs using several GCPs. If only two GCPs are available, the offsets and scale factors of image line and sample are updated. If we have more than three GCPs, four parameters of the offsets and scale factors of image line and sample are refined first, and then six parameters of the offsets and scale factors of latitude, longitude and height are updated. The stereo images acquired by IKONOS satellite are tested using six ground points. First, the RPCs model was refined using 2 GCPs and 4 check points acquired by GPS. The results from IKONOS stereo images are reported and these show that the RMSE of check point acquired from left images and right are 1.021m and 1.447m. And then we update the RPCs model using 4 GCPs and 2 check points. The RMSE of geometric accuracy is 0.621 m in left image and 0.816m in right image.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.299-307
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• 2009

We count the isomorphism classes of elliptic curves over finite fields $\mathbb{F}_{3^{n}}$ and list a representative of each isomorphism class. Also we give the number of rational points for each supersingular elliptic curve over $\mathbb{F}_{3^{n}}$.