• Korean Journal of Computational Design and Engineering
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• v.6 no.1
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• pp.31-39
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• 2001

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set. The circles are located in a Euclidean plane, the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work when the correct topology of the Voronoi diagram was given. Given three circle generators, the position of the Voronoi vertex is computed by treating the plane as a complex plane, the Z-plane, and transforming it into another complex plane, the W-plane, via the Mobius transformation. Then, the problem is formulated as a simple point location problem in regions defined by two lines and two circles in the W-plane. And the center of the inverse-transformed circle in Z-plane from the line in the W-plane becomes the position of the Voronoi vertex. After the correct topology is constructed with the geometry of the vertices, the equations of edge are computed in a rational quadratic Bezier curve farm.

• Journal of Practical Engineering Education
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• v.7 no.1
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• pp.1-9
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• 2015

STEM Education in the US and Korean STEAM are reviewed. The present STEM education focuses on K-12 and it does not concern STEM education in university. In this paper, we define a STEM education that can be made available in university and we establish a way of teaching and learning differential equations based on the STEM education. The class provides students with a chance to explore the capstone design projects that are developed by seniors and do hands-on activities. We introduce and set a Mobius strip with an instant delivery pathway to solve real problems as a symbol of STEM education.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.59-64
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• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• Journal of the Institute of Convergence Signal Processing
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• v.21 no.3
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• pp.142-147
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• 2020

The Internet of Things is valuable as a means of solving social problems such as personal, public, and industrial. Recently, the application of IoT technology to the healthcare industry is increasing. It is important to ensure reliability and security in IoT-based healthcare services. Communication protocols, wireless transmit/receive techniques, and reliability-based message delivery are essential elements in IoT healthcare devices. The system was designed and implemented to measure body temperature and activity through body temperature and acceleration sensors and deliver them to the oneM2M-based Mobius platform.

• The Journal of Korean Society for Radiation Therapy
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• v.32
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• pp.53-59
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• 2020

Purpose: The purpose of this study is to compare and analyze the difference between the MLC log file-based software (Mobius) and the conventional phantom-ionization chamber (ArcCheck) dose verification method according to the change of target volume. Material and method: Radius 0.25cm, 0.5cm, 1cm, 2cm, 3cm, 4cm, 5cm, 6cm, 7cm, 8cm, 9cm, 10cm with a Sphere-shaped target Twelve plans were created and dose verification using Mobius and ArcCheck was conducted three times each. The irradiated data were compared and analyzed using the point dose error value and the gamma passing rate (3%/3mm) as evaluation indicators. Result: Mobius point dose error values were -9.87% at a radius of 0.25cm and -4.39% at 0.5cm, and the error value was within 3% at the remaining target volume. The gamma passing rate was 95% at a radius of 9cm and 93.9% at 10cm, and a passing rate of more than 95% was shown in the remaining target volume. In ArcCheck, the average error value of the point dose was about 2% in all target volumes. The gamma passing rate also showed a pass rate of 98% or more in all target volumes. Conclusion: For small targets with a radius of 0.5cm or less or a large target with a radius of 9cm or more, considering the uncertainty of DQA based on MLC log files, phantom-ionized DQA is used in complementary ways to include point dose, gamma index, DVH, and target coverage. It is believed that it is desirable to verify the dose delivery through a comprehensive analysis.

• Information and Communications Magazine
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• v.32 no.5
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• pp.16-22
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• 2015

사물인터넷은 실세계와 가상세계에 존재하는 사물들을 네트워크로 상호 연결하여 사람과 사물, 사물과 사물간에 언제 어디서나 서로 소통할 수 있도록 하는 미래 인터넷 기술이다. 본 고에서는 글로벌 표준단체 및 산업체 컨소시엄을 중심으로 이뤄지고 있는 오픈소스 기반 사물인터넷 플랫폼 개발 동향을 알아보고, OCEAN 연합체를 중심으로 2015년 1월 공개된 oneM2M 릴리즈1 기술규격에 기반한 사물인터넷 공통플랫폼 Mobius, &Cube 개발 및 오픈소스 공개 내용과 향후 추진방향에 대해서 살펴본다.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.307-317
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• 2004

In the setting of the half-plane of the complex plane, we show that for $r\geq0$, the dual space of the weighted bergman spaces B$^{1}{\gamma}$ is the Bloch space of the half-plane and we study some bounded linear operators induced by radial derivatives.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.387-396
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• 2005

In the setting of the half-plane of the complex plane, we introduce a modified reproducing kernel and we show that for $r>-1/2,\;B^{1,r}-cancellation$ property holds and the Bloch space is the dual space of $B^{1,r}$.

• The Mathematical Education
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• v.38 no.1
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• pp.87-94
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• 1999

A multimedia CD title is developed for learning simple closed curve and Mobius band which are one of mathematics contents in the first grade of middle school. This title visualizes various figures through graphics and animations so that students can easily understand the relevant concepts and learn them with fun. It is shown that 88.6% of 30 sampled teachers are positive for the title and that 86.7% want to use it as a teaching tool in their classes.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.