• Publications of The Korean Astronomical Society
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• v.25 no.4
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• pp.113-118
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• 2010

The Henyey-Greenstein (H-G) phase function, which is characterized by a single parameter, has been generally used to approximate the realistic dust-scattering phase function in investigating scattering properties of the interstellar dust. Draine (2003) proposed a new analytic phase function with two parameters and showed that the realistic phase function is better represented by his phase function. If the H-G and Draine's phase functions are significantly different, using the H-G phase function in radiative transfer models may lead to wrong conclusions about the dust-scattering properties. Here, we investigate whether the H-G and Draine's phase functions would indeed produce significant differences in radiative transfer calculations for two simple configurations. For the uniformly distributed dust with an illuminating star at the center, no significant difference is found. However, up to ~ 20% of difference is found when the central star is surrounded by a spherical-shell dust medium and the radiation of $\lambda$ < $2000\;{\AA}$ is considered. It would mean that the investigation of dust-scattering properties using the H-G phase function may produce errors of up to ~ 20% depending on the geometry of dust medium and the radiation wavelength. This amount of uncertainty would be, however, unavoidable since the configurations of dust density and radiation sources are only approximately available.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.1
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• pp.27-36
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• 1998

A three-dimensional numerical model of water circulation has been developed. The model employs the equations on $\sigma$-coordinate and the finite element method for numerical integration. To verify accuracy of the model, a series of numerical experiments have been conducted. The experiments include wind-driven currents in an one-dimensional channel, wind-driven currents in a square lake, and tidal current distributions in Masan-Jinhae Bay. The simulation results showed good agreements with the analytic solutions for wind-driven current and the field data sets in Masan-Jinhae Bay. The model can be used widely for modeling of water circulation in the waters with a complex geometry.

• Nuclear Engineering and Technology
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• v.21 no.1
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• pp.32-39
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• 1989

A method for determining the optimum ideal MHD $\beta$limit and the operation conditions is presented for an axisymmetric tokamak reactor with a circular cross section. The $\beta$limit is calculated under the constraints of ideal MHD instability criteria with varying the operation conditions which depend on the toroidal current density distributions. Semiempirical laws deduced from experimental observations are used for the toroidal current density distributions. Analytic derivations of various equations required to determine the $\beta$limit are carried out from the empirical equations. Various distributions of the $\beta$limit are obtained by the numerical calculations for different distributions of the toroidal current density. The resulting values of the maximum $\beta$limited by ideal MHD instabilities are expressed by a scaling law in terms of the tokamak geometry and the safety factor.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.3
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• pp.41-50
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• 1993

This paper compares various potential based panel methods for the analysis of two-dimensional hydrofoil. The strength of singularity on each panel is assumed to be constant or linear. Robin boundary condition as well as Neumann and Dirichlet boundary conditions are applied to various formulations to evaluate the accuracies of the methods. Pressures and lifts are computed for various two-dimensional hydrofoil geometries and are compared with the analytic solutions. Extensive studies are performed on the local errors near the trailing edge, known to be sensitive to the foil geometry with sharp trailing edge and high camber. Robin boundary condition with the perturbation velocity potential formulation shows the best accuracy and convergence rate.

• School Mathematics
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• v.9 no.1
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• pp.119-139
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• 2007

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.

• School Mathematics
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• v.18 no.3
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• pp.589-609
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• 2016

In this study, researchers have modernly reinterpreted geometric solving of cubic equations presented by an arabic mathematician, Omar Khayyam in medieval age, and have considered the pedagogical significance of geometric solving of the cubic equations using two conic sections in terms of analytic geometry. These efforts allow to analyze educational application of mathematics instruction and provide useful pedagogical implications in school mathematics such as 'connecting algebra-geometry', 'induction-generalization' and 'connecting analogous problems via analogy' for the geometric approaches of cubic equations: $x^3+4x=32$, $x^3+ax=b$, $x^3=4x+32$ and $x^3=ax+b$. It could be possible to reciprocally convert between algebraic representations of cubic equations and geometric representations of conic sections, while geometrically approaching the cubic equations from a perspective of connecting algebra and geometry. Also, it could be treated how to generalize solution of cubic equation containing variables from geometric solution in which coefficients and constant terms are given under a perspective of induction-generalization. Finally, it could enable to provide students with some opportunities to adapt similar solving procedures or methods into the newly-given cubic equation with a perspective of connecting analogous problems via analogy.

• The Journal of the Korea Contents Association
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• v.22 no.10
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• pp.132-142
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• 2022

The purpose of this study is to interpret the MCU's universal worldview from the perspective of geometry and to storytell narrative elements with mathematical imagination. For storytelling, data from the Phase 3 series aired from 2016 to 2019 was used. The Phase 3 series stimulates the imagination of the public with the sense of reality shown in the narrative and images based on geometrical theory and various predictions about future technology. Imagination is the driving force for diverse and original thinking about the unexperienced, and the ability to find order in chaos and create new perceptions of matter. The power of imagination is very necessary not only in artistic activities, but also in the scientific field where logic and rationality are important. Bachelard's imagination aims for art, the primitive realm of human beings, and contains sincerity and passion for the wonders of nature and all things. By exploring the MCU's worldview and superhero narrative through geometrical logic and imagination-driven imagery, you can understand the cosmic messages and laws in the film. From a convergence point of view of art and science, various and original techniques based on mathematics and scientific imagination used in MCU video production will help to improve the quality of video analysis.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.1
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• pp.9-15
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• 2005

Most of location systems use RF signal. Because multipath is too severe at indoor environment, RF signal are usually used in outdoor positioning such as GPS. To overcome the difficulty at indoor positioning, m positioning is recently developed and is being vigorously studied. Some standardizations on UWB are in progress at IEEE 802.15 committee. In developing UWB positioning system, we should consider the synchronization of sensor network, positioning algorithm, sensor allocation, and so on. This paper presents a comparison of TDOA positioning algorithms that are widely used in location systems. Two algorithms are compared; one is derived by linearization, and the other is by analytic solution(CH algorithm). Simulation results show that the CH algorithm is superior to the linearized least square at indoor environment in that CH algorithm shows consistent positioning performance regardless of the visibility and geometry of basestations.

• Korean Journal of Optics and Photonics
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• v.23 no.5
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• pp.179-188
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• 2012

Lenses with an ultra wide angle of view are usually called fisheye lenses since a fish can see an ultra wide panoramic view under water. As the angle of view for these kinds of lenses reaches a wide angle, the illumination on an image sensor is reduced by a rapid drop. In this paper, we discuss the causes and the ways to correct for a rapid drop. First, it is treated for the sign convention of directional cosine vectors and normal vectors on the curved surface by means of analytic geometry. And, from the fundamental discussion for these vectors, the rapid illumination drop is numerically analyzed for various kinds of causes by utilizing geometrical optics and radiometry as well as Fresnel equations derived from electromagnetic boundary conditions. As a result, we are able to get the full understanding for the rapid illumination drop and to propose ways to correct effects due to an wide angle of view.

• Journal of Korean Dental Science
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• v.4 no.2
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• pp.52-58
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• 2011

Purpose: Modifications of implant design have been related to improving initial stability. The purpose of this study was to investigate their respective effect on initial stability between two tapered implant systems (self-tapping vs. non-self-tapping) in medium density bone using three different analytic methods. Materials and Methods: Self-tapping implant (GS III$^{(R)}$; Osstem Implant Co., Busan, Korea) and non-self-tapping implant (Replace Select$^{(R)}$; Nobel Biocare, G$\H{o}$teborg, Sweden) were investigated. In Solid rigid polyurethane blocks of artificially simulated Quality 2 bone, each of the 5 implants was inserted according to the manufacturer's instructions for medium-bone drilling protocol. Evaluation of initial stability was carried out by recording the maximum insertion torque (IT) and performing the resonance frequency analysis (RFA), and the pull-out test. Results: The IT and RFA values of self-tapping implant were significantly higher than those of non self-tapping implant (P=.009 and P=.047, respectively). In the pull-out values, no significant differences were found in implants between two groups (P=.117). Within each implant system, no statistically significant correlation was found among three different outcome variables. Conclusions: These findings suggest that design characteristics of implant geometry significantly influence the initial stability in medium bone density.