• Korean Journal of Mathematics
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• v.20 no.3
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• pp.361-369
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• 2012

We get a theorem which shows the existence of at least six solutions for the semilinear wave equation with nonlinearity crossing three eigenvalues. We obtain this result by the variational reduction method and the geometric mapping defined on the finite dimensional subspace. We use a contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three-dimensional subspace with three axes spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one-dimensional subspace.

• Journal of The Korean Digital Architecture Interior Association
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• v.12 no.4
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• pp.97-105
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• 2012

This study aims to evaluate Rietveld's creative design style and concepts. To this end, I looked into the evaluation of major researchers on Rietveld, classified all his works into four groups according to the design types and analyzed them. As follows: based on the results of the analysis of works I concluded. First, Rietveld created the concept of the spatial extension to the ingenious joint which had the structural node formed of three listels with quadrangular section. It is the design innovation that led to liberate the closed construction. Second, Rietveld had opened up the possibility to neutralize the gravitational three-dimensional works. He subtracted the weight in the direction of gravity from the three-dimensional structure of the works and painted the three primary colors on them partially to get rid of the original material color. Therefore they looked like the forms liberated from gravity. Third, Rietveld ripped off the surfaces of cube through several formative experiments and decomposed the volume into the tesseract. Through this method of realizing the new plastic concepts, he completed the architectural models of weightlessness. Fourth, Rietveld opened the possibility of the realization of the three-dimensional works integrated all space and time in the one-pieced works and the folded works. Fifth, Rietveld steadily experimented and realized the internal and external integration of time and space in his later works.

• Bulletin of the Korean Space Science Society
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• 2011.04a
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• pp.28.2-28.2
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• 2011

Coronal Mass Ejections (CMEs) are enormous eruptions of plasma ejected from the Sun into interplanetary space, and mainly responsible for geomagnetic storms and solar energetic particle events. It is very important to infer their direction of propagation, speed and their 3-dimensional configurations in terms of space weather forecast. Two STEREO satellites provide us with 3-dimensional stereoscopic measurements. Using the STEREO observations, we can determine the 3-dimensional structure and radial velocity of the CME. In this study, we applied three different methods to the 2008 April 26 event: (1) Ice cream Cone Model by Xue (2005) using the SOHO/LASCO data, (2) Flux rope model by Thernisien (2009) using the STEREO/SECCHI data, (3) Flux rope model with zero angle using the STEREO/SECCHI data. The last method in which separation angle of flux rope is zero, is similar to the ice cream cone model morphologically. The comparison shows that the radial speeds from three methods are estimated to be about 750km/s and are within ${\pm}120km/s$. We will extend this comparison to other CMEs observed by STEREO and SOHO/LASCO.

• Journal of the Korea Furniture Society
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• v.23 no.1
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• pp.75-83
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• 2012

Space dominates all the art activities human do and plays a role of providing aesthetic emotion. Architecture, sculpture, painting, and furniture, etc. these two and three dimensional works are represented in space and interpreted the role of its form, structure and function. Each area is different, but space has been studied in philosophy, physics, geometry, and mathematical studies, etc. and has been consistently interpreted and represented relating to a variety of human creative activity. Furniture is also three dimensional art being dependent on space. In the United States in 2004, I made the living room bench by applying the spatial concept at Rochester Institute of Technology. Two years later, this design was adopted by wendell Castle Collection, an American furniture company, then prototype were made and tested three times during a year, and then since 2007 as indoor benches it has been manufactured in the United States. The study's purpose is to order the process of its development based on the experience of bench production applied the spatial concept, and by analyzing the properties of spatial concept, I am planning to propose a new concept on interaction with the space and furniture for next.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.507-515
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• 2012

We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three dimensional subspace with three axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.95.1-95.1
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• 2012

Halo coronal mass ejections (HCMEs) are major cause of geomagnetic storms and their three dimensional structures are important for space weather. In this study, we compare three cone models: an elliptical cone model, an ice-cream cone model, and an asymmetric cone model. These models allow us to determine the three dimensional parameters of HCMEs such as radial speed, angular width, and the angle (${\gamma}$) between sky plane and cone axis. We compare these parameters obtained from three models using 62 well-observed HCMEs from 2001 to 2002. Then we obtain the root mean square error (RMS error) between maximum measured projection speeds and their calculated projection speeds from the cone models. As a result, we find that the radial speeds obtained from the models are well correlated with one another (R > 0.84). The correlation coefficients between angular widths are less than 0.53 and those between ${\gamma}$ values are less than 0.47, which are much smaller than expected. The reason may be due to different assumptions and methods. The RMS errors of the elliptical cone model, the ice-cream cone model, and the asymmetric cone model are 213 km/s, 254 km/s, and 267 km/s, respectively. Finally, we discuss their strengths and weaknesses in terms of space weather application.

• Magazine of korean Tunnelling and Underground Space Association
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• v.4 no.3
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• pp.38-48
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• 2002

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1167-1177
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• 2001

The groups generated by reflections in faces of Coxeter polyhedra in three-dimensional Thurstons spaces are considered. We develop a method for finding of finite index subgroups of Coxeter groups which uniformize three-dimensional manifolds obtained as two-fold branched coverings of manifolds of Heegaard genus one, that are lens spaces L(p, q) and the space S$^2$$\times$S$^1$.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.1-5
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• 2012

We study surfaces of revolution in the three dimensional Euclidean space $\mathbb{R}^3$ with two distinct axes of revolution. As a result, we prove that if a connected surface in the three dimensional Euclidean space $\mathbb{R}^3$ admits two distinct axes of revolution, then it is either a sphere or a plane.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.547-557
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• 2018

We establish some characterizations of isoparametric surfaces in the three-dimensional Euclidean space, which are associated with the Laplacian operator defined by the so-called II-metric on surfaces with non-degenerate second fundamental form and the elliptic linear Weingarten metric on surfaces in the three-dimensional Euclidean space. We also study a Ricci soliton associated with the elliptic linear Weingarten metric.