• 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 Chungcheong Mathematical Society
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• v.15 no.2
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• pp.57-66
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• 2003

The various deformation spaces associated with maximal geometric structures on closed oriented 3-manifolds was studied in [2], leaving out the geometry of $\mathbb{R}^3$. In this paper, we study the Weil spaces and Teichm$\ddot{u}$ller spaces of non-orientable 3-dimensional flat Riemannian manifolds. In particular, we find the Teichm$\ddot{u}$ller spaces are homeomorphic to the Euclidean spaces $\mathbb{R}^4$ or $\mathbb{R}^3$ depending on the holonomy group $\mathbb{Z}_2$ or $\mathbb{Z}_2{\times}\mathbb{Z}_2$ respectively.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.175-177
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• 1989

The following is the basic problem about the stability in Riemannian Geometry; given a Riemannian manifold N, find all stable complete minimal submanifolds of N. As answers of this problem, do Carmo-Peng [1] and Fischer-Colbrie and Schoen [3] showed that the stable minimal surfaces in R$^{3}$ are planes and Schoen-Yau [5] and Fischer-Colbrie and Schoen [3] gave a solution for the case where the ambient space is a three dimensional manifold with nonnegative scalar curvature. In this paper we will remove the assumption of finite absolute total curvature in [3, Theorem 3].

• Proceedings of the Optical Society of Korea Conference
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• 2005.07a
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• pp.150-151
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• 2005

Integral imaging is one of the three-dimensional(3D) display methods, which is an autostereoscopic method. The integral imaging system can provide volumetric 3D image which has both vertical and horizontal parallaxes. The elemental image which is obtained in the pickup process by lens array has the 3D information of the object and can be used for the depth perception and the 3D correlation. Moreover, the elemental image which represents a cyber-space can be generated by computer process.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.253-264
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• 2015

In the present paper, we consider a position vector of an arbitrary curve in the three-dimensional Galilean space $G_3$. Furthermore, we give some conditions on the curvatures of this arbitrary curve to study special curves and their Smarandache curves. Finally, in the light of this study, some related examples of these curves are provided and plotted.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.537-554
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• 2017

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.85-92
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• 1994

It is well known that there exist no closed minimal surfaces in a 3-dimensional Euclidean space R$^{3}$. Myers [4] generalized the result to the case of the higher dimension and proved that there are no closed minimal hypersurfaces in an open hemisphere. The complete and non-compact version concerning Myers' theorem is recently considered by Cheng [1] and the following theorem is proved.

• Korean Institute of Interior Design Journal
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• v.19 no.6
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• pp.112-120
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• 2010

Human can recognize the environment by detecting spatial perception, and most of environmental perception depends on visual perception. In view that the acquisition of spatial information is accomplished through visual recognition, analysis of visual structure contained in the space is thought to be very important sector in studying the characteristic of the space. The history of studies on visual structure of space, however, wasn't too long, and furthermore most of the theories up to now focused on static and planar principles. Under this circumstance, this study is intended to suggest new theory by combining Isovist theory and VGA theory that have been actively discussed as the theory on visual perception-based spatial structure and supplementing them between each other to expand into 3-dimensional model. The suggested theory is a complex principle in dimensional and dynamic form in consideration of visual direction, which forms 3-dimentional virtual model that enables visualization of the property of spatial structure as the routine discriminating whether visual connection is made between viewing point and target point, and the target point is included in the visual field quadrangular pyramid or not. Such model was built up by an analysis application where four probe paths were applied to simulate the visual structure that occurs in virtual space, and then the characteristics were analyzed through quantification. In result, in spite of the path with equal space and equal length, significant difference in the acquired quantity of spatial information could be found depending on the probe sequence. On the contrary, it was found that probe direction may not affect the acquired quantity of information and visual property of the space.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.4
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• pp.543-552
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• 1996

The goal of this paper is to developed a DSP based power analyzing and control system by 3-Dimensional (3-D) space current co-ordinates. A developed system is made up of 486-PC and DSP (Digital Signal Processor) board, Active Power Filter, Non-linear thyristor load, and Power analyzing and control program for Windows. Power is analyzed using signal processing techniques based on the correlation between voltage and current waveforms. Since power analysis algorithm is performed by DSP, power analysis is achieved in real-time even under highly dynamic nonlinear loading conditions. Combining control algorithm with power analysis algorithm is performed by DSP, power analysis is achieved in real-time even under highly dynamic nonlinear loading conditions. Combining control algorithm with power analysis algorithm, flexibility of the proposed system which has both power analysis mode and control mode, is greatly enhanced. Non-active power generated while speed of induction motor is controlled by modulating firing angle of thyristor converter, is compensated by Active Power Filter for verifying a developed system. Power analysis results, before/after compensation, are numerically obtained and evaluated. From these results, various graphic screens for time/frequency/3-D current co-ordinate system are displayed on PC. By real-time analysis of power using a developed system, power quality is evaluated, and compared with that of conventional current co-ordinate system. (author). refs., figs. tabs.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.567-589
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• 2004

In the present paper, we treat an infinite series ($\alpha$, $\beta$)-metric L =$\beta$$^2$/($\beta$-$\alpha$). First, we find the conditions that a Finsler metric F$^{n}$ with the metric above be a Berwald space, a Douglas space, and a projectively flat Finsler space, respectively. Next, we investigate the condition that a two-dimensional Finsler space with the metric above be a Landsbeg space. Then the differential equations of the geodesics are also discussed.