• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.115-122
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• 1998

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future(or past) complete Lorentzian metrics on $M{\;}={\;}[a,{\;}{\infty}){\times}_f{\;}N$ with specific scalar curvatures.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.625-635
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• 2016

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ on ${\mathbb{R}}^2{\times}N$, where $x_1$, $x_2$ are the local coordinates on ${\mathbb{R}}^2$ and ${\tilde{g}}$ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.95-101
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• 1999

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future complete Lorentzian metrics on $M{\;}={\;}[\alpha,\infty){\times}_f{\;}N$ with specific scalar curvatures.

• Journal of Industrial Technology
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• v.28 no.A
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• pp.35-42
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• 2008

Recently, there are a lot of multimedia products to using image interpolation system. However, most interpolation systems in existence suffer visually to some extents the effects of blurred edges and jagged artifacts in the image. I in this paper, we propose the adaptive linear interpolation system that uses the sub-pixel. We system calculate the warped distance among the pixels of an image, and use data for Optimize length parameter. Our experimental results show that our new algorithm significantly outperforms linear interpolation in subjective quality, and in most cases, in terms of PSNR as well.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.5-15
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• 2005

The conharmonic transformation is a conformal trans-formation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishii and we have generalized his results. Twisted product space is a generalized warped product space with a warping function defined on a whole space. In this paper, we partially classified the twisted product space and obtain a sufficient condition for a twisted product space to be locally Riemannian products.

• Proceedings of the Korea Contents Association Conference
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• 2003.11a
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• pp.367-372
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• 2003

In the framework of Lorentzian warped products, we study the Friedmann - Robertson - Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In particular we analyze non-smooth features of the spatially flat Friedmann-Robertson-Walker universe by introducing double discontinuities occurred at the radiation- matter and matter-lambda phase transitions in astrophysical phenomenology.

• Proceedings of the Korea Contents Association Conference
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• 2003.05a
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• pp.470-473
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• 2003

We have the index form of the multiply warped products manifold. From this result we will investigate the physical properties on the Robertson-Walker spacetime. The singularly thorem are usually interpreted as an indication that black hole exist and that there has been a big bang. This paper include necessary condition for the Robertson-Walker spacetime with singularly.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.45 no.6
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• pp.9-16
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• 2008

Recently, there are a lot of multimedia products using image interpolation system. However, most interpolation systems in existence suffer visually to some extents from the effects of blurred edges and jagged artifacts in the image. In this paper, we propose a new adaptive linear interpolation system that uses the sub-pixel. The proposed system calculate the warped distance among the pixels of an image by optimizing length parameter. A new cost function is introduced to reflect frequency properties of the origin data in order to improve image quality. Experimental results show that our new algorithm significantly outperforms conventional interpolation methods in subjective quality, and in most cases, in terms of PSNR as well.

• Journal of the Korean Wood Science and Technology
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• v.42 no.4
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• pp.407-419
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• 2014

The analysis of shape before and after heating, Surface moisture content, Moisture weight change and surface heat distribution by fixed type microwave heating in forms of flat veneer and veneer roll of Korean pine, pitch pine, larch and yellow poplar was conducted. The results were as follows: In case of flat veneer, the quality after microwave heating was comparatively good, but it was somewhat warped. These phenomena may be due to transformation by nonuniform drying stress and stronger effect of local irradiation on the veneers when heating veneer owing to the characteristics of fixed type microwave equipment. In case of the features of roll-shaped veneer heated by microwave, the quality after heating was comprehensively excellent. Especially there was no warping unlike flat veneer. Heat distribution and diffusion were also very stable for roll-shaped veneer and such heat distribution had much influence on surface moisture content and moisture weight loss. Accordingly, the veneer roll would show sufficient drying efficiency in fixed type microwave equipment through a scrutinized examination on generating power and irradiation time according to species and thickness of veneer.