• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1285-1325
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• 2011

We solve the isoperimetric problem, the least-perimeter way to enclose a given area, on various Euclidean, spherical, and hyperbolic surfaces, sometimes with cusps or free boundary. On hyperbolic genus-two surfaces, Adams and Morgan characterized the four possible types of isoperimetric regions. We prove that all four types actually occur and that on every hyperbolic genus-two surface, one of the isoperimetric regions must be an annulus. In a planar annulus bounded by two circles, we show that the leastperimeter way to enclose a given area is an arc against the outer boundary or a pair of spokes. We generalize this result to spherical and hyperbolic surfaces bounded by circles, horocycles, and other constant-curvature curves. In one case the solution alternates back and forth between two types, a phenomenon we have yet to see in the literature. We also examine non-orientable surfaces such as spherical M$\ddot{o}$obius bands and hyperbolic twisted chimney spaces.

• Journal of Environmental Science International
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• v.21 no.2
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• pp.203-215
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• 2012

In order to clarify the impacts of thermal difference in atmospheric boundary layer due to the different sophistication of building information in Busan metropolitan areas, several numerical simulations were carried out. ACM (Albedo Calculation Model) and WRF (Weather Research and Forecasting) was applied for estimating albedo and meteorological elements in urban area, respectively. In comparison with coarse aggregated and small buildings, diurnal variation of albedo is highly frequent and its total value tend to be smaller in densely aggregated and tall buildings. Estimated TKE and sensible heat flux with sophisticatedly urban building parameterization is more resonable and valid values are mainly induced by urban building sophistication. The simulation results suggest that decreased albedo and increased roughness due to skyscraper plays an important role in the result of thermal change in atmospheric boundary layer.

• Wind and Structures
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• v.12 no.3
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• pp.281-283
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• 2009

Marquardt method is used to estimate the aerodynamic parameters in urban area of Beijing City, China, including displacement length (d), roughness length ($z_0$) and friction velocity (u*) and drag coefficient. The surface drag coefficient defined as the ratio between friction velocity and mean wind speed is 0.125 in our research, which is close to typical urban area value. The averaged d and $z_0$ are 1.2 m and 7.6 m. d and $z_0$ change with direction because of the surface heterogeneity over urban surface and reach their maximum values at S-SW sector, this tendency agrees with the surface rough element distribution around the observation tower.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.11C
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• pp.898-904
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• 2008

In this paper, we propose a fast algorithm to generate the array of elemental image in a computer generated integral imaging system. It generates the array of elemental image using depth information, needs less computing time to produce the result by using the concept of boundary area and computing the voxel within boundary area. By comparing the computing time of proposed algorithm with that of the existing algorithm theoretically and experimently, we proved the efficiency of this algorithm.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.4
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• pp.332-337
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• 2002

The applicability of models based on fractal geometry to characterize the surface of the EL devices was investigated. Insulating layer and phosphor layer of EL devices were deposited on ITO glass using e-beam method. The images of phosphor layer by scanning electron microscope(SEM) were transformed to binary coded data. The relations between fractal geometry and electrical characteristics of EL devices were investigated. When the fractal dimension of $Cas:EuF_3$ EL device was 1.82 and its grain boundary area was 19%, the brightness of $Cas:EuF_3$ EL device was 261 cd/$\textrm{m}^2$.

• Korean Journal of Hydrosciences
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• v.5
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• pp.45-55
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• 1994

A new method to estimate the mean areal precipitation using kriging is developed. Urlike the conventional approach, points for double and quadruple numerical integrations in the kriging equation are selected randomly, given the boundary of area of interest. This feature eliminates the conventional approach's necessity of dividing the area into subareas and calculating the center of each subarea, which in turn makes the developed method more powerful in the case of complex boundaries. The algorithm to select random points within an arbitrary boundary, based on the theory of complex variables, is described. The results of Monte Carlo simulation showed that the error associated with estimation using randomly selected points is inversely proportional to the square root of the number of sampling points.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.1107-1119
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• 2024

Consider a two dimensional smooth convex body with a marked point on the boundary of it, sitting tangentially at the marked point over a base curve in 𝔼², ℍ² or 𝕊² and the image of this body by the reflection with respect to the tangent line of the base curve at the marked point. When we roll these two bodies simultaneously along the base curve, the trajectories of the marked point bound a closed region. We show that the area of the closed region is independent of the shape of the base curve if the base curve is not highly curved with respect to the boundary curve of the convex body.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2003.04a
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• pp.277-281
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• 2003

We fused RADARSAT image and SPOT panchromatic image by wavelet transform in order to improve the accuracy of classification on the water area. Fused image in water not only maintained the characteristic of SAR image (low pixel value)but also had boundary information improved. This leads to accurate method to classify water areas.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.1 no.1
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• pp.35-43
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• 1997

Handling the emergency problems such as Chemobyl accident require real time prediction of pollutants dispersion. One-point real time sounding at pollutant source and simple model including turbulent-radiation process are very important to predict dispersion at real time. The stability categories obtained by one-dimensional numerical model (including PBL dynamics and radiative process) are good agreement with observational data (Golder, 1972). Therefore, the meteorological parameters (thermal, moisture and momentum fluxes; sensible and latent heat; Monin-Obukhov length and bulk Richardson number; vertical diffusion coefficient and TKE; mixing height) calculated by this model will be useful to understand the structure of stable boundary layer and to handling the emergency problems such as dangerous gasses accident. Especially, this simple model has strong merit for practical dispersion models which require turbulence process but does not takes long time to real predictions. According to the results of this model, the urban area has stronger vertical dispersion and weaker horizontal dispersion than rural area during daytime in summer season. The maximum stability class of urban area and rural area are 'A' and 'B' at 14 LST, respectively. After 20 LST, both urban and rural area have weak vertical dispersion, but they have strong horizontal dispersion. Generally, the urban area have larger radius of horizontal dispersion than rural area. Considering the resolution and time consuming problems of three dimensional grid model, one-dimensional model with one-point real sounding have strong merit for practical dispersion model.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2002.10a
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• pp.71-74
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• 2002