• ETRI Journal
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• v.38 no.6
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• pp.1135-1144
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• 2016

Fractal antenna arrays are geometry-based thinned arrays having multiband applications. The major challenge of these arrays is their large number of elements at higher expansion factors. This article presents the thinning of fractal antenna arrays while maintaining an appropriate balance between the side lobe level and beam width by using various quantized fractal distribution functions. A 2D square fractal antenna array and 3DSierpinski gasket antenna array are considered in this article to validate the proposed distribution functions. Nearly one third of the antenna elements are thinned in each successive iteration except in the case of a one-count distribution function. The proposed technique can simplify practical implementation and exhibits better performance for various parameters such as the side lobe level, side lobe angle, and half power beam width than fully populated fractal antenna arrays.

• Korean Journal of Soil Science and Fertilizer
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• v.43 no.1
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• pp.1-7
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• 2010

This study was carried out to investigate plow pan characteristics and to grasp the relationship between its particle size distribution fractal dimension ($D_m$) and water transport in paddy plow pan. Twenty four soil sampling sites with different management groups, ordinary and sandy-textured, were selected and investigated for physical properties of soils such as Yamanaka hardness in April, non-submerged condition, before rice seedling transplanting. The plow pan appearing depth and thickness was determined by penetration resistance profile. Undisturbed core samples with five replicates were sampled at plow pan layerwith 2 inch cores for measuring soil bulk density and saturated hydraulic conductivity. The particle size distribution fractal dimension ($D_m$) was calculated by the method following the procedure Tylerand Wheacraft (1992), using the USDA-based particle size analysis datawith fractions of 0-0.002, 0.002-0.053, 0.053-0.1, 0.1-0.25, 0.25-0.5, 0.5-1.0, and 1.0-2.0 mm. The plow pan of investigated fields appeared at a range from 5 to 30 cm depth, showing minimum value in sandy-textured management group and maximum value in ordinary management group. The thickness of plow pan were distributed from 5 to 17 cm, showing both minimum and maximum values in sandy-textured management group. Averagely, the plow appearing depth were deeper in ordinary management group than in sandy-textured management group, whereas the reverse in the thickness of plow pan. The particle size distribution fractal dimension ($D_m$) had higher value with finer textures, with higher fractality in coarser texture. Saturated hydraulic conductivities, $K_s$, of plow pan soils distributed from 0.5 to 1420 mm $day^{-1}$, having the highest value in sandy skeletal soils. The $K_s$ decreased with decreasing clay content and $D_m$, showing power function relationships. The coefficient of determination, $R^2$, of the fitted power functions were higher in $D_m$ as x-axis than in clay content. This means that $D_m$ could give us more effective estimation than clay content. Especially, sandy-textured paddy soils had higher $R^2$, compared to ordinary paddy soils. $K_s$ of relatively coarse-textured soils with less than 18%of clay content, therefore, was more dependent on particle size distribution than that of relatively fine-textured soils. From these results, it could be concluded that the fractal scaling gives us a unique quantity describing particle size distribution and then can be applied to estimate saturated hydraulic conductivity, especially more effective in coarse-textured soils.

• Journal of the Korean Geographical Society
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• v.40 no.3 s.108
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• pp.253-273
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• 2005

In recent years, there are strong social demands to characterize the spatial distribution of mountains in Korea. This study aims to develop a 'Sanjulgi-Jido(mountain ridge map)' that might be used not only to satisfy these social demands but also to effectively present the spatial distribution of mountains and drainage basins in the Korean Peninsular. The 'Sanjulgi-Jido' developed in this study is a map that presents the continuity of mountains based on the drainage divides that are delineated by a pre-defined drainage basin size and elevation. This study first validated the Bakdudaegan system through the analyses of a digital elevation model. The Bakdudaegan system has long been recognized as the Koreans traditional conceptual framework to characterize the spatial distribution of mountains. The analyses showed that the Bakdudaegan system has several problems to represent the mountain systems in Korea, which includes 1) the lack of the representativeness of drainage basins, 2) inaccuracy to depict the boundary of drainage basins, 3) the lack of representativeness of mountains, and 4) geo-polical issue that confines the spatial extent of mountain systems within the Korean Peninsular. In order to represent the mountains system in a more quantitative manner, we applied several terrain analysis techniques to understand the spatial distribution of mountains and drainage basins. Based on these analyses, we developed an hierarchical system to classify the continuity (If mountains, which are presented as the spatial distribution of drainage divides with a certain elevation. The first-order Sanjulgi is the drainage divides whose drainage basin are bigger than $5,000km^2$ and the point elevation is above 100m. The next order Sanjulgi is delineated as the size of drainage basin is successively divided by two. This kind of design is able to provide a logical framework to present the mountain systems at different details, depending on the purpose and scale of maps. We also provide several empirical functions to calculate various geomorphological indices for each order of Sanjulgi. The 'Sanjulgi Jido' is similar with the Bakdudaegan system, since it characterizes the continuity of mountains based on the spatial distribution of the drainage divide. It, however, has more scientific criteria to define the scale and continuity of mountains. It should be also noted that the 'Sanjulgi Jido' proposed has different logical and methodological background, compared with the mountain range map that explains the genesis of mountain systems in addition to the continuity of mountains.