• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.93-93
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• 2012

하천의 수면 폭, 평균수심, 평균유속은 유량과 함께 변화한다. 이들의 관계는 멱함수의 형태로 표현될 수 있으며, 변동성을 바라보는 관점에 따라 두 가지로 구분된다. 하나는 시간에 따른 변동성으로 한 지점에서 서로 다른 주기를 갖는 유량들의 폭, 수심, 유속과의 관계(지점수리기하, at a station hydraulic geometry)이며, 다른 하나는 공간적 변동성으로 하천의 하류 방향으로 가면서 나타나는 유량과 폭, 수심, 유속과의 관계(하류수리기하, downstream hydraulic geometry)이다(Leopold and Maddock, 1953). 두 가지 수리기하의 경우 모두 자연 하천의 프랙털 특성(fractal)을 보여주는 예라 할 수 있다. Dodov and Foufoula-Georgiou (2004)는 Stall and Fok (1968)의 자료를 재분석한 결과, 지점수리기하의 지수 값이 해당 지점에서의 유역면적에 관한 함수로 표현될 수 있음을 발견하였다. 그러나, 이러한 멀티 프랙털 특성은 모든 하천유역에서 발견되는 것은 아니며, Dodov and Foufoula-Georgiou (2004)가 통계적으로 분석한 대상유역의 결과도 그 유의성에 논란의 여지가 있다고 볼 수 있어서, 현대 수문지형학의 남겨진 숙제라고 할 수 있다. 이에 본 연구에서는 수리기하의 멀티 프랙털 특성을 수문학적 동질성 여부라는 측면에서 탐구하였다. 이를 위해 본 연구에서는 기존 수리기하 관계식과 차별되는 무차원변량을 이용한 새로운 관계식을 제안하였으며 이를 관측 자료에 적용하여, 멀티 프랙털 특성의 존재 여부를 고찰하였다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.1
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• pp.33-40
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• 2012

This paper proposes a method to implement biological early warning systems(BEWS). This system generates periodically data event using a monitoring daemon and it extracts the feature parameters from this data sets. The feature parameters are derived with 6 variables, x/y coordinates, distance, absolute distance, angle, and fractal dimension. Specially by using the fractal dimension theory, the proposed algorithm define the input features represent the organism characteristics in non-toxic or toxic environment. And to find a moderate algorithm for learning the extracted feature data, the system uses an extended learning algorithm(UChoo) popularly used in machine learning. And this algorithm includes a learning method with the extended data expression to overcome the BEWS environment which the feature sets added periodically by a monitoring daemon. In this algorithm, decision tree classifier define class distribution information using the weight parameter in the extended data expression. Experimental results show that the proposed BEWS is available for environmental toxicity detection.

• Tunnel and Underground Space
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• v.22 no.3
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• pp.196-204
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• 2012

Quantification of roughness plays an important role in modeling strength deformability and fluid flow behaviors of rock joints. A procedure was suggested to simulate joint roughness, and characteristics of the roughness was investigated in this study. Stationary fractional Brownian profiles with known input values of the fractal parameter and other profile properties were generated based on random midpoint displacement method. Also, a procedure to simulate three dimensional roughness surface was suggested using the random midpoint displacement method. Selected statistical roughness parameters were calculated for the generated self-affine profiles to investigate the attribute of roughness. Obtained results show that statistical parameters applied in this study were able to consider correlation structure and amplitude of the profiles. However, effect of data density should be tackled to use statistical parameters for roughness quantification.

• Communications of Mathematical Education
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• v.27 no.2
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• pp.165-177
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• 2013

Mathematics teaching is often more effective when teachers connect the contents of mathematics with history, culture, and social events. In the history of mathematics, the 'paradigm' theory from Thomas Kuhn's scientific revolution is very effective to explain the revolutionary process of development in mathematics, and his theory has been widely quoted in the history of science and economics. However, it has not been appropriate to use his theory in the other fields. This is due to the fact that the scope of Kuhn's paradigm theory is limited to mathematics and science. In this study, this researcher introduced pan-paradigm as a general concept that encompasses all, since through any relation in the field of mathematics and architecture, Thomas Kuhn's theory of paradigm does not explain the phenomena. That is, at the root of various cultures there exist always a 'collective unconsciousness' and 'demands of the times,' and these two factors by synergism form values and controlling principles common to various parts of the culture, and this synergism leads the cultural activities, the process of which is a phenomenon called pan-paradigm.

• Tunnel and Underground Space
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• v.16 no.1 s.60
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• pp.26-37
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• 2006

This study addresses the applicability of box fractal dimension, $D_B$, as an index of statistical homogeneity of fractured rock mass. The box-count method's capability in quantifying the combined effect of fracture density and size distribution is examined systematically. Total of 129 two-dimensional fracture configurations were generated based on different combinations of fracture size distribution and fracture density. $D_B$was calculated for the generated fracture network systems using the box-counting method. It was found that was standard deviation of trace length and fracture orientation have no effect on calculated $D_B$. The estimated $D_B$ was found to increase with increasing total density and/or mean trace length. To explore the field applicability of this study, the statistical homogeneity of fractured rock mass was investigated at the rock slope and the underground facility using the box-counting method as well as conventional contingency table analysis. The results obtained in this study clearly show that the methodologies given in this paper have the capability of determining the statistical homogeneity of fractured rock mass.

• Economic and Environmental Geology
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• v.42 no.3
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• pp.261-272
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• 2009

An experimental study of the accelerated weathering was performed to investigate the variations of physicomechanical properties of deteriorated rocks due to freeze-thaw weathering for the Jurassic granite specimens from Wonju, Gangwon-do. Each complete cycle of freeze and thaw was lasted 24 hours, comprising 2 hours saturating in vacuum chamber, 8 hours freezing at -20$\pm1^{\circ}C$ and 14 hours thawing at room temperature. Freeze-thaw cycles were implemented with measuring the index physical properties as well as geometries of microfractures. The seismic velocity was found to decrease with increasing freeze-thaw cycles. On the other hand, absorption tends to increase with freeze-thaw cycles. In the end, it was concluded that variations of the index properties of deteriorated specimen depend on its initial properties and flaws in rock. The size and density of the traces of the microfracture on slab specimen were changed continuously with increasing freeze-thaw weathering. The results obtained in this study show that the box fractal dimension($D_B$) has the strong capability of quantifying the combined effect of size and density of the microfractures.

• Tunnel and Underground Space
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• v.19 no.2
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• pp.146-157
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• 2009

An experimental study of accelerated weathering on mudstone sample specimens from Haman, Gyeongnam was performed to investigate the variations of physico-mechanical properties of deteriorated rocks due to freeze-thaw weathering. Each complete cycle of freeze and thaw lasted 24 hours, comprising 2 hours of saturating in vacuum chamber, 8 hours of freezing at $-16{\pm}1^{\circ}C$ and 14 hours of thawing at room temperature. Total of 55 cycles of freeze-thaw were completed with measuring the index properties as well as geometries of microfractures. The measured specific gravity and P-wave velocity found to decrease with increasing freeze-thaw cycles. On the other hand, absorption ratio and effective porosity were continuously increased with increasing freeze-thaw cycles. It was found that the index properties of deteriorated sample specimen depend on its initial properties and flaws in rock. The size and density of the traces of the microfracture on slab specimen exhibited abrupt changes after 30 cycles of freeze-thaw weathering. The results obtained in this study show that the box fractal dimension($D_B$) given in this paper has the strong capability of quantifying the size and density of the microfracture.

• Korean Journal of Agricultural and Forest Meteorology
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• v.9 no.2
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• pp.140-148
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• 2007

The remote sensing observations of land surface properties are inevitably influenced by the landscape heterogeneity. In this paper, we introduce a geostatistical technique to provide a quantitative interpretation of landscape heterogeneity in terms of key land surface parameters. The study areas consist of the two KoFlux sites: (1) the Gwangneung site, covered with temperate mixed forests on a complex terrain, and (2) the Haenam site with mixed croplands on a relatively flat terrain. The semivariogram and fractal analyses were performed for both sites to characterize the spatial heterogeneity of two radiation parameters, i.e., land surface temperature (LST) and albedo. These parameters are the main factors affecting the reflected longwave and shortwave radiation components from the two study sites. We derived them from the high-resolution Landsat ETM+ satellite images collected on 23 Sep. 2001 and 14 Feb. 2002. The results of our analysis show that the characteristic scales of albedo was >1 km at the Gwangneung site and approximately 0.3 km at the Haenam site. For LST, the scale of heterogeneity was also >1 km at the Gwangneung site and >0.6 to 1.0 km at the Haenam site. At both sites, there was little change in the characteristic scales of the two parameters between the two different seasons.