• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.341-354
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• 2009

The purpose of this study is to show the Fractals activities for mathematically gifted students, and to analyze the constructions on Fractals of the mathematically gifted. The subjects of this study were 5 mathematically gifted students in the Gifted Education Institut and also 6th graders at elementary schools. These activities on Fractals focused on constructing Fractals with the students' rules and were performed three ways; Fractal cards, colouring rules, Fractal curves. Analysis of collected data revealed in as follows: First, the constructions on Fractals transformed the ratios of lines and were changed using oblique lines or curves. Second, to make colouring rules on Fractals, students presented the sensitivities of initial and fractal dimensions on Fractals. In conclusion, this study suggested the importance of communication and mathematical approaches in the mathematics classrooms for the mathematically gifted.

• Journal of Astronomy and Space Sciences
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• v.23 no.3
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• pp.227-236
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• 2006

The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from SIDC (Solar Influences Data analysis Center) and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89) between the observed and predicted maximum sunspot numbers in the solar cycles.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.4
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• pp.304-309
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• 2000

For understanding the information processing in human brain, we analyze the EEG, a spontaneous electric activity on the scalp of the human. In this paper, we used the mutual information to analyze EEG. The mutual information is used to show the stochastic correlation between signals which are generated in the communication and information theory. The used EEG is evoked by each auditory stimulus in positive and negative emotional states. As a result, we found thet there is some difference at the mutual information in each emotional state.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.215-219
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• 2000

인간의 뇌 정보처리를 이해하기 위한 일환으로서, 많은 연구자들이 사람의 두피에서 자발적으로 발생하는 전기 활동인 뇌파(EEG)를 분석하였다. 측정된 뇌파는 잡음처럼 보이는 비선형적인 거동으로 인하여 단순한 관찰만으로는 그 특징을 분석하기가 매우 어렵다. 따라서 이러한 뇌파를 분석하고 이해하기 위한 방법으로 파워스펙트럼, 바이스펙트럼 등과 같은 스펙트럼 분석과 상관차원, 프랙탈 차원과 같은 비선형 카오스 분석 등과 같은 해석법들이 활발히 연구되어왔다. 본 논문에서는 이러한 기존의 방법 외에 두 신호사이의 통계적 의존성을 측정하는 양인 상호정보를 이용하여 뇌파의 특징을 분석하였다. 뇌파간의 상호정보 분석을 통해 두뇌에서의 정보의 흐름에 관한 특징을 알아보았고, 감성자극에 반응하는 두뇌의 활동영역을 알 수 있었다.

• The Journal of Engineering Geology
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• v.19 no.1
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• pp.51-61
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• 2009

Fractures and segmentation in association with the activities of the Yangsan fault are studied around Mt. Namsan, Gyengju city in the southeastern part of Korea. It is believed that the higher values of joint density and fractal dimension with the approach of the center of the Yangsan fault mean intense fracturing due to the fault activity. The boundary between fault damage zone and host rock is inferred to be placed at about 2.7 km from the center of the Yangsan fault where the values of joint density and fractal dimension abruptly decrease and the orientations of joint are also much dispersed. The small faults within the damage zone of the Yangsan fault are definitely divided into right-lateral and left-lateral strike-slip faults. The former is considered to be formed during the right-lateral movement of the Yangsan fault and the latter during the left-lateral movement. The Yangsan fault is segmented in the study area with obvious evidences as follows: (1) the difference of fault strike between northern and southern segments, (2) The geometry of contractional imbricate fans and syncline plunging $9^{\circ}$, $S85^{\circ}E$ at the end of northern segment, and (3) anticline plunging $28^{\circ}$, $N4^{\circ}W$ at the end of southern segment.

• Economic and Environmental Geology
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• v.45 no.5
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• pp.487-502
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• 2012

This paper is focused on mineral compositions, microstructures and distributional characters of remained grains in the fault rocks collected from a fault developed in Yongdang-ri, Yangbuk-myeon, Gyeongju City, Korea, using X-ray diffraction (XRD), optical microscope, laser grain size analysis and fractal dimension analysis methods. The exposed fault core zone is about 1.5 meter thick. On the average, the breccia zone is 1.2 meter and the gouge zone is 20cm thick, respectively. XRD results show that the breccia zone consists predominantly of rock-forming minerals including quartz and feldspar, but the gouge zone consists of abundant clay minerals such as chlorite, illite and kaolinite. Mineral vein, pyrite and altered minerals commonly observed in the fault rock support evidence of fault activity associated with hydrothermal alteration. Fractal dimensions based on box counting, image analysis and laser particle analysis suggest that mineral grains in the fault rock underwent fracturing process as well as abrasion that gave rise to diminution of grains during the fault activity. Fractal dimensions(D-values) calculated by three methods gradually increase from the breccia zone to the gouge zone which has commonly high D-values. There are no noticeable changes in D-values in the gouge zone with trend being constant. It means that the bulk-crushing process of mineral grains in the breccia zone was predominant, whereas abrasion of mineral grains in the gouge zone took place by continuous fault activity. It means that the bulk-crushing process of mineral grains in the breccia zone was predominant, whereas abrasion of mineral grains in the gouge zone took place by continuous fault activity. Mineral compositions in the fault zone and peculiar trends in grain distribution indicate that multiple fault activity had a considerable influence on the evolution of fault zones, together with hydrothermal alteration. Meanwhile, fractal dimension values(D) in the fault rock should be used with caution because there is possibility that different values are unexpectedly obtained depending on the measurement methods available even in the same sample.

• Communications of Mathematical Education
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• v.38 no.2
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• pp.247-261
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• 2024

This study propose the educational potential of an activity that solves the task of one-stroke drawing of complex figures using a drag-and-drop type educational programming language such as Scratch. The problem of determining whether a given shape is capable of one-stroke drawing is a separate problem from actually finding the path of one-stroke drawing and implementing it through programming. In particular, finding a path that allows one-stroke drawing of complex shapes with regularity and implementing it through programming requires problem-solving capabilities based on the convergence of various mathematical knowledge. Accordingly, in this study, problems related to one-stroke drawing concerning polygon-related shapes, tessellation-related shapes, and fractal shapes were presented, and the results of one-stroke drawing programming of the shapes were exemplified. In addition, the mathematical knowledge and computational thinking elements necessary for the solution of the illustrated problem were analyzed. This study is significant as a new example of the mathematics education that combines mathematics and information.

• Proceedings of the Korean Society of Disaster Information Conference
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• 2015.11a
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• pp.305-306
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• 2015

본 논문은 복잡다단한 환경변화에 효과적으로 대응하기 위하여 오늘날 여러 학문 분야에서 주로 이용되고 있는 복잡계 이론의 사고와 방법론을 기반으로 테러대응을 위한 분야별 제 접근에 대하여 논하는데 그 목적이 있다. 우리는 수많은 테러조직 및 테러환경 요인들과 연결된 복잡한 시스템 속에서 활동하고 있기 때문에 이 모든 것을 이해하고 통제하며 예측하면서 대응한다는 것은 사실상 애초부터 불가능한 일일지도 모른다. 테러대응 역시 테러대응 관계 기관간, 관계 기관 전담 부서 내의 구성원들의 상호작용뿐만 아니라 넓게는 정부, 민간단체, 산업체, 학계, 언론 등 나아가서는 국가간의 이해 관계자, 국제기구 등 테러대응 분야의 다양한 조직들의 참여하에 이들의 상호작용으로 공식적, 비공식적 의사 결정을 통한 방안들을 모색하는 것이 필요할 것이다. 이에 따라 초기조건의 민감성, 프랙탈과 자기유사성, 자기 조직화, 창발, 공진화, 혼돈의 가장자리의 복잡계 이론을 통하여 테러대응 분야의 적용가능성을 은유적으로 탐색할 수 있을 것이다.

• The Korean Journal of Ecology
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• v.23 no.5
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• pp.359-368
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• 2000

Landscape change is the modification and replacement of landscape elements in accordance with human management and natural disturbance on land mosaics. During landscape change, changes in patterns such as heterogeneity, diversity and shape, and juxtaposition of spatial elements are also accompanied. For the sustainable landscape system, therefore, spatial characteristics of the landscape should be considered in implementation of landscape conservation and restoration planning. Short-term changes of land-use and landscape pattern during the 10 years of 1980s and 1990s were investigated in the agriculture-forestry dominated landscape system through the statistics and the analysis of landscape-vegetation map. Study area is Yangdong-myon, Yangpyung-gun (37°27′30"N, 127°46′50"E), Kyonggi-do, in central Korea. Landscape change of this region was significantly related to the recent industrialization according to socio-economic development. Analyses of landscape pattern show that the area of secondary forest sustained by human activity decreased and it was replaced with large exotic plantations during this period. Area of paddy field was also extended. Fractal dimension of the total landscape increased, but that of paddy field area decreased due to rearrangement for mechanized farming. Moreover, the area of landscape management regimes such as plantation and cultivation increased in land mosaics during this period.