• Journal for History of Mathematics
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• v.19 no.2
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• pp.59-76
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• 2006

This research focuses on the relationship between mathematics and visual art from a perspective of chaos theory which emerged under the influence of post-modernism. Culture and history, which transform dynamically with the passing of time, are models of complexity. Especially, when the three periods of Medieval, Renaissance, and 17-18 Centuries are observed, the Renaissance period is phase transition phenomenon era between Medieval and 17-18 Centuries. The transition stage between the late Medieval times and the Renaissance; and the stage between the Renaissance and the Modern times are also phase transitions. These phenomena closely resemble similarity in Fractal theory, which includes the whole in a partial structure. Phase transition must be preceded by fluctuation. In addition to the pioneers' prominent act of creation in the fields of mathematics and visual an serving as drive behind change, other socio-cultural factors also served as motivations, influencing the transformation of the society through interdependency. In particular, this research focuses on the fact that scientific minds of artists in the Renaissance stimulated the birth of Perspective Geometry.

• Korean Institute of Interior Design Journal
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• no.22
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• pp.123-131
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• 2000

The purpose of this study is to propose a new design concept and properties within new paradigm. Contemporary students of architectural design seem to redefine the mechanic and reductive approach to design method based upon Euclidean geometry. In this study, the organic space-time and holistic view-point that constitutes the background for all this is radically different from the modern design. It consists of three sections as follow: First, it presents a concept of complex system and properties of complexity that we find in new natural science and tries to combine that news geometry with architectural design to provide a methodological basis for morphogenesis and transformation. Second, the complexity in architecture is defined as a fractal shape, folded space, and irreducible organic system that cannot be fully understood by modernist idea of architecture. Third, the complexity in architecture is strategy based on the electronic paradigm that would enable the emergence of creative possibility. The complexity theory offer new insights to explain not only natural laws but also define dynamic architecture. In fine, this study places a great emphasis on the organic world-view to the spatial organization, which I hope will contribute to generating a greater number of creative possibilities for design.

• Journal of Digital Contents Society
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• v.9 no.1
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• pp.109-116
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• 2008

The variation of real phenomena and shape of nature in our world is so complicated that some mathematical tools using the traditional geometric methods based on the Euclidean geometry and analytical differential method may be irrelevant or insufficient in some problems. Recently, to deal with these circumstances, one can use the fractal geometric method. As another measures, in this paper we introduce the non-integral order derivative function for the analytical method and construct to facilitate their calculation.

• Journal of KSNVE
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• v.7 no.3
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• pp.439-447
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• 1997

In this study, the dynamic instabilities of a nonlinear elastic system subjected to follower forces are investigated. The two-degree-of-freedom double pendulum model with nonlinear geometry, cubic spring, and linear viscous damping is used for the study. The constant, the initial impact forces acting at the end of the model are considered. The chaotic nature of the system is identified using the standard methods, such as time histories, power density spectrum, and Poincare maps. The responses are chaotic and unpredictable due to the sensitivity to initial conditions. The sensitivities to parameters, such as geometric initial imperfections, magnitude of follower force, direction control constant, and viscous damping, etc., are analysed. Dynamic buckling loads are computed for various parameters, where the loads are changed drastically for the small change of parameters.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.5
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• pp.61-71
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• 1998

Genetic Algorithm(GA) is a method of approaching optimization problems by modeling and simulating the biological evolution. GA needs large time-consuming, so ti had better do on a parallel computer architecture. Our proposed system has a VLSI-oriented interconnection network, which is constructed from a viewpoint of fractal geometry, so that self-similarity is considered in its configuration. The approach to Parallel Genetic Algorithm(PGA) on our proposed system is explained, and then, we construct the classifier system such that the set of samples is classified into weveral classes based on the features of each sample. In the process of designing the classifier system, We have applied PGA to the Traveling Salesman Problem and classified the sample set in the Euclidean space into several categories with a measure of the distance.

• Proceedings of the Korea Information Processing Society Conference
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• 2011.04a
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• pp.1441-1444
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• 2011

본 논문에서는 초등학교 교육과정에서 교육목표로 다루고 있는 창의성이라는 주제와 학교현장에서 초등학생들에게 쉽게 접목시킬 수 있는 교육용 프로그래밍 언어인 LOGO 프로그래밍과 프랙탈 기하이론을 초등학교 컴퓨터교육에 활용하기 위한 방안을 제시한다. 향후 컴퓨터교육과정은 알고리즘과 프로그래밍 영역이 포함될 예정이며, 이러한 알고리즘과 프로그래밍 교육에는 교육용 프로그래밍 언어 사용이 필수적이며 이의 활용에 대한 연구가 시급한 상황이다. LOGO 프로그래밍과 프랙탈을 함께 지도함으로서 규칙성, 반복성, 유사성, 닮음 등 수학적 개념을 쉽게 이해하는 것이 가능하므로, 이를 활용하여 초등학교 수학과 교육과정에서 반드시 학습해야 할 도형, 측정, 규칙성과 문제 해결 영역과 연계하여 지도하면 좋은 효과를 얻을 수 있을 것으로 기대된다.

• Proceedings of the Korean Geotechical Society Conference
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• 2010.09a
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• pp.790-799
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• 2010

The Upper Devonian Grossmont Formation in Alberta, Canada reserves an estimated 50 billion cubic meters of bitumen and possess about 1/6 of the total bitumen resources in northern Alberta. However, unlike the overlying Athabasca oil sands, non conventional bitumen resources has not been developed as yet. The carbonate rocks of Grosmont Formation have been subject to various stages of diagenesis, including dolomatization and karstification with a strong effect on the distribution of porosity and permeability, which resulted in highly heterogeneous reservoirs. An extensive fracture logging and mapping was performed on total of six boreholes located in the study area to explore the characteristics of fracture geometry system and the subsurface structures of carbonates reservoir that holds bitumen. Fractal dimension was used as a measure of the statistical homogeneity of the fractured rock masses. The applicability of random Cantor dust, Dc, as a fractal parameter was examined systematically. The statistical homogeneity of fractured carbonates rock masses was investigated in the study area. The structural domains of the rock masses were delineated depthwise according to estimated Dc. The major fracture orientation was dominated by horizontal beddings having dip of $0-20^{\circ}$. Also, fractures having high dip angles existed with relatively low frequency. Three dimensional fracture network modeling for each structural domain has been performed based on fracture orientation and intensity, and some representative conceptual models for carbonates reservoir in the study area has been proposed. The developed subsurface conceptual models will be used to capture the geomechanical characteristics of the carbonates reservoir.

• 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.

• Korean Journal of Soil Science and Fertilizer
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• v.44 no.3
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• pp.517-526
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• 2011

Soil structure plays an important role in ecological system, since it controls transport and storage of air, gas, nutrients and solutions. The study of soil structure requires an understanding of the interrelations and interactions between the diverse soil components at various levels of organization. Investigations of the spatial distribution of pore/particle arrangements and the geometry of soil pore space can provide important information regarding ecological or crop system. Because of conveniences in image analyses and accuracy, these investigations have been thrived for a long time. Image analyses from soil sections through impregnated blocks of undisturbed soil (2 dimensional image analyses) or from 3 dimensional scanned soils by computer tomography allow quantitative assessment of the pore space. Image analysis techniques can be used to classify pore types and quantify pore structure without inaccurate or hard labor in laboratory. In this paper, the last 50 years of the soil image analyses have been presented and measurements on various soil scales were introduced, as well. In addition to history of image analyses, a couple of examples for soil image analyses were displayed. The discussion was made on the applications of image analyses and techniques to quantify pore/soil structure.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.7
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• pp.1521-1528
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• 2010

This paper examines technical writing and teaching methods based on the perspectives of the complex learning system theory. So, the paper first discusses the constituent elements and characteristics of the complex learning system theory and continues to examine the potential of applying the complex learning system theory to new teaching methods. As a result, not only did the research expand the approach methods of providing technical writing education but also confirmed the potential of actual implementation. Such results will provide a leeway to start applying new teaching methods for technical writing education. Furthermore, the paper proposes more detailed case studies related to this topic as well as development of this research to produce textbooks and other higher level researches.