• 대한수학회지
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• 제40권3호
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• pp.517-561
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• 2003

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in $\mathbb{C}$. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제1권2호
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• pp.163-181
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• 1997

The paper deals with some aspects of early childhood geometry in the Czech Republic. Children's first geometrical experiences come from real life. In our opinion, there exist four types of geometrical experience which can be called the partition of space, the filling of space motion in space and the dimension of space. We distinguish three levels of the mathematical learning process: a spontaneous level, an operational level and a theoretical level.

• Journal of Electrochemical Science and Technology
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• 제1권2호
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• pp.112-116
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• 2010

Fractal property of the passivated steel surface was investigated on the basis of scaling analysis with a special focus on its relationship with corrosion resistance. For this purpose, the surface of stainless steel was intentionally oxidized under a variety of passivation conditions and its scaling property was analyzed by a triangulation method. The morphology of the passivated steel surface was satisfactorily evaluated with fractal dimension. From the chronoamperometry and impedance measurement, it proved that lower fractal dimension leads to more enhanced corrosion resistance. The higher passivity of the steel surface with lower fractal dimension was discussed in terms of active area and structural imperfection.

• 한국안전학회지
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• 제17권4호
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• pp.38-44
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• 2002

The application of fractal concept provides an useful method in the study for the quantitative analysis of irregular variations like the fracture surfaces and crack profiles. Fractal curves have characteristics that represents a self-similarity based on the fractal dimension. The fractal dimensions were obtained by the box counting method. In this report, we obtained the nearly stable fractal dimensions of fracture crack profiles for STS316 with CT specimen as the crack advances and the relationships between crack length and fractal dimension. Moreover fractal fracture parameter that corresponds to J-R curve is shown by the relationships between fractal dimension and crack extension. From the results, we concluded that crack extension of high toughness material also shows the fractal characteristics, which can be used in order to evaluate the crack life precisely.

• 한국정밀공학회지
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• 제17권9호
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• pp.166-173
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• 2000

A system for burr measurement is developed to measure the geometry of the burr formed in metal cutting or shearing operations. laser system is selected according to the required measuring accuracy and burr size. A specific program for calculating the burr geometry from measured laser data is developed. The raw data is obtained by scanning cross the burr. The height and width of burr are calculated. Due to the specific characteristic of laser peak or valley are formed in measuring sharp edges or small sharp cracks. Compensation for the peak or valley is carried out to make it possible to calculate the burr, burr geometry is measured in 3 dimension.

• 지질공학
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• 제3권2호
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• pp.149-165
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• 1993

지하매질의 유동특성을 알기 위한 직접적인 방법은 아직도 현장수리시험에 의존하고 있다. 열극암반에서 유동모델의 개념정립을 위하여는 열극체계분포와 특히, 수리시험해석결과가 중요시되고 있다. 국내에서 수행되고 있는 수리시험은 조사공구간별에 따른 수리전도도를 방사상의 정상류로 가정하여 결과를 해석하고 있다. 또한 시험대상 매질을 균질한 대수층 또는 단순한 기하학적 형태의 매질로 간주하며 구간별 투수량계수는 시험구간을 가로지르는 각 열극의 투수량계수의 합과 같다고 가정한다. 국내 기존의 수리시험 및 해석방법으로는 수리학적 경계면의 영향(boundary effects)이나 유동로의 기하학적 형태(flow geometry)에 대한 자료를 얻기가 힘들며, 일정한 조사공 주변을 벗어나면 투수성열극의 연결성에 대한 정보를 구할 수 없다. 열극특성을 고려한 지하수유동 해석을 위하여 단일공 정압주입시험을 실시하였으며, 비정상류해석방법을 통하여 유동차원(flow dimension)에 대한 분석을 시도하였다. 시추시에는 단일패커시험을 일정구간별로 시행하였으며, 조사공의 시추후에는 이중패커에 의한 구간별 시험을 실시하였다. 비정상류해석으로 구한 수리전도도값은 정상류해석의 결과와 큰 차이(10배 이내)는 없었으나, 정압하에서 도출된 유동량변화곡선에서 유동차원분석이 가능하였다. 상부구간(<10m 깊이)의 단일 및 이중패커시험결과는 모두 정상류의 유동차원이 나타났으며, 이는 영향반경의 경계면이 open system임을 알 수 있다. 15m 깊이에서 도출된 유동량변화곡선은 1차원 유동상태에서 3차원(구상유동)으로 변화하였다. 하부구간(25m 깊이)의 시험결과는 closed system 특성이 관찰되었으며, 이는 조사구간에서 연결된 열극이 수리적으로 격리되어 있음을 알 수 있다. 현장수리시험으로부터 보다 많은 자료를 도출하기 위하여는 무엇보다도 수리시험장비의 보완이 필요하다. 특히 조사구간을 완벽하게 분리할 수 있는 패커장비와 미세한 유동량변화를 계측할 수 있는 유량계의 확보가 필수적이며, 조사구간의 압력변화를 자동기록할 수 있는 계측기기가 필요하였다.

• 한국조경학회지
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• 제34권6호
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• pp.1-9
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• 2007

Land use types within a watershed closely are related with the water quality characteristics of receiving water bodies. Despite of a numerous studies suggesting a strong relationship between water quality and land use, there have been increasing concerns about the geographical variation and a lack of spatial integration in that relationship, which are essential to implementing these findings into land use planning and management. In the meantime, edges mediate the material flux between adjacent systems. This mediating effect of edges is strongly related to the complexity of their shapes. Land use activities within a watershed have a direct impact on the water quality of adjacent aquatic systems, and hydrological processes carry residuals from watershed into adjacent aquatic ecosystems through the edges. Therefore, the geometry of reservoirs theoretically affects the relationship between land uses in the watershed and the quality of receiving bodies of water. In this light, this study integrates the geo-spatial dimensions of land uses in the watershed using GIS and landscape indices in order to explore the relationship between land uses and water quality. Water quality characteristics, land uses and geometry of 133 randomly sampled reservoirs were correlated, based on buffer zones and types of reservoirs. The findings showed that land uses, particularly urban land uses, significantly affect water quality characteristics including BOD, COD, TN and TP, and geometry of reservoirs reduces the concentration of pollutant and nutrients in reservoirs. One of results indicates that the relationship between land use and water quality and effects of spatial dimension may vary with types of reservoirs and pollutants. These results suggest that lakeshore areas are important, particularly for TN reduction and call for a caution to land use activities nearby shoreline areas for sustaining better water quality.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 1999년도 봄 학술발표회 논문집
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• pp.277-284
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• 1999

This study describes the influence factors related to slope failure pattern and dimension in the southern Kyounggi area. Intrusive and metamorphic rocks are distributed in the study area. Geological condition, rainfall property and slope geometry are influence on slope failure characteristics in the study we& Geological factors related to slope failure are rock type, geological structure and weathering condition. Because of deep soil (RS-CW) depth of granite region, circular failure type is major failure pattern in granite region. Almost granite slopes with circular or surface failure pattern are failed during heavy rainfall season. But typical wedge failure type related to geological structure factor is a main failure pattern of metamorphic rock slope. Additionally failure dimension is influenced by geological factors and several factors, i.e. natural slope condition, failure type, rainfall intensity and etc. failure height/width ratio and thickness/length ratio of granite slope are 0.88 and 0.23. But the ratios of metamorphic rock slope are 1.36 and 0.19.

• Current Optics and Photonics
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• 제2권1호
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• pp.69-78
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• 2018

This paper presents a precise edge detection algorithm for the critical dimension (CD) measurement of a Thin-Film Transistor Liquid-Crystal Display (TFT-LCD) pattern. The sigmoid surface function is proposed to model the blurred step edge. This model can simultaneously find the position and geometry of the edge precisely. The nonlinear least squares fitting method (Levenberg-Marquardt method) is used to model the image intensity distribution into the proposed sigmoid blurred edge model. The suggested algorithm is verified by comparing the CD measurement repeatability from high-magnified blurry and noisy TFT-LCD images with those from the previous Laplacian of Gaussian (LoG) based sub-pixel edge detection algorithm and error function fitting method. The proposed fitting-based edge detection algorithm produces more precise results than the previous method. The suggested algorithm can be applied to in-line precision CD measurement for high-resolution display devices.

• Journal of Mechanical Science and Technology
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• 제15권10호
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• pp.1417-1422
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• 2001

Since fracture surface presents clear evidence to describe the circumstances of material failure event, analysis of fracture surface should provide plenty of useful information for failure prevention. Thus if we extract proper information from the fracture surface, the safety evaluation, for plant component could be more accurate. In general, the chaotic morphology of fracture surface is determined by the degree of material degradation as well as by other factors such as type of load, geometry of specimen, notch condition, microstructure of material and environment. In this research, we developed a fractal analysis technology for the fracture surface of aged turbine rotor steel based on the slit-island technique using an image analyzer. Moreover the correlation between the fractal dimension and the aging time was studied.