• Journal of the Korean Chemical Society
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• v.63 no.6
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• pp.473-485
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• 2019

In this study, we investigated the differences of graph constructed by middle school students in daily-life and scientific contexts according to the views on the nature of scientific measurement. A test consisting of three similar data sets regarding daily-life and scientific contexts was developed, and administered to 151 ninth graders. They were expected to construct proportional, inverse-proportional, and increasing and become constant form of graphs for each data set. Graphs constructed were analyzed in the aspects of constructing a trend line (types of a trend line, interpolation/extrapolation), selecting axes variables, scaling axes, and plotting points. Analyses of the results revealed that the students with set paradigm tended to construct a curved trend line, while those with point paradigm constructed a broken trend line in inverse-proportional graph questions. In the aspects of interpolation/extrapolation, most students with set paradigm performed both interpolation and extrapolation better than those with point paradigm in scientific context. Most students with set paradigm performed both interpolation and extrapolation regardless of contexts, while the proportion of interpolation of those with point paradigm was higher in scientific context than in daily-life context. In selecting axes variables, scaling axes, and plotting dots, there were no statistically significant differences between set and point paradigms. On the bases of the results, educational implications for improving graph construction skills of middle school students are discussed.

• The Journal of Engineering Geology
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• v.33 no.3
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• pp.439-459
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• 2023

Numerical analysis has been adopted in nearly all modern scientific and engineering fields due to the rapid and ongoing evolution of computational technology, with the number of grid or mesh points in a given data field also increasing. Some values must be extracted from large data fields to evaluate and supplement numerical analysis results and observational data, thereby highlighting the need for a fast and effective interpolation approach. The quadrilateral irregular network (QIN) proposed in this study is a fast and reliable interpolation method that is capable of sufficiently satisfying these demands. A comparative sensitivity analysis is first performed using known test functions to assess the accuracy and computational requirements of QIN relative to conventional interpolation methods. These same interpolation methods are then employed to produce simple numerical model results for a real-world comparison. Unlike conventional interpolation methods, QIN can obtain reliable results with a guaranteed degree of accuracy since there is no need to determine the optimal parameter values. Furthermore, QIN is a computationally efficient method compared with conventional interpolation methods that require the entire data space to be evaluated during interpolation, even if only a subset of the data space requires interpolation.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.713-719
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• 2011

The problem of approximation from a set of scattered data arises in a wide range of applied mathematics and scientific applications. In this study, we present a quasi-interpolatory approximation scheme for scattered data approximation problem, which reproduces a certain space of polynomials. The proposed scheme is local in the sense that for an evaluation point, the contribution of a data value to the approximating value is decreasing rapidly as the distance between two data points is increasing.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.2
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• pp.94-104
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• 2002

As a part of scientific data visualization automatic generation algorithms for a contour map have been investigated mainly on data which are defined at every lattice point. But in actual situation like weather data measurement. it is impossible to get data defined at every lattice point This is because the exact value on every lattice point can not be obtained due to characteristics in sampling devices or sampling methods. In order to define data on every lattice point where data were not sampled an interpolation method. was applied to the sample data to assign approximate values for some lattice type data but by using the non-lattice type of sample data sets. A triangle data link was defined by using non lattice points directly based on actually sample data set, not by using the pre-processed rectangle lattice points. The suggested algorithm generates a contour map a contour map only by using sample data set which are much smaller than old one without data interpolation and there is no skew on data any more since it does not need any interpolation to get the values of the defined lattice points.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.267-296
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• 2018

This paper studies the Cauchy problem and blow-up phenomena for a new generalized Camassa-Holm equation with cubic nonlinearity in the nonhomogeneous Besov spaces. First, by means of the Littlewood-Paley decomposition theory, we investigate the local well-posedness of the equation in $B^s_{p,r}$ with s > $max\{{\frac{1}{p}},\;{\frac{1}{2}},\;1-{\frac{1}{p}}\},\;p,\;r{\in}[0,{\infty}]$. Second, we prove that the equation is locally well-posed in $B^s_{2,r}$ with the critical index $s={\frac{1}{2}}$ by virtue of the logarithmic interpolation inequality and the Osgood's Lemma, and it is shown that the data-to-solution mapping is $H{\ddot{o}}lder$ continuous. Finally, we derive two kinds of blow-up criteria for the strong solution by using induction and the conservative property of m along the characteristics.

• ETRI Journal
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• v.22 no.2
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• pp.1-10
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• 2000

Pattern recognition is one of the most common problems encountered in engineering and scientific disciplines, which involves developing prediction or classification models from historic data or training samples. This paper introduces a new approach, called the Representational Capability (RC) algorithm, to handle pattern recognition problems using radial basis function (RBF) models. The RC algorithm has been developed based on the mathematical properties of the interpolation and design matrices of RBF models. The model development process based on this algorithm not only yields the best model in the sense of balancing its parsimony and generalization ability, but also provides insights into the design process by employing a design parameter (${\delta}$). We discuss the RC algorithm and its use at length via an illustrative example. In addition, RBF classification models are developed for heart disease diagnosis.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.397-410
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• 2007

Visualization of 2D and 3D data, which arises from some scientific phenomena, physical model or mathematical formula, in the form of curve or surface view is one of the important topics in Computer Graphics. The problem gets critically important when data possesses some inherent shape feature. For example, it may have positive feature in one instance and monotone in the other. This paper is concerned with the solution of similar problems when data has convex shape and its visualization is required to have similar inherent features to that of data. A rational cubic function [5] has been used for the review of visualization of 2D data. After that it has been generalized for the visualization of 3D data. Moreover, simple sufficient constraints are made on the free parameters in the description of rational bicubic functions to visualize the 3D convex data in the view of convex surfaces.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.25 no.3
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• pp.257-266
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• 2007

The research on red tide is generally in progress through field work, such as the naked eye and sampling. It was difficult to forecast exactly the course, from appearance of red tide to disappearance. with the established ways of investigation and analysis. Accordingly it is need to analyze environmental factors in time and space, the appearance of red tide and the path of its migration by more objective and scientific methods. In this study, GIS is applied to analyse the space character of red tide and the interpolation of IDW(Inverse Distance Weight) is applied to assume the density distribution of red tide after gather data by using Arc/Info. After IDW interpolation, the sea area occurred over 1,000 cells/ml of red tide density is extracted with CON and SUM Function of Grid Module, and the density of the sea area is accumulated daily. As a result of this study, the distribution condition of red tide is found timely and spacially by applying GIS to the sea area of red tide, the results indicated that the spatial density and the cumulative frequency about the origin of red tide using GIS, the sea area demonstrated that the maximum density and the maximum frequency varied significantly over the Nammyun of Namhae-Is. with the maximum frequency being 49 times. accordingly if data about the areas of red tide will occur from the present are accumulated, the shifting route of red tide occurrence and extinction can be predicted.

• Journal of computational fluids engineering
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• v.17 no.2
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• pp.35-41
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• 2012

This paper presents incompressible Navier-Stokes solution algorithm for 2D Free-surface flow problems on the Cartesian mesh, which was implemented to run on Graphics Processing Units(GPU). The INS solver utilizes the variable arrangement on the Cartesian mesh, Finite Volume discretization along Constrained Interpolation Profile-Conservative Semi-Lagrangian(CIP-CSL). Solution procedure of incompressible Navier-Stokes equations for free-surface flow takes considerable amount of computation time and memory space even in modern multi-core computing architecture based on Central Processing Units(CPUs). By the recent development of computer architecture technology, Graphics Processing Unit(GPU)'s scientific computing performance outperforms that of CPU's. This paper focus on the utilization of GPU's high performance computing capability, and presents an efficient solution algorithm for free surface flow simulation. The performance of the GPU implementations with double precision accuracy is compared to that of the CPU code using an representative free-surface flow problem, namely. dam-break problem.

• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.238-238
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• 2018

2011년 동일본 대지진으로 발생된 지진해일로 인해 막대한 경제적 손실과 인명피해가 발생하였고, 2차적 사회적 피해가 지속되고 있다. 또한 국내에서도 최근 경주와 포항지역에서 지진이 발생하여 피해가 발생함에 따라 재난의 불확실성에 대한 대비의 중요성이 강조되고 있고, 과거 안전하다고 했던 재난에 대한 위험성에 대해 국민들의 관심이 증대되었다. 피해사례가 2차례 있는 지진해일의 경우도 동일본 대지진 이후로 전 세계적으로 해일에 대한 위험성이 재평가되고 있다. 지진해일은 해저에서 발생하는 지진에 의한 것으로 발생지점 및 강도 등을 예측하기가 쉽지 않으므로, 지진발생에 대한 가상 시나리오를 이용한 연구가 진행되고 있다. 가상 시나리오를 활용하여 현재까지 많은 침수예상도가 제작되었으나, 다양한 시나리오 대해서 검토되지 않았다. 따라서 본 연구에서는 과학적 보간법을 이용하여 수치모형을 수행하지 않고 기수행된 연구 DB를 활용하여 지진해일 피해를 예측하는 기술을 개발하였다. 연구 DB는 국립재난안전연구원에서 수행된 지진해일 자료를 활용하였고, 전국단위를 기반으로 지진규모 7.0~9.0 내에 지진해일을 유발하는 지진에 대해 지진해일의 피해를 예측할 수 있는 기술을 개발하였다. 기술을 검증하기 위해 5개의 진원지에 대하여 과거 발생 지진규모부터 극한의 지진규모를 가정한 수치모의 결과와 본 연구의 결과를 비교하였다. 본 연구는 격자 1km인 광역모형의 모의결과를 활용하였으므로 실제로 해안지역의 침수양상의 정확도가 높지 않지만 향후 고정밀 공간해상도에 대하여 모의를 수행한다면 지진해일로 발생하는 범람 및 침수를 보다 정밀하게 예측할 수 있을 것이라 기대된다.