• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.105-112
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• 1990

Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $\hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(\hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{\infty}$ norms.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.4
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• pp.286-290
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• 2005

We consider the poisson equation where the functions involved are periodic including the solution function. Let $R=[0,1]{\times}[0,l]{\times}[0,1]$ be the region of interest and let $\phi$(x,y,z) be an arbitrary periodic function defined in the region R such that $\phi$(x,y,z) satisfies $\phi$(x+1, y, z)=$\phi$(x, y+1, z)=$\phi$(x, y, z+1)=$\phi$(x,y,z) for all x,y,z. We describe a very simple method for solving the equation ${\nabla}^2u(x, y, z)$ = $\phi$(x, y, z) based on the cubic spline interpolation of u(x, y, z); using the requirement that each interval [0,1] is a multiple of the period in the corresponding coordinates, the Laplacian operator applied to the cubic spline interpolation of u(x, y, z) can be replaced by a square matrix. The solution can then be computed simply by multiplying $\phi$(x, y, z) by the inverse of this matrix. A description on how the storage of nearly a Giga byte for $20{\times}20{\times}20$ nodes, equivalent to a $8000{\times}8000$ matrix is handled by using the fuzzy rule table method and a description on how the shape preserving property of the Laplacian operator will be affected by this approximation are included.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1996.03b
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• pp.121-129
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• 1996

This study aimsdetecting defects for the forming precesses of X2 spline, which is designed by an industry expert. The exist process consists of 3 runs and 7 operations with 3 heat treatments. The rigid-plastic FEM analysis was carried out to design a new process and some defects were found. Thus the design was modified to get better results. it is ocnfirmed that the industry expert agree the possibility of defects derived from the FEM results.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.371-386
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• 2001

In this work we investigate the finite element preconditioning method for the $C^1$-cubic spline collocation discretizations for an elliptic operator A defined by $Au := -{\Delta}u + a_1u_x+a_2u_y+a_0u$ in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.985-994
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• 1994

Boundary value problems are common in nature. Here we restrict our attention to the second order differential equations of the form $$ (1.1) \frac{d^2 y}{dx^2} = P(x)y(x) + Q(x), 0 \leq x \leq 1, $$ $$ y(0) = \alpha, $$ $$ y(1) = \beta, $$ where P(x) and Q(x) are continuous functions with $P(x) \geq 0, x \in [0, 1]$.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.569-573
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• 2001

An approximate representation of discrete functions {f$_{i,j}\mid$｜i, j=-1, 0, 1, …, N+1}in two variables by a fuzzy system is described. We use the cubic B-splines as fuzzy sets for the input fuzzification and spike functions as the output fuzzy sets. The ordinal number of f$_{i,j}$ in the sorted list is taken to be the out put fuzzy set number in the (i, j) th entry of the fuzzy rule table. We show that the fuzzy system is an exact representation of the cubic spline function s(x, y)=$\sum_{N+1}^{{i,j}=-1}f_{i,j}B_i(x)B_j(y)$ and that the approximation error S(x, y)-f(x, y) is surprisingly O($h^2$) when f(x, y) is three times continuously differentiable. We prove that when f(x, y) is a gray scale image, then the fuzzy system is a smoothed representation of the image and the original image can be recovered exactly from its fuzzy system representation when it is a digitized image.e.

• Textile Coloration and Finishing
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• v.2 no.3
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• pp.14-25
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• 1990

An extension method of data points of Munsell color space is described. A cubic spline method is used for this extension and the charts made by the use of these points are recommended for general use in the textile industry in determining the Munsell notation (H, V, C) of a given color sample when the CIE sepcification (Y, x, y) is known. These data points are used for the analysis of the H-C plane of Munsell color space.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.289-292
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• 2002

2계 선형 상미분방정식의 경계치 문제는 보통 해를 구하고자 하는 구간의 양 끝점에서 도함수의 값을 임의로 선정한 후 각 점에서 초기치 문제의 해를 구한 다음 적절한 1차 결합을 이용하여 구하게 된다. 이 경우 초기값과 도함수 값을 사용한 반복연산이 수반되며 따라서 오차의 누적이 불가피 하게 된다. 이 논문에서는 이같은 오차의 누적을 피할 뿐 아니라 3차 Spline 함수를 사용함으로써 오차가 O( $h^2$)인 해를 구하는 방법에 대하여 기술한다 두 개의 경계조건과 근사값을 구하고자 하는 점에서의 함수 값을 "If x is $B_{i}$, then f is $C_{i}$"와 같은 Fuzzy Rule들로 변형하고 주어진 미분방정식을 상수 $C_{i}$들의 관계식으로 변형하여 해를 구하였다. 산출된 결과로부터의 보간 연산은 Fuzzy System사용에 의하여 대체되었다. 이상의 방법으로 산출한 해의 근사오차가 O( $h^2$).임을 증명하였으며 3개의 예제에 대한 계산결과를 4계 Runge-Kutta 방법에 의한 해와 비교하여 기술하였다였다였다였다

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.4 no.4
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• pp.242-249
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• 2011

In this study, The degree of scoliosis, an algorithm that can automatically detect was developed. Developed system was used for X-ray imaging source. The formula for the degree of curvature of the spine of the S <0, and, L> 0 is satisfied with the condition $Y=SX^2+L$ is a function expression. X-axis length can be changed and applied equally in all spline function graph, and the slope is $S=-L/92^2$. The graph on the degree of scoliosis of the differential equation Y'= 2SX could see that the extracted spine wire for the classification and the classification of scoliosis, the degree is determined as the available algorithms.

• Korean Journal of Remote Sensing
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• v.8 no.2
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• pp.131-145
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• 1992

A low cost personal computer and image processing S/W were empolyed to derive Digtal Elevation Model(DEM) of tidal flat from multitemporal LANDSAT TM images, and to create three-dimensional(3D) perspective views of the tidel flat on Komso bay in west coasts of Korea. The method for generation of Digital Elevation Model(DEM) in tidal flat was considered by overlapping techniques of multitemporal LANDSAT TM images and interpolations. The boundary maps of tidal flat extracted from multitemporal images with different water high were digitally combined in x, y, z space with tide in formation and used as an inputcontour data to obtain an elevation model by interpolation using spline function. Elevation errors of less than $\pm$0.1m were achived using overlapping techniques and a spline interpolation approach, respectively. The derived DEM allows for the generation of a perspective grid and drape on the satellite image values to create a realistic terrain visualization model so that the tidal flat may be viewed from and desired direction. As the result of this study, we obtained elevation model of tidal flats which contribute to characterize of topography and monitoring of morphological evolution of tidal flats. Moreover, the modal generated here can be used for simulation of innudation according to tide and support other studies as a supplementary data set.