• Honam Mathematical Journal
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• v.30 no.2
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• pp.233-246
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• 2008

In this paper, we obtain the general solution of the following cubic type functional equation and establish the stability of this equation (0.1) $kf({{\sum}\limits^{n-1}_{j=1}}x_j+kx_n)+kf({{\sum}\limits^{n-1}_{j=1}}x_j-kx_n)+2{{\sum}\limits^{n-1}_{j=1}}f(kx_j)+(k^3-1)(n-1)[f(x_1)+f(-x_1)]=2kf({\sum\limits^{n-1}_{j=1}}x_j)=K^3{\sum\limits^{n-1}_{j=1}[f(x_j+x_n)+f(x_j-x_n)]$ for any integers k and n with k ${\geq}$ 2 and n ${\geq}$ 3.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.7
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• pp.1515-1522
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• 1997

Several image coding algorithms have been developed for the telecommunication and multimedia systems with high image quality and high compression ratio. In order to achieve low entropy and distortion, the system should pay great cost of computation time and memory. In this paper, the uniform cubic lattice is chosen for Lattice Vector Quantization (LVQ) because of its generic simplicity. As a transform coding, the Discrete Wavelet Transform (DWT) is applied to the images because of its multiresolution property. The proposed algorithm is basically composed of the biorthogonal DWT and the uniform cubic LVQ. The multiresolution property of the DWT is actively used to optimize the entropy and the distortion on the basis of the distortion-rate function. The vector codebooks are also designed to be optimal at each subimage which is analyzed by the biorthogonal DWT. For compression efficiency, the vector codebook has different dimension depending on the variance of subimage. The simulation results show that the performance of the proposed coding mdthod is superior to the others in terms of the computation complexity and the PSNR in the range of entropy below 0.25 bpp.

• Environmental and Resource Economics Review
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• v.11 no.4
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• pp.633-657
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• 2002

This study presents a demand modelling for landfill gas, which is used as alternative energy source for district cooling business. By analyzing the cost minimizing behavior of producer facing with three alternative energy sources such as electricity, cooling heat water, and gas, a demand function for landfill gas is derived from the optimal operating time of gas fired production facility, and estimated using unpublished data, which are associated with Seoul city's development plan for Sang-am area. The estimation results repeals that Seoul City could supply the land-fill gas of 13.76 million cubic meters each year at the price of about 16 won per cubic meters. However, if the investment costs associated with installation of gas collecting facilities are treated as sunk costs, annual amount of gas supplied is expected to increase to 14.22 million cubic meters at a lower unit price of 14.76 won.

• 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.

• Korean Journal of Applied Biomechanics
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• v.14 no.3
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• pp.301-311
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• 2004

The purpose of this study was to verify the usefulness of the Mathcad program as a tool for the studying and teaching the sport biomechanics. A projectile motion was analyzed because it is the one of the most popular motion in sports activities. A 3 dimensional CG data for the high jump bar clear phase was used to calculate the initial velocity vector of the CG. Linear regression function and other functions such as cubic spline and derivative of Mathcad were used to calculate this vector. Finally, the approach angle to the bar and peak jump height was calculated. Programming in Mathcad was relatively easy compare to traditional computer language such as Fortran and C, because of the unique documentation method of Mathcad. Additionally the 2 and 3 dimensional graph function was very easy and useful to describe the mechanical data. If the use of Mathcad program is more popular in the field of sport biomechanics, it could greatly contribute to overcome the limit of research caused by the lack of proper programming ability.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.358-363
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• 1998

An algorithm for representing the cubic spline interpolation of differentiable functions by a fuzzy system is presented in this paper. The cubic B-spline functions which form a basis for the interpolation function are used as the fuzzy sets for input fuzzification. The ordinal number of the coefficient cKL in the list of the coefficient cij's as sorted in increasing order, is taken to be the output fuzzy set number in the (k, l) th entry of the fuzzy rule table. Spike functions are used for the output fuzzy sets, with cij's as support boundaries after they are sorted. An algorithm to compute the support boundaries explicitly without solving the matrix equation involved is included, along with a few properties of the fuzzy rule matrix for the designed fuzzy system.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.193-200
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• 1992

This paper uses a piecewise ratonal cubic interpolant to solve the problem of shape preserving interpolation for plane curves; scalar curves are also considered as a special case. The results derived here are actually the extensions of the convexity preserving results of Delbourgo and Gregory [Delbourgo and Gregory'85] who developed a $C^{1}$ shape preserving interpolation scheme for scalar curves using the same piecewise rational function. They derived the ocnstraints, on the shape parameters occuring in the rational function under discussion, to make the interpolant preserve the convex shape of the data. This paper begins with some preliminaries about the rational cubic interpolant. The constraints consistent with convex data, are derived in Sections 3. These constraints are dependent on the tangent vectors. The description of the tangent vectors, which are consistent and dependent on the given data, is made in Section 4. the convexity preserving results are explained with examples in Section 5.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.379-387
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• 2006

Local polynomial regression is widely used because of good properties such as such as the adaptation to various types of designs, the absence of boundary effects and minimax efficiency Choi and Hall (1998) proposed an estimator of regression function using a convex combination idea. They showed that a convex combination of three local linear estimators produces an estimator which has the same order of bias as a local cubic smoother. In this paper we suggest another estimator of regression function based on a convex combination of five local constant estimates. It turned out that this estimator has the same order of bias as a local cubic smoother.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.4
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• pp.241-250
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• 1986

Current distributions are the basis of analyzing and designing the antenna. In this paper, a method of deriving the current distribution of a spiral shaped thin wire scattere is proposed when plane wave is incident on it. The calculated results are also shown for severla spiral sizes and incidence angles selected. For numerical calculation, the method of point matching is used with a cubic B-spline function as a basis function.

• Journal of Korean Society for Quality Management
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• v.25 no.3
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• pp.51-61
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• 1997

We introduce a method of estimating an unknown failure rate function based on sample data. We estimate failure rate function by a function s from a space of cubic splines constrained to be linear (or constant) in tails using maximum likelihood estimation. The number of knots are determined by Bayesian Information Criterion(BIC). Examples using simulated data are used to illustrate the performance of this method.