• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.237-242
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• 1994

An quintic spline interpolate to a function in $C^{10}$[a, b] and its O($h^6$) error behavior are presented when its fourth derivative satisfies some kind of end conditions. The O($h^6$) relations between its derivatives up to fourth order and the m-th derivatives of the given function are also given at the nodes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.2C
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• pp.166-173
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• 2007

In Orthogonal Frequency Division Multiplexing (OFDM) systems, Narrow-Band Jamming (NBJ) over pilot tones used for channel estimation degrades the system performance. In this paper, we propose a new jammed pilot detection and elimination algorithm to overcome this problem. Moreover, the average Mean-Squared Error (MSE) on one OFDM symbol both under jammed and removed pilot subcarrier is analyzed. And then, the Symbol Error Rate (SER) performance of the channel estimation scheme using the proposed algorithm is evaluated by simulation. We can confirm that the channel estimator with the proposed algorithm improves the channel estimation performance at a high jamming power.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Economic and Environmental Geology
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• v.56 no.3
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• pp.331-341
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• 2023

When creating a soil contamination map using geostatistical techniques, there are various sources that can affect prediction errors. In this study, a grid-based soil contamination map was created from the sampling data of heavy metal concentrations in soil in abandoned mine areas using Ordinary Kriging. Five factors that were judged to affect the prediction error of the soil contamination map were selected, and the variation of the root mean squared error (RMSE) between the predicted value and the actual value was analyzed based on the Leave-one-out technique. Then, using a machine learning algorithm, derived the top three factors affecting the RMSE. As a result, it was analyzed that Variogram Model, Minimum Neighbors, and Anisotropy factors have the largest impact on RMSE in the Standard interpolation. For the variogram models, the Spherical model showed the lowest RMSE, while the Minimum Neighbors had the lowest value at 3 and then increased as the value increased. In the case of Anisotropy, it was found to be more appropriate not to consider anisotropy. In this study, through the combined use of geostatistics and machine learning, it was possible to create a highly reliable soil contamination map at the local scale, and to identify which factors have a significant impact when interpolating a small amount of soil heavy metal data.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Journal of Mechanical Science and Technology
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• v.20 no.12
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• pp.2189-2196
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• 2006

The present work is concerned with the development of a procedure for adaptive computations of shear localization problems. The maximum jump of equivalent strain rates across element boundaries is proposed as a simple error indicator based on interpolation errors, and successfully implemented in the adaptive mesh refinement scheme. The time step is controlled by using a parameter related to the Lipschitz constant, and state variables in target elements for refinements are transferred by $L_2$-projection. Consistent tangent moduli with a proper updating scheme for state variables are used to improve the numerical stability in the formation of shear bands. It is observed that the present adaptive mesh refinement procedure shows an excellent performance in the simulation of shear localization problems.

• International Journal of Aeronautical and Space Sciences
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• v.10 no.1
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• pp.1-14
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• 2009

When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect, it's state equation remains always valid, except, it was called by gas calorically imperfect or gas at high temperatures. The purpose of this work is to develop a mathematical model for a normal shock wave normal at high temperature when the stagnation temperature is taken into account, less than the dissociation of the molecules as a generalisation model of perfect for constant heat specific. A study on the error given by the perfect gas model compared to our model is presented in order to find a limit of application of the perfect gas model. The application is for air.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.267-272
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• 1993

This paper presents the performance and problems in analysis method and testing system of Electronic Speckle Pattern Interferometry (ESPI) method, in measuring two-dimensional in-plane displacement. The anyalysis result of measurement by ESPI is quite comparable to that of measurement by strain gauge method. This implieds that the method of ESPI is a very effective tool in non-contact two-dimensional in-planc strain analysis. But there is a controversal point,measurment error. This error is discussed to be affected not by ESPI method itseif, but by its analysis scheme of the interference fringe,where the first-order interpolation has been applied to the points of strain measured. In this case, it is turned out that the more errors would be occured in the large interval of fringe. so, this paper describes a computer method for drawing when the height is available only for some arbitary collection of points, the method is based on a distance-weighted, least-squares approximation technique, with the weight varying with the distance of the data points.

• Journal of the Korean Statistical Society
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• v.14 no.2
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• pp.63-75
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• 1985

This paper considers a statistical calibration problem in which the standard as wel as the nonstandard measurement is subject to error. Since the classicla approach cannot handle this situation properly, a functional relationship model with additional feature of prediction is proposed. For the analysis of the problem four different approaches-two estimation techniques (ordinary and grouping least squares) combined with two prediction methods (classical and inverse prediction)-are considered. By Monte Carlo simulation the perromance of each approach is assessed in term of the probability of concentration. The simulation results indicate that the ordinary least squares with inverse prediction is generally preferred in interpolation while the grouping least squares with classical prediction turns out to be better in extrapolation.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.12
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• pp.134-137
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• 1994

In this paper, we describe an approach to ECG data coding based on a fractal theory of iterated contractive transformations defined piecewise. The main characteristic of this approach is that it relies on the assumption that signal redundancy can be efficiently captured and exploited through piecewise self-transformability on a block-wise basis. The variable range size technique is employed to reduce the reconstruction error. Large ranges are used for encoding the smooth waveform to yield high compression efficiency, and the smaller ranges are used for encoding rapidly varying parts of the signal to preserve the signal quality. The suggested algorithm was evaluated using MIT/BIH arrhythmia database. A high compression ratio is achieved with a relatively low reconstruction error.