• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.182-185
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• 2005

Satellite cameras are calibrated before launch in detail and in general, but it cannot be guaranteed that the geometry is not changing during launch and caused by thermal influence of the sun in the orbit. Modem satellite imaging systems are based on CCD-line sensors. Because of the required high sampling rate the length of used CCD-lines is limited. For reaching a sufficient swath width, some CCD-lines are combined to a longer virtual CCD-line. The images generated by the individual CCD-lines do overlap slightly and so they can be shifted in x- and y-direction in relation to a chosen reference image just based on tie points. For the alignment and difference in scale, control points are required. The resulting virtual image has only negligible errors in areas with very large difference in height caused by the difference in the location of the projection centers. Color images can be related to the joint panchromatic scenes just based on tie points. Pan-sharpened images may show only small color shifts in very mountainous areas and for moving objects. The direct sensor orientation has to be calibrated based on control points. Discrepancies in horizontal shift can only be separated from attitude discrepancies with a good three-dimensional control point distribution. For such a calibration a program based on geometric reconstruction of the sensor orientation is required. The approximations by 3D-affine transformation or direct linear transformation (DL n cannot be used. These methods do have also disadvantages for standard sensor orientation. The image orientation by geometric reconstruction can be improved by self calibration with additional parameters for the analysis and compensation of remaining systematic effects for example caused by a not linear CCD-line. The determined sensor geometry can be used for the generation? of rational polynomial coefficients, describing the sensor geometry by relations of polynomials of the ground coordinates X, Y and Z.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.5
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• pp.279-286
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• 2020

In this study, we investigate the accuracy of higher order derivatives in the moving least square (MLS) difference method. An interpolation function is constructed by employing a Taylor series expansion via MLS approximation. The function is then applied to the mixed variational theorem in which the displacement and stress resultants are treated as independent variables. The higher order derivatives are evaluated by solving simply supported beams and cantilevers. The results are compared with the analytical solutions in terms of the order of polynomials, support size of the weighting function, and number of nodes. The accuracy of the higher order derivatives improves with the employment of the mean value theorem, especially for very high-order derivatives (e.g., above fourth-order derivatives), which are important in a classical asymptotic analysis.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.780-785
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• 2002

As the KOMPSAT-1 satellite can roll tilt up to $\pm$45$^{\circ}$, we have analyzed some EOC images taken at different tilt angles fur this study. The required ground coordinates for bundle adjustment and geometric accuracy, are read from the digital map produced by the National Geography Institution, at a scale of 1:5, 000. These are the steps taken for the tilting angle of KOMPSAT-1 satellite to be present in the evaluation of the accuracy of the geometric of each different stereo image data: Firstly, as the tilting angle is different in each image, the satellite dynamic characteristic must be determined by the sensor modeling. Then the best sensor modeling equation is determined. The result of this research, the difference between the RMSE values of individual stereo images is due more the quality of image and ground coordinates than to the tilt angle. The bundle adjustment using three KOMPSAT-1 stereo pairs, first degree of polynomials for modeling the satellite position were sufficient.

• Journal of Information Processing Systems
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• v.10 no.3
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• pp.395-411
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• 2014

Temporal medical data is often collected during patient treatments that require personal analysis. Each observation recorded in the temporal medical data is associated with measurements and time treatments. A major problem in the analysis of temporal medical data are the missing values that are caused, for example, by patients dropping out of a study before completion. Therefore, the imputation of missing data is an important step during pre-processing and can provide useful information before the data is mined. For each patient and each variable, this imputation replaces the missing data with a value drawn from an estimated distribution of that variable. In this paper, we propose a new method, called Newton's finite divided difference polynomial interpolation with condition order degree, for dealing with missing values in temporal medical data related to obesity. We compared the new imputation method with three existing subspace estimation techniques, including the k-nearest neighbor, local least squares, and natural cubic spline approaches. The performance of each approach was then evaluated by using the normalized root mean square error and the statistically significant test results. The experimental results have demonstrated that the proposed method provides the best fit with the smallest error and is more accurate than the other methods.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.89-100
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• 2001

The Ritz method Is applied In a three-dimensional (3-D) analysis to obtain accurate frequencies for thick. linearly tapered. annular plates. The method is formulated for annular plates haying any combination of free or fixed boundaries at both Inner and outer edges. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate. and a1gebraic polynomials in the radial and thickness co-ordinates. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant figures is demonstrated. Comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2-D classical thin place theory. Extensive and accurate ( four significant figures ) frequencies are presented 7or completely free. thick, linearly tapered annular plates haying ratios of average place thickness to difference between outer radius (a) and inner radius (b) radios (h$_{m}$/L) of 0.1 and 0.2 for b/L=0.2 and 0.5. All 3-D modes are included in the analyses : e.g., flexural, thickness-shear. In-plane stretching, and torsional. Because frequency data liven is exact 7o a\ulcorner least four digits. It is benchmark data against which the results from other methods (e.g.. 2-D 7hick plate theory, finite element methods. finite difference methods) and may be compared. Throughout this work, Poisson\`s ratio $\upsilon$ is fixed at 0.3 for numerical calculations.s.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Korean Journal of Soil Science and Fertilizer
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• v.36 no.4
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• pp.181-192
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• 2003

We developed a mathematical simulation model to portray the vertical distribution of soil water from the measured weather data and the known soil hydraulic properties, and then compared simulation results with the periodically measured soil water profiles obtained on Jungdong sandy loam to verify the model, In this model, we solved potential-based Richards' equation by the implicit finite difference method superimposed on the predictor-corrector scheme. We presumed that: soil hydraulic properties are homogeneous; soil water flows isothermally; hysteresis is not considered; no vapor flows; no heat transfers into the soil profiles; and water added to soil surface is distributed along the soil profile following partial displacement principle. The input data were broadly classified into two groups: (1) daily weather data such as rainfall, maximum and minimum air temperatures, relative humidity and solar radiation and (2) soil hydraulic data to approximate unsaturated hydraulic conductivity and water retention. Each hydraulic polynomial function approximated using the Chebyshev polynomial and least square difference technique in tandem showed a fairly good fit of the given set of data. Vertical distribution of soil water as approximations to the Richards' equation subject to changing surface and phreatic boundaries was solved numerically during 53 days with a comparatively large time increment, and this pattern agreed well with field neutron scattering data, except for the surface 0.1 m slab.

• Water for future
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• v.28 no.5
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• pp.151-162
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• 1995

A two-dimensional stream tube dispersion model is developed to simulate accurately transverse dispersion processes of pollutants in natural channels. Two distinct features of the stream tube dispersion model derived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in a natural coordinate system which follows the general direction of the channel flow. In the model studied, Eulerian-Lagrangian method is used to solve the stream tube dispersion equation. The stream tube dispersion equation is decoupled into two components by the operator-splitting approach; one is governing advection and the other is governing dispersion. The advection equation has been solved using the method of characteristics and the results are interpolated onto Eulerian grid on which the dispersion equation is solved by centered difference method. In solving the advection equation, cubic spline interpolating polynomials is used. In the present study, the results of the application of this model to a natural channel are compared with a steady-state flow measurements. Simulation results are in good accordance with measured data.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.8
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• pp.691-697
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• 2002

Myocardial ischemia is a disorder of cardiac function caused by insuficient blood flow to the muscle tissue of the heart. We can diagnose myocardial ischemia by observing the change of ST-segment, but this change is temporary. Our primary purpose is to detect the temporary change of the 57-segment automatically In the signal processing, the wavelet transform decomposes the ECG(electrocardiogram) signal into high and low frequency components using wavelet function. Recomposing the high frequency bands including QRS complex, we can detect QRS complex more easily. Amplitude comparison method is adopted to detect QRS complex. Reducing the effect of noise to the minimum, we grouped ECG by 5 data and compared the amplitude of maximum value. To recognize the ECG .signal pattern, we adopted the polynomial approximation partially and statistical method. The polynomial approximation makes possible to compare some ECG signal with different frequency and sampling period. The ECG signal is divided into small parts based on QRS complex, and then, each part is approximated to the polynomials. After removing the distorted ECG by calculating the difference between the orignal ECG and the approximated ECG for polynomial, we compared the approximated ECG pattern with the database, and we detected and classified abnormality of ECG.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.78.2-78.2
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• 2019

We develop an Alcock-Paczynski (AP) test method that uses the evolution of redshift-space two-point correlation function (2pCF) of galaxies. The method improves the AP test proposed by Li et al. (2015) in that it uses the full two-dimensional shape of the correlation function. Similarly to the original method, the new one uses the 2pCF in redshift space with its amplitude normalized. Cosmological constraints can be obtained by examining the redshift dependence of the normalized 2pCF. This is because the 2pCF should not change apart from the expected small non-linear evolution if galaxy clustering is not distorted by incorrect choice of cosmology used to convert redshift to comoving distance. Our new method decomposes the redshift difference of the 2-dimensional correlation function into the Legendre polynomials whose amplitudes are modelled by radial fitting functions. The shape of the normalized 2pCF suffers from small intrinsic time evolution due to non-linear gravitational evolution and change of type of galaxies between different redshifts. It can be accurately measured by using state of the art cosmological simulations. We use a set of our Multiverse simulations to find that the systematic effects on the shape of the normalized 2pCF are quite insensitive to change of cosmology over \Omega_m=0.21 - 0.31 and w=-0.5 - -1.5. Thanks to this finding, we can now apply our method for the AP test using the non-linear systematics measured from a single simulation of the fiducial cosmological model.