• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.627-644
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• 2009

The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method to prove optimal accuracy via energy estimate. The main key in this proof is to construct the intermediate equation which is formed to gauge-Uzawa algorithm. We will estimate velocity errors via comparing with the intermediate equation and then evaluate pressure errors via subtracting gauge-Uzawa algorithm from Navier-Stokes equations.

• Korean Journal of Optics and Photonics
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• v.13 no.3
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• pp.182-188
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• 2002

We have analyzed the phase-calculation-error of a three-dimensional shape measurement system using the projection of phase shifted fringe patterns. In this study, we have dealt various errors; an error caused by the variation of quantization levels, an error caused by the defocus of fringe pattern projected images, an error caused by phase-shifting errors, an error caused by the intensity variation of the background and modulation amplitude of fringe pattern projected images during the projection of multiple patterns, an error caused by the distortion of sinusoidal shape of a fringe pattern. The results will contribute to the design of a three-dimensional shape measurment system and give an important meaning to the calculation and the analysis of the accuracy of a system.

• The korean journal of orthodontics
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• v.33 no.2 s.97
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• pp.73-84
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• 2003

This study was performed to find out how much projection errors in the cephalometric measurements were made by vertical head rotation in taking posteroanterior cephalograms. 25 adults without any apparent facial asymmetry or severe sagittal skeletal discrepancy were selected and the posteroanterior cephalograms were taken with the head rotated $5^{\circ},\;10^{\circ}$ superior and inferior each to the reference $position(0^{\circ})$. The 7 height, 5 width and 6 angular measurements were taken at each 5 positions. Through the statistical analysis of all measurements taken at each rotated position, folowing results were obtained.1. The projection errors of height measurements were remarkably target than those of width or angular measure nents. f. Among the height measurements, the farther to the rotation axis the measurements were, the larger the projection errors were. 3. Among the width measurements, mandibular width and mandibular width of mandibular first molars showed significant differences between the values taken at each rotated position, while nasal width, maxillary width and intermolar width of maxillary first molars did not. 4. Among the angular measurements, the angle between horizontal reference line and the line that is connected to crista galli and antegonion or maxillare showed significant differences between the values taken at each rotated Position. The above results suggest that it is needed to the effort to keep constant head position for taking the useful posteroanterior cephalogra, because projection errors are caused by vertical head rotation.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.16 no.2
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• pp.327-335
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• 1998

Many kinds of map projection have been used, since this cannot be done without a distortion and seemless representation of the globe. To overcome the continues representation of large digital terrain information by the global coordinate system , to find out the sources of projection error and optimizing method, and to increase the map accuracy, specific map projection researches are needed. In this study, improvements of map projections are suggested for small scale mapping which covering entire Korean peninsula based on theoretical evaluation and limits of current map projection. Furthermore, distortion factors, positional errors, and accuracy increasing method are evaluated.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.34 no.2
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• pp.171-183
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• 2016

Small-scale maps currently used are made by scanning and editing printed maps and its shortcoming is accumulated errors at the time of editing and low accuracy. TM projection method is used but its accuracy varies. In addition, small-scale maps are made without consideration of usability and compatibility with other scale maps. Therefore, it is necessary to suggest projection and coordinates system improvement methods in consideration of usability and compatibility between data. The results of this study reveal that in order to make the optimum small-scale map, projection that fits the purpose of map usage in each scale, coordinate system and neat line composition should be selected in consideration of interrelation and compatibility with other maps. Conic projection should be used to accurately illustrate the entire country, but considering usability and compatibility with other maps, traversing cylindrical projection should be used instead of conic projection. For coordinates system of the small-scale map, Universal Transverse Mercator (UTM-K) based on the World Geodetic System should be used instead of conventional longitude and latitude coordinate system or Transverse Mercator.

• The korean journal of orthodontics
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• v.30 no.1 s.78
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• pp.53-66
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• 2000

This study was performed to find out the effect of projection errors on cephalometric linear and angular measurements according to head rotation during taking lateral cephalometric radiographs. Seventeen skulls with permanent dentition and no gross asymmetry were obtained from the Department of Anatomy, Medical School, Chosun University. Total 527 x-ray films were taken with $1^{\circ}$ interval from the reference position($0^{\circ}$) to ${\pm}15^{\circ}$ around the vertical axis (Z axis) which is perpendicular to the midpoint of the line connecting the center of two ear rods in submento-vertex direction. Statistical analysis was performed by paired t-test if there were statistically significant differences between the mean of the reference position($0^{\circ}$) and that of each rotation angle. The following results were obtained. 1. The projection errors of angular measurements were smaller than those of linear measurements. 2. The projection errors of angular measurements including midline landmarks were smaller than those including bilateral landmarks. 3. The horizontal linear measurements were gradually decreased when the stroll was rotated toward the film, but slightly increased and then decreased when the skull was rotated toward the focal spot. However, the changes were smaller in focal direction. 4. The projection errors of horizontal linear measurements were larger than those of vertical linear measurements. 5. The projection errors of vertical linear measurements were increased with increased distance from the rotation axis to vertical measurements. It is concluded that the use of angular measurements rather than linear measurements is recommended to minimize the projection errors.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.43-56
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• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.125-150
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• 2013

The stabilized Gauge-Uzawa method (SGUM), which is a second order projection type algorithm to solve the time-dependent Navier-Stokes equations, has been newly constructed in 2013 Pyo's paper. The accuracy of SGUM has been proved only for time discrete scheme in the same paper, but it is crucial to study for fully discrete scheme, because the numerical errors depend on discretizations for both space and time, and because discrete spaces between velocity and pressure can not be chosen arbitrary. In this paper, we find out properties of the fully discrete SGUM and estimate its errors and stability to solve the evolution Navier-Stokes equations. The main difficulty in this estimation arises from losing some cancellation laws due to failing divergence free condition of the discrete velocity function. This result will be extended to Boussinesq equations in the continuous research (part II) and is essential in the study of part II.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.9
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• pp.148-156
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• 2014

In the MVDR (minimum variance distortionless response) adaptive array, its performance could be greatly deteriorated in the presence of steering vector errors as the desired signal is treated as an interference. This paper suggests an computationally simple adaptive beamforming method which is robust against these errors. In the proposed method, a minimization problem that is formulated according to the DCB (doubly constrained beamforming) principle is solved to find a solution vector, which is in turn projected onto a subspace to obtain a new steering vector. The minimization problem and the subspace projection are dealt with using some principal eigenpairs, which are obtained using a modified PASTd(projection approximation subspace tracking with deflation). We improve the existing MPASTd(modified PASTd) algorithm such that the computational complexity is reduced. The proposed beamforming method can significantly reduce the complexity as compared with the conventional ones directly eigendecomposing an estimate of the corelation matrix to find all eigenvalues and eigenvectors. Moreover, the proposed method is shown, through simulation, to provide performance improvement over the conventional ones.

• The Journal of Korean Society for Radiation Therapy
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• v.11 no.1
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• pp.100-105
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• 1999

Purpose : When the value of X,Y,Z coordination of the isocenter are reallocated from an arbitrary point using DRR (Digitally Reconstructed Radiographs) image in CT Simulation, conventional simulation is normally performed to verify the accuracy of this reallocation of the isocenter through the fluroscopy. The purpose of our experiment is to determine whether repeated test of the verification is necessary or not, and to analyze errors of reallocation with respect to the body region and the beam projection, if necessary, Material and Method : For 200 simulation patient, an arbitrary point is marked on each body and axial scaning is performed using CT, and treatment planing is done by drawing tumor and target volume on each slice. Using the planing data and the reallocated point of the isocenter, DRR image can be obtained and the final isocenter are marked on the patient's skin. In order to verify this reallocation of X,Y.Z coordination from CT simulation, We measure and evaluate the errors of these value on the fluoroscopy monitor and systematize them by classifying according to each body region (Brain, Neck and SCL, Lung, Esophagus, abdomen, Breast and Pelvis) and each beam projection {AP(PA), Supine, Prone and conformal : etc. } Conclusion : Isocenters are shifted by 3-5 mm in the case of Neck & SCL, Breast. at Abdomen, while noticeable differences are not found in other regions. Also, there are not correlations between the errors and the body regions or beam projections. However, our experiment intends to decide whether the procedure of verification is necessary on the vase of time and economy. It is regretful that we could not fully analyze the geometrical errors of DRR image and visual errors from the divergence. In conclusion, according to how much doctor consider tumor margin in drawing tumor and target volume, the meaning of analysis on the reallocation of isocenter should be reinterpreted, (which depends on the experience and capability of doctors)