• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• Progress in Medical Physics
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• v.28 no.3
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• pp.111-121
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• 2017

Verification of dose distribution is an essential part of ensuring the treatment planning system's (TPS) calculated dose will achieve the desired outcome in radiation therapy. Each measurement have uncertainty associated with it. It is desirable to reduce the measurement uncertainty. A best approach is to reduce the uncertainty associated with each step of the process to keep the total uncertainty under acceptable limits. Point dose patient specific quality assurance (QA) is recommended by American Association of Medical Physicists (AAPM) and European Society for Radiotherapy and Oncology (ESTRO) for all the complex radiation therapy treatment techniques. Relative and absolute point dose measurement methods are used to verify the TPS computed dose. Relative and absolute point dose measurement techniques have a number of steps to measure the point dose which includes chamber cross calibration, electrometer reading, chamber calibration coefficient, beam quality correction factor, reference conditions, influences quantities, machine stability, nominal calibration factor (for relative method) and absolute dose calibration of machine. Keeping these parameters in mind, the estimated relative percentage uncertainty associated with the absolute point dose measurement is 2.1% (k=1). On the other hand, the relative percentage uncertainty associated with the relative point dose verification method is estimated to 1.0% (k=1). To compare both point dose measurement methods, 13 head and neck (H&N) IMRT patients were selected. A point dose for each patient was measured with both methods. The average percentage difference between TPS computed dose and measured absolute relative point dose was 1.4% and 1% respectively. The results of this comparative study show that while choosing the relative or absolute point dose measurement technique, both techniques can produce similar results for H&N IMRT treatment plans. There is no statistically significant difference between both point dose verification methods based upon the t-test for comparing two means.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.553-562
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• 2005

It is well-known that the smoothness of 4-point interpolatory Deslauriers-Dubuc(DD) subdivision scheme is $C^{1}$. N. Dyn[3] proved that 4-point interpolatory subdivision scheme is $C^{1}$ by means of eigenanalysis. In this paper we take advantage of Laurent polynomial method to get the same result, and give new way of strict proof on Laurent polynomial method.

• Korean Management Science Review
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• v.21 no.1
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• pp.77-86
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• 2004

In this paper, we present a methodology for solving the multicommodity network flow problems using interior point methods. In our method, the minimum cost network flow problem extracted from the given multicommodity network flow problem is solved by primal-dual barrier method in which normal equations are solved partially using preconditioned conjugate gradient method. Based on the solution of the minimum cost network flow problem, a warm-start point is obtained from which Castro's specialized interior point method for multicommodity network flow problem starts. In the computational experiments, the effectiveness of our methodology is shown.

• Journal of Advanced Marine Engineering and Technology
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• v.2 no.1
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• pp.3-14
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• 1978

The authors have developed a calculating method of propeller shaft alignment by the finite element method. The propeller shaft is divided into finite elements which can be treated as uniform section bars. For each element, the nodal point equation is derived from the stiffness matrix, the external force vector and the section force vector. Then the overall nodal point equation is derived from the element nodal point equation. The deflection, offset, bending moment and shearing force of each nodal point are calculated from the overall nodal point equation by the digital computer. Reactions and deflections of supporting points of straight shaft are calculated and also the reaction influence number is derived. With the reaction influence number the optimum alignment condition that satisfies all conditions is calculated by the simplex method of linear programming. All results of calculation are compared with those of Det norske Veritas, which has developed a computor program based on the three-moment theorem of the strength of materials. The authors finite element method has shown good results and will be used effectively to design the propeller shaft alignment.

• Journal of Computational Design and Engineering
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• v.1 no.3
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• pp.202-212
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• 2014

To survive in the current shipbuilding industry, it is of vital importance for shipyards to have the ship components' accuracy evaluated efficiently during most of the manufacturing steps. Evaluating components' accuracy by comparing each component's point cloud data scanned by laser scanners and the ship's design data formatted in CAD cannot be processed efficiently when (1) extract components from point cloud data include irregular obstacles endogenously, or when (2) registration of the two data sets have no clear direction setting. This paper presents reformative point cloud data processing methods to solve these problems. K-d tree construction of the point cloud data fastens a neighbor searching of each point. Region growing method performed on the neighbor points of the seed point extracts the continuous part of the component, while curved surface fitting and B-spline curved line fitting at the edge of the continuous part recognize the neighbor domains of the same component divided by obstacles' shadows. The ICP (Iterative Closest Point) algorithm conducts a registration of the two sets of data after the proper registration's direction is decided by principal component analysis. By experiments conducted at the shipyard, 200 curved shell plates are extracted from the scanned point cloud data, and registrations are conducted between them and the designed CAD data using the proposed methods for an accuracy evaluation. Results show that the methods proposed in this paper support the accuracy evaluation targeted point cloud data processing efficiently in practice.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.85-94
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• 2016

In this paper, we first propose a fast one-parameter relaxation (FOPR) method with a scaled preconditioner for solving the saddle point problems, and then we present a formula for finding its optimal parameter. To evaluate the effectiveness of the proposed FOPR method with a scaled preconditioner, numerical experiments are provided by comparing its performance with the existing one or two parameter relaxation methods with optimal parameters such as the SOR-like, the GSOR and the GSSOR methods.

• Journal of the Korea Computer Graphics Society
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• v.29 no.1
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• pp.1-11
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• 2023

Deep-learning-based image segmentation is one of the most widely employed lane detection approaches, and it requires a post-process for extracting the key points on the lanes. A general approach for key-point extraction is using a fixed threshold defined by a user. However, finding the best threshold is a manual process requiring much effort, and the best one can differ depending on the target data set (or an image). We propose a novel key-point extraction algorithm that automatically adapts to the target image without any manual threshold setting. In our adaptive key-point extraction algorithm, we propose a line-level normalization method to distinguish the lane region from the background clearly. Then, we extract a representative key point for each lane at a line (row of an image) using a kernel density estimation. To check the benefits of our approach, we applied our method to two lane-detection data sets, including TuSimple and CULane. As a result, our method achieved up to 1.80%p and 17.27% better results than using a fixed threshold in the perspectives of accuracy and distance error between the ground truth key-point and the predicted point.

• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.