• The Korean Journal of Applied Statistics
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• v.18 no.3
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• pp.583-595
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• 2005

Contingency tables are used to compare counts of n-grams to determine if the n-gram is a true collocation, meaning that the words that make up the n-gram are highly associated in the text. Some statistical methods for identifying collocation are used. They are Kulczinsky coefficient, Ochiai coefficient, Frager and McGowan coefficient, Yule coefficient, mutual information, and chi-square, and so on. But the main problem is that these measures are based ell the assumption of a nor-mal or approximately normal distribution of the variables being sampled. While this assumption is valid in most instances, it is not valid when comparing the rates of occurrence of rare events, and texts are composed mostly of rare events. In this paper we have simply reviewed some statistics about testing association of two words. Some randomization tests to evaluate the significance level in analyzing collocation in large corpora are proposed. A related graph can be used to compare different lest statistics that ran be used to analyze the same contingency table.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.36 no.6
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• pp.621-628
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• 2018

More than four visible GPS (Global Positioning System) satellites are required to obtain absolute positioning. However, it is not easy to satisfy this condition when a rover is in such unfavorable condition as an urban area. As a consequence, clock-aided positioning has been used as an alternative method especially when the number of visible satellites is three providing that receive clock error information is available. In this study, LSC (Least-Squares Collocation) method is proposed to interpolate clock errors for clock-aided positioning after analyzing the characteristics of receiver clock errors. Numerical tests are performed by using GPS data collected at one of Korean CORS (Continuously Operating Reference Station) and a nearby GPS station. The receiver clock errors are obtained through the DGPS (Differential GPS) positioning technique and segmentation procedures are applied for efficient interpolation. Then, LSC is applied to predicted clock error at epoch which clock information is not available. The numerical test results are analyzed by examining the differences between the original and interpolated clock errors. The mean and standard deviation of the residuals are 0.24m and 0.49m, respectively. Therefore, it can be concluded that sufficient accuracy can be obtained by using the proposed method in this study.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.4B no.4
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• pp.180-183
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• 2004

This paper presents a description of the point collocation method and its application to the electromagnetic field computation. The interpolation scheme is based on the fast moving least square reproducing kernel approximation. In the method, the integration cell is not required and the essential boundary conditions can be enforced directly. Numerical simulations on 1-D and 2-D problems are carried out to validate the method. It is found that computational efficiency is higher than the general mesh-free methods.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.263-284
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• 2012

This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov's partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.

• Journal of the Society of Disaster Information
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• v.12 no.1
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• pp.69-73
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• 2016

In this study, the applicability and validity of collocation method to nonlinear vibration issues in comparison to other solutions are confirmed, and the applicability of collocation method to nonlinear dynamic response issues in comparison to the response curve with F.E.M results is examined. Also, it is also examined how the influence of axial inertia varies according to the size of slenderness ratio.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1101-1123
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• 2011

Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.203-224
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• 2014

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• Journal of Astronomy and Space Sciences
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• v.25 no.4
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• pp.361-374
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• 2008

Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.193-213
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• 2017

We investigate an efficient approximation of solution to stochastic Burgers equation driven by an additive space-time noise. We discuss existence and uniqueness of a solution through the Orstein-Uhlenbeck (OU) process. To approximate the OU process, we introduce the Karhunen-$Lo{\grave{e}}ve$ expansion, and sparse grid stochastic collocation method. About spatial discretization of Burgers equation, two separate finite element approximations are presented: the conventional Galerkin method and Galerkin-conservation method. Numerical experiments are provided to demonstrate the efficacy of schemes mentioned above.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.365-372
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• 2006

A new meshfree formulation is developed for material discontinuity problems. A local interfacial jump function which is defined as hyperplane function is embedded in the meshless approximation and the approximation accurately models functions with jumps in the displacement and the derivative fields. Diffuse derivative technique copes with difficulty due to complexity of derivative computation of meshfree approximation. Collocation method with diffuse derivative accelerates computing speed for numerical solution. By solving inclusion and composite material problems, the robustness and effectiveness of the method are verified.