• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.175-177
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• 2003

The convergence characteristics of the LV scheme for the Euler equations have been investigated by using the Von Neumann stability analysis. The results indicated that the convergence rate is governed by a specific combination of CFD parameters. Based on this insight, it is shown that the convergence characteristics of the LV scheme is not deteriorated at any grid aspect-ratio as long as the local time step is defined based on the parameter combination. The numerical results demonstrated that this time step definition provide a uniform convergence for grid aspect-ratios between one to$1{\times}10^{4}$.

• Journal of computational fluids engineering
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• v.2 no.1
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• pp.13-20
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• 1997

A fundamental study for the numerical scheme to simulate unsteady nonlinear waves by solving Euler equations is presented. First a conservation form and a non-conservation form of the Euler equations with a free surface fitted coordinate system are compared. Next, a time splitting fractional step method and an alternating direction implicit(ADI) method for the time integration are compared. For the comparative study, flow calculations around a bottom bump in a channel and a NACA 0012 hydrofoil in a flume are performed. The results show that the ADI method with a third order upwind differencing scheme is very efficient in reducing the computing time with keeping the accuracy, And, there is no distinct difference between two expression forms except that the non-conservative form shows faster wave propagating velocity than the conservation form. Some results are compared with experiments and show good agreement.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.623-630
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• 1995

The impulse response functions (force-strain relations) for Euler-Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force is numerically obtained with the convolution approach using the impulse response function obtained by Laplace transform. Using this relation, the impact force history is determined in the time domain and results are compared with those from Hertz's contact law. The parameters of timpact force model are identified using the recovered force and compared with the Hertz's contact model. In order to verify the proposed algorithm, measurements were done using an impact hammer and a steel ball drop test and these results are also compared with the simulated values.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.1
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• pp.130-137
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• 2009

This paper deals with the comparisons of methodologies to express finite rotations accounting for analysis of the rotor system. Researches have been made to predict a behavior of its rotational motion by introducing Euler angles which turned out to be lack in consistency and exactness of the analysis. To overcome this deficiency a new methodology is applied by using both spherical coordinate and quaternion in the rotor rotation and shows its superiority over choices of the Euler angle in terms of kinetic energy and rotation velocity. It is found through numerical examples that quaternion is a more useful and valid tool to derive the ideal numerical model of the rotor system.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.101-107
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• 2013

The Gamma function ${\Gamma}$ which was first introduced b Euler in 1730 has played a very important role in many branches of mathematics, especially, in the theory of special functions, and has been introduced in most of calculus textbooks. In this note, our major aim is to explain the convergence of the Euler's Gamma function expressed as an improper integral by using some elementary properties and a fundamental axiom holding on the set of real numbers $\mathbb{R}$, in a detailed and instructive manner. A brief history and origin of the Gamma function is also considered.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.11
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• pp.1053-1059
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• 2010

This paper treats the DIS (Digital Image Stabilization) problem subject to base motions such as translation, rotation and zoom. For the local motion estimation from a raw image, the Harris corner detection algorithm is exploited to extract feature points, and comparing those of consecutive images, the zoom ratio (scale factor) is computed. For the global motion estimation, an equivalent model is derived to account for a 3-dimensional composite motion from which the center point and Euler angle can be determined. Finally, the motion compensation follows. To show the effectiveness of the present DIS scheme, experimental results for synthetic images are illustrated.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.103-110
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• 2005

This paper is aimed at studying a historical background of graph theory and we deal with the computer representation of graph through a simple example. Graph is represented by adjacency matrix, edge table, adjacency lists and we study the matrix representation by Euler circuit. The effect of the matrix representation by Euler circuit economize the storage capacity of computer. The economy of a storage capacity has meaning on a mobile system.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1503-1520
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• 2013

For multi-line insurance companies, allocating the risk capital to each line is a widely-accepted risk management exercise. In this article we consider several applications of the Euler capital allocation. First, we propose visual tools to present the diversification and the line-wise performance for a given loss portfolio so that the risk managers can understand the interactions among the lines. Secondly, on theoretical side, we prove that the Euler allocation is the directional derivative of the marginal or incremental allocation method, an alternative capital allocation rule in the literature. Lastly, we establish the equivalence between the mean-shortfall optimization and the RORAC optimization when the risk adjusted capital is the expected shortfall, and show how to construct the optimal insurance business mix that maximizes the portfolio RORAC. An actual loss sample of an insurance portfolio is used for numerical illustrations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.279-286
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• 2006

The main purpose of this paper is to apply differential transformation method(DTM) and generalized differential quadrature method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated. Numerical calculations are carried out and compared with previous published results.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.6
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• pp.778-784
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• 2011

This paper presents the study on orientations interpolation of 6-axis articulated robot using quaternion. In this paper, we propose a control algorithm between given two orientations of 6-axis articulated robot by using a quaternion with spherical linear interpolation. In order to study the quaternion interpolation, We created Inverse kinematics program and Interpolation program using LabVIE$^{(R)}$. The rotation angle of each axis were calculated using both euler orientations interpolation program and quaternion orientations interpolation program. The proposed control algorithm is shown to be effective in terms of motor angles and torques when compared to a conventional Euler angle interpolation, by using both LabVIEW$^{(R)}$ and RecurDyn$^{(R)}$.