• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.231-236
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• 2007

This paper presents the effect of the center of the series on convergence in solving vibration problems by Differential Transformation Method(DTM) to the transverse vibration of the Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of the Euler-Bernoulli beam under varying axial force is derived. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previously published results. The effect of the center of the series on convergence in solving the problem by DTM is discussed.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.10
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• pp.27-36
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• 1992

This paper proposes a numerical method of motion planning for manipulators using Foruier series. For a redundant manipulator, we predetermine the trajectories of redundant joints in terms of the Nth partial sum of the fourier series. then the optimal coefficients of the fourier series are searched by the Powell's method. For a nonredundant or redundant manipulator, CS02T-continuous smooth joint trajectory for a point-to-point task can be obtained while considering the frequency response. We apply the proposed method to the 3-link planar manipulator and the PUMA 560 manipulator. To show the validity of the proposed method, we analyze solutions by the Fast Fourier Transform (FFT). Also, several features are discussed to obtain an optimal solution.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.3 no.1
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• pp.8-13
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• 2000

The singularity system to represent two circular cylinders poised under different ambient flow fields is considered in the present research. The singularity system, being composed of a series of singularities, has to be truncated for numerical calculations. A rational criterion to determine how many terms of this series should be retained to maintain the prescribed accuracy is provided through analysis of the converging property of the series. A particular emphasis is put to how to deal with the discrete vortex model of a boundary layer, this possibility being the basis for the development of a tool to simulate vortex shedding from a structure composed of two circular cylinders. The principle to obtain the present singularity system can be applied to more-than-cylinders structure. Only th series become much more complex with increase of the number of cylinders.

• International Journal of Naval Architecture and Ocean Engineering
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• v.4 no.2
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• pp.83-95
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• 2012

In the present study, the structural response of breakwaters installed on container carriers against green water impact loads was numerically investigated on the basis of the fluid-structure interaction analysis. A series of numerical studies is carried out to induce breakwater collapse under such conditions, whereby a widely accepted fluid-structure interaction analysis technique is adopted to realistically consider the phenomenon of green water impact loads. In addition, the structural behaviour of these breakwaters under green water impact loads is investigated simultaneously throughout the transient analysis. A verification study of the numerical results is performed using data from actual collapse incidents of breakwaters on container carriers. On the basis of the results of a series of numerical analyses, the pressure distribution of green water was accurately predicted with respect to wave mass and velocity. It is expected that the proposed analytical methodology and predicted pressure distribution could be used as a practical guideline for the design of breakwaters on container carriers.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.1-22
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• 2023

Let L(s, χ) be the Dirichlet L-series associated with an f-periodic complex function χ. Let P(X) ∈ ℂ[X]. We give an expression for ∑^f_n=1 χ(n)P(n) as a linear combination of the L(-n, χ)'s for 0 ≤ n < deg P(X). We deduce some consequences pertaining to the Chowla hypothesis implying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least 65% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. We also show that a generalized Chowla hypothesis holds true for at least 72% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than 2·10⁵.

• Proceedings of the Korean Nuclear Society Conference
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• 2001.05a
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• pp.147.1-147
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• 2001

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.253-260
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• 2014

The intraclass correlation model has a long history of applications in several fields of research. Case deletion diagnostic methods for the intraclass correlation model are proposed. Based on the likelihood equations, we derive a formula for a case deletion diagnostic method which enables us to investigate the influence of observations on the maximum likelihood estimates of the model parameters. Using the Taylor series expansion we develop an approximation to the likelihood distance. Numerical examples are provided for illustration.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.429-437
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• 2001

In [1, 2], described a Chebyshev series method for the numerical solution of integral equations with three automatic algorithms for computing tow regularization parameters, C/sub f/ and r. Here we describe a Fourier series expansion method for a class singular integral equations with Hilbert kernel and constant coefficients with using a new automatic algorithm.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.2 no.4
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• pp.33-37
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• 1991

The problem of radiation from a flanged parallel-plate waveguide is re-examined. The technique of the Fourier transform is used to represent the radiation fields in the spectral domain. The simultaneous equations for the radiation field coefficients are formulated and solved to give an asymptotic seolution. The asymptotic series solution is compared with other results, thus clarifying the discrepancy among different numerical approaches.

• Journal of The Korean Astronomical Society
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• v.40 no.2
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• pp.49-60
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• 2007

This paper deals with the theory for rotational motion of a two-layer Earth model (an inelastic mantle and liquid core) including the dissipation in the mantle-core boundary(CMB) along with tidal effects produced by Moon and Sun. An analytical solution being derived using Hori's perturbation technique at a second order Hamiltonian. Numerical nutation series will be deduced from the theory.