• Journal of Ocean Engineering and Technology
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• v.16 no.6
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• pp.25-31
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• 2002

A system identification method is introduced to increase the prediction accuracy of a ship's maneuverability in PMM test, analysis. To improve the accuracy of linear hydrodynamic coefficients, the analysis techniques of pure sway and yaw tests are developed, and confirmed. In the analysis of sway tests, accuracy to linear hydrodynamic coefficients depends on the frequency of sway motion. To obtain nonlinear hydrodynamic coefficients for large drift angles, a combined yaw test is introduced. Using this system identification method, runs of PMM test can be reduced while retaining sufficient accuracy, compared to the Fourier integration method. Through the comparisons with sea trial results and the Fourier integration method, the accuracy and efficiency of the newly proposed system identification method, based on least square method, has been validated.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.533-543
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• 2002

In this paper we propose a change-point estimator with left and right regressions using the sample Fourier coefficients on the orthonormal bases. The window size is different according to the data in the left side and in the right side at each point. The asymptotic properties of the proposed change-point estimator are established. The limiting distribution and the consistency of the estimator are derived.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.481-488
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• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.207-217
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• 1996

The problem of detecting change with independent data is considered. The asymptotic distribution of the sample change process with the sample Fourier coefficients is shown as a Brownian Bridge process. We suggest to use dynamic statistics such as a sample Brownian Bridge and graphs as statistical animation. Graphs including change PP plots are given by way of illustration with the simulated data.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.599-619
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• 2005

We define the convolutions of Fourier hyperfunctions and show that every strongly decreasing Fourier hyperfunction is a convolutor for the space of Fourier hyperfunctions and the converse is true. Also we show that there are no differential operator with constant coefficients which have a fundamental solution in the space of strongly decreasing Fourier hyperfunctions. Lastly we show that the space of multipliers for the space of Fourier hyperfunctions consists of analytic functions extended to any strip in $\mathbb{C}^n$ which are estimated with a special exponential function exp$(\mu|\chi|)$.

• Journal for History of Mathematics
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• v.27 no.1
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• pp.81-93
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• 2014

The $L^1$-convergence of Fourier series problems through additional assumptions for Fourier coefficients were presented by W. H. Young in 1913. We say that they are the classical results. Using modified trigonometric series is the convenience method to study the $L^1$-convergence of Fourier series problems. they are called the neoclassical results. This study concerns with the $L^1$-convergence of Fourier series. We introduce the classical and neoclassical results of $L^1$-convergence sequentially. In particular, we investigate $L^1$-convergence results focused on the results of Bhatia's studies. In conclusion, we present the research minor lineage of Bhatia's studies and compare the classes of $L^1$-convergence mutually.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2614-2616
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• 2000

This paper presents the Walsh-Fourier conversion algorithm and Signal Analysis Technique. The Fourier coefficients are determined as the combinations of the Walsh coefficients in terms of the new Walsh-Fourier conversion algorithm. This paper checks the analysis of the Walsh-Fourier spectra and the approximate synthesis of the waveform via one example.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• Journal of Advanced Marine Engineering and Technology
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• v.8 no.1
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• pp.100-111
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• 1984

The methods solving the 2nd order linear ordinary differential equations of the form y"+H(x)y'+G(x)y=P(x) using Fourier series are presented in this paper. These methods are applied to the differential equations of which the exact solutions are known, and the solutions by Fourier series are compared with the exact solutions. The main results obtained in these studies are summarized as follows; 1) The product and the quotient of two functions expressed in Fourier series can be expressed also in Fourier series and the relations between the Fourier coefficients of the series are obtained by multiplying term by term. 2) If the solution of the 2nd order lindar ordinary differential equation exists in a certain interval, the solution can be obtained using Fourier series and can be expressed in Fourier series. 3) The absolute errors of Fourier series solutions are generally less in the center of the interval than in the end of the interval. 4) The more terms are considered in Fourier series solutions, the less the absolute errors.rors.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.141-146
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• 2013

This research investigates the stability analysis for the rotating and the stationary grooved journal bearing. The dynamic coefficients of the journal bearing are calculated by using FEM and the perturbation method. When journal bearing is in whirling motion, the dynamic coefficients have time-varying components as a sine wave due to the reaction force of oil film toward the center of journal even in the steady state. The solutions for the equations of motion can be assumed as the Fourier series expansion. The equations of motion can be rewritten as the linear algebraic equations with respect to the Fourier coefficients. Then, stability of the grooved journal bearing can be calculated by Hill's infinite determinant. The periodic function of dynamic coefficients is derived using Fourier Fast Transform(FFT).The stability of journal bearing is determined as rotating speed increases and the stability of rotating grooved journal bearing is compared and discussed with the stability of stationary grooved journal bearing.