• Journal of KSNVE
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• v.4 no.2
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• pp.137-146
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• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.921-925
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• 2003

An analytical method for the free vibration of single circular plate submerged in a fluid-filled rigid cylindrical vessel was developed by the Rayleigh-Ritz method based on the Fourier-Bessel series expansion. It was assumed that the plate is clamped at an offcentered location of the cylinder, and the non-viscous incompressible fluid contained in the cylinder is bisected by the plate. It was found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis results. The offcentered distance effect on the natural frequencies was also observed.

• Journal of the Korean Mathematical Society
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• v.15 no.2
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• pp.167-176
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• 1979

• Proceedings of the KIEE Conference
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• 1986.07a
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• pp.293-295
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• 1986

• Proceedings of the KSRS Conference
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• 1999.11a
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• pp.429-432
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• 1999

Vegetation cover classification is examined based on a time series NOAA/AVHRR data. Time series data analysis methods including Fourier transform, Auto-Regressive (AR) model and temporal signature similarity matching are developed to extract phenological features of vegetation from a time series NDVI data from NOAA/AVHRR and to classify vegetation types. In the Fourier transform method, typical three spectral components expressing the phenological features of vegetation are selected for classification, and also in the AR model method AR coefficients are selected. In the temporal signature similarity matching method a new index evaluating the similarity of temporal pattern of the NDVI is introduced for classification.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.551-566
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• 2022

We apply Fourier-Legendre-based integration methods that had been given by Campbell in 2021, to evaluate new rational double hypergeometric sums involving ${\frac{{1}}{\pi}}$. Closed-form evaluations for dilogarithmic expressions are key to our proofs of these results. The single sums obtained from our double series are either inevaluable $_2F_1({\frac{4}{5}})$- or $_2F_1({\frac{1}{2}})$-series, or Ramanujan's ₃F₂(1)-series for the moments of the complete elliptic integral K. Furthermore, we make use of Ramanujan's finite sum identity for the aforementioned ₃F₂(1)-family to construct creative new proofs of Landau's asymptotic formula for the Landau constants.

• Nuclear Engineering and Technology
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• v.23 no.3
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• pp.316-320
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• 1991

The Core Operating Limit Supervisory System (COLSS) is digital computer based on-line monitoring system that is designed to assist the operator in monitoring of the Limiting Conditions for Operation. A current COLSS calculates axial power distribution based on in-core detector signals using 5th order Fourier series method. It was found that the 5th elder Fourier series method was not accurate for certain axial power shapes, especially saddle power shapes, resulting in thermal margin decrease. A cubic spline synthesis was applied to the COLSS in order to improve the axial power distribution monitoring for the various axial power shapes. The results showed that the cubic spline synthesis simulated more accurately the axial power shapes, up to 5% in RMS errors, compared to those of the Fourier series.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• The Mathematical Education
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• v.41 no.1
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• pp.91-100
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• 2002

The purpose of this study is to help the students understand the concepts for the series and calculate the sum of series with diverse methods --- a) High School Algebraic Technique, b) Using Bernoulli Number, c) Integral Method, d) Euler Formular, e) Fourier Series

• Structural Engineering and Mechanics
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• v.16 no.6
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• pp.655-674
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• 2003

Investigated in this study are the natural vibration characteristics of the coaxial cylindrical shells coupled with a fluid. Theoretical method is developed to find the natural frequencies of the shell using the finite Fourier series expansion, and their results are compared with those of finite element method to verify the validation of the method developed. The effect of the fluid-filled annulus and the boundary conditions on the modal characteristics of the coaxial shells is investigated using a finite element modeling.