• Proceedings of the Optical Society of Korea Conference
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• 2009.02a
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• pp.167-168
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• 2009

We propose a new computing method for Fourier hologram of 3D objects captured by lens array. Fourier hologram of the two objects which positioned at different distances can be calculated using multiple orthographic view images. The size of the Fourier hologram is in proportion to the number of the orthographic view images. By repeating the orthographic view images, the size of the Fourier hologram can be increased. The principle is verified by numerically reconstructing the hologram which is synthesized from the orthographic images captured optically.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.579-595
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• 1997

In this paper, we establish an $L_p$ analytic Fourier-Feynman transform theory for a class of cylinder functions on an abstract Wiener space. Also we define a convolution product for functions on an abstract Wiener space and then prove that the $L_p$ analytic Fourier-Feyman transform of the convolution product is a product of $L_p$ analytic Fourier-Feyman transforms.

• Proceedings of the Korean Geotechical Society Conference
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• 2010.09a
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• pp.1182-1189
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• 2010

The mechanical behavior of a granular material is governed by the applying effective stresses and its skeletal structure which is considered to be the packing of particles giving overall density and degree of anisotropic. Factors that affect soil packing are the particle size, size distribution and shape, and the arrangement of grain contact. Soil particle size and shape are the most important factor, but difficult to quantify. In this study, 2D Fourier analysis is applied to quantify the shape of granular particles. Jumunjin sand was used in the experiment and particle images are captured using an optical microscope. The results showed that three lower order Fourier descriptor are closely related with roundness, sphericity of the granular particle. Also statistical approach is used to determine roundness, form factor, elongation ratio, roughness of Jumunjin sand.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.35-42
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• 2010

A goal of Magnetic Resonance Imaging is reproducing a spatial map of the effective spin density from the measured Fourier coefficients of a specimen. The imaging procedure can be done by inverse Fourier transformation or backward fast Fourier transformation if the data are sampled on a regular grid in frequency space; however, it is still a challenging question how to reconstruct an image from a finite set of Fourier data on irregular points in k-space. In this paper, we describe some mathematical and numerical properties of imaging techniques from non-uniform MR data using the pseudo-inverse or the diagonal-inverse weight matrix. This note is written as an easy guide to readers interested in the non-uniform MRI techniques and it basically follows the ideas given in the paper by Greengard-Lee-Inati [10, 11].

• 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.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.75-90
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• 2007

Huffman, Park and Skoug introduced various results for the $L_p$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra S introduced by Cameron and Strovic. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class $F_{A_1,A'_2}$ containing F(B). In this paper, we establish various interesting relationships and expressions involving the first variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in $F_{A_1,A_2}$.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.259-274
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• 2013

In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the ${\diamond}$-convolutions. Further, we give an approach to solution of the Schr$\ddot{o}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential. The Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.28 no.2
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• pp.339-353
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• 1998

The purpose of this study was to investigate whether a radiographic estimate of osseous fractal dimension and power spectrum of 2D discrete Fourier transform is useful in the characterization of structural changes in bone. Ten specimens of bone were decalcified in fresh 50 ml solutions of 0.1 N hydrochloric acid solution at cummulative timed periods of 0 and 90 minutes. and radiographed from 0 degree projection angle controlled by intraoral parelleling device. I performed one-dimensional variance. fractal analysis of bony profiles and 2D discrete Fourier transform. The results of this study indicate that variance and fractal dimension of scan line pixel intensities decreased significantly in decalcified groups but Fourier spectral analysis didn't discriminate well between control and decalcified specimens.

• Journal of KSNVE
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• v.6 no.6
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• pp.771-779
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• 1996

In this paper, double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.