• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.373-386
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• 2014

Let (R,m) be a commutative Noetherian local ring. In this paper we show that a finitely generated R-module M of dimension d is Cohen-Macaulay if and only if there exists a proper ideal I of R such that depth($M/I^nM$) = d for $n{\gg}0$. Also we show that, if dim(R) = d and $I_1{\subset}\;{\cdots}\;{\subset}I_n$ is a chain of ideals of R such that $R/I_k$ is maximal Cohen-Macaulay for all k, then $n{\leq}{\ell}_R(R/(a_1,{\ldots},a_d)R)$ for every system of parameters $a1,{\ldots},a_d$ of R. Also, in the case where dim(R) = 2, we prove that the ideal transform $D_m(R/p)$ is minimax balanced big Cohen-Macaulay, for every $p{\in}Assh_R$(R), and we give some equivalent conditions for this ideal transform being maximal Cohen-Macaulay.

• Journal of Information Processing Systems
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• v.16 no.5
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• pp.1129-1144
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• 2020

The thangka image inpainting method based on wavelet transform is not ideal for contour curves when the high frequency information is repaired. In order to solve the problem, a new image inpainting algorithm is proposed based on edge structural constraints and wavelet transform coefficients. Firstly, a damaged thangka image is decomposed into low frequency subgraphs and high frequency subgraphs with different resolutions using wavelet transform. Then, the improved fast marching method is used to repair the low frequency subgraphs which represent structural information of the image. At the same time, for the high frequency subgraphs which represent textural information of the image, the extracted and repaired edge contour information is used to constrain structure inpainting in the proposed algorithm. Finally, the texture part is repaired using texture synthesis based on the wavelet coefficient characteristic of each subgraph. In this paper, the improved method is compared with the existing three methods. It is found that the improved method is superior to them in inpainting accuracy, especially in the case of contour curve. The experimental results show that the hierarchical method combined with structural constraints has a good effect on the edge damage of thangka images.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.10 s.113
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• pp.913-919
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• 2006

This paper presents a technique for motion compensation of ISAR(Inverse SAR) images for a moving target. If a simple fourier transform is employed to obtain ISAR image for a moving target, the image is usually blurred. These images blurring problem can be solved with the time-frequency transform. In this paper, motion compensation algorithms of ISAR image such as STFT(Short Time Fourier Transform), GWT(Gabor Wavelet Transform) are described. In order to show the performances of each algorithm, we use scattering wave of the ideal point scatterers and simulated MIG-25 to obtain motion compensated ISAR image, and display the resolution of STFT and GWT ISAR image.

• Advances in nano research
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• v.8 no.2
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• pp.169-182
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• 2020

This study presents the hygro-thermo-electromagnetic mechanical vibration attributes of elastically restrained piezoelectric nanobeam considering effects of beam surface for various elastic non-ideal boundary conditions. The nonlocal Eringen theory besides the surface effects containing surface stress, surface elasticity and surface density are employed to incorporate size-dependent effects in the whole of the model and the corresponding governing equations are derived using Hamilton principle. The natural frequencies are derived with the help of differential transformation method (DTM) as a semi-analytical-numerical method. Some validations are presented between differential transform method results and peer-reviewed literature to show the accuracy and the convergence of this method. Finally, the effects of spring constants, changing nonlocal parameter, imposed electric potential, temperature rise, magnetic potential and moisture concentration are explored. These results can be beneficial to design nanostructures in diverse environments.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.639-650
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• 2018

Finding a solution for the Legendre equation is difficult. Especially if it is as a part of the Laplace equation solving in the electric fields. In this paper, first a problem of the generalized differential transform method (GDTM) is solved by the Sturm-Liouville equation, then the Legendre equation is solved by using it. To continue, the approximate solution is compared with the nth-degree Legendre polynomial for obtaining the inner and outer potential of a sphere. This approximate is more accurate than the previous solutions, and is closer to an ideal potential in the intervals.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.484-490
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• 2008

For CSLDV, the Chebyshev demodulation (or polynomial) technique and Hilbert transform approach have been used for mode shape reconstruction with harmonic excitation. In this paper, the Hilbert-Huang transform approach was applied as an alternative to impact excitation cases in terms of a numerical approach. The vibration of the tested structure is modeled using impulse response functions. In order to verify this technique, a simply supported beam was chosen as the test rig. With additional innovative steps which are the ideal-band pass filter and the nodal point determination, Hilbert-Huang transformation can be used for a good mode shape reconstruction even in the impact excitation case.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.197-198
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• 2008

Even if the DFT calculation is one of the general method to do phasor estimation, it can't adapt to alteration of the frequency. The Frequency is fastened to 60Hz in the ideal power system. However the frequency is not constant in real power system and fluctuates more followed by conditions of the power system. In these cases, the accurate phasor estimation is impossible by using a common DFT calculation, so that a frequency - adaptive phasor estimation method based on the fourier transform is proposed in this paper.

• The Transactions of the Korean Institute of Power Electronics
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• v.20 no.1
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• pp.72-80
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• 2015

In distributed generation systems, a grid-connected inverter should operate with synchronization to grid voltage. Considering that synchronization requires the phase angle of grid voltage, a phase locked loop (PLL) scheme is often used. The synchronous reference frame phase locked loop (SRF-PLL) is generally known to provide reasonable performance under ideal grid voltage. However, this scheme indicates performance degradation under the harmonic distorted or unbalanced grid voltage condition. To overcome this limitation, this paper proposes a phase and harmonic detection method of grid voltage using fast Fourier transform (FFT). To reduce the calculation time of FFT algorithm, minimum sampling data is taken from the voltage measurement to determine the phase angle and the magnitude of harmonic components. An experimental test setup for a grid-connected inverter system has been constructed. By comparative simulations and experiments under various abnormal grid voltage conditions, the proposed scheme has been proven to effectively track the phase angle of the grid voltage.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.12B
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• pp.2369-2381
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• 1999

In this paper, we propose an iterative algorithm for reducing the blocking artifact in block transform-coded images by using a wavelet transform. In the proposed method, an image is considered as a set of one-dimensional horizontal and vertical signals and one-dimensional wavelet transform is utilized in which the mother wavelet is the first order derivative of a Gaussian like function. The blocking artifact is reduced by removing the blocking component, that causes the variance at the block boundary position in the first scale wavelet domain to be abnormally higher than those at the other positions, using a minimum mean square error (MMSE) filter in the wavelet domain. This filter minimizes the MSE between the ideal blocking component-free signal and the restored signal in the neighborhood of block boundaries in the wavelet domain. It also uses local variance in the wavelet domain for pixel adaptive processing. The filtering and the projection onto a convex set of quantization constraint are iteratively performed in alternating fashion. Experimental results show that the proposed method yields not only a PSNR improvement of about 0.56-1.07 dB, but also subjective quality nearly free of the blocking artifact and edge blur.