• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.247-262
• /
• 2016

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• East Asian mathematical journal
• /
• v.31 no.5
• /
• pp.685-693
• /
• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• Geophysics and Geophysical Exploration
• /
• v.8 no.2
• /
• pp.170-176
• /
• 2005

Recently the velocity stack inversion is having many attentions as an useful way to perform various seismic data processing. In order to be used in various seismic data processing, the inversion method used should have properties such as robustness to noise and parsimony of the velocity stack result. The IRLS (Iteratively Reweighted Least-Squares) method that minimizes ${L_1}-norm$ is the one used mostly. This paper introduce another method, CGG (Conjugate Guided Gradient) method, which can be used to achieve the same goal as the IRLS method does. The CGG method is a modified CG (Conjugate Gradient) method that minimizes ${L_1}-norm$. This paper explains the CGG method and compares the result of it with the one of IRSL methods. Testing on synthetic and real data demonstrates that CGG method can be used as an inversion method f3r minimizing various residual/model norms like IRLS methods.

• Journal of IKEEE
• /
• v.20 no.2
• /
• pp.136-142
• /
• 2016

This paper presents a non-local means (NLM) denoising algorithm based on a new weighting function using a mixed norm. The fidelity of the difference between an anchor patch and the reference patch in the NLM denoising depends on noise level and local activity. This paper introduces a new weighting function based on a mixed norm type of which the order is determined by noise level and local activity of an anchor patch, so that the performance of the NLM denoising can be enhanced. Experimental results demonstrate the objective and subjective capability of the proposed algorithm. In addition, it was verified that the proposed algorithm can be used to improve the performance of the other $l_2$ norm based non-local means denoising algorithms

• Journal of the Korean Institute of Landscape Architecture
• /
• v.30 no.6
• /
• pp.38-46
• /
• 2003

Perceived crowding is known as a necessary method to evaluate social carrying capacity in recreational settings. But according to the results of previous research, perceived crowding, use density, and satisfaction have shown weak and indirect correlations. The theory of visitors’ adjustment is one of several possible explanations for this poor relation. But the validity of the visitors’ adjustment theory has not been not inspected clearly. Therefore, the purposes of this study are to understand visitors’ adjustment theory and to examine visitors’ adjustment to the overuse of recreational settings. Study hypotheses were formulated through literature review and related to visitors’ adjustment in recreation density. Pour hypotheses were established and inspected with the case study, i.e., Rationalization : Visitors’ satisfaction isn't related to use density in recreation setting, 2) Product-shift : Preference norm is related to current use density, 3) Self-selection : Visitors’ satisfaction for the use level is generally high, and 4) Displacement : Norm interference is related to willingness to revisit. The case study was conducted during May and June,2001. According to the results of this survey, visitors adjust to overuse of recreation setting through rationalization and product shift (hypotheses l/2 acceptance). Current use density isn't related to visitors’ satisfaction and willingness to revisit (see table 3). And visitors’ preference norm is modified by situation (see table 4). Visitors’ satisfaction and willingness to revisit don't show a high correlation but moderately high (see table 5, hypothesis 3 acceptance). Differences between visitors’ preference norm and current use density is norm interference. Norm interference isn't related to willingness to revisit (see table 7). Therefore, the norm interference concept is not a useful method to explain visitors’ adjustment to the degree of overuse in a recreational setting (hypothesis 4 rejection). As for future directions, the following are proposed: 1) correctly understanding and reestablishing the visitor norm and norm interference concept, 2) introducing a composite research method to monitor visitors’ behavior and survey visitors’ attitudes and coping responses. These efforts would be helpful in the Planning and management of recreational settings to improve the quality of visitors’ experiences.

• Geophysics and Geophysical Exploration
• /
• v.19 no.4
• /
• pp.220-227
• /
• 2016

Marine seismic data have not only primary signals from subsurface but also ghost signals reflected from the sea surface. The ghost decreases temporal resolution of seismic data because it attenuates specific frequency components. For eliminating the ghost signals effectively, the exact ghost delaytimes and reflection coefficients are required. Because of undulation of the sea surface and vertical movements of airguns and streamers, the ghost delaytime varies spatially and randomly while acquiring seismic data. The reflection coefficient is a function of frequency, incidence angle of plane-wave and the sea state. In order to estimate the proper ghost delaytimes considering these characteristics, we compared the ghost delaytimes estimated with L-1 norm, L-2 norm and kurtosis of the deghosted trace and its autocorrelation on synthetic data. L-1 norm of autocorrelation showed a minimal error and the reflection coefficient was calculated using Kirchhoff approximation equation which can handle the effect of wave height. We applied the estimated ghost delaytimes and the calculated reflection coefficients to remove the source and receiver ghost effects. By removing ghost signals, we reconstructed the frequency components attenuated near the notch frequency and produced the migrated stack section with enhanced temporal resolution.

• ETRI Journal
• /
• v.36 no.1
• /
• pp.42-50
• /
• 2014

Orthogonal frequency division multiplexing (OFDM) is a modulation technique that allows the transmission of high data rates over wideband radio channels subject to frequency selective fading by dividing the data into several narrowband and flat fading channels. OFDM has high spectral efficiency and channel robustness. However, a major drawback of OFDM is that the peak-to-average power ratio (PAPR) of the transmitted signals is high, which causes nonlinear distortion in the received data and reduces the efficiency of the high power amplifier in the transmitter. The most straightforward method to solve this problem is to use a nonlinear mapping algorithm to transform the signal into a new signal that has a smaller PAPR. One of the latest nonlinear methods proposed to reduce the PAPR is the $L_2$-by-3 algorithm, which is based on the discrete sliding norm transform. In this paper, a new algorithm based on the $L_2$-by-3 method is proposed. The proposed method is very simple and has a low complexity analysis. Simulation results show that the proposed method performs better, has better power spectral density, and is less sensitive to the modulation type and number of subcarriers than $L_2$-by-3.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.4
• /
• pp.1724-1731
• /
• 2018

The conventional polynomial neural network (PNN) is a classical flexible neural structure and self-organizing network, however it is not free from the limitation of overfitting problem. In this study, we propose a space search-optimized polynomial neural network (ssPNN) structure to alleviate this problem. Ranking selection is realized by means of ranking selection-based performance index (RS_PI) which is combined with conventional performance index (PI) and coefficients based performance index (CPI) (viz. the sum of squared coefficient). Unlike the conventional PNN, L2-norm regularization method for estimating the polynomial coefficients is also used when designing the ssPNN. Furthermore, space search optimization (SSO) is exploited here to optimize the parameters of ssPNN (viz. the number of input variables, which variables will be selected as input variables, and the type of polynomial). Experimental results show that the proposed ranking selection-based polynomial neural network gives rise to better performance in comparison with the neuron fuzzy models reported in the literatures.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1209-1219
• /
• 2018

We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky [7]: let H be the Hilbert transform and let a, b be real constants. Then for 1 < p < ${\infty}$ the norm of the operator aI + bH from $L^p(\mathbb{R})$ to $L^p(\mathbb{R})$ is equal to $$\({\max_{x{\in}{\mathbb{R}}}}{\frac{{\mid}ax-b+(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}ax-b-(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p}{{\mid}x+{\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}x-{\tan}{\frac{\pi}{2p}}{\mid}^p}}\)^{\frac{1}{p}}$$. Our proof avoids passing through the analogous result for the conjugate function on the circle, as in [7], and is given directly on the line. We also provide new approximate extremals for aI + bH in the case p > 2.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.5 no.2
• /
• pp.25-37
• /
• 2001

We consider the finite element method applied to nonlinear Sobolev equation with smooth data and demonstrate for arbitrary order ($k{\geq}2$) finite element spaces the optimal rate of convergence in $L_{\infty}\;W^{1,{\infty}}({\Omega})$ and $L_{\infty}(L_{\infty}({\Omega}))$ (quasi-optimal for k = 1). In other words, the nonlinear Sobolev equation can be approximated equally well as its linear counterpart. Furthermore, we also obtain superconvergence results in $L_{\infty}(W^{1,{\infty}}({\Omega}))$ for the difference between the approximate solution and the generalized elliptic projection of the exact solution.